subfolder
stringclasses 367
values | filename
stringlengths 13
25
| abstract
stringlengths 1
39.9k
| introduction
stringlengths 0
316k
| conclusions
stringlengths 0
229k
| year
int64 0
99
| month
int64 1
12
| arxiv_id
stringlengths 8
25
|
|---|---|---|---|---|---|---|---|
1206
|
1206.4585_arXiv.txt
|
Steady accretion of a radiating gas onto a central mass point is described and compared to classic Bondi accretion. Radiation losses are essential for accretion flows to be observed. Unlike Bondi flows, radiating Bondi flows pass through a sonic point at a finite radius and become supersonic near the center. The morphology of all radiating flows is described by a single dimensionless parameter proportional to ${\dot M}/MT_s$ where $T_s$ is the gas temperature at the sonic point. In radiating Bondi flows the relationship between the mass accretion rate and central mass, ${\dot M} \propto M^p$ with $p \sim 1$, differs significantly from the quadratic dependence in classical Bondi flows, ${\dot M} \propto M^2$. Mass accretion rates onto galaxy or cluster-centered black holes estimated from traditional and radiating Bondi flows are significantly different. In radiating Bondi flows the gas temperature increases at large radii, as in the cores of many galaxy groups and clusters, allowing radiating Bondi flows to merge naturally with gas arriving from their cluster environments. Some radiating flows cool completely before reaching the center of the flow, and this also occurs in cooling site flows, in which there is no central gravitating mass.
|
Bondi flow describes the steady spherical inflow of an adiabatic gas toward an accreting mass point. As gas flows radially toward the gravitating mass, its density increases due to tidal compression by the gravity field and consequently its temperature also increases. Gas at rest at infinity with uniform temperature and density accelerates steadily as it flows inward toward the central mass. In Bondi flow the mass of flowing gas is assumed to be small so its self-gravity can be neglected and the central mass can be regarded as constant during relevant flow times (Bondi 1952). Conventional non-radiating Bondi flows are often used in computational studies of massive black hole growth during galaxy formation or to detect errors in hydrocodes. Bondi flows are also often used to estimate black hole accretion rates from X-ray observations of gas near central black holes in galaxies and galaxy clusters. However, Bondi flows do not radiate. For more realistic astrophysical applications, such as the flow of hot intracluster gas toward a cluster-centered black hole, the gas must radiate as it flows inward. Our purpose here is to illustrate that steady spherical accretion flow solutions with radiative losses differ fundamentally from the traditional Bondi solution. A large family of morphologically varied radiating solutions are possible, all characterized by a single dimensionless parameter. But the most important difference is that the often-assumed quadratic Bondi relation between the mass accretion rate and the central mass, ${\dot M} \propto M^2$, no longer holds. Instead, radiating flows require ${\dot M} \propto M^p$ with $p \sim 1$. Unlike classical Bondi flow, the gas temperature in radiating solutions always increases at large radii, allowing more natural fits to the hot gas cores in galaxy groups and clusters that also have positive temperature gradients. Radiating Bondi flows can also accommodate larger accretion rates ${\dot M}$ due to gas flowing in from an extended cluster environment. To be useful in cosmological evolutionary computations and in interpreting accretion rates from X-ray observations, it is useful to keep our solutions as simple and general as possible. Consequently, our radiating steady solutions do not include spatially distributed mass of stars or dark matter (e.g. Yahil \& Ostriker 1973; Cowie \& Binney 1977; Fabian \& Nulsen 1977; Mathews \& Bregman 1978; Quataert \& Narayan 2000; Guo, Oh, \& Ruszkowski 2008), feedback energy, or rotation (Park 2009; Brighenti et al. 2009; Narayan \& Fabian 2011). When radiative losses are included, an initially hot gas can sometimes cool to zero temperature before it reaches the concentrated mass at the center, particularly if the central mass is sufficiently small or if there is no central gravitating mass at all. This latter type of flow toward a cooling site in the absence of gravity experiences no tidal compression so the gas temperature decreases continuously toward the origin, becoming supersonic before cooling to zero temperature. Cooling site flows may describe the appearance and evolution of cool, non-central low-entropy gas often observed in galaxy clusters far from the gravitating cluster core.
|
Gas flowing near accreting black holes can only be observed with radiation that necessarily carries entropy away from the flow, in violation of the adiabatic assumption inherent in traditional Bondi flows. However, when radiative cooling is included, the accretion flow solutions are qualitatively different, not merely perturbations or limiting cases of the original Bondi flow. Nevertheless, radiating solutions have widely varying morphologies that depend on a single dimensionless parameter and they all must pass through a sonic point. Although the gas density (entropy) decreases (increases) monotonically with radius, many solutions exhibit a broad temperature minimum. Far from the mass point the temperature and entropy increase, allowing fits to be made to gas flowing subsonically in from a deeper potential well having a larger virial temperature. Some radiating accretion flows do not pass through a temperature minimum, but instead cool completely before reaching the central mass. In ``cooling site'' flows, in which there is no central mass, total cooling occurs at a non-zero radius within the sonic point. Of particular interest is the failure of traditional Bondi flows to accurately relate the mass accretion rate to the central mass. The traditional Bondi result ${\dot M} \propto M^p$ with $p = 2$ is certainly incorrect for radiating flows. The examples we consider indicate much smaller values $p \sim 1$ in which the precise value of $p$ is somewhat sensitive to the flow morphology. The idealized radiating Bondi flow we describe here, while certainly an improvement over the classic adiabatic Bondi flow, cannot be valid within some radius. Any small rotation in the initial gas must ultimately flow into a disk. Nevertheless, these idealized spherical radiating solutions may provide a useful framework for understanding more realistic flows that include rotation, magnetic fields, viscosity, feedback, etc. They may also be useful in evaluating the performance of central or non-central cooling in numerical computations.
| 12 | 6 |
1206.4585
|
1206
|
1206.6580_arXiv.txt
|
We show that suppression of the baryon energy gaps, caused by the relative motion of superfluid and normal liquid components, can substantially influence dynamical properties and evolution of neutron stars. This effect has been previously ignored in the neutron-star literature.
|
According to numerous microscopic calculations (e.g., \citealt*{yls99, ls01} and references therein), nucleons and hyperons in the internal layers of neutron stars (NSs) can become superfluid at temperatures $T \la 10^8 \div10^{10}$~K. Superfluidity has a strong impact on the thermal evolution of NSs, their oscillations, and (most probably) leads to such observational phenomena as glitches (\citealt*{ai75}) and pulsar spin precession (\citealt*{shaham77, lc02}). Recent real-time observations (\citealt*{hh10}) of a cooling NS in Cassiopea A supernova remnant give strong arguments that the star has superfluid core (\citealt{syhhp11,ppls11}). The aim of this short note is to point out the importance of one effect related to superfluidity of baryons in NSs that has usually been ignored in the NS literature. In Sec.\ II we outline the effect. In Sec.\ III we demonstrate its efficiency. In Sec.\ IV we discuss possible consequences for the physics of NSs and in Sec.\ V we conclude. We use the system of units in which $k_{\rm B}=\hbar=1$.
|
The baryon energy gaps depend on the relative velocity between the superfluid and normal components ($\Delta {\pmb V}$-effect). We propose, for the first time, that this effect may have a strong impact on the dynamical properties of NSs. We illustrate this point by considering radial oscillations of an NS with superfluid nucleon core and a nonsuperfluid crust. However, we stress that the $\Delta {\pmb V}$-effect should be equally important in the crust of NSs where superfluid neutrons are present, as well as in the interiors of hyperon and quark stars. Although we discussed some immediate applications in Sec.\ IV, it is clear that more efforts are needed to analyze all possible consequences of this effect on the evolution of NSs.
| 12 | 6 |
1206.6580
|
1206
|
1206.3646_arXiv.txt
|
Using the Subaru 8.2m Telescope with an IRCS Echelle spectrograph, we obtained high-resolution ($R=$10,000) near-infrared (1.01-1.38$\mu$m) spectra of images A and B of the gravitationally lensed QSO B1422+231 ($z=3.628$) consisting of four known lensed images. We detected \ion{Mg}{2} absorption lines at $z=3.54$, which show a large variance of column densities ($\sim$0.3 dex) and velocities ($\sim$10 km s$^{-1}$) between the sightlines A and B with a projected separation of only $8.4h_{70}^{-1}$ pc at the redshift. This is the smallest spatial structure of the high-$z$ gas clouds ever detected after Rauch et al. found a 20-pc scale structure for the same $z=3.54$ absorption system using optical spectra of images A and C. The observed systematic variances imply that the system is an expanding shell as originally suggested by Rauch et al. By combining the data for three sightlines, we managed to constrain the radius and expansion velocity of the shell ($\sim$50-100 pc, 130 km s$^{-1}$), concluding that the shell is truly a supernova remnant (SNR) rather than other types of shell objects, such as a giant \ion{H}{2} region. We also detected strong \ion{Fe}{2} absorption lines for this system, but with much broader Doppler width than that of $\alpha$-element lines. We suggest that this \ion{Fe}{2} absorption line originates in a localized \ion{Fe}{2}-rich gas cloud that is not completely mixed with plowed ambient interstellar gas clouds showing other $\alpha$-element low-ion absorption lines. Along with the Fe richness, we conclude that the SNR is produced by an SNIa explosion.
|
Gravitationally lensed QSOs provide us precious opportunities to study spatial structures of high-$z$ gas clouds which intersect the multiple sightlines toward the QSO \citep[e.g.,][]{wey83,fol84,sme95,rau99,rau01a,rau01b,rau02,kob02,chu03a,ell04,lop05,mon09}. By comparing the profiles of absorption lines between multiple sightlines, we can study the density and velocity gradients of intersecting gas clouds directly even at high redshift. Such spatial properties of absorbing gas at high redshift may provide a key to understand the galaxy formation processes. The statistical studies of absorption line systems with the gravitationally lensed QSOs have revealed that the \ion{Mg}{2} systems, which trace low-ionization systems are relatively small ($<$ a few hundred pc) and have clumpy spatial structures \citep{rau02,ell04}, in contrast to the \ion{C}{4} systems which are typically a few kpc in size and have fewer structures \citep{rau01a,ell04}. Studies of single line-of-sight observations and CLOUDY photoionization modeling \citep{fer98} also suggest that the Fe-rich low-ionization systems should be as small as 10 pc \citep{rig02,nar08}. Thus, low-ionization systems appear to have small clumpy spatial structures that directly relate to star forming activities, such as giant molecular clouds. It is important to investigate their spatial properties with multiple sightlines of gravitationally lensed QSOs, since only the gravitational lens can directly reveal fundamental parameters such as the size and kinematics of gas clouds. The quadruple gravitationally lensed QSO B1422+231 \citep{pat92} is one of the best objects for such a study because of the relatively small separations among multiple sightlines due to the large distance between the lense galaxy \citep[$z=0.339$; ][]{kun97,ton98} and the QSO ($z=3.628$). This QSO has been observed frequently as one of the most luminous gravitationally lensed high-$z$ QSOs \citep{jil95,son96,pet98,rau99,rau01a,rau01b}. \citet[][, hereafter RSB99]{rau99} obtained high-resolution optical spectra of images A and C of B1422+231 using Keck HIRES \citep{vog94} and detected \ion{C}{4}, \ion{Si}{4}, \ion{C}{2}, \ion{Si}{2}, and \ion{O}{1} absorption lines from the $z=3.54$ absorption system originally identified by \citet{son96} with strong Ly$\alpha$ and Ly$\beta$ absorption lines. The projected separation between A and C sightlines is only 22.2$h^{-1}_{70}$pc at the redshift. RSB99 suggested that the absorption system is an expanding shell of mass ejection or supernova remnants (SNRs) by analyzing the differences of the absorption profiles of lower ionization species between the images A and C. \begin{figure}[t] \centering \includegraphics[width=7cm,clip]{B1422Vcc_trim_1005.eps} \caption{\textit{HST} F555W image of B1422+231 from CASTLES homepage (http://www.cfa.harvard.edu/castles). North is up, east is to the left. Four white point sources show gravitationally lensed images A, B, C and D. The extended object (G) to the northwest of image D shows the lensing galaxy of this system. We obtained spectra of the two brightest and closest components, A and B.} \label{img} \end{figure} In this paper, we report the results of the Subaru near-infrared spectroscopic observations of images A and B of B1422+231. Previous studies of low ionization gas with \ion{Mg}{2} QSO absorption lines were limited to the optical wavelength range and thus to redshifts $<2.5$, beyond which this transition moves into the infrared waveband. Thanks to the advent of highly sensitive near-infrared high-resolution spectroscopy with 8-10 m class telescope, it is possible now to study this unexplored redshift range. We are conducting a systematic high-resolution spectroscopic survey of high-$z$ \ion{Mg}{2} systems with the Subaru IRCS Echelle spectrograph. We observed B1422+231 as one of the initial targets, and detected \ion{Mg}{2} doublet and \ion{Fe}{2} absorption lines for the $z=3.54$ system. Moreover, we succeeded in spatially resolving spectra of images A and B owing to the high spatial resolution in the infrared and the very good seeing of the Subaru Telescope site. This paper is composed as following. The details of our observations are summarized in \textsection 2. The data reduction and calibration of spectra are described in \textsection 3. In \textsection 4, we show the properties of detected \ion{Mg}{2} and \ion{Fe}{2} absorption lines. We interpret the properties as signatures of a Type Ia supernova (SN Ia) remnant, which is discussed in \textsection 5 in detail. \textsection 6 is the summary of this paper. We adopt a standard cosmology with $\Omega _\Lambda = 0.7$, $\Omega _m = 0.3$, $\Omega _k = 0$ and $H_0 = 70 h_{70} = 70 $ km s$^{-1}$ Mpc$^{-1}$ throughout this paper.
|
\subsection{Small-scale Structure of Absorbing Gas Cloud at $z=3.54$} By comparing the results for images A and B, considerable differences of the column densities of \ion{Mg}{2} absorption lines ($\log (N_A / N_B) \sim$ 0.20$\pm 0.12$ dex and 0.37 $\pm 0.08$ dex for component 2 and component 3, respectively) and considerable velocity shears ($|v_A - v_B| \sim$ 7.0$\pm 5.8$ km s$^{-1}$ and 12.3$\pm0.8$ km s$^{-1}$ at $z=3.53850$ for component 2 and component 3, respectively) are found as shown in Figure \ref{compABC}. Considering the alignment of three images A, B, and C, the differences were as expected from RSB99's interpretation of their optical spectra of images A and C in that the relations of the column densities and the relative velocities among three images are $\log N_A > \log N_B > \log N_C$ (assuming $\log N(\text{\ion{Mg}{2}})/N(\text{\ion{C}{2}})$ is equal for both images B and C ) and $|v_A| < |v_B| < |v_C|$ for both components 2 and 3. The projected distances at $z=3.54$ between images are $d_{AB} = 8.4 h_{70}^{-1}$ pc and $d_{AC} = 22.2 h_{70}^{-1}$ pc. This very high spatial resolution (10 pc at $z=3.54$ corresponds to $\sim$ 1 mas angular resolution for direct imaging) shows the power of the gravitational lensing (RSB99). B1422+231 also has a QSO absorption system at slightly higher redshift (z=3.624) and the transverse distance reaches 1 pc, which is the smallest separation for QSO absorption systems ever studied with gravitationally lensed QSOs \citep{jil95, rau01a}, though the system shows few variations of absorption lines among multiple images \citep[see Figure 5 of][]{rau01a} and this system is likely to be associated with the QSO itself. Therefore, the $\sim$ 10 pc structure for the $z=3.54$ system is the smallest spatial structure ever detected for QSO absorption systems. \citet{ell04} observed three lensed images of gravitationally lensed QSO APM08279+5255(z=3.911) with \textit{Hubble Space Telescope (HST)}. They detected many metal absorption lines at $1.1 < z < 3.8$, which correspond to the transverse distance, from 30 $h_{70}^{-1}$ pc to 2.7 $h_{70}^{-1}$ kpc. They found large variations of EWs for lower ionization systems, which are traced with \ion{Mg}{2} doublet lines, even on the spatial scale of a few hundred pc while the higher ionization systems, which are traced with \ion{C}{4} doublet lines, show less variations of EWs \citep{rau01a,ell04}. Therefore, low ionization systems should reflect small scale gas clouds, which are likely to be related to star formation activities in galaxies. Because this $z=3.54$ system's spatial scale ($\sim$ 10 pc) corresponds to that of the typical Galactic gas clouds, such as giant molecular clouds, \ion{H}{2} regions, and SNRs \citep{rau99}, the $z=3.54$ system toward B1422+231 is a very precious target that enables the study of such Galactic-scale objects in detail at the galaxy-forming epoch. \begin{figure*} \centering \includegraphics[width=6cm,clip]{shell_3dver2.eps} \includegraphics[width=5cm,clip]{shell_3dver2_sightlines.eps} \includegraphics[width=6cm,clip]{shell_3dver_circle_1005.eps} \caption{Images of the expanding shell to illustrate the formulation in the text (Section 5.2.1) for the case where information from three sightlines, A, B, and C, is available. Left panel: the 3D image of sightlines that pass through the shell. Middle panel: the expanding shell seen from the direction of sightlines, showing the definitions of $d_A, d_B, d_C$, and $ \phi$. Right panel: the cross-section of the shell that contains the sightline of image A and the center of the shell, showing the definition of $\theta _A$. Similarly, $\theta _B$ and $\theta _C$ are defined for the sightlines of images B and C, respectively.} \label{shell3d} \end{figure*} \begin{figure*} \centering \includegraphics[width=6cm,clip]{shell_2dver3.eps} \includegraphics[width=5cm,clip]{shell_2dver3_sightlines.eps} \includegraphics[width=6cm,clip]{shell_2dver_circle_1005.eps} \caption{Images of the expanding shell to illustrate the formulation in the text (Section 5.2.1) for the case where information from two sightlines, A and C, is available. Left panel: the 3D image of sightlines that pass through a circle that is off the center of the shell. Middle panel: the expanding shell seen from the direction of sightlines, showing the definition of $\Theta$. The radius of the cross-section is $R\sin \Theta$. Right panel: the cross-section of the shell that contains the sightlines of images A and C. Though we can constrain $R\sin \Theta$ and $v\sin \Theta$, we cannot infer the radius $R$ and expansion velocity $v$ due to the lack of information of another independent sightline, such as the sightline B.} \label{shell2d} \end{figure*} \subsection{Expanding SNR Shell} \subsubsection{Shell Model} The column densities and the velocities of \ion{Mg}{2} absorption lines of components 2 and 3 vary among three sightlines as $\log N_A > \log N_B > \log N_C$ and $|v_A| < |v_B| < |v_C|$. What types of object can generate these \textit{systematic} variances on such a small scale? Based on the nearly symmetric velocity profiles of components 2 and 3 with respect to the systemic velocity that corresponds to $z=3.53850$ that are seen in optical spectra of both images A and B (see the profiles for \ion{C}{2} and \ion{Si}{2} in Figure \ref{spectra}), RSB99 suggested that the components 2 and 3 of the $z=3.54$ system can be an expanding shell, such as an SNR. When the sightline passes through the center of a gas cloud of the expanding shell, the observed velocity becomes highest because the gas expands along the direction of the sightline while the column density becomes lowest because the path of the sightline in the shell is shortest at the center. On the other hand, when the sightline passes through the outer edge, the observed velocity becomes lowest, while the column density becomes highest. Applying this model to the $z=3.54$ system, RSB99 found that the sightlines of images A and C pass near the outer edge and near the center of an expanding gaseous shell, respectively. The absorption lines of image B, which is newly observed in this study, shows intermediate values for both column density and relative velocity; this systematic kinematics seen in this gas cloud support the idea of RSB99 that this $z=3.54$ system is truly an expanding shell. Although a contracting (or collapsing) shell is an alternative choice, such an astronomical object is unlikely because the central object of the shell has to pull all the gas symmetrically in a subtle manner: normally such gas should fall through a disk or infalling envelope (not a shell). In fact, no such object is known in the Galaxy and near-by galaxies (see the listed examples of astronomical objects in Section 5.2 in \citealt{rau02}). Following RSB99 and \citet{rau02}, we will consider a model of a three-dimensional (3D) expanding shell (Figure \ref{shell3d}) that has a radius of $R$ and an expansion velocity of $v_{\text{exp}}$. Those parameters can be constrained by two kinds of observables: the physical distance between two sightlines at the redshift (e.g., $d_{AB}$) and the velocity difference of the two absorption components seen in a single sightline (e.g., $\Delta v_A$). In case only two sightlines are available, only the parameters for the expansion ``ring'' that is on the plane of the two sightlines can be constrained: one is the radius of the ring ($R\sin\Theta$) and the other is the expansion velocity of the ring ($v_{\text{exp}}\sin\Theta$), where $\Theta$ is the declination of the ring on the sphere (Figure \ref{shell2d}). Although the relation between $R\sin\Theta$ and $v_{\text{exp}}\sin\Theta$ can be obtained, the 3D radius ($R$) and the expansion velocity ($v_{\text{exp}}$) can never be determined because of the complete lack of the information on the absolute location of the ring ($\Theta$) on the sphere: only the possible range of $R\sin\Theta$ and the lower-limit of $v_{\text{exp}}\sin\Theta$ can be obtained (RSB99). On the other hand, in case {\it three} independent sightlines (not on a single plane) are available, we can put a strong constraint on the expanding sphere. Since the absolute location of the planes that contain the sightlines cannot be determined in a unique way, $R$ and $v_{\text{exp}}$ still cannot be determined. {\it However}, if the $R$ value is fixed, the other parameter $v_{\text{exp}}$ is determined because two $\Theta$s for the sets of two sightlines (e.g., A/B and B/C) can be determined from the two equations for two rings. Therefore, the relation between $R$ and $v_{\text{exp}}$, which is useful to elucidate the astronomical nature of the shell, can be obtained as a final product (see the detailed description in Appendix of \citealt{rau02}). In fact, \citet{rau02} suggested that the $z=0.5656$ absorption system in the three sightlines of gravitationally lensed QSO Q2237+0305 is also an expanding shell because the absorption lines showed variances similar to those of the $z=3.54$ system. They analysed the relation between the radius and expansion velocity of the 3D shell and concluded that the expanding shell at $z=0.5656$ can be interpreted as a supershell or a superbubble of 1-2 kpc size that is frequently observed in the Galaxy and extra-galaxies. Based on the radial velocities in the two lines of sight (images A and C), RSB99 managed to constrain the parameters in a ring for the $z=3.54$ system as 9 $h_{70}^{-1} < R\sin\Theta <$ 34 $h_{70}^{-1}$ pc and $v_{\text{exp}}\sin\Theta > 98\ \text{km s}^{-1}$. Now, with the additional information of image B, we can obtain the relation of $R$ and $v_{\text{exp}}$ of the expanding shell at $z=3.54$. Note that the model parameters can be completely determined if we have four independent sightlines. Because B1422+231 has four independent gravitationally lensed images, future observations of the fourth image would be very valuable. We formulated the geometry of the expanding shell as shown in Figure \ref{shell3d} to obtain the radius-velocity relation of the $z=3.54$ system. The difference of velocities of components 2 and 3 in the sightline of image A, $(\Delta v)_A$, and the distance from the center of the shell to the sightline A, $d_A$, can be expressed as \begin{gather} (\Delta v)_A = 2 v_{\text{exp}} \cos \theta _A \\ d_A = R \sin \theta _A , \end{gather} where $\theta _A$ is the angle from the center of the shell to the sightline A (see Figure \ref{shell3d}). The equations for images B and C can be given similarly, resulting in six equations in total. Next, we can derive two equations about the geometry of triangle ABC : \begin{gather} d_A^2 = d_B^2 + \overline{AB}^2 + 2d_B \overline{AB} \cos{\phi} \\ d_C^2 = d_B^2 + \overline{BC}^2 + 2d_B \overline{BC} \cos{[\angle ABC - \phi]} , \end{gather} where $\overline{AB}$ and $\overline{BC}$ are projected distances between images at $z=3.54$, $\phi$ is the angle between BA and BO, and $\angle ABC$ is the angle between BA and BC. Now, the parameters $(\Delta v)_A$, $(\Delta v)_B$, $(\Delta v)_C$, $\overline{AB}$, $\overline{BC}$, $\angle ABC$, are observed and the nine parameters $R$, $v_{\text{exp}}$, $d_A$, $d_B$, $d_C$, $\theta _A$, $\theta _B$, $\theta _C$, $\phi$ are not determined. If these eight equations are combined, the $R(v_{\text{exp}})$ relation can be obtained as a solution\footnote{The analytic solution is given in Equation (A5) in \citet{rau02}.}. For the $z=3.54$ system, the projected distances are $\overline{AB} = 8.4 h_{70}^{-1} $ pc, $\overline{BC} = 14.4 h_{70}^{-1} $ pc, and $\overline{AC} = 22.2 h_{70}^{-1} $ pc at $z=3.54$. The angle between AB and BC is 153$^\circ$. The velocity differences between components 2 and 3 are $(\Delta v)_A = 168\pm1$ km s$^{-1}$, $(\Delta v)_B = 188 \pm 3$ km s$^{-1}$, and $(\Delta v)_C = 197\pm1$ km s$^{-1}$. By putting those values into the equations, we obtained the function $R(v_{\text{exp}})$ that is shown with a solid line in Figure \ref{rad-vel} along with two dashed lines that show the 1$\sigma$ uncertainty range of our calculation : each line corresponds to the cases of $(\Delta v)_B =$ 185 km s$^{-1}$, 191 km s$^{-1}$. Here, we are only concerned with the uncertainty of $(\Delta v)_B$ because it is the largest among six observables : the available spectrum of image B is only our lower-resolution near-infrared data while the available spectra of the other two images A and C are higher-resolution optical data of RSB99. \begin{figure}[t] \centering \includegraphics[width=9cm,clip]{RV_HII_SNR_1111.eps} \caption{Relation of radius and expansion velocity of the expanding shell model. The solid line shows the relation for the $z=3.54$ system in the case of $(\Delta v)_B=188$ km s$^{-1}$, which is the most likely value from the observation (see Section 5.2.1 for detail). The dotted lines along the solid line are the case of $(\Delta v )_B=185,191$ km s$^{-1}$, showing 1$\sigma$ uncertainty of our calculation. The filled and open circles show the radius and expansion velocity of the observed SNRs and \ion{H}{2} regions in our Galaxy \citep{koo91,shi90,kot02,arn07,dai07,cap08,cic08}.} \label{rad-vel} \end{figure} \subsubsection{The SNR Origin of the Shell} Figure \ref{rad-vel} shows that the radius of the shell is larger than $\sim20$ pc and the expansion velocity is larger than $\sim120$ km s$^{-1}$. Although there is no a priori constraints, the shortest radius ($R \le 30$ pc) is unlikely because it requires: (1) an exact alignment of the shell with the three sightlines that have similar separations as the shell diameter and (2) very high velocity ($v_{\text{exp}} >200$ km s$^{-1}$) that appears to be too fast for an \ion{H}{1} shell. The largest radius ($R \gg 100$ pc) is also unlikely since it requires similarly very high expansion velocity and all three sightlines must pass near the edge of expanding shell, exactly. Therefore, the bottom of the curve ($R \sim50-100$ pc, $v_{\text{exp}}\sim130$ km s$^{-1}$) would be the natural choice of the radius and the expansion velocity of the shell (see the original discussion in \citealt{rau02} for another QSO absorption system). To compare to the known astronomical shell-like objects, we also plotted the radii and expansion velocities observed for the Galactic \ion{H}{2} regions (\citealt{shi90,kot02,arn07,dai07,cap08,cic08}) and SNRs that have a structure of expanding shell: the data points of SNR are from \citet{koo91}, who observed 15 old SNRs with \ion{H}{1} 21cm line in the disk of our Galaxy. As a result, the location of the $z=3.54$ system on the plot is found to be quite consistent with SNRs while all the \ion{H}{2} regions show much smaller expansion velocity less than 20 km s$^{-1}$. In fact, the distributions of SNRs match well with the bottom of the curve for the $z=3.54$ system, which is quite consistent with the above consideration that the bottom of the curve is the most likely location of the shell. Therefore, we concluded that the shell is truly an SNR shell, confirming RSB99's initial suggestion in more solid way. \subsubsection{Physical Parameters of the SNR Shell} Assuming $R=50-100$ pc and $v_{\text{exp}}=130$ km s$^{-1}$ as the radius and the expansion velocity of the observed shell, we compare the observed SNR shell with the typical self-similar expansion model to estimate the main physical parameters of the shell. Then, we compare the estimated physical parameters to those of typical SNRs to check the consistency of the SNR interpretation. In the following, we will utilize the formulation described in text-books by \citet{tie05} and \citet{dra11} to first estimate the age ($t$) of the SNR shell, and finally the total energy ($E$) of the shell, along with an independent estimate of mass ($M$) of the shell from the column densities of the absorption lines. If the self-similar concept is introduced with a simple power laws ($R \propto t^{\eta}$), the age of the shell can be roughly estimated from $R$ and $v_{\text{exp}}$ as $t\sim 10^5 $yr for $z=3.54$ system since $t\sim R/v_{\text{exp}}$. The SNR shell of this age is in the radiative expansion phase (snowplow phase) rather than adiabatic expansion phase (Sedov phase). In this case, $\eta = 2/7$ and the age $t$ can be derived with \begin{equation} t = 1.1 \times 10^5 \text{yr} \left( \frac{R}{50\text{pc}}\right) \left( \frac{v_{\text{exp}}}{130 \text{km s}^{-1}} \right) ^{-1} . \label{age} \end{equation} For the observed $v_{\text{exp}}$ (130 km s$^{-1}$) and the range of $R$ (50 - 100 pc), the age of the $z=3.54$ shell is estimated as: \begin{equation} 1.1 \times 10^5 \text{yr} \leq t \leq 2.2 \times 10^5 \text{yr} . \end{equation} In this snowplow phase, the radius and expansion velocity are modeled as \begin{equation} R(t) = 21.6 \text{pc} \left( \frac{E_0}{10^{51} \text{erg}} \right)^{\frac{11}{45}} \left( \frac{n_0}{1\text{cm}^{-3}}\right) ^{-\frac{11}{45}} \left( \frac{v_{\text{exp}}(t)}{250\,\text{km s$^{-1}$}} \right) ^{-\frac{2}{5}} ,\label{radius} \end{equation} where $E_0$ is the total energy of a supernova, $n_0$ is the number density of the interstellar gas {\it before the supernova explosion}. Next, we will discuss the mass of the shell ($M_{\text{tot}}$). RSB99 estimated the number density ($n$) and the size along the line of sight ($L$) for the component 3 of image A using photoionization model as \begin{gather} 0.16 \text{ cm}^{-3} \leq n \leq 1.6 \text{ cm}^{-3} \label{numberR} \\ 0.015 \text{ pc} \leq L \leq 1.6 \text{ pc} . \label{thickR} \end{gather} From these parameters, RSB99 estimated the mass of a gas cloud ($M_{\text{tot}}$) assuming two geometrical cases ; first is a homogeneous cylindrical slab with a thickness $L$ and radius $\overline{AC}$ as a lower limit of the mass; second is a spherical cloud with a radius $\overline{AC}$ as an upper limit of the mass: \begin{equation} 0.4M_\odot \leq M_{\text{tot}} \leq 2700M_\odot . \label{rsbmass} \end{equation} Here, we newly obtained an additional constraint on the radius $R$ of the gas cloud as $R \sim 50 - 100$ pc. Assuming that the gas cloud has a shape of spherical shell with an average radius of $R$, thickness of $L$, and number density of $n$, we can calculate the total mass $M_{\text{tot}}$ of the shell with \begin{equation} M_{\text{tot}} = 4 \pi R^2 L n m_{\text{\ion{H}{1}}} \mu , \end{equation} where $m_\text{\ion{H}{1}}$ is the mass of a hydrogen atom particle ($m_{\text{\ion{H}{1}}} = 1.66\times 10^{-24} $g) and $\mu$ is the reduced mass ($\mu = 4/3$). Here we ignored the effect of $\cos \theta _A$ on the thickness of the shell (see Figure \ref{shell3d}) in view of the large uncertainty of $L$. Using the value range of $n$ and $L$ (Equation \ref{numberR} and \ref{thickR}) and our result on the radius ($50 <R< 100\ \text{pc}$), $M_{\text{tot}}$ is estimated as: \begin{equation} 25 M_\odot \leq M_{\text{tot}} \leq 1050 M_\odot . \end{equation} This is consistent with the original mass estimate by RSB99 (Equation \ref{rsbmass}), but narrows the mass range by two orders of magnitude. Because the uncertainty of this estimate is quite large, we try an alternative mass estimate in the following. We will estimate the mass in two ways here, using the column density of \ion{H}{1} or \ion{Mg}{2}, in order to check the consistency. In both estimates, we will use the column density of component 3 of image A because the ionization parameter, $\log U$, of this component was specifically estimated as $\log U = -4.4$ (RSB99) which is low enough that we can estimate the mass simply from observed column density without any ionization correction. Although the column density of this component may not be the representative value of the shell, we would not expect a large uncertainty of more than an order of magnitude in view of the column density variation among the components seen in images A, B and C. First, the \ion{H}{1} mass of the shell can be simply calculated as : \begin{equation} M_{\text{\ion{H}{1}}} = 4 \pi R^2 N_{\text{\ion{H}{1}}} m_{\text{\ion{H}{1}}} \label{himass} \end{equation} where $R$ is the size of the shell and $N_{\text{\ion{H}{1}}}$ is the observed \ion{H}{1} column density. Using $\log N$(\ion{H}{1})=$16.05 \pm 0.15$ for component 3 of image A (RSB99), the \ion{H}{1} mass is calculated as \begin{equation} 2.8 M_\odot \leq M_{\text{\ion{H}{1}}} \leq 11 M_\odot \label{mass_hi} \end{equation} Because this gas cloud is optically thin, almost all of the hydrogen is likely to be ionized. To estimate the total mass of the shell from the \ion{H}{1} mass, we must evaluate the degree of ionization. In \citet{don91}, the fraction of \ion{H}{1} is calculated with \begin{equation} \frac{n(\text{\ion{H}{1}})}{n_H} = (4.6\times 10^{-6}) U ^{-1.026}, -4.7 < \log U < -1.8, \end{equation} where $n$(\ion{H}{1}) is the number density of only \ion{H}{1} and $n_\text{H}$ is the total number density of hydrogen atom that includes \ion{H}{2}. Since the ionization parameter of the component 3 of image A is estimated as $\log U = -4.4$ (RSB99), $n(\text{\ion{H}{1}}) / n(\text{H})$ is calculated as 0.15. Then, the total hydrogen mass is estimated as: \begin{equation} 19 M_\odot \leq M_H \leq 75 M_\odot . \end{equation} Finally, the total mass of the shell can be calculated by multiplying the reduced mass, $\mu$, as: \begin{equation} 25 M_\odot \leq M_{\text{tot}} \leq 99 M_\odot. \label{totmasshi} \end{equation} This range is consistent with the typical scrambled gas mass of the observed SNR (10 - 1000 $M_\odot$), with a radius from about 10 to a few 100 pc \citep{koo91}. Next, we attempt one more independent estimate of the total mass of the shell based on the column density of \ion{Mg}{2} instead of \ion{H}{1}. The total \ion{Mg}{2} mass in the shell can be estimated using Equation (\ref{himass}) but after replacing \ion{H}{1} to \ion{Mg}{2}. For column density $N_{\text{\ion{Mg}{2}}}$, we use the value of component 3 of image A because this component is examined in detail by RSB99. As a result, the total \ion{Mg}{2} mass is calculated as \begin{equation} 0.06 M_\odot < M_{\text{\ion{Mg}{2}}} < 0.24 M_\odot \label{massofMgII} \end{equation} for the assumed range of radius. The total mass of the shell can be estimated first assuming that all the magnesium is in the form of \ion{Mg}{2}. This assumption is reasonable because the \ion{Mg}{1} absorption lines are not detected (the 3$\sigma$ upper limit is calculated as $\log N (\text{\ion{Mg}{1}}) [\text{cm}^{-2}]< 11.1$; see Section 4.1 or Table \ref{vpfit}. Although the possibility of the existence of a significant amount of \ion{Mg}{3} cannot be dismissed, we ignored the higher ionization states because the ionization parameter $\log U$ of this component is estimated to be quite low as $\log U = -4.4$ (RSB99) based on the photoionization modeling of \citet{don91}. We assumed the solar abundance, which is suggested by RSB99 for component 3 based on the photoionization modeling by \citet{don91}. With the solar abundance of magnesium \citep[0.13\% in mass; ][]{gre10}, the total mass $M_{\text{tot}}$ is estimated from Equation (\ref{massofMgII}) as \begin{equation} 47 M_\odot < M_{\text{tot}} < 188 M_\odot. \label{mass_tot} \end{equation} This mass range is pretty much consistent with the estimate from \ion{H}{1} column density, Equation (\ref{totmasshi}). From the estimated radius and expansion velocity, we can finally constrain the energy of supernova explosion using Equation (\ref{radius}). The remaining parameter in this equation, $n_0$, which is the number density of interstellar medium around the supernova before explosion, can be estimated assuming that the shell consists of all of the gas that existed in the sphere with radius $R$ before explosion, with the following equation: \begin{equation} n_0 = \frac{3M_{\text{tot}}}{4 \pi R^3 m_H \mu}. \end{equation} With the range of $50 \leq R \leq 100 \text{ pc}$ and $M_{\text{tot}}$ from Equation (\ref{mass_tot}), $n_0$ is calculated as: \begin{equation} 1.8 \times 10^{-3} \text{cm}^{-3} < n_0 < 3.6 \times 10^{-3} \text{cm}^{-3} \end{equation} Then, the energy of supernova explosion, $E_0$, is calculated with Equation (\ref{radius}): \begin{equation} 3.8 \times 10^{49} \text{erg} < E_0 < 3.2 \times 10^{50} \text{erg} \label{energySNR} \end{equation} The estimated energy is roughly consistent with the energy of supernova explosion, $\sim 10^{51}$ erg \citep{tie05,dra11}. The slight difference can be attributed to the left-over gas inside the shell \citep[see e.g.,][]{koo91} that can effectively increase $n_0$, thus $E_0$ through Equation (\ref{radius}). In this subsection, we have gone through the physical parameters of the $z=3.54$ system as an expanding shell of an SNR. The expanding shell model and estimated physical parameters appear to be quite consistent with the properties of SNRs observed in the galaxy. With our calculation, this system is likely to be an SNR of about 0.1 Myr with a radius of 50 $-$ 100 pc, an expansion velocity of about 130 km s$^{-1}$, and the total energy of $10^{50}$ erg. Therefore, we conclude that this $z=3.54$ system is truly an SNR. \begin{figure} \centering \includegraphics[width=8cm,clip]{narayanan_1008Mg.eps} \caption{$N$(\ion{Mg}{2}) vs. $N$(\ion{Mg}{2})/$N$(\ion{Fe}{2}) of weak \ion{Mg}{2} systems. The crosses are from \citet{nar08}, the squares are from \citet{rig02}, and a filled circle shows the component 3 of image A of the $z=3.54$ system. The filled squares show confirmed Fe-rich systems while a open square shows confirmed non Fe-rich system \citep{rig02}. The dotted line shows the solar abundance ratio \citep{asp05}. The $z=3.54$ system (filled circle) is located in a horizontal branch near the solar value, where the confirmed Fe-rich systems (filled squares) are distributed.} \label{narayanan} \end{figure} \subsection{Type Ia Supernova ?} Recall the very broad profile of \ion{Fe}{2} absorption lines of component 3 in image A, which is described in Section 4.2. What does this feature mean in the SNR interpretation of the $z=3.54$ system? To answer this question, we first discuss the iron richness of the SNR shell, then examine the broad absorption feature in a more rigorous way to suggest that the iron is localized in the SNR shell. Finally, we conclude that the SNR shell is related to an SN Ia. \subsubsection{Fe Richness} The amount of iron in the gas cloud is crucial to investigate the chemical enrichment by supernovae. Figure \ref{narayanan} shows the distribution of $\log N(\text{\ion{Mg}{2}}) / N(\text{\ion{Fe}{2}})$ versus $\log N$(\ion{Mg}{2}) for weak \ion{Mg}{2} systems. The crosses are from \citet{nar08}, who studied 100 weak \ion{Mg}{2} systems at $0.4<z<2.4$ using VLT data. The four squares are weak \ion{Mg}{2} systems studied with Keck data by \citet{rig02}. Note that neither sample includes the systems whose \ion{Fe}{2} are not detected. The filled and open squares are confirmed Fe-rich and non-Fe-rich systems based on their photoionization modeling using CLOUDY, respectively. The filled circle shows the $z=3.54$ system ($\log N(\text{\ion{Mg}{2}}) / N(\text{\ion{Fe}{2}})$=0.31$\pm$0.07). The dotted line shows the solar abundance ratio, $\log [N(\text{Mg}) / N(\text{Fe})]_\odot$ = 0.08 \citep{asp05} for the case that all Mg and Fe atoms are in the \ion{Mg}{2} and \ion{Fe}{2} ionization states. The value of the $z=3.54$ system is found to be closer to the solar value than those for the other weak \ion{Mg}{2} systems with similar $N$(\ion{Mg}{2}). \citet{nar08} suggested that any system near the solar value (dashed line in Figure \ref{narayanan}) are truly Fe-rich systems. \citet{rig02} suggested that their three Fe-rich systems ($N$(\ion{Fe}{2})$\sim$$N$(\ion{Mg}{2})) have small sizes of $\sim 10$pc, and high metallicity of $> 0.1 Z_\odot$ (see filled squares in Figure \ref{narayanan}). They specifically predicted that the $z=3.54$ system toward B1422+231 should show strong \ion{Fe}{2} lines ($N$(\ion{Fe}{2}) $\sim$ $N$(\ion{Mg}{2})) in view of the small spatial structure ($\sim$10 pc) and high metallicity inferred by RSB99. In fact, $\log N(\text{\ion{Mg}{2}}) / N(\text{\ion{Fe}{2}})$ of the $z=3.54$ system is found to be similarly Fe-rich as the three Fe-rich systems (see Figure \ref{narayanan}), suggesting solar to sub-solar metallicity. All those results support the iron-richness of the SNR shell at $z=3.54$. The high iron abundance of the SNR naturally suggests that it is an SN Ia. In fact, \citet{rig02} suggested that the three iron-rich systems in their samples have [$\alpha$/Fe]$<0$ and have been enriched by SNe Ia because high iron column density that is similar to magnesium column density cannot be explained by other enrichment processes such as SNe II. Therefore, it is highly likely that the $z=3.54$ system is a gas cloud enriched by SNe Ia. More detailed arguments based on abundance estimate using CLOUDY photoionization modeling will be presented in our separate paper (S. Kondo et al. in preparation). If the gas cloud was truly enriched by SNIa explosion, the total amount of the iron in the gas should be consistent with the yield of the iron from SNIa explosion. Assuming the \ion{Fe}{2} absorbing gas is in the form of shell with $R=50-100$ pc as Equation (\ref{himass}), the \ion{Fe}{2} mass is estimated as 0.07-0.29 $M_\odot$ from the component 3 of image A. Our estimated \ion{Fe}{2} mass is consistent with the observed mass of SNeIa. \citet{sca10} and \citet{sil11} suggest that the estimated mass of radio active $^{56}$Ni (eventually decays to $^{56}$Fe) ejected from an SN Ia ranges from 0.02 $M_\odot$ to 1.7 $M_\odot$. Note that the slightly low estimated energy of the SN (Section 5.2.3) also favors an SNIa interpretation rather than other types of SN with more energetic explosions. Because our estimate does not include the iron in other ionization states, such as \ion{Fe}{3}, within the shell as well as the iron \textit{inside} the shell, the total mass of iron is expected to be more than the estimated value. \subsubsection{Fe Localization} Another characteristic of the \ion{Fe}{2} absorption line is the Doppler width ($23\pm6$ km s$^{-1}$) that appears to be unusually broad compared with that of $\alpha$-element (e.g., $b_{\text{\ion{Mg}{2}}} \sim 9$ km s$^{-1}$). This is quite strange for a QSO absorption system, because the mass of an iron atom is much heavier than that of $\alpha$ elements, thus the width of an \ion{Fe}{2} absorption line should be smaller than that of $\alpha$ elements. We first compared the widths of \ion{Mg}{2} and \ion{Fe}{2} lines of the $z=3.54$ system with the past surveys of weak \ion{Mg}{2} systems \citep{rig02,chu03,nar08}. Figure \ref{dopplar} shows correlation of the Doppler widths of \ion{Mg}{2} and \ion{Fe}{2} lines of weak \ion{Mg}{2} systems. The points should be located below the dotted line ($b_{\text{\ion{Mg}{2}}} = b_{\text{\ion{Fe}{2}}}$) because iron is heavier than magnesium. In fact, most data points from the literatures are distributed along or below the dotted line. However, the $z=3.54$ system is found to be located significantly above the line even considering the uncertainty, suggesting the uniqueness of this system. We first checked the possibility of blending of other absorption lines on the \ion{Fe}{2} absorption lines. For example, if \ion{Mg}{2} absorption systems existed at $z=$3.22 and $z=$2.87, strong metal absorption lines \ion{Mg}{2} $\lambda \lambda$2796, 2803 would blend with the \ion{Fe}{2} $\lambda$2600 ($\lambda = 11804$ \r{A}) and $\lambda$2383 ($\lambda = 10814$\r{A}) lines, respectively. However, such absorption systems have not been reported in \citet{son96} and \citet{rau01a}, who detected many Lyman series lines and \ion{C}{4} absorption lines of B1422+231. Therefore, we conclude that the broad features of \ion{Fe}{2} lines are real. Here we try to evaluate the excess \ion{Fe}{2} absorption by decoupling the broad feature into two sub-components. If we compare the \ion{Mg}{2} and \ion{Fe}{2} profiles, the excess exists on the blue side of the \ion{Mg}{2} absorption peak (Figure \ref{Fecomb}). Then, we fitted two velocity components to both \ion{Fe}{2} $\lambda$2600 and $\lambda$2383 lines with the fixed Doppler widths of 9 km s$^{-1}$ , which is the upper limit estimated from the Doppler width of \ion{Mg}{2} ($\sim 9$ km s$^{-1}$). The results are shown in the bottom panel of Figure \ref{vpfitcomp}. The black line shows the component whose redshift is fixed to the value of the \ion{Mg}{2} absorption line during the fitting, while the gray line shows the other excess component, for which the redshift was not fixed. The resultant difference of peak velocity between the two velocity components is $26\pm7$ km s$^{-1}$, and the column densities of blue and red components are $\log N$ [cm$^{-2}$] = $12.3 \pm 0.2$ and $12.5\pm0.1$, respectively. This fitting appears to match well with the observed data for both \ion{Fe}{2} $\lambda$2600 and $\lambda$2383 lines. Now, the question is what is the blue component ? Because there is no obviously corresponding $\alpha$-element absorption lines, this iron gas cloud is inferred to be localized in the shell. The localization of iron in the SNR also supports the SNIa origin of the SNR shell: the \ion{Fe}{2} features imply the ejection of the mass from the SN Ia, while the other $\alpha$-element absorption lines are likely to be the interstellar gas scrambled by the shock of the SNR. In our Galaxy, \citet{ham97} observed SN1006, which is an SN Ia remnant, with absorption lines on a spectrum of Schweizer and Middleditch star, whose sightline intersects near the center of SN1006. Despite the age difference ($\sim$1000 yr for SN1006, $\sim 10^5$ yr for the $z=3.54$ system), it would be useful to compare those two objects in detail to infer the nature of the $z=3.54$ SNR shell because the geometrical configuration is very similar. For SN1006, very broad ($\sim$ 5,000 km s$^{-1}$) \ion{Fe}{2} absorption line is detected at the systemic velocity while the ejected \ion{Si}{2} shows a redshift of $\sim$ 5,000 km s$^{-1}$. This suggests that the mixing of ejected iron with interstellar gas occurs after the mixing of ejected $\alpha$-elements. The two velocity sub-components of \ion{Fe}{2} absorption lines of component 3 of image A can be interpreted as meaning that the red component with the same velocity as the $\alpha$-element lines comes from Fe gas that mixed with the scrambled interstellar gas, and the blue component comes from Fe gas that has not been mixed with it yet (Figure \ref{shellfe}). Therefore, we might witness the mixing process of ejected iron with interstellar gas at $z=3.54$. \begin{figure} \centering \includegraphics[width=8cm,clip]{dopplar.eps} \caption{Correlation of Doppler widths of \ion{Mg}{2} and \ion{Fe}{2} absorption lines of weak \ion{Mg}{2} systems. The crosses are from \citet{rig02}, \citet{chu03}, \citet{nar08}, while the filled circle shows the $z=3.54$ system (component 3 of image A). The dotted line shows the location where the widths of \ion{Mg}{2} and \ion{Fe}{2} are identical. While the crosses are distributed along or below the dotted line, the point of the $z=3.54$ system is located above the line with a large offset.} \label{dopplar} \end{figure} \begin{figure} \centering \includegraphics[width=8cm,clip]{comp_MgII_FeII5_1112.eps} \caption{Voigt profile fitting to the \ion{Mg}{2} $\lambda$2803 (bottom), \ion{Fe}{2} $\lambda$2600 (middle) and $\lambda$2383 (top) absorption lines of component 3 of image A. The thin lines show the observed spectra. The solid thick lines show the fitted Voigt profiles with the Doppler width and redshift fixed to the values of \ion{Mg}{2} absorption lines. The gray lines show the fitted Voigt profiles to the residual absorption. The dashed lines show the combined profiles of black and gray components.} \label{vpfitcomp} \end{figure} \begin{figure} \centering \includegraphics[width=8cm,clip]{shell_fe5.eps} \caption{Schematic image of the SNR shell of the $z=3.54$ system. The Fe-rich gas clouds are localized in the expanding shell, while the $\alpha$ element gas clouds, such as \ion{Mg}{2}, are distributed homogenously in the expanding shell.} \label{shellfe} \end{figure} \subsubsection{SNe Ia at High Redshift} In this section, we saw the evidence of the richness and localization of iron in the SNR shell at $z=3.54$. The detected iron richness cannot be explained by processes other than SN Ia. Moreover, the suggested localization of iron in the shell supports the SN Ia interpretation. From these facts, we conclude that the $z=3.54$ system is an SN Ia remnant. The extragalactic SN Ia has been studied extensively for the supernova cosmology \citep{goo11}. However, even the most distant SN Ia event ever detected is at $z=1.55$ \citep{rod11} and more distant objects that are important for the study of cosmic chemical enrichment history are hard to detect and with 8-10 m class telescopes. For studying such high-$z$ SNe Ia, absorption systems toward gravitational-lensed QSO may serve as good targets as is the case for this $z=3.54$ system toward B1422+231. Even for the single sightline, the Fe-rich absorption systems as seen in Figure \ref{narayanan} would become good targets for studying chemical enrichment history at high-redshift ($z>2$) with more data available with sensitive high-resolution spectroscopy with adaptive optics \citep[see][]{kob05}.
| 12 | 6 |
1206.3646
|
1206
|
1206.2476_arXiv.txt
|
We have implemented non-ideal Magneto-Hydrodynamics (MHD) effects in the Adaptive Mesh Refinement (AMR) code RAMSES, namely ambipolar diffusion and Ohmic dissipation, as additional source terms in the ideal MHD equations. We describe in details how we have discretized these terms using \m{the} adaptive Cartesian mesh, and how the time step is \m{diminished} with respect to the ideal case, in order to perform a stable time integration. We have performed a large suite of test runs, featuring the Barenblatt diffusion test, the Ohmic diffusion test, the C-shock test and the Alfven wave test. For the latter, we have performed a careful truncation error analysis to estimate the magnitude of the numerical diffusion induced by our Godunov scheme, \m{allowing us} to estimate the spatial resolution that is required to address non-ideal MHD effects reliably. We show that our scheme is second-order accurate, and is therefore ideally suited to study non-ideal MHD effects in the context of star formation and molecular cloud dynamics.
|
The impact of magnetic fields on various objects in astrophysics is now well established. They play a major role \m{on} a wide range of scales, from the study of the early universe, the stellar and intergalactic medium to the formation and interiors of stars or the accretion flows around stellar objects. They are difficult to study both \m{from an observational} and a theoretical (and numerical) point of view. Several implementations of ideal MHD have been performed since the last decade (\citet{fromang}, \citet{StoneNorman}, \citet{Machida2005} among others), and numerical issues concerning the divergence free condition \m{have now been resolved}. However, ideal magnetohydrodynamics (MHD) is in many circumstances a poor approximation and non-ideal MHD effects need to be thoroughly considered. Ambipolar diffusion is expected to play a major role in star formation (\citet{MestelSpitzer56}), at the scale of molecular clouds by enabling the collapse of otherwise magnetically supported clouds (\citet{BasuCiolek04}) and at the scale of the first Larson's core with the formation of a centrifugally supported disk and the well-known {\it fragmentation crisis} (\citet{HennebelleTeyssier2008}). \m{Ambipolar diffusion is also important in protoplanetary disks} as they are in general only partially ionised. The microscopic and entropic heating resulting from the drift and collision between neutral and charged species is another very important \m{and relatively unknown} aspect which is \m{crucial} as soon as cooling or heating of the gas (thus radiative transfert) is taken into account (in contrast it is not relevant \m{when using} a barotropic equation of state). Magnetic resistivity effects range from prohibiting long-term MHD turbulence in molecular clouds (\citet{BasuDapp2010}) to preventing the {\it magnetic braking catastrophe} on small scales (\citet{DappBasu2010}). Its importance is also crucial in order to study disk formation around protostellar objects (\citet{Krasnopolsky}) and the physics of binary formation and brown dwarfs. Thus, it appears necessary to introduce the ambipolar and Ohmic diffusion in a 3D MHD code. Before exploring the astrophysical impact of such a study, however, the accuracy of the treatment of the complete MHD set of equations must be unambiguously assessed. This is the very aim of the present paper, in which we describe a prescription to incorporate ambipolar and Ohmic diffusion in the multi-dimensional MHD AMR code {\ttfamily RAMSES} (\citet{teyssier}), extending the ideal MHD version presented in \citet{teyssierMHD} and \citet{fromang}. Several numerical treatments have been derived from ideal MHD models, following different aims and thus \m{using} different methods. \label{rev3}\rev{The first attempt to implement ambipolar diffusion in a code was made by \citet{BlackScott1982} using an iterative approximation in an implicit first-order code. \citet{toth1994} used a semi-explicit method in a two-dimensional code to investigate instabilities in C-schocks. \citet{McLow} presented a widely used explicit method (\citet{Choietal}, \citet{MellonLi2009}, \citet{LiKrasnopolskyShang}) to implement single-fluid ambipolar diffusion in the strong coupling limit, and then developed a two-fluid model in order to capture shock instabilities. \citet{TilleyBalsara2008} and more recently \citet{TilleyBalsara2011} presented a semi-implicit scheme for solving two-fluid ambipolar diffusion, arguing that the single fluid approximation does not carry the full set of MHD waves that can propagate in a poorly ionized system. Multi-fluid approaches including ambipolar diffusion and Ohmic diffusion have been suggested by \cite{Falle2003}, or \cite{Osullivan2006} and then investigated by e.g. \citet{KunzMouschovias2009}. Recently, \citet{LiKrasnopolskyShang} used the single-fluid approach including more realistic resistivities based on a multi-fluid approach for ambipolar diffusion, Ohmic diffusion and Hall effect in two-dimensional (axi-symmetric) calculations. Another approach has been used by \citet{Machida_etal06} was to describe both ambipolar diffusion and Ohmic diffusion in one single Laplace operator $\eta \Delta B$, with $\eta$ taking into account every diffusive process at stake.} \m{These numerous studies have also given rise to several numerical tests, a number of which we will either perform directly or slightly modify to assess the accuracy of our treatment.} Our current study focusses on the one-fluid approximation (\citet{Shu_etal87}), as in previous calculations by \citet{McLow} and \citet{DuffinPudritz}. \label{revv1}\revv{We used a direct explicit method to implement non-ideal MHD terms in both the induction and energy equations (\citet{McLow}) in an AMR framework. We did not choose to account for non-ideal effects by adding ambipolar diffusion and Ohmic dissipation in a single Laplace operator as \citet{Machida_etal06}. Instead we kept the full expressions and proceeded separately for each non-ideal effect.} The paper is organized as follows. In \S~\ref{amb}, we first derive the equations for ambipolar diffusion in the single fluid approximation. We then describe the various tests we have performed, first without the hydrodynamics and then in a complete MHD situation, exploring in particular the propagation of Alfv\'en waves. Comparisons with existing analytical or benchmark solutions are presented in details, demonstrating the validity and the accuracy of our scheme. \S~\ref{mag} addresses the case of Ohmic diffusion, following the same procedure as for ambipolar diffusion, while \S~\ref{concl} is devoted to the conclusion.
|
\label{concl} In this paper we have described a numerical method to implement the treatment of the two important terms of non-ideal MHD, namely ambipolar diffusion and Ohmic dissipation, into the multi-dimensional AMR code {\ttfamily RAMSES}. For ambipolar diffusion, we have used a single fluid approach, which is valid when the Lorentz force and the neutral-ion drag force are comparable, corresponding to a domain of strong coupling between the fluid and the field lines. The situations where such an approximation can be made are numerous, \m{of which} cloud collapse or certain protoplanetary disks are two typical examples. The accuracy of our numerical resolution of the MHD equations \m{was} examined by performing a diversity of tests, for which either analytical or benchmark solutions exist. For both ambipolar and Ohmic diffusion, we first explored the purely magnetic case, without any coupling to the hydrodynamics. For ambipolar diffusion, this \m{was} done by comparing the evolution of a Dirac pulse to the solution provided by Barenblatt while for Ohmic diffusion, the solution is confronted to the well known heat diffusion equation. In a second step, we studied the full MHD case \m{(coupling the fluid to the magnetic field)} by considering first an oblique shock, and then the behavior of propagating and standing Alfv\'en waves. For all these tests \m{the solutions obtained with our method show excellent agreement with the analytical predictions, typically} within a few tenths of a percent on average, \m{showcasing} the validity and the robustness of our method. We have also carefully analyzed the main source of numerical error using the Modified Equation framework. \m{In order to} estimate the spatial resolution that is required to model non-ideal MHD effects reliably. This opens the avenue to a vast domain of astrophysical applications, in particular cloud collapse, pre-stellar core formation and protostellar disks where ambipolar and Ohmic diffusion processes \m{are believed to} play a dominant role. Such astrophysical applications of the non-ideal MHD equations with {\ttfamily RAMSES} will be explored in forthcoming papers. \bigskip
| 12 | 6 |
1206.2476
|
1206
|
1206.0703_arXiv.txt
|
Using the observed rate of short-duration gamma-ray bursts (GRBs) it is possible to make predictions for the detectable rate of compact binary coalescences in gravitational-wave detectors. These estimates rely crucially on the growing consensus that short gamma-ray bursts are associated with the merger of two neutron stars or a neutron star and a black hole, but otherwise make no assumptions beyond the observed rate of short GRBs. In particular, our results do not assume coincident gravitational wave and electromagnetic observations. We show that the non-detection of mergers in the existing LIGO/Virgo data constrains the progenitor masses and beaming angles of gamma-ray bursts (e.g., $\theta_j>4^\circ$ for $M_{\rm total}\ge20\msun$, for uniform component mass), although these limits are fully consistent with existing expectations. We make predictions for the rate of events in future networks of gravitational-wave observatories, finding that the first detection of a NS--NS binary coalescence associated with the progenitors of short GRBs is likely to happen within the first 16 months of observation, even in the case of a modest network of observatories (e.g., only LIGO-Hanford and LIGO-Livingston) operating at modest sensitivities (e.g., advanced LIGO design sensitivity, but without signal recycling mirrors), and assuming a conservative distribution of beaming angles (e.g. all GRBs beamed with $\theta_j=30^\circ$). Less conservative assumptions reduce the waiting time until first detection to a period of weeks to months. Alternatively, the compact binary coalescence model of short GRBs can be ruled out if a binary is not seen within the first two years of operation of a LIGO-Hanford, LIGO-Livingston, and Virgo network at advanced design sensitivity. We also demonstrate that the rate of GRB triggered sources is less than the rate of untriggered events if $\theta_j\lesssim30^\circ$, independent of the noise curve, network configuration, and observed GRB rate. Thus the first detection in GWs of a binary GRB progenitor is unlikely to be associated with the observation of a GRB.
|
\label{sec:intro} The LIGO and Virgo collaborations have recently released results from roughly a half year of observations, investigating the gravitational wave (GW) sky at unprecedented levels of sensitivity~\citep{LIGO:2012aa}. They did not identify any gravitational wave sources, and thereby established new upper limits on the rates of a variety of possible GW events in the nearby ($<200\,\mbox{Mpc}$) Universe~\citep{abadie:2011wc}. One of the most promising sources for GWs detectable by these ground-based observatories is the coalescence and merger of a compact binary system: two neutron stars (NS), two black holes (BH), or one of each. There has been an active program of observing gamma-ray bursts (GRBs), focusing on rapid follow-up to determine afterglows and identify host galaxies~\citep{2006ApJ...650..261S,2006MNRAS.367L..42P,2007ApJ...664.1000B,2009ApJ...696.1871P}. As a result, there is growing evidence that short/hard gamma-ray bursts are associated with the mergers of either two neutron stars, or a neutron star with a black hole~\citep{2010ApJ...708....9F,2011MNRAS.413.2004C,Berger:2011il}. This consensus is based on noting that the physical timescales are commensurate, the short GRBs do not appear to be associated with star formation (and therefore are unlikely to be associated with supernovae), and the GRBs occur far from the centers of their host galaxies. These studies have also provided redshifts for a subsample of short GRBs, thereby providing preliminary estimates for the rate densities of these events~\citep{Nakar:2005bs,Dietz:2011by}. There is great interest in gravitational wave/electromagnetic multi-messenger observations of these GRBs \citep{2012ApJ...746...48M,Evans:2012ta,Briggs:2012vj}, as such systems would help confirm the first detections of GWs, elucidate the properties of GRBs, and potentially provide interesting measurements of the Hubble constant and the dark energy equation-of-state \citep{Schutz:1986bz,2005ApJ...629...15H,PhysRevD.74.063006,2010ApJ...725..496N}. One of the most important properties of GRBs is the beaming of the gamma rays. This beaming directly relates to the total electromagnetic energy of the explosion, as well as the intrinsic event rate of the sources (as compared to the observed rate, which is a function of the ones that happen to point at us). Recent observations of a jet break in the short-duration gamma-ray burst GRB 111020A suggests a beaming opening angle of $\theta_j\sim3$--$8^{\circ}$~\citep{Fong:2012wz}. Other GRBs (e.g., GRB 070714B, GRB 070724A, and GRB 071227) have been found with beaming angles in the range $1$--$30^{\circ}$~\citep{Fong:2012wz,Coward:2012uz}, while non-detection of a jet break in the light curve of GRB 050724A places a lower limit on the beaming of that burst of $\theta_j\ge 25^{\circ}$~\citep{Grupe:2006uc}. Numerical studies, on the other hand, find $\theta_j\le 30^{\circ}$~\citep{Popham:1998ab,Rosswog:2002rt,Janka:2005yh,Rezzolla:2011da}. In this paper we estimate the limits that arise on the beaming of short-duration GRBs based on the non-detection of GWs from associated binary systems in the recent LIGO/Virgo science run. We also make projections for the detection rate of binary systems, as a function of mass and beaming angle, for future networks of GW observatories. We take a conservative lower limit on the observed rate density of local short GRBs of ${\cal R}_{\rm GRB}= 10\,\mbox{yr}^{-1}\mbox{Gpc}^{-3}$ \citep{Nakar:2005bs,Dietz:2011by,Coward:2012uz}, based primarily on BATSE and {\em Swift}\/ observations. We emphasize that this rate is determined purely through observations, although it is broadly consistent with the rates arising from population synthesis~\citep{2006ApJ...648.1110B,OShaughnessy:2008bb,2010ApJ...715L.138B,Abadie:2010fn,Dominik:2012vs}. The gravitational-wave limits presented here are based on observed GRB rates, and are therefore independent of, and complementary to, estimates based on population synthesis modeling. We assume that all short GRBs are associated with low-mass compact binary coalescence. There is developing evidence that this is the case, with perhaps a small sample of nearby GRBs occurring from other mechanisms, such as flares from soft gamma repeaters~\citep{Levan:2008hl,Abbott:2008kg}. While it is conceivable that not all short GRBs are the result of binary coalescences, it is perhaps even more likely that not all binary coalescences result in GRBs. We thus expect that our limits on the minimum beaming angle in Sec.~\ref{sec:S6} are low, and our estimates of the maximum wait time in Sec.~\ref{sec:aLIGO} are high.
|
We have explored the connection between the observed short GRB rate, the beaming angle of short GRBs, and the predicted rate of detectable binary systems associated with progenitors of GRBs in networks of gravitational-wave observatories. We have shown that existing LIGO/Virgo data provides preliminary constraints on the beaming angle and mass distribution of short GRB progenitor systems. For example, we find that short GRB progenitors of mass $M_{\rm total}>20\,\msun$ (uniformly distributed in component mass) and with beaming angles of $\theta_j<4^\circ$ are ruled out by existing LIGO/Virgo data. These constraints, while novel, are fully consistent with our current understanding of the short GRB engine and rates. We have analyzed the observed rate of short GRB progenitors in future networks of GW detectors. We find that, even in the pessimistic case of only two detectors (HL) operating at conservative sensitivity (without a signal recycling mirror), in 90\% of cases we would expect a first detection of a binary within 16 months if the GRBs are beamed within $\theta_j=30^\circ$, and within 55 days if $\theta_j=10^\circ$. The expected event rates are $1.7\,\mbox{yr}^{-1}$ ($\theta_j=30^\circ$) and $15\,\mbox{yr}^{-1}$ ($\theta_j=10^\circ$). We find that the HLV network, operating at zero-detuning and high laser power, would shorten these times to 4.9 months ($\theta_j=30^\circ$) and 17 days ($\theta_j=10^\circ$), with corresponding event rates of $5.6\,\mbox{yr}^{-1}$ and $49\,\mbox{yr}^{-1}$. Alternatively, the binary coalescence model for short GRB progenitors can be ruled out if an HLV network does not observe a binary within the first two years of observation. Finally, we have shown that the rate of GRB triggered observations of GW systems associated with GRBs is lower than the rate of untriggered observations if $\theta_j\gtrsim30^\circ$. This result is independent of network, noise curve, and GRB rate, and when coupled with recent observations of small beaming angles for short GRBs, suggests that the first detections of GRB progenitors with advanced GW networks will not involve the observation of GRBs. We conclude that, assuming short GRBs are the result of the merger of compact objects, and assuming that the resulting gamma-rays are beamed, the first detection of gravitational-waves from binary coalescence associated with a GRB progenitor will be untriggered, and may occur within months of operation of a modest network of ground-based gravitational wave observatories.
| 12 | 6 |
1206.0703
|
1206
|
1206.5917_arXiv.txt
|
{We statistically study the property of emerging flux regions (EFRs) and the upper solar atmosphere response to the flux emergence by using data from the Helioseismic and Magnetic Imager (HMI) and the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). Parameters including the total emerged flux, the flux growth rate, the maximum area, the duration of the emergence and the separation speed of the opposite polarities are adopted to delineate the property of the EFRs. The response of the upper atmosphere is addressed by the response of the atmosphere at different wavelengths (and thus at different temperatures). According to our results, the total emerged fluxes are in the range of (0.44 -- 11.2)$\times$10$^{19}$ Mx while the maximum area ranges from 17 to 182 arcsec$^2$. The durations of the emergence are between 1 and 12 hours, which are positively correlated to both the total emerged flux and the maximum area. The maximum distances between the opposite polarities are 7 -- 25 arcsec and are also correlated to the duration positively. The separation speeds are from 0.05 to 1.08 km s$^{-1}$, negatively correlated to the duration. The derived flux growth rates are (0.1 -- 1.3)$\times$10$^{19}$ Mx hr$^{-1}$, which are positively correlated to the total emerging flux. The upper atmosphere responds to the flux emergence in the 1600\AA\ chromospheric line first, and then tens and hundreds of seconds later, in coronal lines, such as the 171\AA\ (T=10$^{5.8}$ K) and 211\AA\ (T=10$^{6.3}$ K) lines almost simultaneously, suggesting the successively heating of atmosphere from the chromosphere to the corona.
|
% \label{sect:intro} The ubiquitous emerging flux regions (EFRs) on the Sun with variety of size, lifetime, total magnetic flux and field strength have been widely discussed. Magnetic features with large scale such as sunspots have fluxes of about 10$^{22}$ Mx (Maxwell) and generally exist in active regions (Thornton \& Parnell 2011). Magnetic features with small scale such as network fields and intranetwork (IN) fields have fluxes of 10$^{18}$ -- 10$^{19}$ Mx (Martin 1988; Wang et al. 1995) and 10$^{16}$ -- 10$^{18}$ Mx (Livingston \& Harvey 1975; Zirin 1985, 1987; Keller et al. 1994; Wang et al. 1995) respectively and generally exist in the quiet Sun. Using data from high-resolution Hinode (Kosugi \etal\ 2007) Solar Optical Telescope (SOT, Tsuneta \etal\ 2008), Thornton \& Parnell (2011) developed two different feature identification methods to determine the flux emergence rate of small-scale magnetic features in the quiet Sun. Combined with previous results, they found that the emergence frequency followed a power-law distribution with fluxes which ranged from 10$^{16}$ to 10$^{23}$ Mx . Simon \etal\ (2001) investigated the bipoles in the photosphere from emerging to splitting and then ending up in the magnetic network. They assumed a flux emergence rate of 7$\times$10$^{22}$ Mx d$^{-1}$ (consistent with that indicated by others for ephemeral regions (ERs)) that could keep the solar surface at a steady state. Hagenaar (2001) also examined a large number of ERs and obtained the total amount of flux emergence to be 5$\times$10$^{23}$ Mx d$^{-1}$ . They concluded that the magnetic field in the quiet Sun could be replaced in 14 hours with this emergence rate. When EFRs go through the atmosphere of the Sun, they produce various solar activities including ellerman bombs, blinkers, transient brightenings in small scale and solar flares, filament eruptions and coronal mass ejections (CMEs) in large scale as viewed by Low(1996) and heat the upper atmosphere (Li \etal\ 2007; Li \& Li 2010). When a new EFR appears, it may interact with pre-existing surrounding region and produce a tiny two-ribbon flare (Sakajiri \etal\ 2004) or an EFR-surge which is the first signature of magnetic flux emergence in many EFRs (Kurokawa \& Kawai 1993). The evolution of two consequent dipoles in the coronal hole (CH) is first reported by Yang \etal\ (2009). The two dipoles interacted with each other and produced a jet and a plasma eruption. Their work is meaningful for the investigation of the CH evolution. Using the multi-wavelength observations combined with a nonlinear force-free extrapolation, Valori \etal\ (2012) provided a coherent picture of the emergence process of small-scale magnetic bipoles, which subsequently reconnected to form a large scale structure in the corona. Granular-scale flux emergence, which leaded to cancellation at the penumbral boundary was studied by Lim \etal\ (2011). They used data from the New Solar Telescope (NST, Goode \etal\ 2010) at Big Bear Solar Observatory (BBSO, Cao \etal\ 2010) with high spatial and temporal resolution. A bright point (BP) developed in their case due to the cancellation. They thought the scale of ER in their work was about 0.5 -- 1 arcsec, which was not detected in a magnetogram obtained with the Helioseismic and Magnetic Imager (HMI, Schou \etal\ 2011). Hagenaar \etal\ (2008) investigated the evolution of magnetic network elements in the quiet-Sun photosphere with data from Michelson Doppler Imager (MDI, Scherrer \etal\ 1995) and found that the ER emergence rate is higher in flux-balanced regions. Wang \etal\ (2012) studied the solar IN magnetic elements. They found the flux emergence in these regions were mainly in the form of cluster emergence of mixed polarities and IN ERs. The samples in their work have an average separation of 3 -- 4 arcsec and lifetime of 10 -- 15 min, which are relatively small. Zhang \etal\ (2009) selected 6 events from Hinode Spectro-Polarimeter (SP, Lites \etal\ 2001) data to investigate the interaction between granulation and small-scale magnetic flux. Their result implies that the granule evolves quite differently according to the topology and emergence location of the EFR. Meanwhile, the granular flow also influences the development of EFR. With BBSO data, Zhang \etal\ (2006) compared the distribution of magnetic flux in a CH and a quiet region (QR). Their result demonstrates a balanced flux distribution in the QR and an imbalanced distribution in the CH, for IN fields and network fields . Yang \etal\ (2012) also statistically investigated the ERs in the quiet Sun and found two types of ERs: normal ERs and self-cancelled ERs. Their results also reveal that the ERs with higher magnetic flux tend to be self-cancellation easier. Statistical study about EFRs has also been done with SOT onboard the Hinode satellite by Otsuji \etal\ (2007, 2011). In the first paper they found the two polarities separated each other at a speed of 4.2 km s$^{-1}$ during the initial phase and then the separation speed decreased to about 1 km s$^{-1}$ ten minutes later. In the second paper, they demonstrated that the maximum spatial distance between two main polarities, the magnetic flux growth rate and the mean separation speed follow a power-law distribution with the total emerged flux. More works about magnetic fields can also be found in the review of Fang \etal\ (2011) and other references. EFRs are probably the brightest features in the non-flaring solar corona (Schmieder \etal\ 2004). Responding to flux emergence, the coronal loops may appear bright in all temperatures. Yohkoh Soft X-ray Telescope (SXT, Tsuneta \etal\ 1991) has observed many transient brightenings (Shimizu \etal\ 1992, 1994) in multi-wavelength coordinated observations, which are located in EFRs. The close relation between the emerging flux and transient brightenings has been extensively studies (Mein \etal\ 2001; Kubo \etal\ 2003). Zhang \etal\ (2012) carried out a detailed multi-wavelength analysis of two coronal bright points (CBPs) and proposed that the gentle brightenings and the CBP flashes might be due to null-point reconnection and the separatrix reconnection, respectively. Even though the SOT has observed many EFRs and some statistical work has been done to study EFR's properties (Otsuju \etal\ 2011), more work is still needed since the results are far from determined due to the wide span of their lifetimes, total fluxes, areas, \etc. Meanwhile, due to the intimate association of EFRs with various solar activities, statistical study of the properties of EFRs and the resultant response of the upper atmosphere is important to understand the physics of solar active regions and activities. In this paper, we use data from the HMI and the Atmospheric Imaging Assembly (AIA, Lemen \etal\ 2011) on board the Solar Dynamics Observatory (SDO, Pesnell \etal\ 2011) to study the property of EFRs and corresponding response of the upper solar atmosphere. In Section \ref{sect:Obs}, we will introduce the observations and data reduction. We give one example to demonstrate our study as a case and the statistical results in Section \ref{sect:result}. Our discussion and summary are presented in Section \ref{sect:sum}. \begin{figure} % \center{\resizebox{\textwidth}{!}{\includegraphics{ms1119fig1.ps}}} \caption{LOS magnetograms obtained with SDO/HMI. It lasted from 2010 September 5 07:00 UT to 12:00 UT , which covers the time range of the studied EFR in the paper. The scale bar in the middle indicates the magnetic field strength in Gauss.} \label{fig.hmi} \end{figure} \begin{figure} % \center{\resizebox{\textwidth}{!}{\includegraphics{ms1119fig2.ps}}} \caption{Evolution of response in the upper atmosphere from AIA/1600\AA (left column), 171\AA (middle column), 211\AA (right column) lasts from 07:00 UT to 11:00 UT in the same region as in Figure \ref{fig.hmi}. The contours overlaid on the 10:00 UT panels are the LOS magnetic field with strength of 80, 250, -80, -250G. The white and gray lines correspond to positive and negative polarities, respectively. } \label{fig.aia} \end{figure} \begin{figure} % \center{\resizebox{\textwidth}{!}{\includegraphics{ms1119fig3.ps}}} \caption{LOS magnetogram and its corresponding AIA intensity maps in 1600\AA, 304\AA, 171\AA, 193\AA, and 211\AA, respectively. The region is a little smaller than the ones in Figure \ref{fig.hmi} and Figure \ref{fig.aia}. The contours overlaid on the intensity maps are the LOS magnetic field with strength of 80, 160, -80, -160G. The white and gray lines correspond to positive and negative polarities, respectively.} \label{fig.over} \end{figure}
|
\label{sect:sum} Using the LOS magnetic field data from SDO/HMI, we statistically studied the properties of EFRs through the seven parameters mentioned above. The inferred relationship of these parameters are generally consistent with previous results (e.g. Otsuji \etal\ 2007, 2011). We found that the durations have a larger range (1--12 hours) in our case. All the parameters show a weak positive correlation with total emerged flux except the separation speed, which decreases as the emerged flux increases. This is consistent with the conclusion that tubes of larger EFR are anchored in deeper layers (Javaraiah \etal\ 1997). Meanwhile, for EFRs with flux less than 10$^{19}$ Mx in our cases the upper atmosphere does not shown apparent brightness enhancement in coronal lines, indicating small EFRs tend to interact with low-layer magnetic structure around. However, the heating effect for the lower atmosphere by EFRs with flux less than 10$^{19}$ Mx is not persistent but fluctuant. We deduce that in the lower atmosphere, the magnetic structures around tend to be smaller and lower, when small EFRs which are comparable with surrounding magnetic structures appear, the interaction between them will greatly change the morphologies of both. This will not guarantee the continuously heating. But when the EFR is larger (here we say with flux greater than 10$^{19}$ Mx), the interaction between the EFR itself and the surrounding magnetic structures may not change the morphology of EFR catastrophically and when it emerges into corona where the surrounding magnetic structures are quite larger and higher, the surrounding magnetic structures may ensure the successive heating. All of these guesses need simulation to prove it out. In previous papers of Otsuji \etal\ (2007, 2011), they used data from Hinode/SOT which only observes partial area of the sun during a certain time frame. So the parameters that they considered may be not as much as ours, since the data obtained by SOT probably not cover the whole duration of the event , just like missing the beginning phase or didn't contain the phase when magnetic flux reached the maximum. However, we can get the entire information of an EFR as long as we download abundant data thanks to the continuously observing of SDO. Therefor, our statistical result may be more reliable since we have data covering the entire process of the emergence. The statistical research for response of upper atmosphere has already been studied by Li \etal\ (2007) and Li \& Li (2010), and their works either did not have magnetic information (Li \& Li 2010) or the time resolution was too low (Li \etal\ 2007). In this paper, we have both the LOS magnetogram and five channels of UV/EUV observations for the chromosphere and corona with a time resolution of 12 second. The result shown in Figure \ref{fig.resp} (right panel) manifests that the emerging flux should first reach and heat the chromosphere, and then move to the corona and cause the coronal brightening. It is also mentioned in Li \etal\ (2007) that one could expect that the chromosphere displays enhanced brightening in the Ca II H line earlier than the corona in soft X-ray (SXR), but later than the increase of the integrated magnetic flux. It also manifests that the response time delay is much longer for larger emerged flux. A larger EFR interacts with the surroundings for a longer time and subsequently the heating process lasts a longer time. It should be mentioned that in our study, we use 12 min cadence HMI LOS magnetic field data, which is relatively small compared with the durations of the EFRs and certainly has some effect on our results, which may induce an uncertainty of 12 min for the time delay between flux emergence and upper response. But it is still relatively small when compared with the response time in this paper. The threshold (20\% of the maximum enhancement) used to define the start time of EUV response could also slightly affect the time delay. However, these do not change our results as a whole. In summary, from this statistical study we found that the derived parameters for EFRs generally have a large range, and all the durations, areas, separations, flux growth rates and average field strength are in weak positive correlation with the total emerged flux. EUV emissions are also related to the total emerged flux and delay with respect to the flux emergence by minutes to hours. The chromosphere responds to flux emergence first and then the corona. The delayed time increases with the temperature of the EUV emission, suggesting the successive heating of the upper atmosphere.
| 12 | 6 |
1206.5917
|
1206
|
1206.6809_arXiv.txt
|
% Weakly Interacting Massive Particles (WIMPs) may constitute most of the matter in the Universe. While there are intriguing results from DAMA/LIBRA, CoGeNT and CRESST-II, there is not yet a compelling detection of dark matter. The ability to detect the directionality of recoil nuclei will considerably facilitate detection of WIMPs by means of "annual modulation effect" and "diurnal modulation effect". Directional sensitivity requires either extremely large gas (TPC) detectors or detectors with a few nanometer spatial resolution. In this paper we propose a novel type of dark matter detector: detectors made of DNA could provide nanometer resolution for tracking, an energy threshold of 0.5 keV, and can operate at room temperature. When a WIMP from the Galactic Halo elastically scatters off of a nucleus in the detector, the recoiling nucleus then traverses thousands of strings of single stranded DNA (ssDNA) (all with known base sequences) and severs those ssDNA strands it hits. The location of the break can be identified by amplifying and identifying the segments of cut ssDNA using techniques well known to biologists. Thus the path of the recoiling nucleus can be tracked to nanometer accuracy. In one such detector concept, the transducers are a few nanometer-thick Au-foils of 1m$\times$1m, and the direction of recoiling nuclei is measured by "DNA Tracking Chamber" consisting of ordered array of ssDNA strands. Polymerase Chain Reaction (PCR) and ssDNA sequencing are used to read-out the detector. The detector consists of $\sim 1$ kg of gold and 0.1 kg of DNA packed into (1m)$^3$. By leveraging advances in molecular biology, we aim to achieve about 1,000-fold better spatial resolution than in conventional WIMP detectors at reasonable cost.
|
Introduction} The Milky Way, along with other galaxies, is well known to be encompassed in a massive dark matter halo of unknown composition. Only 5\% of the Universe consists of ordinary atomic matter, while the remainder is 23\% dark matter and 72\% dark energy \cite{Komatsu:2010fb}. Identifying the nature of this dark matter is the longest outstanding problem in modern physics. Leading candidates for this dark matter are Weakly Interacting Massive Particles (WIMPs), a generic class of particles that includes the lightest supersymmetric particle. These particles undergo weak interactions and their expected masses range from 1~GeV to 10~TeV. These particles, if present in thermal equilibrium in the early universe, annihilate with one another so that a predictable number of them remain today. For a wide range of parameters, the relic density of these particles is found to be roughly in agreement with the value measured by WMAP. Thirty years ago, Refs. \cite{Drukier:1983gj, Goodman:1984dc} first proposed that the most efficient laboratory mechanism for detecting weakly interacting particles, including WIMPs, is via coherent scattering with nuclei. Soon after \cite{DFS} computed detection rates in the context of a Galactic Halo of WIMPs. Then development of ultra-pure Ge detectors permitted the first limits on WIMPs \cite{Ahlen:1987mn}. Since that time, a multitude of experimental efforts to detect WIMPs has been underway, with some of them currently claiming detection. The basic goal of direct detection experiments is to measure the energy deposited when weakly interacting particles scatter off of nuclei in the detector, depositing 1-10 keV in the nucleus. Numerous collaborations worldwide have been searching for WIMPs using a variety of techniques to detect the nuclear recoil. The most difficult aspect of these experiments is background rejection. To avoid cosmic rays (CR), the experiments are placed deep underground. Yet radioactive backgrounds persist; fast neutrons produced by CR are particularly difficult to differentiate from WIMPs. Important tools in isolating a WIMP signal are the annual and diurnal modulations (AME and DME) that would be expected for WIMPs but not for most backgrounds. \medskip\noindent {\bf Annual Modulation Effect:} Three of us showed in 1986 that the count rate in WIMP direct detection experiments will experience an annual modulation \cite{DFS,Freese:1987wu} as a result of the motion of the Earth around the Sun: the relative velocity of the detector with respect to the WIMPs depends on the time of year. Thus the count rate in detectors should change with a cosine dependence on time. For the past ten years the DAMA experiment \cite{DAMA} has been claiming detection of an annual modulation. This experiment consists of a large number of NaI crystals situated in the Gran Sasso Tunnel and currently reports a 9$\sigma$ detection. Recently the CoGeNT experiment \cite{COGENT}, made of germanium, also reported annual modulation, at the 2.8~sigma level. A third experiment, dilution-refrigerator based CRESST-II \cite{CRESST}, has also announced anomalous results. There has been much discussion as to whether or not the three experiments may be consistent with the same WIMP parameter range, {\it e.g.} \cite{Kelso:2011gd, Fox:2011px} Yet CDMS II sees no annual modulation \cite{Ahmed:2012vq}, and both CDMS II \cite{Ahmed:2010wy} and XENON \cite{Angle:2011th} find null results that appear to be in conflict with the other three experiments. The situation is perplexing. \medskip\noindent {\bf Diurnal Modulation Effect:} A major step forward in the field of direct detection would be the development of detectors with directional capability ~\cite{spergel}, i.e., the capability to determine which direction the WIMP came from. As a result of the elastic scattering of WIMP off of a nucleus in the detector, the nucleus gets kicked in a particular direction (typically forward). Thus by determining the track of the nucleus one could identify the direction of the incoming WIMP (Figure 1). The WIMP flux in the lab frame is peaked in the direction of motion of the Sun (which happens to be towards the constellation Cygnus). Hence the recoil spectrum for most energies should be peaked in the direction opposite to this. The event rate in the backward direction is expected to be $\sim 10$ times larger than that in the forward direction~\cite{spergel,gondolo}. A directional detector which could measure the direction of the recoiling nuclei from the interaction is required to detect this 'head-tail' asymmetry. Given the capability of ascertaining this asymmetry, the statistical requirements to show a WIMP detection would only require $\sim$ 10-100 WIMPs \cite{copi:krauss, ck2, pap1}. In a second generation of directional detection experiments, the measurement of the diurnal variation of the count rate due to the daily rotation of the Earth could provide further information. Measurements of both the annual and diurnal modulations could then provide a "smoking gun" for the existence of WIMPs. In addition, any galactic substructure in the WIMP density, such as tidal streams, could show up as spikes coming from one particular direction in a directional detector. \begin{figure}[diurnal] \includegraphics[width=0.4\textwidth,height=0.3\textheight]{diurnal.pdf} \caption{Diurnal modulation of WIMPs: the Sun orbits around the Galactic Center (in a direction that happens to be towards the constellation Cygnus), therefore experiencing a WIMP wind, for which the orientation relative to the laboratory frame depends on the rotation of the earth, and hence time of day.} \label{fig6} \end{figure} \medskip\noindent {\bf Limitations of existing detectors:} The goal is to obtain the track of the recoiling nucleus after it has been hit by a WIMP. Yet in existing detectors the track length is shorter than the resolution of the detectors. Nuclei with high atomic number A also have high atomic charge $Z$; the density is high, $>$ 10 g/cc; and the energy deposition is proportional to $Z^2$. Thus the range of recoiling nuclei is super-short, often below 10 nm, while existing detectors have spatial resolution of a few microns. In both typical solid state detectors as well as liquid detectors, the range is 100 times shorter than the spatial resolution. As a consequence, in prior designs of "directional detectors", the density of the detectors must be brought low enough to increase the recoil range. For example, it is proposed to use Xe gas pumped to 0.1 Atmosphere \cite{Alner:2005, ahlen, Battat:2010ip}. Such a huge volume of gas must be placed underground and shielded against radioactivity. \medskip\noindent {\bf DNA based detector:} In this paper we describe a smaller and less expensive alternative: detectors made of DNA may provide nanometer resolution for tracking, energy threshold below 0.5 keV, and can operate at room temperature. One implementation consists of a large number of thin foils of gold (Au) with strings of single stranded DNA (ssDNA) hanging down from them as shown in Figure 2. The required amount of material is roughly 1kg of gold and 0.1kg of ssDNA. The DNA strands all consist of identical sequences of bases (combinations of A,C,G,T), with an order that is well known. An incoming WIMP from the Halo of our Galaxy strikes one of the gold nuclei and knocks it out of the plane with $\sim$ 10 keV of energy. The Au nucleus traverses a few hundred DNA strands before stopping. Whenever it hits the DNA, it severs the ssDNA strand. The cutoff segment of DNA falls down onto a capture foil and is periodically removed. The locations of the breaks are easy to identify via a plurality of techniques: the broken segments can be copied using Polymerase Chain Reaction (PCR), thus amplifying the signal a billion fold; then the collection of amplified cut-off ssDNA becomes what biologists call a "DNA ladder". It can be sequenced with single base accuracy, i.e. $\sim$ nm precision. Thus the path of the recoiling nucleus can be tracked to nanometer accuracy. More details of this particular detector design are presented below. Alternative detector designs may be implemented instead, but the important new development is the idea of using DNA in lieu of more conventional detector materials to provide thousand-fold better tracking resolution, so that directionality of the WIMPs can be determined. There are many advantages to this new technology of using DNA: \begin{enumerate} \item Nanometer spatial resolution enables directional detection with detector mass of 1 kg (much lower than any alternative proposal); \item Operates at room temperature; \item Low energy threshold of 0.5 keV, allowing for study of low mass $<10$GeV WIMPs; \item Flexibility of materials: One may choose from a variety of elements with high atomic mass ({\it e.g.} Au) to maximize the spin-independent scattering rate. Given a variety of materials one can also extract information about the mass and cross section of the WIMPs; \item One can also select materials with high spin to maximize spin-dependent interaction rate; \item Signal may be amplified by a factor of $10^9$ by using PCR; \item Excellent background rejection, by using dE/dx in vertex and $> 10^{16}$ physical granularity of the detector, i.e. there are $10^{16}$ voxels in a (1m)$^3$ detector. \end{enumerate} The nanometer tracking described in this paper may have many uses beyond dark matter detection as will be studied in future work.
|
Summary} A major step forward in the field of direct detection would be the development of detectors with directional capability. By contrasting the count rates in a detector in the direction toward and away from the Galactic WIMP "wind" that the Sun is moving into, the statistical requirements on the number of detected WIMPs drops to $\sim 100$ rather than thousands without the directional sensitivity. In the paper we proposed using DNA as a detector material that can provide nanometer resolution tracking. We presented a particular design consisting of modules of thin gold planes with single stranded DNA hanging down from each plane. The required amount of material is $\sim$ 1kg of gold and 0.1kg of ssDNA. The DNA strands all consist of (almost) identical sequences of bases (combinations of A,C,G,T), with an order that is well known. An incoming WIMP from the Halo of our Galaxy strikes one of the gold nuclei and knocks it out of the plane with $\sim$ 10 keV of energy. The Au nucleus moves forward into the strands of DNA, traverses thousands of these strands, and whenever it hits one, breaks the ssDNA. The locations of the breaks are easy to identify, using PCR to amplify the broken segments a billion fold followed by DNA sequencing to locate the break. In this way the path of the recoiling nucleus can be tracked to nanometer accuracy. We note that this design is not restricted to the use of Au nuclei, which can be interchanged with many different nuclei with high atomic number (so as to maximize the SI interaction rate). By using a variety of different materials, it should be possible to identify the mass and cross-section of the interacting WIMP. In addition, although the specific detector design may be modified, the important new development is the idea of using DNA in lieu of other detector materials to provide better tracking resolution so that directionality of the WIMPs can be determined. More generally, it is easy to imagine multiple applications for nanometer tracking beyond that of WIMP detection.
| 12 | 6 |
1206.6809
|
1206
|
1206.6662_arXiv.txt
|
We present the implementation of an \textit{\textbf{im}plicit-\textbf{ex}plicit} (IMEX) Runge-Kutta numerical scheme for general relativistic hydrodynamics coupled to an optically thick radiation field in two existing GR-(magneto)hydrodynamics codes. We argue that the necessity of such an improvement arises naturally in most astrophysically relevant regimes where the optical thickness is high as the equations become stiff. By performing several simple one dimensional tests we verify the codes' new ability to deal with this stiffness and show consistency. Then, still in one spatial dimension, we compute a luminosity versus accretion rate diagram for the setup of spherical accretion onto a Schwarzschild black hole and find good agreement with previous work which included more radiation processes than we currently have available. Lastly, we revisit the supersonic \textit{\textbf{B}ondi\textbf{ H}oyle \textbf{L}yttleton} (BHL) accretion in two dimensions where we can now present simulations of realistic temperatures, down to $T\sim 10^6$\,K or less. Here we find that radiation pressure plays an important role, but also that these highly dynamical set-ups push our approximate treatment towards the limit of physical applicability. The main features of radiation hydrodynamics BHL flows manifest as (i) an effective adiabatic index approaching $\gamma_{\rm eff}\sim 4/3$; (ii) accretion rates two orders of magnitude lower than without radiation pressure, but still super-Eddington; (iii) luminosity estimates around the Eddington limit, hence with an overall radiative efficiency as small as $\eta_{_{\cal BHL}}\sim 10^{-2}$; (iv) strong departures from thermal equilibrium in shocked regions; (v) no appearance of the flip-flop instability. We conclude that the current optically thick approximation to the radiation transfer does give physically substantial improvements over the pure hydro also in set-ups departing from equilibrium, and, once accompanied by an optically thin treatment, is likely to provide a fundamental tool for investigating accretion flows in a large variety of astrophysical systems.
|
The field of numerical relativistic hydrodynamics has recently seen much progress in treating astrophysical systems under more and more realistic conditions. Because of the large computational costs involved, the inclusion of multi-dimensional \textit{\textbf{g}eneral \textbf{r}elativistic \textbf{r}adiation\textbf{ h}ydro\textbf{d}ynamics} (GR-RHD) has been postponed for a long time, with the remarkable exception of neutrino transport in the context of supernovae simulations [see \citet{Lentz2012} and references therein]. However, due to the increasing power of supercomputers, the situation has started changing significantly in the last few years, and the inclusion of a photon-field is no longer regarded as a remote possibility. This delay has, however, not been due to the fact that dynamical radiation fields are not regarded as a main ingredient, rather it is the inherent difficulty of solving the radiation transfer equation\footnote{ See \cite{pomraning_1973_erh} and \cite{Mihalas84} for a comprehensive treatment of radiation hydrodynamics and \cite{Schweizer1988} for the extension to the relativistic case. }. The cooling time-scales of a dynamical fluid may easily vary over several orders of magnitude within the computational domain. This then leads to characteristic propagation speeds for the photons in optically thin regions that are much higher than the coupled fluid/photon speeds in optically thick regions. Not only are time-scales vastly different, but also additional spatial resolution is required whenever the coupling to the photon field induces small scale instabilities and turbulence. In addition, surfaces of astrophysical structures are typically not in \textit{\textbf{l}ocal \textbf{t}hermal \textbf{e}quilibrium} (LTE) and can cool very efficiently, usually on much shorter time scales than the dynamical ones. This problem becomes particularly severe when performing global simulations of astrophysical systems in which the principal force is gravity. In these cases, the spatial domain must firstly be large enough to contain the entire astrophysical structure and secondly, it needs to resolve the influence of gravity\footnote{ A complementary approach, which is not covered here, is to model not a global system, but only a small, representative region e.g. a shearing box.}. Any such multi-scale problem is numerically extremely costly and it is thus important to formulate efficient algorithms that include at least a leading order approximation to the various physics while still remaining computationally affordable. One of the most successful strategies was, and still is, represented by the so called projected symmetric trace-free (PSTF) moment formalism introduced by \cite{Thorne1981}. By defining moments of the radiation field similarly to how density, momentum and pressure of a fluid are defined as velocity moments of the corresponding distribution function, such a formalism provides an accurate, though still reasonably cheap, approximation to the solution of the radiation transfer equations. This approach is particularly appealing in the case of an optically thick medium, characterized by a strong coupling between matter and radiation. \citet{Farris08} were first to undertake the implementation of the corresponding radiation hydrodynamics equations in a general relativistic framework. A further step has been taken by \cite{Shibata2011}, who adopted the variable Eddington factor approach of \citet{Levermore1984} to solve the relativistic radiation-hydrodynamics equations both in the optically thin and in the optically thick limit. This represents a significant progress with respect to simplified treatments, where effective cooling functions are introduced. In spite of all this progress, major numerical difficulties still prevent the application of such schemes to realistic astrophysical systems; one of them being the presence of stiff source terms. For example, in \citet{Zanotti2011} (hereafter paper{\sc I}), after implementing and testing the framework suggested by \citet{Farris08}, we studied the \textit{\textbf{B}ondi \textbf{H}oyle \textbf{L}yttleton} (BHL) accretion flow onto a black hole, but we could only treat unrealistically high fluid temperatures of the order of $\sim 10^9$\,K or above. Though simplified, the BHL flow can effectively help our understanding of those compact sources accreting matter with a reduced amount of angular momentum, and is currently applied to the study of both High Mass X-ray Binaries \citep{Hadrava2012} and of the merging of supermassive black hole binaries [see \citet{Pfeiffer2012} and references therein]. In this paper, we address the problem of treating the optically thick regime compatible with the conservative formulation used in Eulerian GR-MHD codes, while at the same time coping with the stiffness of the source terms. As a stiff solver, we choose the \textit{\textbf{im}plicit-\textbf{ex}plicit} (IMEX) scheme by \citet{pareschi_2005_ier}, implement it in both {\sc Whisky}\footnote{\texttt{www.whiskycode.org}} and {\sc Echo}\footnote{\citet{DelZanna2007}}, and test the codes against each other. As the two codes contain internal differences, such as scheduling and general infrastructure, it is very useful to validate them both at this stage, even though the main part of the simulations shown in this paper are performed with {\sc Echo}, because of its spherical, non-uniform grid\footnote{{\sc Whisky} uses Cartesian adaptive mesh refinement, which is less suited for spherical models.}. The paper is organized as follows. In Sec.~\ref{Radiation_hydrodynamics_in_the_stiff_regime} we describe the treatment of the radiation stiff source terms. We detail an IMEX Runge Kutta scheme as our time integration stiff-solver. Sec.~\ref{Verification_of_the_scheme} presents the verification of our new scheme through a selected sample of stiff shock tube problems. Turning towards astrophysical applications, we first present in Sec.~\ref{sec:spherical} the results for spherical accretion in a regime that was constructed to be particularly challenging for the numerics. We also present a physical Michel solution and compare it with previous results. Abandoning spherical symmetry, we devote Sec.~\ref{sec:bh} to the study of the radiation hydrodynamics of BHL accretion in two dimensions. Finally, in Sec.~\ref{sec:conclusions} we offer a brief summary and our conclusions. Throughout the paper, we set the speed of light $c=1$, and the gravitational constant $G$ to a pure number. We extend the geometric units by setting $m_p/k_B=1$, where $m_p$ is the mass of the proton, while $k_B$ is the Boltzmann constant. However, we have maintained $c$, $G$, and $k_B$ in a explicit form in those expressions of particular physical interest. We refer the interested reader to Appendix~\ref{appendixA} of paper{\sc I} for the system of extended geometrized units.
|
\label{sec:conclusions} In this paper, we have revisited the optically thick, thermal radiation transfer in GR. First, we addressed the numerical problem of stiff source terms; proposed a numerical treatment, implemented and verified it. As we chose an IMEX Runge-Kutta scheme, we needed to isolate the principal stiff parameters, which were found to be the (density-weighted) opacities. After applying the new IMEX method to the one-dimensional problem of spherical accretion, we compared our results with those obtained earlier by \citet{Nobili1991} and found good agreement. In this spherical, stationary scenario the current formulation of the GR-RHD equations is fully applicable as long as the solution remains optically thick. We remark that there is not a unique stiffness threshold, valid for any physical scenario, at which the purely explicit scheme fails and the IMEX becomes necessary. In the case of a purely explicit RK scheme, when the source terms become stiff, it is possible to a certain extent to lower the $\cfl$ factor and obtain a stable evolution. However, the stiffness parameter can become very large, so the time-step very tiny. That is of course inefficient, and resorting to a stiff solver is the only way out. In general, if a problem can be solved with a purely explicit RK scheme, this is to be preferred as it is CPU-faster. However, we believe that most non-trivial radiation applications will exhibit stiffness and lead to code crashes with standard explicit RK schemes. We then revisited the Bondi Hoyle Lyttleton accretion in 2D for an astrophysical, dynamical problem. Here, we could show that: \begin{itemize} \item The IMEX scheme allows us to evolve models with realistic choice of parameters, of the order of $T\sim10^6$\,K; \item the dynamics of the flow are significantly affected by the radiation pressure, yielding super-Eddington accretion rates in the range $\dot{M}\sim[62,135]\dot{M}_{\rm Edd}$ and Eddington limited luminosities; \item the fluid and the radiation depart strongly from thermal equilibrium in shocked regions, particularly in the shock cone downstream of the accretor. \end{itemize} Our analysis has substantially benefited from the ability of our scheme to treat stiff source terms. However, we should also state a few words of caution as to the current shortcomings and necessary future improvements of our scheme: \begin{itemize} \item The optically thin regime cannot be treated yet, and further steps are required to incorporate the variable-Eddington factor approach. \item Temperatures of order $T<10^5$\,K, as they appear in small regions of the domain, require the inclusion of bound-free opacities, which are currently neglected. \item The only dissipative mechanism is currently thermal conductivity. Other types of viscosity such as an effective viscosity related to magnetic turbulence would be beneficial. Coupling the current equations to MHD represents another direction of future research. \item Since we currently cannot extract the luminosity in regions where the optical depth is low, we must trace a geometrical surface of constant $\tau\geq1$. However, it remains an uncertainty as to where such a surface should be placed, and the computed luminosities are therefore affected by at least one order of magnitude uncertainty. \end{itemize} Even in the presence of these limitations, our analysis may become relevant for the study of merging supermassive black-hole binaries, which have been attracting a lot of interest for the possible joint measure of electromagnetic and gravitational wave signal (in the context of multi-messenger astronomy). Neglecting the back-reaction of radiation onto matter, \citet{Farris:2009mt} already considered the BHL solution in a binary system, finding that luminosities as high as $10^{43}{\rm erg}\,s^{-1}$ can be obtained in a hot gas cloud of temperatures $T\sim 10^6$\,K. Such estimates are compatible with our calculations, but a dedicated work will be presented in the future.
| 12 | 6 |
1206.6662
|
1206
|
1206.0044_arXiv.txt
|
We investigate the possibility that a magnetic field may be present in the star $o-$Ceti (hereafter, Mira) and that the field plays a role in the star's mass loss. The model presented here is an application of an earlier derived theory that has been successfully employed for intermediate and high-mass evolved stars, and is now extended to the low-mass end. The modelling shows that it is possible to obtain a hybrid magnetohydrodynamic-dust-driven wind scenario for Mira, in which the role of a magnetic field in the equatorial plane of the star is dynamically important for producing a stellar wind. The wind velocity and the temperatures obtained from the model appear consistent with findings elsewhere.
|
\label{sec:intro} Mira (omicron-Ceti) is a relatively close evolved star that is in its asymptotic giant branch (AGB) infancy. It is the template upon which the class of stars called \emph{Mira variables} are based, which are characterised most strikingly, by large-amplitude long period variability. Mira varies with a period of about $332$ days \citep[e.g.][]{Lopez1997}. Observations of emission due to vibrational-rotational transitions in the CO molecule have not only revealed that the envelope of Mira is mildly asymmetric, possibly due to a bipolar outflow, perhaps due to an equatorial magnetic field \citep[see for e.g.][]{Planesas1990a,Planesas1990b, Lopez1997} but also CO transition line observations have also enabled a variety of different estimates of the wind velocity ranging from $4.8$ km/s \citep[see][]{Young1995} to $2.5$ km/s for the envelope's expansion at intermediate distances of $100-1000 R_0$ \citep[see][]{Ryde2000,Ryde2001}. Elsewhere, there is evidence for double winds \citep[see][]{Knapp1998} with a fast wind of about $6.7$ km/s, and a slow component of about $2.5$ km/s. Meanwhile, observations in the infrared at around $11 \mu$m, have revealed that the inner radius for the dust around Mira is at around $3 R_0$ \citep[see for e.g.][]{Bester1991,Lopez1997}, where $R_0$ is the photospheric radius. These observations have also been modelled with success \citep[see][]{Lopez1997} using an additional dust shell at $12 R_0$, as well as with dust clumps with photospheric spots. SiO-maser observations of the molecular shell close to the photosphere of Mira have revealed that the star may be rotating with a period of about $89 \times \sin(i)$ years \citep[see][]{Cotton2006}, where $i$ is the angle between the line of sight and the rotation axis. SiO maser polarisation studies on the other hand, indicate that Mira may harbour a predominantly radial magnetic field in its atmosphere \citep[e.g.][]{Cotton2004,Cotton2006}. Elsewhere, recent observations of masers have been instrumental in establishing the dynamic role that magnetic fields play in the atmospheres of evolved stars \citep[see for e.g.][]{Amiri2012,Vlemmings2011,Herpin2006} and theoretical efforts \citep[see][]{Busso2007} have delineated their role in transport of material in AGB stellar interiors with surface fields of $\stackrel{_<}{_\sim} 20$~G. Imaging of Mira in the near infrared (IR) and optical wavelengths has provided tools for measuring the diameter of the star \citep[see for e.g.][]{Haniff1995, van_Leeuwen1997}. \cite{Perrin2004} find that by varying the opacity of the molecular layer just ahead of the photosphere, they were able to account for the apparent changes in the diameter of Mira, arriving at an estimate of $\approx 350 R_{\odot}$, over the entire variability cycle of Mira. From the brief discussion of the literature presented above, it appears that the role that magnetic fields may play in shaping the outflow and influencing certain dynamic features of the envelope cannot be ignored. In the current study we present a rudimentary model integrating the effects of rotation, an equatorial magnetic field and the usual dust-driving picture into one cohesive scenario for Mira's outflow. The work presented here represents an extension of our earlier theory \citep[see][]{Thirumalai2010, TH2012} to the low-mass end of AGB stars; viz., Mira which is about $1.5 M_{\odot}$ \citep[e.g.][]{Martin2007}. Now that stellar rotation may have been detected in Mira, the aim of the current work is to raise the question, \emph{how important is the magnetic field in the stellar outflow and can Mira be a magneto-dusty rotator, given the current observations?}
|
\label{sec:results} Along with the basic ingredients of the model listed in Table~1, the set of parameters $\{ B_0, u_0, u_a, r_a, \gamma, \Gamma_d, i \}$ are varied until a critical solution to Eq.~(\ref{eq:1}) is obtained that satisfies the following criteria. \begin{enumerate} \item[1.]{The solution passes through all three critical points; the sonic point, the radial Alfv\'{e}n point and the fast point} \item[2.]{The solution is continuous through the radial Alfven point.} \item[3.]{The velocity profile starts at the base of the wind sub-sonic and attains a super-Alfv\'{e}nic terminal velocity at large distances} \item[4.]{The temperature range in the dust condensation region (within a few stellar radii from the photosphere) is consistent with observations.} \item[5.]{The gas terminal velocity is consistent with observations.} \end{enumerate} This optimisation procedure carried out in tandem with integrating the differential equation in Eq.~(\ref{eq:1}) results in a picture of a hybrid MHD-dust-driven wind for Mira as shown in Figure~ \ref{fig:figure1}. The critical wind solution is shown as the solid red line, which comprises of two parts, $L_1$ and $C_2$. These two lines intersect at the dust formation radius $r_d$, which in the current model is located at $3 R_0$. In the region $r \geq r_d$ Eq.~(\ref{eq:1}) is integrated with the presence of the dust parameter $\Gamma_d$, which represents dust grain drag acting on the gas; it is this part of the solution that is labelled $C_2$. On the other hand, inside $r \leq r_d$ there is no dust and as a result Eq.~(\ref{eq:1}) is integrated in this latter region without the dust parameter, as a pure WD solution. This part of the solution is labelled as $L_1$. Thus in the region $R_0 \leq r \leq r_d$, a pure WD mechanism is responsible for transport of stellar material. Together, $L_1 + C_2$ forms the combined hybrid MHD-dust-driven wind. \begin{figure} \begin{center} \includegraphics[width=3.5in, scale=0.9]{Fig1.eps} \end{center} \caption{Hybrid wind solution is shown for Mira with parameters $u_A \approx 0.14 v_{esc, 0}$, $r_A \approx 43.47 R_0$ and for $\Gamma_d \approx 0.06$ and remaining parameters as given in Tables 1 and 2. The red solid line ($L_1+C_2$) traces the hybrid MHD-dust-driven wind solution for Mira. The decreasing blue solid line traces the temperature and should be interpreted using the right hand y-axis.} \label{fig:figure1} \end{figure} The radial Alfv\'{e}n point and the fast point lie nearly coincident upon one another; shown by the black dashed vertical line at $r \approx 43 R_0$. Theoretically speaking, if we assume that dust condensation occurs at the photosphere, then we would obtain the combined solution $C_1 + C_2$ by integrating Eq.~(\ref{eq:1}) with the dust parameter, over the entire domain $R_0 \leq r \leq 100 R_0$. However, in the atmosphere of Mira, dust formation occurs at the dust condensation radius $r=r_d$ and not at the photosphere. Therefore, inside the dust radius, $r \leq r_d$, the wind starts off at the photosphere at some velocity $u_0$, and proceeds outwards along the trajectory $L_1$, and after dust condensation at $r=r_d$, the solution then switches to proceed outward along $C_2$, rather than continue along the unphysical solution $L_2$. Thus, it is seen explicitly, that without the onset of dust formation at $r=r_d$, there would not be any efflux from Mira, since there is only one solution ($C_2$) that passes through all three critical points, and emerges super-Alfv\'{e}nic at large distances. As can be seen, the gas terminal velocity is about 5~km/s in the equatorial plane, which is in reasonably good agreement with estimates of the wind velocity of Mira \citep[e.g.][]{Young1995,Martin2007}. The dust velocity profile is also shown in Figure~\ref{fig:figure1} as the brown dot-dashed line. This is computed according to Eq.~(\ref{eq:4}), once the gas velocity profile is known. The dust velocity is slightly larger than the gas velocity, as expected, in a dust-driven wind. The red dashed line represent the azimuthal velocity profile of the gas. This profile is typical for a magneto-centrifugal wind. The blue solid line shows the temperature profile in the atmosphere of Mira and should be interpreted using the right hand side axis. The photospheric temperature is about $2500$ K for the model shown. Finally, the green shaded area shows the so called \emph{hybrid region}. This region is bounded to the left by $r=r_d^{in} \approx 2.6 R_0$, this is the lower limit for the inner dust radius as given by \cite{Danchi1994}. To the right, the hybrid region is bounded by the sonic point of the pure WD magneto-centrifugal model. The sonic point of the hybrid model lies at $r \approx 5.61 R_0$; just inside the hybrid region. As seen in our earlier study \citep[see][]{Thirumalai2010}, one of the ways in which a hybrid wind is possible is if the sonic point of the hybrid model lies within the sonic point of the pure WD model; i.e., $r_s < r_s^{WD}$. Moreover, the dust formation radius must also then lie inside $r \leq r_s$. The temperature in the hybrid region can be inferred from the temperature profile shown, to be about $1000 \stackrel{_<}{_\sim} T \stackrel{_<}{_\sim} 1300 $ K, which is well within the observed range of temperatures at this distance from the star \citep[e.g.][]{Lopez1997, Bester1991, Danchi1994, Perrin2004}. Finally the optimised values for the different variable parameters in the model are given in Table 2. Notice that the surface radial magnetic field at the photosphere is obtained to be about $4$ G, which is within the range of field strengths estimated by \cite{Herpin2006} and \cite{Busso2007} for AGB stars. Presently, we turn our attention to the question of hot spots on the photosphere of Mira, and the related question of the influence of the spot on the stellar wind, ahead of the spot in the atmosphere. Figure~\ref{fig:figure2}(a) shows a hybid MHD-dust-driven wind model where the photospheric temperature is increased to about $2700$ K. However, in this second model instead of formulating a hybrid wind model as before, with dust formation occurring within the sonic point, we chose a different scenario. Our motivation here was to investigate the possibility regarding dust formation at around $12 R_0$, at which distance \cite{Lopez1997} model a second dust shell. \begin{figure} \begin{center} \includegraphics[width=3.5in, scale=0.9]{Fig2.eps} \end{center} \caption{(a) Hybrid wind solution is shown for a scenario with a hot spot at the photosphere of Mira. This model has parameters $u_A \approx 0.15v_{esc, 0}$, $r_A \approx 29.21 R_0$ and $\Gamma_d \approx 0.1$ and remaining parameters as given in Table 1. The surface magnetic field was found to be $B_0 \approx 1.15$G. The decreasing blue solid line traces the temperature and should be interpreted using the right hand y-axis. (b) Gas velocities obtained by perturbing the solution in the vicinity of $r_A$ and (c) the corresponding dust velocities.} \label{fig:figure2} \end{figure} Within the framework of the current theory, we found that the only way to have a viable wind scenario with dust formation at this distance, was by collocating the dust formation radius with the radial Alfv\'{e}n point. However, in this case, as can be seen from Figure~\ref{fig:figure2}, the solution is not smooth at the radial Alfv\'{e}n point. In this scenario, the solution need not be smooth at $r=r_A$, as this also happens to be the dust formation radius, hence a kink in the solution is allowed. It is possible that the dust formation can occur outside the fast point, by fine tuning the parameters of the model. This would place the dust formation radius in the vicinity of about $20-30 R_0$. While we do not show such a scenario in Figure~\ref{fig:figure2}, it is to be acknowledged that it may be possible within the framework of the hybrid MHD-dust-driven wind theory. Our objective here was to formulate a model with dust formation occurring at a distance of about $12 R_0$, to be consistent with other models for dusty shells or clumps \citep[e.g.][]{Lopez1997}, while obtaining temperatures in agreement with observations. In Figure~\ref{fig:figure1} it can be seen that the temperature at the left bound of the hybrid region ($r=r_d^{in}=2.6 R_0$) is about $\sim 1300$ K. This same temperature is calculated to be at a distance of about $2.9 R_0$ in Figure~\ref{fig:figure2}. Thus, ahead of a hot spot in the atmosphere, the viable dust formation region moves further out from the photosphere, as would be expected. In Figure~\ref{fig:figure2} the temperature at the sonic point is seen to be about $\sim 900$ K. Thus the range of temperature in this model is similar to that for the hybrid region in Figure~\ref{fig:figure1}, therefore it is still possible to formulate a hybrid wind scenario with dust formation occurring within the sonic point, as was shown in Figure~\ref{fig:figure1}. However, as mentioned earlier, in the current model our goal is to locate a second dust shell outside the sonic point at around $12R_0$ \citep[see][]{Lopez1997} and not within it. In this scenario, with a short-lived hot spot on the photosphere, the temperature in the gas is about $800$ K at the radial Alfv\'{e}n point ($r=r_A$). Thus, the observed temperature for the dust of about $600$ K at this distance is quite feasible \citep[e.g.][]{Lopez1997}. Overall, for the lifetime of the hot spot, it is possible to sustain a hybrid wind with dust forming at $12 R_0$. A pure WD mechanism transports stellar material from the photosphere, through the sonic point and out to the radial Alfv\'{e}n point. After dust formation at this location, the MHD-dust-driven wind then negotiates its way through the remaining critical point; the fast point and leaves the star super-Alfv\'{e}nic. Comparing Figure~\ref{fig:figure2}(a) with Figure~\ref{fig:figure1} reveals that the hybrid model is quite sensitive to changes in the photospheric temperature and the magnetic field. For the model shown in Figure~\ref{fig:figure2}, the surface radial magnetic field strength was found to be $\approx 1.15$ G. The dust parameter ($\Gamma_d$) was found to be about $0.1$; a little higher than in the previous model (c.f. Table~2). With these parameters, the terminal wind velocity is also concomitantly higher, at around $11$ km/s in the equatorial plane. In comparison to the time for one stellar rotation, since the hot-spot at the photosphere would be short-lived, therefore the hot spot model described above would be valid for the duration of the spot. In this regard, there are some concerns that are inherited from collocating the dust formation and radial Alfv\'{e}n points. In the main, dust formation and growth is a stochastic process that is not completely understood. Particularly, for the wind ahead of a short-lived hot spot in the atmosphere, the physical processes may be quite dynamic over time-scales comparable to the spot lifetime. As a result small changes in the wind velocity in the vicinity of the radial Alfv\'{e}n point can result in a drastically different wind velocity profile and indeed the wind may not be able to navigate through the fast point. This is shown in Figure~\ref{fig:figure2}(b) and (c). We have perturbed the gas velocity by a small amount ($\stackrel{_<}{_\sim} 0.01\%$) ahead of the radial Alfv\'{e}n point and then integrated the perturbed solution outwards. Figure~\ref{fig:figure2}(b) shows the unperturbed solution as the red solid line and the perturbed wind solutions as the dashed lines. We see that this perturbation of the gas velocity results in the wind becoming either a failed wind, where it does not pass through the fast point (the dashed lines below the solid red line) or the wind becomes an unphysical double valued wind (dashed lines above the the red solid line that form loops). In either case, this suggests that minor perturbations of the wind velocity around the radial Alfv\'{e}n point will drastically change the nature of the outflow. Figure~\ref{fig:figure2}(c) shows the corresponding dust velocity profile for both the unperturbed and the perturbed solutions. Should the dust follow any of the perturbed trajectories then it will not leave the star and can lead to instabilities in the flow. Therefore, while it is possible that in the atmosphere of Mira, conditions ahead of a mild hot spot may result in a hybrid wind with dust formation at around $12 R_0$, these conditions would be limited by the life-time of the spot, and as such cannot be classified as steady-state, even when compared to the stellar rotation time. Such a localised phenomenon ahead of a hot spot may be able to account for clumpiness of the dust distribution and even spatially distinct dust shells around Mira \citep[e.g.][]{Lopez1997}. We shall end this discussion by cautioning the reader that fully dynamic 2- or 3-D modelling would be needed for establishing the importance of such dynamic short time-scale phenomena, which cannot be entirely gleaned from the simplistic theory presented here. \begin{table} \centering \label{tab:Table2} \caption{Optimised values of the variable parameters for the star Mira.} \begin{tabular}{@{}ll@{}} \hline \hline Parameter & Value \\ \hline \hline $B_0$ & $\approx 4.11$ G\\ $u_0$ & $\approx 5.89 \times 10^{-6}$ km/s \\ $u_A$ & $\approx 4.93$ km/s \\ $r_A$ & $\approx 43.47 R_0$ \\ $\gamma$ & $\approx 1.06$ \\ $\Gamma_d$ & $\approx 0.06$ \\ $i$ & $\approx 26.60^{\circ} \approx 0.46 $ rad \\ \hline \hline \end{tabular} \end{table} The conclusions of the current work are summarised in the following section.
| 12 | 6 |
1206.0044
|
1206
|
1206.0428_arXiv.txt
|
Accurate distances to pulsars can be used for a variety of studies of the Galaxy and its electron content. However, most distance measures to pulsars have been derived from the absorption (or lack thereof) of pulsar emission by Galactic \hi\ gas, which typically implies that only upper or lower limits on the pulsar distance are available. We present a critical analysis of all measured \hi\ distance limits to pulsars and other neutron stars, and translate these limits into actual distance estimates through a likelihood analysis that simultaneously corrects for statistical biases. We also apply this analysis to parallax measurements of pulsars in order to obtain accurate distance estimates and find that the parallax and \hi\ distance measurements are biased in different ways, because of differences in the sampled populations. Parallax measurements typically \emph{under}estimate a pulsar's distance because of the limited distance to which this technique works and the consequential strong effect of the Galactic pulsar distribution (i.e. the original Lutz-Kelker bias), in \hi\ distance limits, however, the luminosity bias dominates the Lutz-Kelker effect, leading to \emph{over}estimated distances because the bright pulsars on which this technique is applicable are more likely to be nearby given their brightness.
|
\label{sec:intro} The rotation of pulsars, which causes their continuous emission to be observed as highly regular pulses, makes these objects highly useful probes of any dispersive phenomena in interstellar space. Combined with an accurate and precise distance, pulsar emission (specifically its dispersion and Faraday rotation) provides crucial information for modelling of the Galactic electron distribution and magnetic field. Parallax measurements are non-trivial undertakings and only very few significant parallax measurements \citep{gtwr86,bmk+90a} were made within the first two decades after pulsars were discovered. Another method to determine a pulsar's distance is based on Galactic \hi\ spectra in the direction to the pulsar. This method (known as the \emph{kinematic} or \hi\ method) compares the \hi\ spectrum on-pulse (when the pulsar emission is seen) and off-pulse (when the pulsar emission beam is turned away). Any observed pulsar absorption must originate in gas lying closer than the pulsar; while gas located farther than the pulsar will \emph{not} exhibit absorption. The velocities of these respective \hi\ regions are subsequently derived from the spectrum and translated to distances with help of a Galactic rotation model. The distance of the furthest \hi\ gas that appears in absorption then provides a lower limit $D_{\rm low}$ on the pulsar distance, while the distance of the nearest gas that only appears in emission, is interpreted as an upper limit $D_{\rm up}$ on the pulsar distance. Roughly two decades after the discovery of pulsars, \citet[henceforth FW90]{fw90} collated all published pulsar distances, which at the time consisted of 50 \hi\ distances, three parallax measurements and 20 distances by association. Given the importance of \hi\ distances, they critically investigated the various measurements and defined a set of criteria that has been used in almost all subsequent publications. Progress in both interferometric hardware (at the Long Baseline Array in the South and the Very Long Baseline Array in the North) and in the sensitivity of pulsar timing, subsequently allowed an exponential increase in the number of measured pulsar parallaxes so that currently 57 parallaxes are measured. This led \citet[henceforth VLM10]{vlm10} to collate those distances and investigate the statistical bias predicted by \citet{lk73}. The work presented by \citetalias{vlm10} was based on a Bayesian analysis that took into account both the Galactic distribution of pulsars (which is the actual bias first discussed by Lutz and Kelker in 1973\nocite{lk73}) and the intrinsic pulsar luminosity distribution; but they only considered parallax measurements. In this paper, we present an update of the work done by \citetalias{fw90}: we list all 80 published distances to pulsars and other neutron stars, based on \hi\ measurements or associations with objects having \hi\ distances, and evaluate them based largely on the criteria laid out by \citetalias{fw90}. We then improve the analysis of \citetalias{vlm10} by deriving fully analytic solutions that replace the need for (approximate) Monte-Carlo simulations. Also, the \citetalias{vlm10} analysis is expanded to incorporate information provided by \hi\ distance limits; and to provide bias-corrected \emph{distances} in addition to parallaxes. As in the case of \citetalias{vlm10}, the present paper bases its bias-correction method on empirical models for the Galactic pulsar distribution and luminosity function. These models do add an unquantified level of uncertainty to the analysis, but can easily be updated as our knowledge about the pulsar population grows through pulsar surveys. The evaluation of \hi\ distance limits is presented in Section~\ref{sec:HID}; the likelihood analysis to correct for the biases is derived in Section~\ref{ssec:Bayes}. Bias-corrected parallaxes and distances are given in tables~\ref{tbl:dist} and \ref{tbl:vlm10} and a summarising discussion is found in Section~\ref{sec:results}.
|
\label{sec:results} Of the 80 pulsars with \hi\ distance limits, all but one have post-correction distances consistent (at the 1$\,\sigma$ level assuming the uncertainties derived from our analysis) with the \hi\ limits published. The exception is PSR~J2018+2839 (PSR~B2016+28), which has a lower distance limit of $3.2\pm 2.1$\,kpc, but a parallax measurement of $1.03\pm 0.10$\,mas \citep{bbgt02}, which dominates the result and therefore makes the \hi\ distance limit irrelevant. Furthermore, there is a single source that is beyond the upper \hi\ distance limit (though within 1$\,\sigma$): this is XTE J1810-197, for which we determine a bias-corrected distance of $3.7\pm 0.5$\,kpc, which is just beyond the upper distance limit of $3.4\pm 0.6$\,kpc derived from \hi\ observations. Since for this neutron star both the lower and the upper limit are equal; and because no radio luminosity is available, the volumetric term determines the slightly higher distance. For 20 sources, the bias-corrected distance is closer than the lower \hi\ distance limit (though within 1$\,\sigma$) and 59 (or three out of four) sources are completely within the distance limits, with typically bias-corrected distances close to the lower \hi\ distance limit. The fact that our analysis finds sources are more likely to be closer to the lower rather than upper \hi\ distance limit (or, indeed, closer even than the lower limit), is unexpected when seen from the perspective presented by \citet{lk73}. There are two reasons for this. First, the upper \hi\ distance limits are mostly past the tangent point. This means that the volumetric term peaks within -- or close to -- the range allowed by the \hi\ limits, which causes the volumetric bias to be either very weak or non-existent. Second, the pulsars to which \hi\ distance limits have been measured, are mostly bright sources, with the exception of the flaring neutron stars and those neutron stars that have \hi\ limits derived from associations with supernova remnants. The brightness of these pulsars implies a luminosity term that peaks at very small distances. Comparing the results in Table~\ref{tbl:dist} and the discussion above with the results in Table~\ref{tbl:vlm10}, it is clear that the types of neutron star distance estimates (parallax and \hi\ measurements) suffer from different statistical biases, although the magnitude of the biases is limited in both cases. While parallax measurements are typically biased towards smaller distances (i.e. the sources are actually \emph{further} away than suggested by the measurement) because of the relatively limited distance to which this technique works (and the consequential strong effect of the volumetric term), the \hi\ measurements are typically biased towards larger distances (i.e. the sources are often \emph{closer} than suggested by the measurement) because the volumetric term has little impact and the luminosity term dominates the analysis. Finally, of the eight pulsars with both \hi\ distance limits and parallax distances, only PSR J1857+0943 (B1855+09) has a bias-corrected parallax that is \emph{in}consistent with the parallax measurement. The published value of $1.1\pm 0.2$\,mas \citep{vbc+09} is found to be considerably larger than the most likely value of $0.6^{+0.2}_{-0.1}$\,mas, which is partly because of the volumetric information \citepalias[as already found by][who derived a value of $0.9\pm 0.2$\,mas]{vlm10}, but also because of the \hi\ limits, which place the pulsar well beyond 1\,kpc.
| 12 | 6 |
1206.0428
|
1206
|
1206.2936_arXiv.txt
|
We give analytic expressions for image properties of objects seen around point mass lenses embedded in a flat $\Lambda$CDM universe. An embedded lens in an otherwise homogeneous universe offers a more realistic representation of the lens's gravity field and its associated deflection properties than does the conventional linear superposition theory. Embedding reduces the range of the gravitational force acting on passing light beams thus altering all quantities such as deflection angles, amplifications, shears and Einstein ring sizes. Embedding also exhibits the explicit effect of the cosmological constant on these same lensing quantities. In this paper we present these new results and demonstrate how they can be used. The effects of embedding on image properties, although small i.e., usually less than a fraction of a percent, have a more pronounced effect on image distortions in weak lensing where the effects can be larger than 10\%. Embedding also introduces a negative surface mass density for both weak and strong lensing, a quantity altogether absent in conventional Schwarzschild lensing. In strong lensing we find only one additional quantity, the potential part of the time delay, which differs from conventional lensing by as much as 4\%, in agreement with our previous numerical estimates.
|
Recently we have investigated the quantitative effect of embedding on gravitational lensing observations by resorting to a mixture of analytic work with a few numerical applications \cite{Kantowski10,Chen10,Chen11}. The analytic results for quantities like the bending angle $\alpha$ produced by a point mass were given as functions of two impact variables $r_0$ and $\pht$ (see Fig.1). These two parameters are not independent if the source and deflector redshifts are fixed. Because of the non-linearity of the expressions we were only able to give an iterative procedure that allowed us to numerically evaluate the conventional minimum impact Schwarzschild coordinate $r_0$ as a function of $\pht$ \cite{Chen11}. We have since been able to analytically carry out this iterative procedure (see Eq.\,(\ref{r0}) in the appendix) and hence obtain all lensing properties such as position, shear, etc., as functions of the single impact angle $\pht$. The solution of the embedded lens equation and comparison with classical lensing theory is therefore greatly simplified. Because the dependence of observable quantities on this angle is highly nonlinear, we are not able to eliminate $\pht$ in favor of $r_0$. Derivations of our current results follow the steps given in \cite{Kantowski10,Chen10,Chen11} which we will not repeat but we will instead simply present the new results and use them on two examples. The point mass lens is the simplest lens to use to demonstrate the effects of embedding; however, all lenses will require corrections. An embedded point mass lens is constructed by condensing a comoving sphere of pressureless dust of a standard homogeneous cosmology to a singular point mass m at the sphere's center, a construction first made by Einstein himself \cite{Einstein45,Schucking54,Kantowski69,Kantowski95}. When the cosmology contains a cosmological constant $\Lambda$ the gravity field inside the evacuated sphere is described by the Kottler metric \cite{Kottler18,Dyer74} rather than the Schwarzschild metric. In this paper we restrict ourselves to a flat background cosmology whose Friedman-Lema\^itre-Robertson-Walker (FLRW) metric is \be ds^2=-c^2dT^2+R(T)^2\left[{d\chi^2}+\chi^2(d\theta^2+\sin^2\theta d\phi^2)\right]. \label{FLRW} \ee The embedded condensation is described by the Kottler or Schwarzschild-de Sitter metric \be \label{Kottler} ds^2=-\gamma(r)^{-2}c^2dt^2+ \gamma(r)^2dr^2+ r^2(d\theta^2+\sin^2\theta\, d\phi^2), \ee where $\gamma^{-1}(r)\equiv\sqrt{1-\beta^2(r)}$ and $\beta^2(r)\equiv r_s/r+\Lambda r^2/3$. The constants $r_s$ and $\Lambda$ are the Schwarzschild radius ($2G{\rm m}/c^2$) of the condensed mass and the cosmological constant respectively. By matching the first fundamental forms at the Kottler-FLRW boundary, angles $(\theta,\phi)$ of equations (\ref{FLRW}) and (\ref{Kottler}) are identified and the expanding Kottler radius $r_b$ of the void is related to its comoving FLRW boundary $\chi_b$ by \be\label{rb-T} r_b=R(T)\chi_b. \ee By matching the second fundamental forms the comoving FLRW radius $\chi_b$ is related to the Schwarzschild radius $r_s$ of the Kottler condensation by \be\label{second-form} r_s=\Omega_{\rm m}\frac{H_0^2}{c^2}(R_0\chi_b)^3. \ee Here $H_0$ is the familiar Hubble constant and the cosmological constant $\Lambda$ is constrained to be the same inside and outside of the Kottler hole. \begin{figure*} \includegraphics[width=0.8\textwidth,height=0.26\textheight]{fig1.eps} \caption{A photon travels left to right entering a Kottler hole at $r=r_1,\, \phi=\pi-\tilde{\phi}_1$ and returns to the FLRW dust at $r=r_1+\Delta r,\, \phi=\tilde{\phi}_1 +\Delta\phi$. The photon's orbit has been chosen symmetric in Kottler about the point of closest approach $r=r_0$, $\phi=\pi/2$. Due to the cosmological expansion, $\Delta r>0$. The slope of the photon's co-moving trajectory in the x-y plane is $\xi_1$ when incoming and $\xi_1+\alpha$ after exiting. The resulting deflection angle as seen by a comoving observer in the FLRW background is $\alpha$, which is negative by convention. Expressions for $r_1,$ $\Delta r,$ $\xi_1,$ $\Delta\phi,$ and $\alpha$ as functions of the two impact parameters, $r_0$ and $\pht$, can be found in \cite{Kantowski10,Chen10,Chen11}.} \label{fig:fig1} \end{figure*} In the following sections we will give image locations and image properties of small sources seen through Kottler voids in an otherwise flat FLRW universe (an embedded lens). We assume that the source and deflector are located at fixed FLRW comoving distances $\chi_s$ and $\chi_d$ from the observer which correspond to angular diameter distances $D_s$ and $D_d$, and redshifts $1+z_s=R_0/R_s$ and $1+z_d=R_0/R_d$, see Fig.\,2. These quantities are computed just as if the void didn't exist. Any quantity with a subscript `$d$' means that it is evaluated at redshift $z_d$ when the radius of the universe was $R_d=R(T_d)=R_0/(1+z_d)$. We give lensing properties such as the bending angle $\alpha$ of Eq.\,(\ref{alpha}) that are a series of smaller and smaller terms, sufficient to see both the shielding effect of embedding and the effect of the expansion rate $\beta_d=v_d/c$ of the void's Kottler radius $r_d=R_d\chi_b$ that existed at FLRW time $T_d$. The expansion rate $v_d$ is the speed of the expanding void boundary as measured by a stationary Kottler observer at $r_d$. It is given by evaluating $\beta(r)$ defined below Eq.\,(\ref{Kottler}) at $r=r_d$ \be \beta_d=\sqrt{\sd+\Ldfr}. \label{beta_d} \ee When expanding quantities such as $\alpha$ in a series we have taken parameters $\beta_d$ and $\chi_b/\chi_d=r_d/D_d$ (the angular radius of the Kottler hole, see Fig.~\ref{fig:fig2}) to be first order and $r_s/r_d$ and $\Lambda r_d^2/3$ to be second order. In our results, e.g., Eq.\,(\ref{alpha}), we have used a parameter $\bdelt$ to keep track of each order. In Table 1 we give values for these and other parameters for two lens masses, ${\rm m}=10^{12}M_\odot$ (a large galaxy) and ${\rm m}=10^{15}M_\odot$ (a rich cluster) both at redshift $z_d=0.5$ in a flat $\Omega_{\rm m}=0.3$, $\Omega_\Lambda=0.7$ universe with $H_0=70\, \rm km\, s^{-1}\,Mpc^{-1}$. We refer to these as the galaxy lens and the cluster lens throughout the paper. \begin{figure*} \includegraphics[width=1.0\textwidth,height=0.17\textheight]{fig2.eps} \caption{A photon travels from a source at comoving distance $\chi_s$ from the observer and then enters a Kottler hole of comoving radius $\chi_b$ centered at comoving distance $\chi_d$ from the observer. The photon is deflected by an angle $\alpha <0$ and returns to the FLRW dust on its way to the observer. Because this is a comoving picture the orbit inside the void is only representative and because the true orbit inside the void is symmetric about $\phi=\pi/2$ (see Fig. 1) the optical axis is rotated clockwise by the angle $-\rho$ (see Eq.\,(14) of \cite{Chen11}).} \label{fig:fig2} \end{figure*} \begin{table} \caption{\label{tab:parameters}Embedded lens parameters for two deflectors (a galaxy and a cluster) at $z_d=0.5$ when viewing a source at $z_s=1.0$ in a $\Omega_{\rm m}=0.3$, $\Omega_\Lambda=0.7$ universe with $H_0=70\, \rm km\, s^{-1}\,Mpc^{-1}$. Choosing $R_0=1$, gives $\chi_d=1.89\times 10^{3}$ Mpc and $\chi_s=3.31\times 10^{3}$ Mpc.} \begin{ruledtabular} \begin{tabular}{cccccccc} Lens & m & $\beta_d$ & $r_d/D_d=\chi_b/\chi_d$ & $r_s/r_d$ & $\Lambda r_d^2/3$ & $\theta_E$(rad) & $\tilde{\phi}_E$(rad) \\ galaxy& $10^{12}M_\odot$ & $3.67\times 10^{-4}$&$9.54\times 10^{-4}$&$7.98\times 10^{-8}$&$5.51\times 10^{-8}$&$8.07\times 10^{-6}$&$8.45\times 10^{-3}$\\ cluster& $10^{15}M_\odot$& $3.67\times 10^{-3}$&$9.54\times 10^{-3}$&$7.98\times 10^{-6}$&$5.51\times 10^{-6}$&$2.55\times 10^{-4}$&$2.65\times 10^{-2}$\\ \end{tabular} \end{ruledtabular} \end{table} Shielding typically causes the most significant embedding effect on images (i.e., the lowest order effect) and analytically appears as combinations of trig functions of the impact angle $\pht$ in quantities like the bending angle $\alpha$ (see the first $\ctocu $ term in Eq.\,(\ref{alpha}) below). This decrease in $\alpha$ is caused by the shortened period a passing photon is influenced by the mass condensation (recall that in conventional lensing the deflecting force has $``\infty$'' range). Corrections caused by the presence of $\Lambda$ first appear in the void's expansion rate $\beta_d$ and are typically smaller than shielding corrections (i.e., are higher order). It was the search for $\Lambda$'s effect on light deflections \cite{Rindler07,Sereno08,Ishak08a,Ishak08b,Sereno09,Ishak10a,Ishak10b} that prompted investigations of embedded lensing \cite{Schucker09a,Schucker09b,Kantowski10,Boudjemaa}.
|
This paper is one of a series of investigations of the differences in image properties caused by including the gravitational lens's mass in the cosmic mean density. We call such a lens an embedded lens. In this paper we have eliminated one of the two impact parameters previously required to give embedded point mass lensing quantities such as the bending angle $\alpha$ and the lens equation itself. The theory remains more complicated than the conventional lensing theory, but is now much easier to use. The new analytical expressions for image properties agree with the lowest order results given in \cite{Chen11}. They can also be compared with the higher order results in \cite{Kantowski10,Chen10} that were given as functions of the two impact parameters $r_0$ and $\pht$. To eliminate $r_0$ in our prior results for quantities such as $\alpha(\pht,r_0)$ in Eq.~(32) of \cite{Kantowski10} and obtain results such as Eq.\,(\ref{alpha}) given in this paper we had to analytically iterate Eq.~(17) of \cite{Chen11} to determine $r_1(\pht)$ and then use the orbit equation (11) of \cite{Kantowski10} to determine $r_0(\pht)$. The result is given in Eq.\,(\ref{r0}) of the appendix for completeness and to allow the reader to eliminate $r_0$ in other quantities of interest. We have found that with the exception of the potential part of the time delay and the effective surface mass density $\kappa$, strong lensing quantities are only minimally altered by making the lens mass a contributor to the mean mass density of the universe. Even there the effect is less than 5\% on the time-delay for a huge cluster lens, see Fig.\,6. For weak lensing most effects are also small; however, shear and image ellipticity begin to differ significantly ($>10$\%, see Fig.\,5) for large impact angles $\pht>45^\circ$. The one quantity that doesn't vanish in embedded point mass lensing is $\kappa$. It turns out to be negative, presumably accounting for the missing FLRW mass density in the Kottler void. All results given here depend on having a flat ($\Omega=1$) background. Extending them to $\Omega\ne1$ is clearly possible. We expect that many results will differ trivially from what we have given here. The applicability of all results given here also depends on the lens being sufficiently condensed so as to be approximated by a point mass. The effects of embedding on extended lenses remains to be investigated \cite{Schucker10b}. To correct for embedding we have used the Swiss cheese cosmologies which are commonly criticized for their unrealistic mass distributions, i.e., holes with masses at their centers that abruptly appear in otherwise uniform backgrounds. The abrupt discontinuity that appears in the cheese is certainly an unrealistic representation of the true matter distribution; however, this is primarily an aesthetic complaint. Fortunately for Swiss cheese, its purpose is not to represent the mass distribution but instead to account for the effects of mass inhomogeneities on the local/global dynamics of the geometry and on the optics of transiting light rays. In those two aspects Swiss cheese does quite well. The real shortcoming of a simple Swiss cheese type embedded lens (a single condensation moving with the Hubble flow) is the absence of any shear at the site of the embedded lens. For such a simple embedded lens, neighboring inhomogeneities can only be distributed so as to produce a homogenized gravity field at the lens site. Consequently the accuracy of our predictions can be questioned. Stated simply, the shortcoming of our lens model, and with standard Swiss cheese itself, is that neighboring and distant inhomogeneities produce an homogenized background at the point where the lens inhomogeneity is inserted. We suspect this ``average'' lens is not representative because it does not account for effects of local shear. We currently do not have a good estimate of how much de-homogenization alters the shielding radius (which is the major source of embedding effects) because there are no simple Einstein solutions which accurately model local distortions. Such distortions can easily be accommodated in conventional lensing theory, but how they would alter the embedding radius is completely unknown. Exact Einstein solutions containing a local shear can be constructed by using hierarchical models built from Swiss cheese itself. Such a construction will probably be necessary to dependably estimate how the spherical shielding radius $r_d$ is distorted and possibly extended by a local shear and hence how it modifies predictions made here.
| 12 | 6 |
1206.2936
|
1206
|
1206.0334_arXiv.txt
|
We formulated tidal decay lifetimes for hypothetical moons orbiting extrasolar planets with both lunar and stellar tides. Previous work neglected the effect of lunar tides on planet rotation, and are therefore applicable only to systems in which the moon's mass is much less than that of the planet. This work, in contrast, can be applied to the relatively large moons that might be detected around newly-discovered Neptune-mass and super-Earth planets. We conclude that moons are more stable when the planet/moon systems are further from the parent star, the planets are heavier, or the parent stars are lighter. Inclusion of lunar tides allows for significantly longer lifetimes for a massive moon relative to prior formulations. We expect that the semi-major axis of the planet hosting the first detected exomoon around a G-type star is 0.4-0.6 AU and is 0.2-0.4 AU for an M-type star.
|
The first discovery of an extrasolar planet in orbit around a main-sequence star was made by \citet{1995Natur.378..355M}. Since then, more than 700 extrasolar planets\footnote{http://exoplanet.eu/} have been discovered. Although extrasolar moons have not yet been detected, they almost certainly exist. Most of the planets in our solar system have satellites. Even Pluto, though no longer officially a planet, has three moons \citep{2006Natur.439..943W}. It is likely that the mechanisms for moon formation in our solar system (impact, capture, and coaccretion) prevail beyond it\citep{2011arXiv1108.4070M}. The Earth's obliquity, or axial tilt, is stabilized by the Moon \citep{1993Natur.361..615L}. Mars, on the other hand, has relatively small satellites, and its obliquity changes chaotically, fluctuating on a 100,000-year timescale \citep{1993Natur.361..608L}. Stable obliquity in its star's habitable zone may be necessary for a planet to support life. An Earth-size planet with no moon, or a relatively small one, may be subject to large fluctuations in obliquity. In such a case, favorable conditions may not last long enough for life to become established. In the same way, orbital longevity is required for any life form to have time to become established. Hence, the prospects for habitable planets may hinge on moons \citep{2000rewc.book.....W}; but see also \citep{2012Icar..217...77L}. In 2005, \citet{2005ApJ...634..625R} discovered Gliese 876 d, the first super-Earth around a main sequence star. To date more than thirty super-Earths have been discovered\footnote{http://exoplanet.eu/}. The discovery of Kepler 22-b in the habitable zone gives rise to the possibility of life beyond our Solar System \citep{2012ApJ...745..120B}. It is important to know the lifetime of moons orbiting super-Earths in the habitable zone: while the planet might be unsuited to the evolution of life, its moons might be. Moons with masses of at least one third $M_{\bigoplus}$, and orbiting around gas giant planets in the habitable zone may have habitable environments \citep{1997Natur.385..234W}. The moon's orbital stability plays a role in habitability as well. Clearly, if the moon leaves orbit, it will probably leave the habitable zone. Although extrasolar moons have not yet been found, several methods to detect them have been investigated. After \citet{2010ApJ...712L.125K}, the following methods can detect extrasolar moons: \begin{enumerate} \item Transit timing variations \citep{1999A&AS..134..553S, 2005MNRAS.359..567A, 2005Sci...307.1288H}. \item Transit duration variations \citep{2009MNRAS.396.1797K}. \item Light curve distortions \citep{2006A&A...450..395S}. \item Planet-moon eclipses \citep{2007A&A...464.1133C}. \item Microlensing \citep{2008ApJ...684..684H}. \item Pulsar timing \citep{2008ApJ...685L.153L}. \item Distortion of the Rossiter-McLaughlin effect of a transiting planet \citep{2009EM&P..105..385S}. \end{enumerate} Considering the speed at which observational instrumentation has developed, it is only a matter of time before extrasolar moons are discovered. Tidal torque is important to the long-term orbital stability of extrasolar moons. A binary system can be in tidal equilibrium only if coplanarity (the equatorial planes of the planet and moon coincide with the orbital plane), circularity (of the orbit), and corotation (the rotation periods of the planet and moon are equal to the revolution period) have been fulfilled. Further, stability occurs only if the orbital angular momentum exceeds the sum of the spin angular momenta of the planet and moon by more than a factor of three \citep{1980A&A....92..167H}. \citet{1973ApJ...180..307C} studied the stability of these equilibria only with respect to coplanarity and circularity. He pointed out that in a planet-moon system with lunar\footnote{In this paper, we use ``lunar" as the adjective of any moons, not just the Moon} tides, there are three possible evolutionary states. Counselman state (i):the semi-major axis of the moon's orbit tidally evolves inward until the moon hits the planet. Example:Phobos around Mars. Counselman state (ii):the semi-major axis of the moon's orbit tidally evolves outward until the moon escapes from the planet. No solar system examples are available. But this result would happen to the Earth-Moon if Earth's present rotation rate were doubled. Counselman state (iii):lunar orbital and planetary spin angular velocities enter mutual resonance and are kept commensurate by tidal forces. Example:Pluto and Charon. This Counselman state is static, while state (i) and (ii) are evolutionary. Here, we consider a star-planet-moon system with stellar tides. Although they did not consider the effects of lunar tides or maximum distance from the planet, \cite{1973MNRAS.164...21W} examined the impact of solar tides on planetary rotation in a limited star-planet-moon system. \citet{2002ApJ...575.1087B} considered a similar case, considering the maximum distance of the moon but neglecting the lunar tide's effect on planetary rotation. They found just two possible final states:the moon may either hit the planet or escape from it. In this paper, we consider a star-planet-moon system with both stellar and lunar tides, and lunar maximum distance from the planet. Stellar and lunar tides both affect planetary spin, whereas stellar and lunar tides affect planet and moon orbits, respectively. We do not consider the effect of stellar tides on the moon's rotation. Stellar tides should sap angular momentum from the system but this effect is less important if the mass of the planet is at least ten times greater than the mass of the moon. We apply tidal theory and set up a system of differential equations that govern the planetary rotational rate and orbital mean motion as well as the orbital mean motion of the moon. The system of differential equations is solved numerically. Finally, a formula for the length of time the moon will stably orbit is found. We then apply this result to hypothetical extrasolar planet moon systems.
|
We derive analytical expressions for determining the lifetime of hypothetical moons in star-planet-moon systems. Our solutions allow us to find the type of system and the lifetime of the moon without the need to numerically solve a system of differential equations. We first determine whether the moon remains within the planet's outermost stable orbit. If not, the moon is lost and the system is Type IV. If the moon remains in orbit, there are three possible outcomes: Types I, II, and III. In Type I, the planet is tidally locked with the moon. In Type II, the planet is tidally locked first with the star, and later with the moon. In Type III, the planet is not tidally locked with the moon. The type of system depends on characteristics of the star, planet, and moon (mass, radius, Love number $Q_{p}$, etc.) as well as the initial conditions of the planet and the moon. Once we determine the system type, we can calculate the lifetime of the moon. To find the type of system and the lifetime of the moon, we need $T1$, which is the time when the spin angular velocity of the planet is equal to the angular velocity of the moon; See Fig.\ref{fig:TyIC1}, Fig.\ref{fig:T123} and Fig.\ref{fig:TypeIII}. We should use a numerical method to find $T1$. Our results are extension of \cite{1973MNRAS.164...21W} and \citet{2002ApJ...575.1087B}. At the range that they considered, our results agree to their results. \cite{1973MNRAS.164...21W} considered Type III without critical mean motion. In this case, the planet will lose its moon only if the moon collides with the planet. \citet{2002ApJ...575.1087B} considered Type III with critical mean motion. In this case, the moon may either hit the planet or escape from it. In both cases, the planet and moon are asynchronous. \citet{2002ApJ...575.1087B} concluded that the heavier the moon, the shorter the lifetime of the moon. Because they considered only systems of Type III, this result agree to our result (Fig.\ref{fig:MmColor}). On the other hand, the heavier the moon, the longer the lifetime of the moon for Type I and II. Our Moon stabilizes Earth obliquity - a key reason for the development of life on Earth \citep{2000rewc.book.....W}. Stable obliquity in its star's habitable zone may be necessary for a planet to support life. An extrasolar moon of sufficient mass could stabilize the obliquity of an Earth-size extrasolar planet. However even if a planet has a relatively large moon like the Earth does, the planetary obliquity may not be stable in some cases such as the moon is far from the planet, the planet is close to the star, there is a Jupiter-size-planet close enough to the planet, etc \citep{2012Icar..217...77L}. On the other hand, Mars has relatively small satellites, and its obliquity changes chaotically, fluctuating on a 100,000-year timescale \citep{1993Natur.361..608L}. Having a relatively large moon is not enough in and of itself to provide a sufficient condition for an extrasolar planet to stabilize its obliquity meaning support life. Hence, our results give a condition needed to support life on a planet in the habitable zone. Suppose we find a Jupiter-size planet in the habitable zone. This planet may have an Earth-sized moon. If the lifetime of that extrasolar moon is equal to or greater than the age of Earth, then the moon may support life. Hence, our results gives a condition needed for potentially habitable moons. In the third example, we show the moon stability lines for 1 to 10 Gyr applied to types of planet/moon systems. We define the `moon stability line' to be the location beyond which a moon is stable for the life of the stellar system. In general, the moon stability line moves inward for more massive planet, for a less massive parent star, and for younger systems. In other words, moons are more stable when the planet/moon systems are further from the parent star, the planets are heavier, or the parent stars are lighter. We expect that the semi-major axis of the planet for the first extramoon of a G-type star will be 0.4-0.6 AU and for an M-type star 0.2-0.4 AU. This lays the ground work for the tidal evolution of a star-planet-moon system and makes it possible to classify star-planet-moon systems and providing useful estimates of the lifetime of a moon. In some cases, we may not necessarily be able to accurately predict the long-term survival of the moon. The value of $Q_{p}$, the specific dissipation function of the planet, is assumed to be constant in time. However, $Q_{p}$ is not known theoretically, and may depend on the planetary internal structure. For the sake of simplicity, we considered a star-planet-moon system with a single planet and a single moon. But we do not consider any interactions between the star and the moon. This deficiency may be addressed in future work. Gravitational perturbations caused by other planets or moons may be significant. For close-in planets, the stellar gravitational perturbations of the moon's orbit are important \citep{2009ApJ...704.1341C}. In these situations, our method may not predict the lifetime of the moon accurately. Despite its shortcomings, our approach provides an important step toward understanding the tidal evolution and longevity of extrasolar moons, and will form both a basis for future theoretical investigations and direction for future searches to detect extrasolar moons. \begin{figure}[hbt] \begin{center} \includegraphics[width=100mm]{Chart.pdf} \end{center} \caption{Flow-chart for calculating moon lifetimes in a star-planet-moon system. First, check the type of system. Then, calculate the lifetime of the moon.} \label{fig:sum} \end{figure}
| 12 | 6 |
1206.0334
|
1206
|
1206.1809_arXiv.txt
|
{Many modifications of gravity introduce new scalar degrees of freedom, and in such theories matter fields typically couple to an effective metric that depends on both the true metric of spacetime and on the scalar field and its derivatives. Scalar field contributions to the effective metric can be classified as conformal and disformal. Disformal terms introduce gradient couplings between scalar fields and the energy momentum tensor of other matter fields, and cannot be constrained by fifth force experiments because the effects of these terms are trivial around static non-relativistic sources. The use of high-precision, low-energy photon experiments to search for conformally coupled scalar fields, called axion-like particles, is well known. In this article we show that these experiments are also constraining for disformal scalar field theories, and are particularly important because of the difficulty of constraining these couplings with other laboratory experiments. }
|
Light scalar fields are both extremely common and extremely annoying in the study of cosmology and modifications of gravity. They are often invoked as quintessence fields to explain the late time acceleration of the expansion of the universe, and in many modifications of gravity, from $f(R)$ theories, through DGP to theories of massive gravity additional light scalar degrees of freedom appear in the gravity sector. The existence of new dynamical degrees of freedom makes these theories distinguishable from standard general relativity and $\Lambda$CDM cosmology. However the consequence of introducing new light scalar degrees of freedom is that the scalar field will mediate a new long range fifth force and we know this to be incompatible with experimental tests to a high degree of precision. In such theories Standard Model matter fields feel an effective metric $\tilde{g}_{\mu\nu}$ that depends on the true metric $g_{\mu\nu}$, which determines the geometry of space, and on the scalar fields and their derivatives. It was shown by Bekenstein \cite{Bekenstein:1992pj} that the most general metric that can be constructed from $g_{\mu\nu}$ and a scalar field, and that respects causality and the weak equivalence principle is\footnote{In his analysis Bekenstein excludes the possibility of including scalars with more than one derivative apiece because they were expected to give rise to ghost degrees of freedom. Recent developments, including the Galileon models \cite{Nicolis:2008in}, have shown that higher derivative terms are not automatically problematic, so it is possible that Bekenstein's metric can be extended in this way. However no such extensions are currently known so we concentrate our analysis on the metric in Equation (\ref{eq:bekenstein}).} \begin{equation} \tilde{g}_{\mu\nu}=A(\phi,X)g_{\mu\nu} +B(\phi,X)\partial_{\mu} \phi\partial_{\nu}\phi\;, \label{eq:bekenstein} \end{equation} where $X=-(\partial \phi)^2/2$, and $|B|=-B$. The metric (\ref{eq:bekenstein}) now defines the geodesics and light cones for the particles of the Standard Model. The first term in this expression is known as the conformal term, and the case $A\equiv A(\phi)$ and $B\equiv 0$ has been much studied. For light, $m<(1\mbox{ mm})^{-1}$, conformally coupled scalars laboratory searches for a fifth force constrain the strength of the coupling to be $M\gtrsim10^5 M_P$ \cite{Adelberger:2009zz}. This transplanckian energy scale is problematic if we want to construct a natural quantum theory for such scalar fields and is a new fine tuning issue for any such theory. Conformally coupled scalar fields can be experimentally acceptable without fine tuning however if we allow for the theory to be non-linear. Non-linear mass terms (in the Chameleon model \cite{Khoury:2003rn,Brax:2004qh}), non-linear forms of the coupling function $A(\phi)$ (in the symmetron \cite{Pietroni:2005pv,Olive:2007aj,Hinterbichler:2010es} and dilaton \cite{Damour:1994zq,Brax:2010gi} models), and non-linear kinetic terms (in the Galileon model \cite{Nicolis:2008in,Deffayet:2009wt} which has a Vainshtein mechanism \cite{Vainshtein:1972sx,Deffayet:2001uk}) can all have the consequence that although the scalar mediated fifth force is large in vacuum it is dynamically suppressed in dense environments, and so does not give rise to noticeable effects in experimental tests. The second term in equation (\ref{eq:bekenstein}) is the disformal term. On its own, when $A\equiv\mbox{ const}$, this term is not problematic for fifth force experiments because as we will see a scalar field that couples to matter in this way is not sourced by a static non-relativistic mass distribution. All of the objects used in searches for fifth forces are indeed static and non-relativistic, and so such experiments cannot probe these couplings. Scalar fields that give rise to disformal metrics have appeared in a number of circumstances including: \begin{itemize} \item In theories of massive gravity \cite{deRham:2010ik}. A massive graviton can be decomposed into one helicity-two mode, two helicity-one modes and a helicity-zero mode. Matter couples to a metric \begin{equation} h_{\mu\nu}=\hat{h}_{\mu\nu}+\pi\eta_{\mu\nu}+\frac{(6c_3-1)}{\Lambda^3_3}\partial_{\mu}\pi\partial_{\nu}\pi\; , \end{equation} where $\hat{h}_{\mu\nu}$ and $\pi$ are the canonically normalised helicity-two and helicity-zero modes respectively\footnote{We have quoted the standard expression for massive gravity where the fields are expressed in a dimensionless way (this is also true of the DBI-Galileon case that follows). This is in contrast to the expressions we give in the rest of this article where the scalar fields have dimensions of mass.}. $c_3$ is an order one dimensionless constant and $\Lambda^3_3= M_Pm^2$, where $m$ is the mass of the graviton\footnote{To be precise this is the metric in the low energy decoupling limit of the theory where $m\rightarrow 0$, $M_P\rightarrow \infty$ keeping $\Lambda_3=(M_Pm^2)^{1/3}$ fixed.}. \item In the probe brane world construction of the unified DBI-Galileon model \cite{deRham:2010eu}, where the scalar field $\pi$ describes the location of the brane in a flat bulk space time. The metric that is induced on the brane is \begin{equation} g_{\mu\nu}=e^{-2\pi/l}\eta_{\mu\nu}+\partial_{\mu}\pi\partial_{\nu}\pi \;. \end{equation} \item Disformal couplings arise in theories in which Lorentz invariance is broken spontaneously on a non-trivial background \cite{Brax:2012hm}. \item The effects of including disformal couplings in chameleon theories were considered in \cite{Noller:2012sv}. \item Scalar fields with disformal couplings have been used to give rise to unusual forms of cosmic acceleration, called disformal inflation \cite{Kaloper:2003yf} in the early universe and disformal quintessence \cite{Koivisto:2008ak} in the late universe. The absence of fifth forces for a disformal quintessence model was discussed in \cite{Koivisto:2012za}. \item Disformal scalar fields have also been used previously to give rise to varying speed of light cosmologies \cite{Clayton:1999zs,Drummond:1999ut}, although these are now in some tension with observations \cite{Magueijo:2003gj}. \end{itemize} These theories have many other interesting properties, but in this article we are only interested in the consequences of a disformal coupling to matter. As we have said previously, fifth force experiments do not constrain disformal couplings, however in models motivated by Galileon theories and massive gravity some constraints have been put on the theories from studying gravitational lensing and the velocity dispersion of galaxies \cite{Wyman:2011mp,Sjors:2011iv}. Fluctuations of these disformally coupled scalar fields do not propagate on geodesics of the metric (\ref{eq:bekenstein}). Instead their motion is described by a metric that depends on the geometric metric $g_{\mu\nu}$, on the background configuration of the scalar field and on the background distribution of matter fields. Understanding how disformally coupled scalar fields propagate on non-trivial backgrounds is one of the aims of this paper. If the scalar field also has non-canonical kinetic terms, as in the massive gravity and Galileon cases, then these terms give additional contributions to the metric describing the propagation of scalar fluctuations, detailed discussion of this point can be found in references \cite{Babichev:2007dw,Burrage:2011cr}. Fifth force searches are not the only way to study new scalar fields. Another extremely fruitful approach is to look for the effects of the mixing of these scalar fields with photons. Until now the focus of this study has been on scalar fields that couple without derivative terms, which are referred to as axion-like particles or ALPs because their coupling to photons has the same form as that of the Pecci-Quinn axion. Conformally coupled scalars are perfect examples of axion-like particles\footnote{The kinetic term for photons is actually conformally invariant, and so at first glance it seems that a conformally coupled scalar field should not be an axion-like particle. However as the Standard Model is not conformally invariant a coupling between the scalar field and photons is always generated \cite{Brax:2010uq}.}. In the presence of a magnetic field photons can convert into these scalar fields and vice versa \cite{Raffelt:1987im}. If the probability of this conversion is small then this generates rotation and ellipticity of the polarisation of the light beam, if the probability of conversion is large it can lead to the dimming of a light beam. The mixing can also lead to more exotic effects such as `light shining through walls', \cite{Redondo:2010dp}, where a magnetic field is used to convert photons into scalar fields which can pass through solid objects that would be impermeable to photons, a second magnetic field on the far side of the wall is used to convert the scalar field back into a photon giving the appearance that the light has travelled through the wall. Currently the strongest experimental constraints on the effects of scalars on the polarisation of photons are from the PVLAS experiment at the Laboratori Nazionali di Legnaro \cite{Zavattini:2007ee}, and for light shining through walls the best constraints come from the ALPS experiment at the Deutsches Elektronen Synchrotron DESY \cite{Ehret:2010mh}. A nice review of this subject is given in \cite{Jaeckel:2010ni}. For canonically coupled scalar fields the constraints of photon laboratory experiments either looking for changes in the polarisation of light shone through a magnetic field or for light shining through wall effects are far from being as stringent as those from fifth force experiments. However their potential for constraining disformally coupled scalar fields has so far not been considered, this is the aim of this paper. In the next section we begin by setting up the disformal scalar field theory we intend to study, and reviewing in Section \ref{sec:fifthforces} why there are no constraints on disformal couplings from fifth force experiments. In Section \ref{sec:photons} we show how such a scalar field couples to photons and derive the coupled equations of motion for photons and scalars. In Section \ref{sec:magneticfield} we specialise to the case where photons and scalar fields are propagating through a homogeneous constant background magnetic field, and in Section \ref{sec:eom} we solve the equations of motion. In Section \ref{sec:labconstraints} we derive the constraints that photon experiments place on disformally coupled scalar fields, for the ALPS experiment in Section \ref{sec:ALPS} and for the PVLAS experiment in Section \ref{sec:PVLAS}. We conclude in Section \ref{sec:conc}. We take the signature of the metric to be $(-+++)$.
|
\label{sec:conc} Disformal couplings between scalar fields and matter have many motivations particularly in the field of modified gravity. However unlike most other modifications of gravity it is difficult to search for disformal couplings with static non-relativistic fifth force experiments. In this paper we have shown that high-precision low-energy photon experiments offer a complimentary opportunity to search for and constrain disformal couplings in the laboratory. In the region of parameter space interesting for theories of modified gravity the ALPS experiment, which looks for the effects of scalar fields mixing with photons by trying to shine light through walls, is the most constraining. We have shown that for strong conformal couplings the null results of this experiment constrain the parameter that controls the strength of the disformal coupling to be $M\lesssim 10^{-11}\mbox{GeV}$, which reaches the massive gravity coupling strength $M\sim (M_P H_0)^{1/2}$. However for weaker conformal couplings the experiment is not able to constrain the disformal coupling. Unfortunately when the disformal terms dominate the mixing between scalar fields and photons they act to suppress the strength of the mixing, which means that significant improvement in experimental accuracy would be needed to enable us to detect these fields. The mixing between axion-like particles and photons also leads to interesting astrophysical and cosmological effects, as the properties of light from astrophysical sources are altered when photons propagate through galactic, intracluster or intergalactic magnetic fields. It will be interesting to explore the observational consequences of disformal couplings in these environments and at these frequencies, and we intend to return to this topic in future work.
| 12 | 6 |
1206.1809
|
1206
|
1206.4930_arXiv.txt
|
We present empirical relations for determining the amount by which the effective temperatures and radii---and therefore the estimated masses---of low-mass stars and brown dwarfs are altered due to chromospheric activity. We base our relations on a large set of low-mass stars in the field with \ha\ activity measurements, and on a set of low-mass eclipsing binaries with X-ray activity measurements from which we indirectly infer the \ha\ activity. Both samples yield consistent relations linking the amount by which an active object's temperature is suppressed, and its radius inflated, to the strength of its \ha\ emission. These relations are found to approximately preserve bolometric luminosity. We apply these relations to the peculiar brown-dwarf eclipsing binary \2m, in which the active, higher-mass brown dwarf has a cooler temperature than its inactive, lower-mass companion. % The relations correctly reproduce the observed temperatures and radii of \2m\ after accounting for the \ha\ emission; \2m\ would be in precise agreement with theoretical isochrones were it inactive. The relations that we present are applicable to brown dwarfs and low-mass stars with masses below 0.8 \msun\ and for which the activity, as measured by the fractional \ha\ luminosity, is in the range $-4.6 \lesssim \log$~\lha/\lbol\ $\lesssim -3.3$. We expect these relations to be most useful for correcting radius and mass estimates of low-mass stars and brown dwarfs over their active lifetimes (few Gyr) and when the ages or distances (and therefore luminosities) are unknown. We also discuss the implications of this work for improved determinations of young cluster initial mass functions.
|
} Observational evidence strongly indicates that the fundamental properties of low-mass stars can be altered in the presence of strong magnetic activity \citep[e.g.][]{morales08,lopez07,ribas06}. In particular, observations of numerous active, low-mass eclipsing binary (EB) stars have found the empirically measured stellar radii ($R$) to be inflated by $\approx$10\%, and the empirically measured stellar effective temperatures (\teff) to be suppressed by $\approx$5\%, relative to the predictions of standard theoretical stellar evolution models, which better match the properties of inactive objects \citep[see][and references therein]{coughlin11,kraus11,morales10,torres10}. Because the mass-radius and mass-\teff\ relationships are central to our understanding of stellar evolution, resolving these discrepancies will be critical to the ongoing development of accurate theoretical stellar models \citep[for a discussion, see][]{stassun10}. Accurate estimates of stellar radii are especially important in the context of searches for transiting exoplanets, which rely upon the assumed stellar radius/density to infer the planet radius/density. Activity effects also lead to errors in object masses ($M$) when these are derived from \teff. A particularly salient example is \2m, an EB in the Orion Nebula Cluster (age $\sim$1 Myr) comprising two brown dwarfs \citep{stassun06,stassun07}. The primary and secondary brown dwarf (BD) components of \2m\ have dynamically measured masses of 60$\pm$3 and 39$\pm$2 \mjup, respectively, and \teff\ ratio of $T_1 / T_2 = 0.952 \pm 0.004$ \citep{gomez09}. That is, the system exhibits a reversal of the usual $M$-\teff\ relation, such that the primary component is cooler than its companion. This behavior is not predicted by theoretical models for coeval BDs. Figure~\ref{fig:2m0535} shows the \2m\ system on the Hertzsprung-Russell (H-R) diagram compared to the 1~Myr isochrone of \citet{baraffe98}. The secondary BD's \teff\ and bolometric luminosity (\lbol, calculated directly from the empirically measured \teff\ and $R$) place it at a position that is consistent with that predicted by the model isochrone. In contrast, the primary is far displaced from its expected position, and so {\it appears} to have a mass of only $\sim$25 \mjup---more than a factor of 2 lower than its true mass---on the basis of its low \teff. \citet{reiners07} used spectrally resolved H$\alpha$ measurements to show that, whereas the secondary BD in \2m\ is chromospherically quiet, the primary BD is highly chromospherically active, perhaps a consequence of its rapid rotation \citep{gomez09}. Thus, magnetic activity in the primary BD could be responsible for its highly suppressed \teff, similar to what has been seen for low-mass stellar EBs in the field. Given the exhibition of activity-related \teff\ suppression in \2m, the first and only EB containing an active BD, it is likely that this phenomenon extends to other active BDs and low-mass stars in star forming regions and in the field. This has important implications for estimating masses from the H-R diagram, as is often necessary at the youngest ages. When the distance of a low-mass main-sequence star is known, mass can be estimated from its luminosity either via empirical mass--magnitude relations or model mass-\lbol\ relations, circumventing the need to use \teff. However, the use of luminosities can be problematic for very young objects, because they are sensitive to age, accretion, disk excess, and extinction---although careful evaluation of these parameters can mitigate these problems \citep[e.g.,][]{dario12}. For low-mass stars, \teff-derived parameters are useful on the pre--main-sequence, during which they evolve along nearly vertical tracks on the H-R diagram, and also while they remain active on the main-sequence lifetime. The activity timescale is relatively short at higher masses ($\lesssim$1~Gyr for spectral types $\leq$M2) but increases substantially at lower masses ($\gtrsim$7~Gyr for spectral types M5--M7) \citep{west08}. For substellar objects, determining physical properties is more complicated because such objects never reach a stable main sequence. Even with an accurately known distance and thus \lbol, the mass and age will be degenerate. Thus, mass estimates for field BDs are generally inaccessible in the absence of age information. At the youngest ages ($\lesssim$100~Myr) the mass-\lbol\ relationship for BDs is substantially flatter as they are still undergoing significant contraction of their radii, so the situation is more akin to pre--main-sequence stars where it is important to know \teff\ accurately. These evolutionary phases are also when BDs are most active, unlike at field ages when they have reached spectral types $\gtrsim$L4 for which activity is very rarely observed \citep[e.g.][]{burgasser02}. Since magnetic activity seems to alter the fundamental properties of both stars and BDs, it would be valuable to have an easily observable empirical metric with which to quantitatively assess the degree to which a given object's \teff\ has been suppressed and its radius inflated. In the absence of a detailed understanding of the underlying physical causes of this effect, such a metric would be a useful ``stop-gap"---it mitigates one source of uncertainty in estimates of fundamental parameters for very low mass objects. The desired metric will allow us to compare magnetically active objects with their inactive counterparts and with non-magnetic evolutionary tracks in order to improve the mass estimates for young low-mass stars and BDs. The aim of this paper is to derive such an empirical metric by relating the degree of \teff\ suppression and radius inflation to the strength of the \ha\ emission line, a commonly used and readily observable tracer of chromospheric activity \citep{scholz07,Berger:2006}. A challenge with any activity-based measure is that most active objects exhibit variability in their activity levels, and the amplitude of this variability can in some cases be quite large. For example, \citet{bell12} found variability of up to 30\% in \ha\ emission among a large sample of M0--M9 dwarfs in the field on timescales of minutes to weeks. Thus, the calibration of \teff\ suppression and $R$ inflation to \ha\ emission requires large statistical samples and/or calibration objects with highly accurate measurements in order to identify robust mean relations. Fortunately for this paper, which is concerned with the most highly active young objects which may experience the most significant \teff\ suppression and $R$ inflation, stronger \ha\ emitters also tend to be less time-variable, with the typical \ha\ variability being less than 10\% for the strongest \ha\ emitters \citep{bell12}. In Sec.~\ref{methods} we describe our approach and the data we use to establish the empirical relationships of $\Delta$\teff\ and $\Delta R$ vs.\ \lha/\lbol. In Sec.~\ref{results} we present the resulting relations and apply them to \2m\ as a test case, finding that the position of the chromospherically active primary BD in the H-R diagram can be fully explained as an offset from its theoretically expected position, due to the effects of activity on its $R$ and \teff\ (Fig.~\ref{fig:2m0535}). In Sec.~\ref{summary} we discuss the broader application of these relations to other low-mass objects, and their possible ramifications for the inferred IMFs of young clusters. We conclude with a summary in Sec.~\ref{conclude}.
|
} In this paper, we have shown that there exists a correlation between the strength of \ha\ emission in active M-dwarfs, and the degree to which their temperatures are suppressed and radii inflated compared with inactive objects and theoretical evolutionary models. By applying these relations, we are able to infer the amount by which an active objects' temperatures have been suppressed, and thereby improve the accuracy of estimates for their masses and radii. We use the brown dwarf eclipsing binary system \2m\ as a benchmark for our model. We expect these relations to be most useful for correcting estimated masses and radii of low-mass stars and brown dwarfs over their active lifetimes \citep[few Gyr;][]{west08} and when the ages or distances (and therefore the luminosities) are unknown. We have shown that failing to account for the effects of activity can cause significant errors in estimates of stellar and substellar masses derived from \teff, and smaller, but systematically biased errors in temperature and radius. If these empirical corrections are corroborated by future observations, they will prove valuable not only for individual objects, but also for studies of stellar populations. In the case of individual objects, reliable stellar properties are invaluable for exoplanetary studies, where exquisite knowledge of the host star is required to infer planet properties. For very young stellar populations, where activity levels are highest, we have shown how underestimated masses can substantially shift the inferred initial mass function. Such a change would necessitate revisions to star formation models and population synthesis models because, e.g., the observed fraction of brown dwarfs and low-mass stars might be substantially altered. While promising, the correlations we have derived contain significant scatter, and they are currently limited by the lack of a single sample of stars with both \ha\ and direct radius measurements. A sample of \ha\ measurements for objects with directly measured radii and temperatures will allow us to better assess our relations and determine if the scatter is intrinsic or if it is caused by the intermediate steps necessary in constructing our relation (e.g., converting \lx\ to \lha). Despite this limitation, we have chosen to pursue a correlation with \ha\ emission (rather than X-ray, or radio, for example) because of the relative ease of its measurement even in the substellar regime. In principle, a reliable activity tracer in the near-IR would prove even more useful by making measurements easier for cooler objects. No such tracer has yet been identified \citep[see, e.g.,][]{Schmidt2012}, although the \ion{He}{1} line at 10830\AA\ may be a possibility \citep[e.g.][]{dupree92}. In order to make progress on understanding how \teff\ suppression and radius inflation relate to chromospheric activity, a larger sample of EBs with precise masses, radii, {\it and} \ha\ measurements are needed. Toward this goal, we encourage other researchers to publish \ha\ measurements for their targets, as this is usually readily available from the spectra used to determine radial velocities. Indeed, a number of low-mass EBs with accurate masses and radii have been published in the last few years \citep[e.g.][]{vaccaro07,irwin09,morales10,kraus11,helminiak11a,helminiak11b,irwin11}, potentially increasing by a factor of 2--3 the small sample that we have used from \citet{lopez07}. We are currently collecting new \ha\ measurements for these published EBs that lack resolved \ha\ measurements in order to improve the empirical relations that we have presented here. Finally, the relations we have determined already indicate quite clearly that the radius inflation and temperature suppression mechanism operates in such a way that the temperature suppression and radius inflation almost exactly cancel in terms of their effect on the bolometric luminosity. Moreover, the relations between activity, \teff\ suppression, and radius inflation do not appear to manifest any obvious discontinuity across the fully convective transition \citep[see also][]{stassun10}; the followup observations we have underway should help to refine this. These are important, fundamental clues to the physical nature of these effects, and should help to constrain theoretical models that are being developed to explain these phenomena \citep[e.g.][]{chabrier07,macdonald2009}.
| 12 | 6 |
1206.4930
|
1206
|
1206.6274_arXiv.txt
|
{ Atmospheric escape has been detected from the exoplanet \object{HD\,209458b} through transit observations of the hydrogen Lyman-$\alpha$ line. Here we present spectrally resolved Lyman-$\alpha$ transit observations of the exoplanet \object{HD\,189733b} at two different epochs. These HST/STIS observations show for the first time, that there are significant temporal variations in the physical conditions of an evaporating planetary atmosphere. While atmospheric hydrogen is not detected in the first epoch observations, it is observed at the second epoch, producing a transit absorption depth of 14.4$\pm$3.6\% between velocities of -230 to -140\,km\,s$^{-1}$. Contrary to HD\,209458b, these high velocities cannot arise from radiation pressure alone and require an additional acceleration mechanism, such as interactions with stellar wind protons. The observed absorption can be explained by an atmospheric escape rate of neutral hydrogen atoms of about 10$^9$\,g\,s$^{-1}$, a stellar wind with a velocity of 190\,km\,s$^{-1}$ and a temperature of $\sim$10$^5$\,K. An X-ray flare from the active star seen with Swift/XRT 8~hours before the second-epoch observation supports the idea that the observed changes within the upper atmosphere of the planet can be caused by variations in the stellar wind properties, or by variations in the stellar energy input to the planetary escaping gas (or a mix of the two effects). These observations provide the first indication of interaction between the exoplanet's atmosphere and stellar variations. }
|
\label{Introduction} Observations of the transiting extrasolar planet \object{HD\,209458b} in the Lyman-$\alpha$ line of atomic hydrogen (\ion{H}{i}) have revealed that this planet is losing gas (Vidal-Madjar et al.\ 2003). Subsequent theoretical studies indicate that atmospheric escape (so-called `evaporation') arises from the intense stellar X-ray and extreme ultraviolet energy input into the upper atmosphere (Lammer et al.\ 2003; Lecavelier des Etangs et al.\ 2004; Yelle 2004), leading to moderate escape rates for massive hot-Jupiters, or to formation of planetary remnants when strong evaporation implies a dramatic change in the planet mass (Lecavelier des Etangs et al.\ 2004, 2007; Charpinet et al.\ 2011). Despite the importance of evaporation on the fate of planets at short orbital distances, the physics of the exospheric gas and role of the star-planet system properties remain debated (Garc\'ia Mun\~oz 2007; Schneiter et al.\ 2007; Holmstr\"om et al.\ 2008; Lecavelier des Etangs et al.\ 2008; Murray-Clay et al.\ 2009; Ben-Jaffel \& Sona Hosseini 2010; Guo 2011). This is further compounded by the limited number of observations (Vidal-Madjar et al.\ 2004; Ballester et al.\ 2007; Ehrenreich et al.\ 2008; Fossati et al.\ 2010; Linsky et al.\ 2010), which include non-spectrally resolved Lyman-$\alpha$ observations of the exoplanet \object{HD\,189733b} (Lecavelier des Etangs et al.\ 2010). \\
|
Whether they are related to the observed X-ray flare or not, the temporal variations in the evaporating atmosphere of HD\,189733b are clearly detected in Lyman-$\alpha$. The variability of the neutral hydrogen cloud around HD\,189733b can explain the high dispersion of absorption depth measurements in spectrally non-resolved Lyman-$\alpha$ observations (Lecavelier des Etangs et al.\ 2010); combining this with the present high signal-to-noise ratio spectrally resolved observations, we conclude that escape signatures are detected in about half of the total five transits observed in Lyman-$\alpha$. More simultaneous X-ray and Lyman-$\alpha$ observations are needed to obtain a better picture of the complex relationship between the stellar energetic input to the planet and the atmosphere's response to it, and to constrain theoretical models of a space weather event on hot-Jupiters ({\it e.g.} Cohen et al.\ 2011). The HD\,189733 system appears to be the target of choice, but future observations should also enlarge the diversity of stellar and planetary system properties to better distinguish the effects of the stellar-planet interactions from the intrinsic variability in the observed atmospheres.
| 12 | 6 |
1206.6274
|
1206
|
1206.1662_arXiv.txt
|
We construct Tully-Fisher relationships (TFRs) in the $u$, $g$, $r$, $i$ and $z$ bands and stellar mass TFRs (smTFRs) for a sample of $25,698$ late spiral type galaxies (with $0.045<z<0.085$) from the Sloan Digital Sky Survey (SDSS) and study the effects of environment on the relation. We use SDSS-measured Balmer emission line widths, $v_{\rm FWHM}$, as a proxy for disc circular velocity, $v_{\rm circ}$. A priori it is not clear whether we can construct accurate TFRs given the small $3''$ diameter of the fibres used for SDSS spectroscopic measurements. However, we show by modelling the H$\alpha$ emission profile as observed through a $3''$ aperture that for galaxies at appropriate redshifts ($z>0.045$) the fibres sample enough of the disc to obtain a linear relationship between $v_{\rm FWHM}$ and $v_{\rm circ}$, allowing us to obtain a TFR and to investigate dependence on other variables. We also develop a methodology for distinguishing between astrophysical and sample bias in the fibre TFR trends. We observe the well-known steepening of the TFR in redder bands in our sample. We divide the sample of galaxies into four equal groups using projected neighbour density ($\Sigma$) quartiles and find no significant dependence on environment, extending previous work to a wider range of environments and a much larger sample. Having demonstrated that we can construct SDSS-based TFRs is very useful for future applications because of the large sample size available.
|
\label{sec:intro} The TFR is an observed correlation between the luminosity and disc circular velocity, $v_{\rm circ}$, of disc type galaxies \citep{1977A&A....54..661T}. This fundamental empirical relationship reflects important physics in galaxy formation (e.g. \citealt{1998MNRAS.295..319M}) and serves as a distance indicator to galaxies (e.g. \citealt{1977A&A....54..661T}, \citealt{2000ApJ...533..744T} and \citealt{2001ApJ...553...47F}). The luminosity of a galaxy is proportional to the stellar mass, while the rotation curve (RC) circular velocity is determined primarily by the dark matter halo (which is significantly more massive), so the TFR is essentially a relation between the dark matter component and the luminous baryonic component of a galaxy. The TFR was discovered by \cite{1977A&A....54..661T} who measured luminosity versus $21$~cm neutral hydrogen emission line width with the $91$~m National Radio Astronomy Observatory (NRAO) for a sample of $10$ spiral galaxies. Using $21$~cm data is advantageous because of the ability of a radio telescope to sample the neutral hydrogen to very large galactic radii, obtaining data up to the plateau of the RC. Since its discovery, the TFR has been investigated using other measures of disc circular velocity as well, such as optical H$\alpha$ emission with long-slit spectroscopy (e.g. \citealt{1997AJ....114.2402C}, \citealt{2002AJ....123.2358K} and \citealt{2007AJ....134..945P}). TFRs have also been reconstructed from optical one-dimensional spectra (integrated line-of-sight velocity widths) for galaxies up to $z\sim 1$ \citep{2006ApJ...653.1027W, 2006ApJ...653.1049W}. There have been many studies of the TFR, each with its own selection criteria, but generally falling in two broad camps.% The first camp is those interested in the physical processes which give rise to the TFR, e.g. \cite{2007AJ....134..945P, 2002AJ....123.2358K, 2001ApJ...550..212B, 2010A&A...510A..68P, 1997AJ....114.2402C} and many others. The introduction to \citealt{1997AJ....114.2402C} gives an excellent review. These surveys tend to have broader selections, for example, \cite{1997AJ....114.2402C} select bright ($m_B < 15.5$), large (diameter $\geq 4\arcmin$), inclined ($55\degr < i < 75\degr$) galaxies from the UGC, eliminating only galaxies with large dust extinction or peculiar/interacting morphologies \citep{1993ApJ...412L..51C}. Scatter in the TFR remains a large uncertainty in its use as a distance indicator, so physical explanations of this scatter such as that of \cite{2002AJ....123.2358K} are a key area of research. % The second camp is interested in the TFR as a empirical law for measuring distances, e.g. \cite{1977A&A....54..661T, 1992ApJS...81..413M, 1996ApJS..107...97M, 2007ApJS..172..599S} and many others. The use of the TFR as a distance indicator is reviewed in \cite{1995PhR...261..271S} and \cite{2000ApJ...533..744T}. To minimise scatter in distance measurements, these studies tend to have narrower selection criteria, preferentially selecting late-type spirals (Sb -- Sd) and luminosity pass-bands where intrinsic scatter is minimised. Despite differences, these two camps are closely linked: a better physical understanding of the TFR provides a better calibration of disk galaxy luminosities and hence more accurate distances. We will make extensive use of one such study here for calibration and comparison: the paper by \cite{2007AJ....134..945P}. That work investigates a broadly selected input sample of $234$ galaxies drawn from the SDSS with $-22 < M_r < -18.5$ to study the intrinsic scatter in the TFR. They obtain reliable H$\alpha$ RCs from long-slit spectroscopic measurements with the Calar Alto $3.5$~m telescope and the MDM $2.4$~m telescope for $162$ galaxies from the sample. This broadly selected sample does, however, contain typical magnitudes of $M_r < -18.5$ and $r$-band scale heights of $8''$, meaning it only samples the brightest and largest low-$z$ galaxies in the SDSS. They find the slope of the TFR systematically steepens from $-5.5\pm0.2$~mag~$(\log_{10} {\rm km}~{\rm s}^{-1})^{-1}$ in the $g$ band to $-6.6\pm0.2$~mag~$(\log_{10} {\rm km}~{\rm s}^{-1})^{-1}$ in the $z$ band. The intrinsic scatter of the TFR is $0.4$~mag in the $g$, $r$, $i$ and $z$ bands, and is attributed to being driven largely by the variations in the ratio of the dark to luminous matter within the disc galaxy population because correlations of the TFR with galaxy properties such as colour, size and morphology were found to be weak. The slope of the TFR derived by \citeauthor{2007AJ....134..945P} is shallower than contemporary studies, which they describe as an effect of Malmquist-type biases for which they include no correction. We have chosen this sample for comparison here because it is based entirely on SDSS data. The large intrinsic scatter in the TFR suggests that the TFR may depend on properties external to the galaxy, such as the environment (i.e., the local number density of galaxies). Environment is known to have a strong impact on galaxy evolution, and, in theory, could have an effect on the TFR. For example, if galaxies in a higher density environment undergo accelerated star formation due to tidal interactions or mergers, then they may be overly luminous for their rotational velocity and the TFR will be altered. Or, a galaxy falling into a cluster can have a significant amount of its gas stripped \citep{1999MNRAS.308..947A}, which can alter the TFR. Studying the TFR as a function of environment hence has implications for galaxy evolution. \cite{2006ApJ...653..861M} conducted two simple tests for an effect of environment on the TFR and found no variation across a range of cluster environments in a sample of 5000 galaxies as a function of clusters. The goal of this paper is the measure the TFR for a large sample ($\sim25,000$) of Sloan Digital Sky Survey \citep[SDSS;][]{2000AJ....120.1579Y} galaxies as a function of environment with very little sample selection criteria except for a colour cut, which will select mostly late disc type galaxies from SDSS. The TFR has not been investigated as a function of environment statistically before, although comparisons have been made between cluster and field TFRs as well as the TFRs for different clusters (see \citealt{1992ApJ...387...47P}, \citealt{2003AJ....126.2622H}, \citealt{2006ApJ...653..861M}, \citealt{2007ApJS..172..599S}, \citealt{2009ApJS..182..474S} and references therein). \cite{2003AJ....126.2622H} gather data on $13$ Coma Cluster S0 galaxies and $8$ Virgo Cluster S0 galaxies to compare their TFRs with the TFRs for late-type spirals and field S0s. They find no difference between the TFRs for field and cluster S0s, and only a small offset from the TFR for late-type spirals. However, the sample size is small. \cite{2006ApJ...653..861M} studies $\sim5000$ field and cluster spiral galaxies that have either $21$~cm or H$\alpha$ line width measurements to investigate the $i$ band TFR. The sample comes from several datasets from the 1990s as well as significant amounts of new data, which are carefully homogenised, and is presented in \citet{2007ApJS..172..599S} (see also the erratum \citealt{2009ApJS..182..474S}). \cite{2006ApJ...653..861M} find a morphological dependence on the TFR: earlier type spirals are observed to be on average dimmer than later type spirals at a fixed velocity width, which results in a shallowing of the TFR slope for earlier type spirals. This is attributed by \cite{2006ApJ...653..861M} to be the reason why field versus cluster TFRs may be different (since early-type spirals are more likely to be found in over-dense regions). However, \cite{2006ApJ...653..861M} find no difference in the slopes, zero points, and scatters of the TFRs for $31$ nearby clusters and groups, and see no trend in the TFR residuals with a galaxy's projected distance from their cluster centre when investigating the impact of environment. In the present work, we directly investigate the TFR as a function of the local density $\Sigma$, determined from the projected distances to the fourth and fifth nearest neighbours, ranging from voids to values typical for clusters for a broad sample of SDSS galaxies. The projected densities have been calculated as in \cite{2006MNRAS.373..469B}, which have been applied in previous studies to examine the environmental dependence of a number of galaxy properties for large samples of SDSS galaxies. \cite{2006MNRAS.373..469B} use $\Sigma$ to find that the fraction of red galaxies increases with increasing $\Sigma$ as well as galaxy mass. \cite{2007MNRAS.382..801M} investigate the stellar mass--metallicity (gas-phase oxygen abundance) relation in star-forming galaxies as a function of projected neighbour density and find no dependence of environment on the relation, and conclude that the evolution of the galaxies is largely independent of their environments. However, \cite{2007MNRAS.382..801M} do find marginal increase in the chemical enrichment level at a fixed stellar mass in denser environments, suggesting that environments can play a moderate role in galaxy evolution. The organization of the paper is as follows. In Section~\ref{sec:why} we show by modelling aperture-biased H$\alpha$ line profiles why we can expect to obtain a TFR using SDSS-observed line widths. In Section~\ref{sec:data} we discuss the data and sample selection used to construct our TFRs. In Section~\ref{sec:results} we investigate the environmental effects on the TFRs in our sample (and find no strong dependence on environment). We find our TFRs are consistent with the TFRs of \cite{2007AJ....134..945P}. In Section~\ref{sec:disc} we discuss the implications of our results and our conclusions. The model details are found in the Appendix, as well as discussion of effects which may affect the sensitivity of our method (seeing, Malmquist bias, rotation curve shape). We use standard cosmological parameters of $H_0=71$~km~s$^{-1}$~Mpc$^{-1}$, $\Omega_{\rm m} = 0.27$ and $\Omega_\Lambda = 0.73$ throughout this paper. All errors are quoted at the $95$ per cent confidence level unless otherwise stated.
|
\label{sec:disc} We have demonstrated that we can use SDSS-measured line widths, which suffer from $3''$ fibre aperture bias, to construct TFRs for galaxies at $z>0.045$, where enough of the galaxy fits inside the fibre so that we can recover its global properties. Hence, the SDSS database can be very useful for studying the TFR on a large sample of galaxies, and one of the best applications is to look at the effects of environmental density on the TFR. We did so, and found the following: \begin{itemize} \item We divided our sample of galaxies into four groups based on density, and found slight steepening of the SDSS-based TFR slope with density in each of the five bands ($ugriz$), but this was attributed (using simulations) to be a consequence of aperture biases affecting the density groups, which had small variations in size distributions. We conclude that there is \textit{no strong or statistically significant environmental effect} at the $95$ per cent level on the TFR in our sample of $25,698$ galaxies and the data is \textit{consistent with the TFR of \cite{2007AJ....134..945P}}. The environments we investigated ranged from void-like regions, with typical $\Sigma$ of $0.05$~Mpc$^{-2}$, to centres of galaxy clusters, with typical $\Sigma$ of $20$~Mpc$^{-2}$. Our method is sensitive enough to allow us to conclude that if there is an effect on the TFR due to environment, the change in the TFR slope or intercept is less than $3$~per~cent. \item Steepening in the TFR is seen on the order of $4$ to $11$ per cent with increasing density, with the relative steepening being larger in the bluer bands. Our simulated populations of model galaxies suggest a steepening of $7\pm 4$ per cent across all bands, accounting for the size change in the groups. One concern, however, may be that perhaps some of the steepening is due to contamination by early type galaxies in our sample, which can have a biasing effect since they tend to be found in denser environments (\citealt{1980ApJ...236..351D}, \citealt{2007MNRAS.382..801M}) and we had only made a simple colour cut to select disc type morphology and may have included some of the less-red ellipticals in our sample. However, repeating the analysis with a stricter colour cut of $u-r<2.00$, we witness the same degree of increase in the TFRs with increasing density ($11.8$, $9.1$, $6.5$, $5.2$ and $4.3$ per cent in the $ugriz$ bands). In addition, there is no significant difference in the concentration indices $c_i=R_{90}/R_{50}$ of the galaxies in the four density groups ($R_{90}$ and $R_{50}$ are the radii enclosing $90$ per cent and $50$ per cent of the $i$-band Petrosian flux). The concentration index is a measure of morphology -- the significance of the bulge -- for galaxies, with $c_i>2.6$ being typical for early-type galaxies and $c_i<2.6$ being typical for late-type galaxies \citep{2001AJ....122.1861S}. Our colour-cut has eliminated the disc galaxies with significant bulges, which is why we do not see a bias in the distribution of $c_i$ across density groups. In addition, we still witness the steepening with density if we make a concentration index cut to select only galaxies with $c_i<2.6$ (most galaxies in our sample have $c_i<2.6$ to begin with). Since our sample primarily contains late disc type galaxies, we are not subject to bias from environmental effects related to the bulges of galaxies (there tend to be more bulges in disc galaxies in higher density environments). We would not detect in our study a trend in the TFR with environment which is really a trend with morphological type, as in the results of \cite{2006ApJ...653..861M}. \item The environmental dependence of the TFR for late-type spirals is small (if any), meaning that the intrinsic properties of a galaxy play a principal role in driving the evolution of disc type galaxies. Our finding agrees with the earlier work by \cite{2006ApJ...653..861M}. \cite{2007MNRAS.382..801M} found no environmental effect on the stellar mass--metallicity relation and conclude that the evolution of the galaxies is largely independent of their environments. They do find marginal increase in the chemical enrichment level at a fixed stellar mass in denser environments, so environments can play a moderate role in galaxy evolution. An alteration in the TFR in denser environments could in theory be due to a temporary increase/accelerated star formation or to photometric or kinematic asymmetry due to dynamical interactions of galaxies. But we do not find strong evidence for this. \item We have established a procedure for ascertaining if any trend in the SDSS-based TFRs with a variable of interest is due to physics or sample bias. In general, it is difficult to convert the observed SDSS-based TFRs as a function of $v_{\rm FWHM}$ to TFRs as functions of $v_{\rm circ}$ in a quick, simple manner because there is a large amount of scatter between $v_{\rm FWHM}$ and $v_{\rm circ}$ due to aperture biases, even at higher redshifts where the apparent sizes of galaxies are smaller. Instead, it is most useful to work in magnitude versus $v_{\rm FWHM}$ space and convert an assumed TFR as a function of $v_{\rm circ}$ into this regime with the aid of simulations of $v_{\rm circ}$ versus $v_{\rm FWHM}$ for the given size distribution of the galaxy sample. Looking at the SDSS line width-based TFR in multiple bands proves to be very useful because given two groups of galaxies which may have disparities in their $v_{\rm circ}$ versus $v_{\rm FWHM}$ relationship due to aperture biases, these disparities (e.g. steepening) should be reflected in the same way in the SDSS-based TFRs in all bands assuming the TFR is the same for both groups. \item Using a steeper TFR for late type galaxies, like that of \cite{2006ApJ...653..861M}, is also consistent with the data. The observed SDSS $v_{\rm FWHM}$-based slopes are still expected to steepen approximately $7$~per~cent from the lowest to the highest density groups due to aperture bias effects. Two different sloped TFRs (as function of $v_{\rm circ}$), if their intercepts are carefully chosen, can predict the same slope and intercept for the observed SDSS $v_{\rm FWHM}$-based TFR. But they would also predict a statistically different distribution of $v_{\rm FWHM}$, which we do not observe across density groups, so both the TFRs of \cite{2006ApJ...653..861M} and \cite{2007AJ....134..945P} cannot be consistent at the same time across different density groups. The choice of a particular TFR does not affect our ability probe for differences in the inferred TFRs across density. \end{itemize}
| 12 | 6 |
1206.1662
|
1206
|
1206.1348_arXiv.txt
|
Using an ionization gasdynamics code, we simulate a model of the wind-blown bubble around a 40 $\msun$ star. We use this to compute the X-ray spectra from the bubble, which can be directly compared to observations. We outline our methods and techniques for these computations, and contrast them with previous calculations. Our simulated X-ray spectra compare reasonably well with observed spectra of Wolf-Rayet bubbles. They suggest that X-ray nebulae around massive stars may not be easily detectable, consistent with observations.
|
\label{sec:intro} Massive stars ($> 8\msun$) lose mass throughout their lifetime, via winds and eruptions, before ending their lives in a cataclysmic supernova (SN) explosion. The interaction of this material with the surrounding medium creates vast wind-blown cavities surrounded by a dense shell, referred to as wind-blown bubbles. Simultaneously, radiation from the star can ionize the surrounding medium. As the star evolves through various stages, the mass-loss parameters, and the ionizing flux or number of ionizing photons, will change, affecting the structure of the bubble. When the star finally explodes, the resulting SN shock wave will expand within the bubble, and the dynamics and kinematics of the shock wave will depend on the bubble parameters \cite{dwarkadas2005}. Similarly, the relativistic blast waves associated with gamma-ray bursts (GRBs) are expected to expand within wind bubbles surrounding Wolf-Rayet (W-R) stars. Thus, it is important to understand the structure of the bubble, as it influences the evolution and emission from SNe and GRBs. The structure of wind bubbles was identified by Weaver et al.~\cite{weaver77}. Proceeding radially outward from the star, 4 regions are delineated: (1) a freely expanding wind region, (2) a shocked wind region, (3) the shocked ambient region, forming a thin dense shell, and (4) the unshocked ambient medium. An inner, `wind termination' shock separates region (1) and (2), a contact discontinuity, regions (2) and (3) and an outer, generally radiative shock, regions (3) and (4). In order to understand the structure of wind-bubbles accurately, models must take into account both the gasdynamics and ionization from the star. Early models that explored the evolution of massive star surroundings \cite{glm96, gml96} had some ionization built in, mainly centered around the Stromgren sphere approximation. They did not model the main-sequence (MS) stage in multi-dimensions. Similar limitations were included in the models of \cite{vanmarleetal05, vanmarleetal06}. A somewhat better treatment of ionization properties was included in \cite{fhy03, fhy06}. Dwarkadas \cite{dwarkadas07a, dwarkadas07c, dwarkadas08} considered the entire evolution in multi-dimensions, and studied the turbulence in the interior, but did not include any ionization in his calculations. 3D simulations carried out by \cite{vanmarleetal11} also do not include ionization. A more complete treatment of both the ionization plus the gasdynamics has been included in the work of Arthur and her group \cite{arthur07, arthur09, ta11}. In this paper we outline a code, AVATAR, that couples the ionization to the gasdynamics, and use it to study the evolution of wind bubbles around a 40 $\msun$ star. We use a tried and tested method, with the goal of having a reasonably accurate description of the wind-blown bubble that is consistent, and at least equivalent to, if not better than, what other groups have done in the recent past. Our purpose is to have a numerical description of the bubble using which we can compute the X-ray emission. Using our code we compute the structure and evolution of the wind-blown bubble, study the dynamics, hydrodynamics and kinematics, the formation of instabilities, growth of small scale structure, and the onset of turbulence. Much of the volume of the wind bubble is occupied by the high-pressure, low density shocked wind. Wind velocities of order 1000-2000 km s$^{-1}$ for O, B and Wolf-Rayet (W-R) stars should conceivably result in post-shock temperatures in the shocked wind of 10$^7$ - 10$^8$ K. It has been assumed in the literature, perhaps rather naively, that the nebulae should therefore be visible as regions of diffuse X-ray emission. However, despite extensive searches around WR and main-sequence stars with Chandra and XMM, diffuse X-ray emission has been detected in only few cases \cite{chuetal03a, chuetal03b, wriggeetal2005}, with observed X-ray luminosities 10-100 times smaller than would be expected given the ``expected'' temperatures and the size of the region. The inferred temperatures for bubbles around two W-R stars, NGC 6888 and S308, are a few times 10$^6$ K, again lower than expected given the wind velocities. Recently, Zhekov \& Park \cite{zp11} have found that about 10\% of the flux in 6888 arises from higher temperature plasma ($>$ 2 keV). It appears that either some of the a-priori assumptions must be incorrect, or perhaps that the thermal energy is converted to some other form of energy. Turbulence has been suggested as one answer. Dwarkadas \cite{dwarkadas08} found, from 2D simulations, that only a small percentage of the energy went into turbulent motions, except in the very last stages of W-R evolution, where the energy in non-radial motions was about 15-20\% of that in the radial flow. Thermal conduction is another suggestion, but given the low densities within the bubble, it seems quite unlikely. This has been quantitatively shown by \cite{ta11}. In order to address questions regarding the X-ray emission, we compute X-ray spectra from our simulations, using the ISIS package \cite{houck2000}. In this first paper, our intention is to outline our work and demonstrate the viability of the techniques involved to compute the X-ray spectra from ionized wind-blown bubbles. We show initial moderate resolution simulations that demonstrate, given the limitations of our method, our hydrodynamic results are consistent, and in some ways better, than others that have been used to compute the hydrodynamics of wind-bubbles around massive stars. We then outline our technique for calculating the X-ray emission, and show how it improves on the work done by other groups. The exciting fact that our simulated spectra seem to be in reasonable agreement with observations suggests that we are on the correct track. We will follow this work with higher resolution simulations and more detailed X-ray calculations in future papers. This paper proceeds as follows: In \S 2 we describe the photoionization code, and in \S 3 the numerical methods. These are then applied to modelling the medium around a 40 $\msun$ star in \S 4, and X-ray spectra computed from the models in \S 5. \S 6 summarizes our work and outlines future development.
|
Using a code that employs a self-consistent method for computing the effects of photo-ionization on circumstellar gas dynamics, we have modeled the formation of wind-driven nebulae around massive stars. Using various X-ray emission models, we have computed detailed X-ray spectra of simulated wind-blown nebulae from a 40 $\msun$ star, as would be seen with the ACIS instrument on Chandra. Comparing with observed X-ray spectra, we find that at certain epochs of the evolution, our synthetic spectra in the Wolf-Rayet (W-R) stage agree quite well with those obtained from observed W-R nebulae. Unlike other calculations, our detailed spectra indicate that diffuse X-ray emission from most main sequence and W-R nebulae would {\em not} be easily observable with currently available X-ray satellites, which is consistent with the observational data \cite{chuetal03a,chuetal03b}. In future we will present calculations for the wind medium around stars of varying initial mass, taking stellar models with rotation and magnetic field into account. We will also compute the X-ray emission using different XSPEC models, study the locations from which the X-ray emission arises, and produce maps showing the cells that are major contributors to the X-ray emission. These can be compared to density and temperature maps to fully understand which regions are the major contributors to the X-ray emission, and why the spectra are so soft.
| 12 | 6 |
1206.1348
|
1206
|
1206.4047_arXiv.txt
|
We present spectroscopic observations in the rest-frame optical and near- to mid-infrared wavelengths of four gravitationally lensed infrared (IR) luminous star-forming galaxies at redshift 1 $< z <$ 3 from the LUCIFER instrument on the Large Binocular Telescope and the Infrared Spectrograph on {\it Spitzer}. The sample was selected to represent pure, actively star-forming systems, absent of active galactic nuclei. The large lensing magnifications result in high signal-to-noise spectra that can probe faint IR recombination lines, including Pa$\alpha$ and Br$\alpha$ at high redshifts. The sample was augmented by three lensed galaxies with similar suites of unpublished data and observations from the literature, resulting in the final sample of seven galaxies. We use the IR recombination lines in conjunction with H$\alpha$ observations to probe the extinction, \Av, of these systems, as well as testing star formation rate (SFR) indicators against the SFR measured by fitting spectral energy distributions to far-IR photometry. Our galaxies occupy a range of \Av\ from $\sim 0$ to 5.9 mag, larger than previously known for a similar range of IR luminosities at these redshifts. Thus, estimates of SFR even at $z \sim 2$ must take careful count of extinction in the most IR luminous galaxies. We also measure extinction by comparing SFR estimates from optical emission lines with those from far-IR measurements. The comparison of results from these two independent methods indicates a large variety of dust distribution scenarios at $1 < z < 3$. Without correcting for dust extinction, the H$\alpha$ SFR indicator underestimates the SFR; the size of the necessary correction depends on the IR luminosity and dust distribution scenario. Individual SFR estimates based on the 6.2 $\micron$ PAH emission line luminosity do not show a systematic discrepancy with extinction, although a considerable, $\sim$ 0.2 dex scatter is observed.
|
The evolution of the star formation rate (SFR) of galaxies is a central topic to the study of galaxy evolution. It is generally agreed that the SFR density of the Universe has declined by an order of magnitude since $z \sim 1$ to the present \citep[e.g.,][]{LeF05, Rujopakarn10, Magnelli11}. The exact epoch of the peak of the SFR history is not known precisely, although it appears to be constrained to be within $1 < z < 3$ \citep[e.g.,][]{PPG05, Reddy08, Rodighiero10, Magnelli11}. At this redshift range, the primary SFR indicators are based on infrared (IR), optical, and extinction-corrected ultraviolet (UV) observations; the resulting SFR estimates commonly disagree with each other by more than a factor of two \citep[e.g.,][]{Reddy08}. The majority of star formation at these redshifts is known to occur in optically extincted star-forming regions in IR luminous galaxies \citep[e.g.,][]{LeF05, Dole06, Berta11}, and the uncertainties resulting from the extinction undermine our ability to understand the SFR history during this era. A better understanding of the SFR history will have important implications on the cosmic stellar mass build-up and metal production. For example, there is a significant discrepancy between the expected metal abundance derived from the SFR history and the observed abundance \citep{Bouche07}, with some studies indicating the difference to be nearly an order of magnitude, and as a result placing the peak of the SFR history as far back as $z \sim 4$ \citep{Kobayashi07}. The situation necessitates more efforts into exploring the nature of optical extinction in high redshift galaxies using unbiased measures as well as studying the effect of extinction on various SFR indicators. Extinction measurements based on optical emission lines could be biased in highly obscured environments because the indicator only probes the outer layer of the star-forming regions, where the extinction is relatively low. This effect is observed locally \citep[e.g.,][]{AH06}, but only because observations are available for longer wavelength IR recombination lines (e.g. Pa$\alpha$ and Br$\alpha$) that are less affected by extinction. In this work, we extend this technique out to $z = 3$ by comparing the strength of the H$\alpha$ line with those of Pa$\alpha$ and Br$\alpha$. Since the latter are in wavelength regions with $10-20$ times less extinction than H$\alpha$, they provide a measurement of extinction through the entire star-forming region. With an unbiased estimate of extinction, we can address its effects on SFR indicators in this critical redshift range. In this paper, we study a wide range of star formation diagnostics in seven gravitationally lensed star-forming galaxies at $1 < z < 3$. We observed four of these galaxies spectroscopically with the LUCIFER1 near-IR imaging spectrograph on the Large Binocular Telescope (LBT) to measure the H$\alpha$ line flux in the near-IR, and with the Infrared Spectrograph (IRS, $5-38$ $\micron$) on the {\it Spitzer} Space Telescope to observe the wavelength regions covering Pa$\alpha$ and/or Br$\alpha$ lines as well as aromatic emission lines and emission complexes (commonly attributed to, and hereafter, polycyclic aromatic hydrocarbons or PAH). The sample comprises Abell 2218b, Abell 2667a, Abell 2218a, and Abell 1835a at redshift 1.03, 1.03, 2.52, and 2.57, respectively (magnification 6$\times$ - 27$\times$). The IRS observations at longer wavelengths are further used to compare SFR estimates from the 6.2 $\micron$ PAH feature. They were carried out under {\it Spitzer} program ID 82, 30775, 50586 (PI G. Rieke); and 40443, and 50372 (PI C. Papovich). Our sample is augmented by three galaxies with similar suites of observations from unpublished data and the literature: SDSSJ120601+5142 (hereafter the Clone), the Lyman break galaxy LBG MS 1512-cB58 (hereafter cB58), and the 8 O'clock arc, at redshift 2.00, 2.73, and 2.73, respectively. Our galaxies were also observed with the MIPS instrument \citep{Rieke04} on {\it Spitzer} at 24 and 70 $\micron$ by \citet{Rigby08}, allowing us to combine the MIPS data with far-IR photometry from the literature to estimate SFR via \LTIR\ obtained by fitting the spectral energy distribution (SED) across the peak of the far-IR emission. In addition, we used the 24 $\micron$ monochromatic indicator \citep{Rujopakarn12} to estimate \LTIR. This paper is organized as follow. We discuss the LBT and {\it Spitzer} observations and data reduction in Section \ref{sec:obs}; extinction, metallicity, \LTIR, and SFR measurements in Section \ref{sec:result}; compare SFR indicators in Section \ref{sec:discuss}; and make concluding remarks in Section \ref{sec:conclusions}. We assume a $\Lambda$CDM cosmology with $\Omega_m = 0.3$, $\Omega_{\Lambda} = 0.7$, and $H_0 = 70$~km~s$^{-1}$Mpc$^{-1}$ throughout this paper.
|
\label{sec:conclusions} We observed four strongly gravitationally lensed star-forming galaxies at $1 < z < 3$ with {\it Spitzer}/IRS and the LBT/LUCIFER to obtain the mid-IR and near-IR spectroscopy. These observations are targeted to cover IR recombination lines, including H$\alpha$ in the near-IR and Pa$\alpha$ or Br$\alpha$ in the mid-IR. We include another three galaxies from the literature with similar suites of observations, yielding a total sample of seven galaxies. Our sample spans the redshift range of $1.03 - 2.73$ and the \LTIR\ range of $1.3 \times 10^{11}$ \Lsun\ to $7.0 \times 10^{12}$ \Lsun. The IR recombination line ratios are used to measure extinction that can probe deep into the highly obscured star-forming regions and thus provide an unbiased measure of extinction under the foreground screen assumption. Independently, we estimate the extinction by comparing the optical and IR SFRs, a method that does not make the foreground screen assumption. The results from the two methods are consistent in three out of four galaxies with good IR recombination line flux measurements, suggesting that the dust extinction in these galaxies is consistent with a foreground screen (i.e. uniform dust distribution). However, in the fourth case, the extinction estimates from two methods disagree by 1.8 mag, indicating a deviation from the uniform dust screen assumption, which suggests an inhomogeneous dust mixture. The extinction range of our sample (assuming a foreground screen) is $\sim 0.0 - 5.9$ mag, which is a larger spread than previously known for intermediate and high redshift galaxies based on measurements with optical emission lines. These results suggest a large diversity in both the extinction levels and dust distribution scenarios at high redshift. We compare the performance of various SFR indicators over the extinction range and find that substantial extinction corrections are required for the H$\alpha$-based SFR indicator. The remaining indicators (1) combined H$\alpha$ and \LMIPS; (2) \LMIPS; and (3) PAH (6.2 $\micron$) all give estimates consistent to within the expected uncertainties of $\sim0.2$ dex. We thank Brian Siana and Eiichi Egami for helpful discussions. WR thanks Alexandra Pope and Philip Choi for data points in Figures \ref{fig_Pope} and \ref{fig_Choi}, respectively, and acknowledges the support from the Thai Government Scholarship. This work is supported by contract 1255094 from Caltech/JPL to the University of Arizona.\\
| 12 | 6 |
1206.4047
|
1206
|
1206.2382_arXiv.txt
|
We present a nonsingular bouncing cosmology using single scalar field matter with non-trivial potential and non-standard kinetic term. The potential sources a dynamical attractor solution with Ekpyrotic contraction which washes out small amplitude anisotropies. At high energy densities the field evolves into a ghost condensate, leading to a nonsingular bounce. Following the bounce there is a smooth transition to standard expanding radiation and matter dominated phases. Using linear cosmological perturbation theory we track each Fourier mode of the curvature fluctuation throughout the entire cosmic evolution. Using standard matching conditions for nonsingular bouncing cosmologies we verify that the spectral index does not change during the bounce. We show there is a controlled period of exponential growth of the fluctuation amplitude for the perturbations (but not for gravitational waves) around the bounce point which does not invalidate the perturbative treatment. This growth induces a natural suppression mechanism for the tensor to scalar ratio of fluctuations. Moreover, we study the generation of the primordial power spectrum of curvature fluctuations for various types of initial conditions. For the pure vacuum initial condition, on scales which exit the Hubble radius in the phase of Ekpyrotic contraction, the spectrum is deeply blue. For thermal particle initial condition, one possibility for generating a scale-invariant spectrum makes use of a special value of the background equation of state during the contracting Ekpyrotic phase. If the Ekpyrotic phase is preceded by a period of matter-dominated contraction, the primordial power spectrum is nearly scale-invariant on large scales (scales which exit the Hubble radius in the matter-dominated phase) but acquires a large blue tilt on small scales. Thus, our model provides a realization of the ``matter bounce" scenario which is free of the anisotropy problem.
|
In this paper we construct a nonsingular bouncing cosmology with an Ekpyrotic contracting phase. The model is free from the problems typically associated with `matter bounce' or pure Ekpyrotic models. Both the matter bounce (see e.g. \cite{RHB2011rev} for a recent review) and the Ekpyrotic scenario (see e.g \cite{Lehners} for an in-depth overview) were proposed as alternatives to inflationary cosmology as an explanation for the origin of the observed structure in the Universe. While these models are faced with serious challenges we show that these challenges can be ameliorated by combining attributes of both scenarios. We begin with a discussion of the successes and problems of the matter bounce model. Some time ago it was realized that curvature fluctuations which originate as quantum vacuum fluctuations on sub-Hubble scales and which exit the Hubble radius during a matter-dominated epoch of contraction acquire a scale-invariant spectrum \cite{Wands, Fabio1}. In a number of toy models, it was shown that this spectrum often persists if the matter-dominated phase of contraction is continued in a nonsingular way to the expanding phase of Standard Big Bang cosmology. A nonsingular bouncing model can be obtained by using Null Energy Condition (NEC) violating matter such as quintom matter \cite{Yifu1, Yifu2} or Lee-Wick matter \cite{Yifu3}, by making use of either a ghost condensate construction \cite{Chunshan}, the ghost-free higher derivative gravity model of \cite{Tirtho1, Tirtho3}, or Galileon fields \cite{Taotao, Damien}, and it arises in Horava-Lifshitz gravity \cite{Horava} in the presence of spatial curvature \cite{HLbounce, HLbounce2}. A nonsingular bounce can also be obtained \cite{Omid, Easson:2007fz, Sahni:2012er} in the context of mirage cosmology \cite{Kehagias:1999vr, Shtanov:2002mb}, by taking into account the effect of extra time-like dimension \cite{Battefeld:2005cj}, by making use of nonconventional K-essence model \cite{Abramo:2007mp, Chimento:2005ua}, or in a universe with nontrivial curved geometries \cite{Martin:2003sf, Solomons:2001ef, Anabalon:2012tu}. In all of these cases it was found (under certain assumptions) that the spectrum of perturbations on scales relevant to current cosmological observations does not change its spectral index during the bouncing phase. Thus, such nonsingular cosmologies provide an alternative to inflation for producing a scale-invariant spectrum of cosmological perturbations today. A difficult problem facing bouncing cosmologies is that the homogeneous and isotropic background cosmological solution is unstable to the development of radiation \cite{Johanna} and anisotropic stress. The latter instability leads to the famous BKL \cite{BKL} mixmaster cosmology, opposed to a homogeneous and isotropic bounce. In the Ekpyrotic scenario \cite{Ekp}, the contracting branch solution is a local attractor \cite{Ekpattr}, similar to the accelerating expanding cosmological solutions in inflationary models. In Ekpyrotic cosmology there is the assumed existence of a matter fluid with an equation of state $w = p / \rho \gg 1$ ($p$ and $\rho$ being pressure and energy densities, respectively). The energy density in this fluid blueshifts faster than the contribution of anisotropic stress in the effective energy density. Thus, the fluid comes to dominate during the contracting phase and prevents the development of the BKL instability. Within the context of a pure Ekpyrotic model, the curvature fluctuations on super-Hubble scales in the contracting phase are not scale-invariant; although, the fluctuation in the Bardeen potential $\Phi$ \cite{Bardeen} \footnote{See \cite{MFB} for an in-depth treatment of the theory of cosmological perturbations and \cite{RHBrev} for an introductory overview.} which describes the metric inhomogeneities in the longitudinal gauge are scale-invariant (see e.g. \cite{Lyth, Fabio2, Hwang, KOST2} for discussions of this issue). The initial Ekpyrotic scenario \cite{Ekp} had a singularity in the effective field theory at the transition point between contraction and expansion. The question of how fluctuations transfer from the contracting to the expanding phase is non-trivial in this context (see e.g. \cite{Durrer} for a detailed discussion). There are prescriptions according to which the spectrum of fluctuations after the bounce is scale-invariant \cite{Tolley}. Also, there are typically entropy modes present in Ekpyrotic models. These entropy modes can acquire a scale-invariant spectrum by the same mechanism that $\Phi$ acquires such a spectrum \cite{Notari, Finelli, Creminelli, Turok, Khoury}, and will then induce a scale-invariant spectrum for the curvature fluctuations by the usual mechanism of isocurvature modes seeding an adiabatic fluctuation. This leads to the so-called ``New Ekpyrotic" scenario \cite{Khoury}. Scale-invariant entropy modes arise from fluctuations of the extra metric fluctuation modes in higher dimensions \cite{Thorsten}, the setting in which the Ekpyrotic scenario was initially proposed. However, in the context of the New Ekpyrotic scenario, one has to worry about instabilities during the bounce phase, an issue recently raised in \cite{BingXue}. The model we propose in this paper is free from the complications associated with entropy modes and the transfer of fluctuations through singular bounces. In this scenario, it is the curvature fluctuations which are scale-invariant. This spectrum is inherited from the phase of matter contraction which preceded the phase of Ekpyrotic contraction. There are no low mass entropy modes leading to the complicated issues existing in pure Ekpyrotic models. The cosmological bounce is nonsingular and hence the transfer of fluctuations from the initial contracting phase to the expanding period can be treated exactly. We find that the spectral index of the fluctuations on infrared scales relevant to current observations does not change during the bounce. The amplitude of the curvature fluctuations are boosted by a significant, scale-independent, factor ${\cal F}$, (for long wavelength modes). We demonstrate that our model is free from the instability problems raised in \cite{BingXue}. In this model the background dynamics before and during the bounce are determined by a single scalar field $\phi$ with non-trivial kinetic action of the form used in ghost condensate \cite{ghost} and Galileon models \cite{Galileon} (see also \cite{Fairlie}). We add to this field a negative exponential potential similar to what is used in the Ekpyrotic scenario. This potential leads to a phase of Ekpyrotic contraction. At high densities, the coefficient of the part of the kinetic term which is standard becomes negative, and this leads to a nonsingular cosmological bounce similar to what is achieved in the New Ekpyrotic scenario \cite{Khoury, Creminelli} and in \cite{Chunshan}. After the bounce, the coefficient of the kinetic term becomes positive again, a period of kinetic-driven expansion sets in, lasting until the radiation and matter dominated periods of Standard Cosmology. We can imagine that the initial contracting phase of the universe mimics our currently observed universe, namely a state filled with regular matter and radiation. Since the kinetic energy density of $\phi$ increases faster in the contracting phase than both that of matter and radiation, eventually $\phi$ will begin to dominate. Given this setup, our model provides a realization of the matter bounce scenario of \cite{Wands, Fabio1, RHB2011rev} which is free from the anisotropy problem which generically affects bouncing cosmologies. The outline of this paper is as follows: In the next section we introduce the model and discuss the cosmological background dynamics, both analytically and numerically. In Section III we show how cosmological fluctuations evolve through the bouncing phase. The final section is reserved for discussion. We defined the reduce Planck mass by $M_{p} = 1/\sqrt{8\pi G}$ where $G$ is Newton's gravitational constant. The sign of the metric is taken to be $(+,-,-,-)$. Note that we take the value of the scale factor at the bounce point to be $a_B = 1$ throughout the paper.
|
In this paper we have presented a single scalar field model which yields a nonsingular bouncing cosmology. It makes use of a negative exponential potential which yields an Ekpyrotic contracting phase. At high energy densities, the scalar field undergoes a phase transition to a ghost condensate. This leads to the violation of the Null Energy Condition which is required to obtain a nonsingular bounce in flat FRW models in General Relativity. Following the bounce, a period of kinetic-driven expansion results. By adding regular matter and radiation to the model, we obtain a realization of the ``matter bounce'' scenario which is free of the anisotropy problem which plagues other realizations of this scenario. The cosmological scenario is therefore as follows: the universe begins in a contracting phase with cold matter dominating over relativistic radiation and over the scalar field. Due to its equation of state $w_c > 1$ the scalar field comes to dominate the universe and leads to an Ekpyrotic-type phase of contraction. This phase of contraction is free from the BKL instability since the energy density in anisotropies grows less fast than that in the scalar field. This phase is followed by the ghost condensate-driven bounce which in turn ends in a kinetic-driven expanding period. Eventually, the usual radiation and matter come to dominate the energy density again, leading to the a Standard Big Bang expanding universe. We have performed a detailed study of the evolution of cosmological fluctuations in our model. We have shown that the spectrum retains its slope through the bounce. Thus, vacuum fluctuations which exit the Hubble radius during the matter-dominated phase of contraction acquire and maintain a scale-invariant spectrum. Thus, our model provides a realization of the ``matter bounce'' alternative to inflation which is free from the anisotropy problem which plagues previous realizations. We have also shown that in the absence of initial matter and radiation dominated phases of contraction, it is possible to obtain a scale-invariant spectrum of fluctuations from initial thermal particle inhomogeneities provided the equation of state during the contracting phase takes on a particular value. We have found that the fluctuation modes undergo a period of exponential growth during the bounce phase. The growth factor ${\cal F}$ of the fluctuation mode during this phase, while being large in amplitude, is independent of $k$. Hence, the spectral shape passes through the bounce without change. The amplitude of scalar modes increases relative to that of tensor modes (for which ${\cal F} \simeq 1$). Hence, a small tensor to scalar ratio results. The increase of the amplitude of the fluctuations during the bounce phase has another implication: the value of the Hubble constant at the transition between matter-dominated contraction and Ekpyrotic contraction can be fairly low. If we compare the final amplitude (\ref{amplitude}) of the curvature power spectrum with what is required to match observations, then with ${\cal F} \sim 1$ we would require a very large value of the Hubble expansion parameter at the beginning of the Ekpyrotic phase. In this context, the anisotropy problem might have reappeared: the initial anisotropies cannot be larger than a critical value such that they begin to dominate at the beginning of the Ekpyrotic phase. In this paper we have focused on adiabatic fluctuations only. It would be interesting to study entropy modes in the model.
| 12 | 6 |
1206.2382
|
1206
|
1206.2661_arXiv.txt
|
{The growth of black holes and the formation and evolution of galaxies appear to be linked at such a fundamental level that we think of the two as `co-evolving.' Recent observations show that this co-evolution may be complex and the result of several different pathways. While it is clear that black hole accretion is linked to specific phases of the evolution of the host galaxy, the impact of the energy liberated by the black hole on the evolutionary trajectory of the host by feedback is less clear. In this contribution, I review the motivations for co-evolution, the current state of the observational picture, and some challenges by black hole feedback. } \FullConference{Frank N. Bash Symposium New Horizons In Astronomy,\\ October 9-11, 2011\\ Austin Texas} \begin{document}
| 12 | 6 |
1206.2661
|
||
1206
|
1206.5331_arXiv.txt
|
The maximum likelihood method is often used for parameter estimation in gravitational wave astronomy. Recently, an interesting approach was proposed by Vallisneri to evaluate the distributions of parameter estimation errors expected for the method. This approach is to statistically analyze the local peaks of the likelihood surface, and works efficiently even for signals with low signal-to-noise ratios. Focusing special attention to geometric structure of the likelihood surface, we follow the proposed approach and derive formulae for a simplified model of data analysis where the target signal has only one intrinsic parameter, along with its overall amplitude. Then we apply our formulae to correlation analysis of stochastic gravitational wave background with a power-law spectrum. We report qualitative trends of the formulae using numerical results specifically obtained for correlation analysis with two Advanced-LIGO detectors.
|
Nowadays, large-scale ground-based laser interferometers such as LIGO \cite{Harry:2010zz}, Virgo \cite{Accadia:2011zzc} and KAGRA (formerly LCGT) \cite{Kuroda:2011zz}, are being upgraded or constructed to realize powerful second generation detectors. It is expected that we will succeed to directly detect gravitational waves (GWs) around 10-1000Hz in this decade. Subsequently, the Laser Interferometer Space Antenna (LISA) \cite{lisa} (see also \cite{AmaroSeoane:2012km} for eLISA/NGO) will explore a new window of GWs around 0.1-100mHz. At the lower frequency regime $\sim 1$nHz, the pulsar timing arrays \cite{Manchester:2011ec,Hobbs:2009yy} have been significantly improving their sensitivities to GWs. Under these circumstances, possibilities of GW astronomy have been actively discussed for these projects, and extracting parameters characterizing GWs is widely recognized as one of the most important tasks. To evaluate the accuracy of parameter estimation, the Fisher matrix approximation is a standard tool and often used in these studies \cite{thorne,Finn:1992wt,Cutler:1994ys,jk}. This method is quite simple to implement, but its performance is known to become worse at lower signal-to-noise ratios (SNRs) \cite{Vallisneri:2007ev}. Unfortunately, a full numerical study mimicking actual data analysis requires a huge computational cost. To fill the gaps between these two methods, Vallisneri \cite{Vallisneri:2011ts} recently proposed an interesting and efficient method to predict distributions of the parameter estimation errors expected for maximum likelihood analyses. He noticed that the mean densities of the local stationary points (peaks, valleys and saddle points) of a likelihood surface can be handled relatively concisely under fluctuations of the surface induced by the detector noises. This is because (i) the dependence of the relevant expressions on the noises is rather simple and (ii) only a small number of independent noise components is involved. In his work, it was suggested that the new method can well reproduce the costly results obtained by fully numerical methods. He also commented that the proposed method can be utilized to analyze multiple local peaks, including not global ones that could cause troubles at the actual parameter estimation. In this paper, we examine this direction, paying attention to geometrical properties of likelihood surfaces, not only their local peaks but also valleys and saddle points. As a first step, our target is limited to a simple model where we estimate only one intrinsic parameter and the overall amplitude of the signal (thus at most two fitting parameters). While we cannot analyze important issues inherent to large dimensionalities of fitting parameters, our study would elucidate basic aspects of parameter estimation with the maximum likelihood method. In this paper, we first present a formal analysis to write down the expected densities of local stationary points of a likelihood surface. Here we assume Gaussian noises, but do not specifically limit our analysis to GW observation. Then we apply our formal results to correlation analysis of stochastic GW background. We assume a power-law spectrum for the background and discuss estimation of the spectral index and the overall amplitude. Many theoretical models of the background predict power-law spectra, reflecting cosmological or astrophysical scale-free processes relevant for generation of GWs, and therefore the assumptions on the spectral shape would be reasonable at least in the frequency band of a detector (see {\it e.g.} \cite{Maggiore:1999vm,Phinney:2001di,Kuroyanagi:2008ye,Nakayama:2008ip,Alabidi:2012ex}). Therefore, the spectral index and the amplitude would be the primary parameters of a background and serve as the key information to discriminate its origin. Since the SNR of the correlation analysis increases with the observation time $T_{\mathrm{obs}}$ as $SNR\propto \sqrt{T_{\mathrm{obs}}}$ \cite{Flanagan:1993ix,Allen:1997ad}, we initially need to deal with a low SNR data. This fact may reduce the validity of the Fisher matrix analysis for the early era of GW astronomy. Given these aspects, our simple analysis by the new method with one intrinsic parameter is not just a toy model, but firmly has a suitable and realistic application. As a concrete model, we examine the correlation analysis with the two Advanced LIGO detectors and evaluate the expected number densities of the local stationary points of the maximum likelihood surface in our parameter space. These results would be useful to discuss the prospects of stochastic GW background measurements with LIGO, and also helps us to grasp qualitative trends of the formal expressions. { We find that, for moderate signal strength $SNR\gsim 5$, there would be vanishingly low probabilities to have multiples peaks on the likelihood surfaces around the true parameters of the GW background. In contrast, false peaks arise mainly by noises at the distant parameter regions where the true signal loses correlation. They typically have low likelihood values and will be safely excluded by setting an appropriate threshold on the likelihood value. We also discuss biases of the fitting parameters estimated with the maximum likelihood method. For $SNR\to \infty$, the biases asymptotically decrease as $1/SNR^2$ relative to the true parameter and would be buried beneath the parameter estimation errors ($\propto1/SNR$). } This paper is organized as follows; in \S II we briefly discuss parameter estimation with the maximum likelihood method. In \S III, we provide formal expressions for densities of the local stationary points. \S IV is devoted to link the results in \S III to the correlation analysis for stochastic GW background. In \S V, we evaluate the densities of the stationary points for the two Advanced LIGO detectors and report the observed trends. We also compare the traditional Fisher matrix approximation with the new predictions. \S VI is a summary of this paper.
|
In this paper, we discussed a simplified model of data analysis where we estimate a single intrinsic parameter $p$ and the overall amplitude $\rho$ of a signal that is contaminated by Gaussian noises. The approach behind our study was recently proposed by Vallisneri \cite{Vallisneri:2011ts}, and based on the fact that the local stationary points on the likelihood surfaces can be studied with a small number of independent noise components. In this paper, we paid special attention to the local geometric aspects of the likelihood surfaces, including valleys and saddle points. With our analytic expressions derived owing to the simplified settings, we can see how the geometrical structure depend on the signal strength, the likelihood value, and correlation between the true and the trial templates. We expect that our qualitative results would provide us useful insights when dealing with more complicated problems of data analysis for GW astronomy (and beyond). In the later half of this paper, we applied our formal expressions to correlation analysis of stochastic GW backgrounds. Considering ubiquitously realized scaling behaviours of cosmological processes (and also astrophysical ones related to GWs), it would be reasonable to assume a power-law spectrum for the background in the frequency regime of a GW detector and discuss accuracy of parameter estimation for the spectral index and the amplitude of the spectrum. Therefore, the correlation analysis for the background can be regarded as an exemplary as well as realistic case for applying our formal expressions. At the same time, this concrete example would conversely help us to see the qualitative trends of the formal results. To link the correlation analysis with the formal results, we provided useful expressions, including ready-to-use fitting formulae for the two LIGO detectors. Then, we numerically evaluated the expected densities of the local peaks/valleys/saddle points of the likelihood surfaces. We find that the abundance of the local valleys is strongly suppressed around the true parameters, indicating prohibition of multiple peaks there. In contrast, at the region where the true signal lose correlation, there appears peaks and valleys mainly caused by the fluctuations of the noise. These false peaks would typically have low likelihood significance due to the lack of the underlying signal correlation. Therefore, they will be safely ruled out in the actual data analysis by setting an appropriate threshold on the value of the likelihood. At $\rho_{\mathrm{t}} \gtrsim 5$, the expansion around the Fisher matrix prediction to the first order in $\rho_{\mathrm{t}}$ is found to approximate the exact results to a good accuracy. { We also analyzed the biases for parameters estimated with the maximum likelihood method. At $\rho_{\mathrm{t}} \gtrsim 5$, our results show good agreements with those obtained in a perturbative method as second order corrections $O(\rho_{\mathrm{t}}^{-2})$ relative to the true parameters. } This work was supported by JSPS grants 20740151, 21684014, and 24540269.
| 12 | 6 |
1206.5331
|
1206
|
1206.2727_arXiv.txt
|
{Accreting Millisecond X-Ray Pulsars (AMXPs) are astrophysical laboratories without parallel in the study of extreme physics. In this chapter we review the past fifteen years of discoveries in the field. We summarize the observations of the fifteen known AMXPs, with a particular emphasis on the multi-wavelength observations that have been carried out since the discovery of the first AMXP in 1998. We review accretion torque theory, the pulse formation process, and how AMXP observations have changed our view on the interaction of plasma and magnetic fields in strong gravity. We also explain how the AMXPs have deepened our understanding of the thermonuclear burst process, in particular the phenomenon of burst oscillations. We conclude with a discussion of the open problems that remain to be addressed in the future.}
|
\label{sec:1} Neutron stars (NSs), amongst the most extreme astrophysical objects in the Universe, allow us to study physics in regimes that cannot be accessed by terrestrial laboratories. They play a key role in the study of fundamental problems including the equation of state (EoS) of ultra-dense matter, the production of gravitational waves, dense matter superfluidity and superconductivity, and the generation and evolution of ultra-strong magnetic fields. Since the discovery of NSs as radio pulsars in 1967~\cite{hew67}, many different classes have been discovered including more than ${\sim}130$ NSs in low mass X-ray binaries (LMXBs). In LMXBs the NS accretes matter from a non-collapsed stellar companion (with mass $M\lesssim 1\,M_{\odot}$) via an accretion disk. This chapter focuses on a subgroup of the LMXBs, the accreting millisecond X-ray pulsars (AMXPs). In the AMXPs, the gas stripped from the companion is channeled out of the accretion disk and onto the magnetic poles of the rotating neutron star, giving rise to X-ray pulsations at the spin frequency. We will explore the details of this process, why it is so rare (the AMXPs are a small class), the physics of the disk-magnetosphere interaction, and how AMXPs can be used to probe extreme physics. Immediately after the discovery of the first millisecond radio pulsar in 1982 \cite{bac82}, LMXBs were identified as possible incubators for millisecond pulsars. It was suggested that LMXBs might be responsible for the conversion of slow NSs with high magnetic field ($B{\sim}10^{12}$~G), into a rapidly spinning objects with a relatively weak magnetic field ($B{\sim}10^8$~G). Two independent papers published in 1982 \cite{alp82, rad82} proposed transfer of angular momentum through accretion as the mechanism responsible for the spin-up of pulsars. This is known as the \emph{recycling scenario} (see \cite{sri10} for an excellent review). This name originates from the fact that radio pulsars switch off their pulsed radio emission after entering the so-called ``pulsar graveyard''. If this happens while the NS is in a binary with a non-collapsed low or intermediate mass stellar companion, binary evolution of the system~\cite{bha91, tau06} can bring the companion into Roche lobe contact and trigger a prolonged epoch of mass transfer from the companion (donor) towards the NS (accretor). The mass is transferred with large specific angular momentum and the NS is spun-up by the resulting accretion torques. Once the mass transfer episode terminates, the NS might eventually switch on again as a ``recycled'' millisecond radio pulsar. The first AMXP (SAX J1808.4--3658), found in 1998 with the \textit{Rossi X-ray Timing Explorer} (\textit{RXTE}) \cite{wij98} provided a beautiful confirmation of the recycling scenario. Fourteen more AMXPs have since been found, with spin frequencies from 182 to 599 Hz. Another important milestone came with the discovery (in 2007) of a binary radio millisecond pulsar (PSR J1023+0038) for which archival optical observations, taken ${\sim}$ 7 years before the radio pulsar discovery, showed evidence for an accretion disk\footnote{a new transition from a radio pulsar to a LMXB has happened and is currently ongoing at the moment of writing this review~\cite{sta13,pat13b}}~\cite{arc09}. This is the first NS observed to have switched on as a radio pulsar after being an X-ray binary. A final confirmation that indeed AMXPs and radio pulsars are related has recently come with the discovery of the system IGR J18245--2452 which has shown both an AMXP and a radio millisecond pulsar phase (see \cite{pap13a} and Section~\ref{sec:18245} for a detailed discussion). The \rxte\, observatory has played an extraordinary role by discovering many systems of this kind and by collecting extensive data records of each outburst detected during its fifteen year lifetime. The excellent timing capabilities of \textit{RXTE} have brought new means to study NSs with coherent X-ray timing, and helped to constrain the long term properties of many AMXPs over a baseline of more than a decade. Observation of the orbital Doppler shift of the AMXP pulse frequency contains information on the orbital parameters of the binary and their evolution in time. Binary evolution has benefited from the study of AMXPs \cite{bil02, nel03, del03} which are now known to include ultra-compact systems (orbital period $P_b\lesssim 80$ min) with white dwarf companions, compact systems ($P_b\simeq1.5-3$ hr) with brown dwarf donors and wider systems ($P_b\simeq3.5-20$ hr) with main sequence stars. Other X-ray and gamma ray space missions like \textit{XMM-Newton}, \textit{INTEGRAL}, \textit{Chandra}, \textit{Swift} and \textit{HETE} have also played an important role in discovering and understanding the spectral and timing properties of these objects. Multiwavelength observations covering radio, infrared, optical and UV wavelengths have also illuminated different aspects of these fascinating systems. Several optical and infrared counterparts have been identified with ground based observations and in some cases have led to the discovery of the spectral type of the donor, while radio and infrared observations have revealed the possible presence of jets. This chapter is structured as follows: \begin{description} \setitemindent{largelabel} \item{\textbf{Section 2.}} An overview of the AMXP family. \item{\textbf{Section 3.}} Observations of individual AMXPs \item{\textbf{Section 4.}} Coherent timing analysis and accretion torques. \item{\textbf{Section 5.}} X-ray pulse properties, their formation and use. \item{\textbf{Section 6.}} Long-term evolution of spins and orbital parameters. \item{\textbf{Section 7.}} Thermonuclear bursts and burst oscillations. \item{\textbf{Section 8.}} Aperiodic phenomena including kilohertz QPOs. \item{\textbf{Section 9.}} Future developments and open questions. \end{description}
| 12 | 6 |
1206.2727
|
|
1206
|
1206.0736_arXiv.txt
|
We study the synthesis of lithium isotopes in the hot tori formed around stellar mass black holes by accretion of the companion star. We find that sizable amounts of both stable isotopes $\lisix$ and $\liseven$ can be produced, the exact figures varying with the characteristics of the torus and reaching as much as 10$^{-2}$ M$_\odot$ for each isotope. This mass output is enough to contaminate the entire Galaxy at a level comparable with the original, pre-galactic amount of lithium and to overcome other sources such as cosmic-ray spallation or stellar nucleosynthesis.
|
\par Lithium is one of the very few elements in our Universe whose abundance is significantly affected by big bang nucleosynthesis (BBN), nuclear spallation processes in cosmic rays, and stellar nucleosynthesis. In particular, its $\liseven$ isotope is observed in the atmosphere of relatively cold stars in our Galaxy, namely halo stars of varying metallicity and stars belonging to globular clusters. The very first observations \cite{Spite:1982} have revealed a remarkable flat trend in the abundance of $\liseven$ vs the metallicity of the target star, known as the ``plateau''; the most recent observations of halo stars (see \cite{Sbordone:2010zi} and references therein) show instead a clear ``meltdown'' of such single abundance value at the lowest metallicities, as well as a moderate, yet non-negligible dispersion at intermediate ones. The ``roof'' of this plateau still sits at a factor $\sim$3 below the prediction from standard BBN, a discrepancy that is known as the ``lithium problem''. If the value of the plateau is of primordial origin, the observations are almost impossible to reconcile with standard BBN, and exotic models are to be invoked \cite{Iocco:2008va, Jedamzik:2009uy}. If that value is the result of processes of stellar origin, it {\it is} possible to set up a stellar mechanism able to deplete the original abundance \cite{Korn:2006tv}, but it is still left to demonstration how this mechanism can act over three orders of magnitude in the metallicity of the star, thus reproducing an almost flat envelope. Cosmic-ray spallations can also destroy $\liseven$, but it seems unlikely that they can reproduce the observed features \cite{Fields:2004ug}. \par The aim of this Letter is not to propose a solution to the so-called ``lithium problem'', but if possible to add another piece to the puzzle, as our results go in the direction of harshening the discrepancy between the BBN value and the one observed in stars. This opens up a scenario that needs to be taken into account in future studies concerning this subject. The existence of stellar mass black holes accreting from companion stars is established through observations of so-called microquasars, visible in X-ray frequencies in our Galaxy \cite{Mirabel:1999fy}. We show that material accreting onto a stellar mass black hole from a companion star, in a disk with characteristics of a hot torus, can undergo nucleosynthesis, and produce sizable quantities of $\lisix$ and $\liseven$. The amount of both isotopes depends on parameters such as the mass of the black hole, the viscosity of the medium, the accretion rate and the expelled fraction, and it can reach up to 10$^{-2}$ M$_\odot$ within the allowed region of the parameter space. \par We first describe the structure of accretion tori around microquasars, and then discuss our implementation of the nuclear reaction network and nucleosynthesis equations. We finally present our results, as well as draw some guidelines and suggestions for future work.
|
\label{secresults} \begin{figure*}[htp] \centering \includegraphics[width=0.4\textwidth,height=0.35\textwidth]{Mdotalpha2_5Msun_new.pdf} \hspace{0.5cm} \includegraphics[width=0.4\textwidth,height=0.35\textwidth]{Mdotalpha2_30Msun_new.pdf} \caption{The mass of $\liseven$ (plus $\beseven$) and $\lisix$ synthesised in a hot torus around a black hole of 5 M$_\odot$ (left) and 30 M$_\odot$ (right). The shadowed area encompasses the Eddington upper limit on the accretion rate $\dot{M}$ assuming accretion efficiencies $0.06\leq \epsilon\leq 0.42$.} \label{fig:Mdotalpha} \end{figure*} \par We have solved the set of coupled Boltzmann equations in a large region of the torus parameter space $(M_{BH},\dot M,\alpha)$. In our default case, we set the initial abundances of light elements to the ones leftover by BBN, namely \cite{Jedamzik:2009uy} $\textrm{D}/\textrm{H}=2.49\times10^{-5}$, $\hethree/\textrm{H}=10^{-5}$, $Y_P=0.2486$, $\liseven/\textrm{H}=5.24\times10^{-10}$ and $\lisix/\textrm{H}$=10$^{-14}$. However, we show later that the initial relative abundances are not crucial for the final amount of lithium isotopes synthesised. The results for sample black hole masses of 5 M$_\odot$ and 30 M$_\odot$ are shown in figure \ref{fig:Mdotalpha} on the plane $\alpha$ vs $\dot M$. It is clear that the nucleosynthesis in the hot torus can produce up to $\gtrsim10^{-4}$ M$_\odot$ of $\liseven$ (plus $\beseven$) and $\lisix$, with little dependence on the black hole mass (the small differences between the two cases arise mainly because of the different size of the torus and inflow time). On the other hand, the Eddington limit $L\equiv \epsilon \dot{M} c^2 \leq L_{Edd}$ -- indicated by the shadowed area in figure \ref{fig:Mdotalpha} with typical black hole accretion efficiencies \cite{ShapiroTeukolsky} $0.06\leq \epsilon\leq 0.42$ -- does depend on $M_{BH}$ and sets the most stringent constraint on the achievable amount of isotopes. We show in figure \ref{fig:MBH} the total produced mass of $\liseven$ (plus $\beseven$) and $\lisix$ as a function of $M_{BH}$ for fixed $\alpha$ and $\dot{m}$. Masses as large as 10$^{-2}$ M$_\odot$ are reached for hundred solar masses black holes. For the case of a 5 M$_\odot$ black hole (left panel in figure \ref{fig:Mdotalpha}), the lithium is produced at a ratio $^{6}\textrm{Li}/(^7\textrm{Li}+^7\textrm{Be})\simeq0.25-0.29$. Our results agree well with \cite{Jin90} when we adopt its equation (7) for the same black hole accretion configuration; however, in figures \ref{fig:Mdotalpha} and \ref{fig:MBH} we show lithium masses according to our equation \eqref{Mli7} that implicitly assumes a uniform ejection of torus material. Computing the expelled mass as if it were ejected mostly from the inner regions yields final masses higher by a factor $\lesssim 10$, which would only strengthen our conclusions. \begin{figure}[htp] \centering \includegraphics[width=0.4\textwidth,height=0.35\textwidth]{MBH_new.pdf} \caption{The mass of $\liseven$ (plus $\beseven$) and $\lisix$ synthesised as a function of $M_{BH}$ for fixed $\alpha$ and $\dot{m}$. Here we take $\epsilon=0.06$.} \label{fig:MBH} \end{figure} \par The nuclear reactions leading the synthesis of the lithium isotopes are the $\alpha+\alpha$ reactions: $\hefour(\alpha,n)\beseven$, $\hefour(\alpha,p)\liseven$, $\hefour(\alpha,d)\lisix$ and $\hefour(\alpha,np)\lisix$. All present similar thermally averaged cross-sections at the temperatures of interest and yield similar outputs of $\lisix$, $\liseven$ and $\beseven$ as shown in figure \ref{fig:Mdotalpha}. Therefore, the final abundance of lithium is sensitive mostly to the content of $\hefour$ present in the plasma. We find that in order to suppress lithium production by a factor $\sim$10$^4$ it is necessary to suppress the original abundance of $\hefour$ by a factor 10$^2$ (notice that the helium abundance enters quadratically in equation \eqref{eqBoltz}). Varying the initial abundances of D, $^3$H and $\hethree$ negligibly affects the final results, and adding an initial abundance of neutrons up to half of the number fraction has no significant effect. These checks show that the synthesis in the hot torus is sensitive mostly to its physical properties rather than the initial conditions of the gas chemistry (modulo the abundance of $\hefour$, which is the fundamental reactant for our purposes). It is worth stressing that synthesis at this level is possible because of the short resilience time of elements inside the hot torus. At photon densities below $\rho/m_p$, such as the ones considered here, the timescale for photodissociation of $\hefour$ in all possible channels (that require non-negligible amounts of photons above the threshold of $\sim$20 MeV) is much larger than the inflow timescale: for the most extreme cases we get $\Gamma^{-1}/t_r\gtrsim 3000$. Analogously, the photodissociation of $\lisix$, $\liseven$ and $\beseven$ is also found to be unimportant since $\Gamma^{-1}/t_r\gtrsim 70$. Together with the low lithium/beryllium densities, this prevents photodissociation from being competitive to the $\alpha+\alpha$ reactions. If we artificially modify the inflow time, we do in fact observe consistent depletion of lithium isotopes for longer inflow times, and enhanced final abundances for shorter resilience times. Furthermore, we find that scaling the photon density by a factor ranging from 10$^{-3}$ up to 10$^3$ has little effect on the lithium synthesis, whereas above 10$^4$ there are substantial variations. This large photon enhancement is rather unlikely if the photons are to be originated in the torus itself; however, if the cool disk surrounding the torus is nearby and produces large amounts of soft photons, these can be upscattered in the torus and induce the spallation of light elements as found in \cite{Mukhopadhyay:1999ut}. \par The results in figures \ref{fig:Mdotalpha} and \ref{fig:MBH} are interesting under many regards. It is to be reminded that the amount of $\liseven$ and $\lisix$ produced by primordial nucleosynthesis, according to the most recent estimates of baryon density, are $\liseven/\textrm{H}=5.24\times10^{-10}$ and $\lisix/\textrm{H}=10^{-14}$; this represents the minimal ``background'' level of lithium isotopes which are present in the Galaxy at the time of its formation. A few simple estimates clarify the relevance of the results presented in this Letter: \begin{itemize} \item It is expected that $10^8-10^9$ stellar mass black holes are present in our Galaxy, see e.g.~\cite{Remillard:2006fc} and references therein. The Milky Way mass in stars and gas is $M_{gal}\sim$ 5$\times$10$^{10}$ M$_\odot$ \cite{Gardner:2010sa}, which means that in principle, if a typical hot torus produces $10^{-4}\textrm{ M}_\odot$ of both $^7$Li and $^6$Li, then only 0.1$-$1\% ($10^{-6}-10^{-5}$\%) of the microquasars in our Galaxy need to host a hot torus so that the synthesised amount of $^7$Li ($^6$Li) is comparable to the BBN ``background'' level. \item The first generation of stars (Population III, Pop.~III) is expected to form in small halos of total baryonic mass $10^5-10^6$ M$_\odot$. Recent numerical simulations of early star formation show evidence for multiple Pop.~III systems, with fragments of masses ranging in the sub-hundred solar masses regime \cite{Turk:2009ae, Smith:2011ac}. It has already been proposed that such systems may give rise to microquasars \cite{Mirabel:2011rx}: what we wish to highlight here is that the production of $10^{-4}-10^{-3}$ M$_\odot$ of $\liseven$ and $10^{-9}-10^{-8}$ M$_\odot$ of $\lisix$ by {\it a single} microquasar is enough to equate the BBN ``background'' level in the halo where the Pop.~III system has formed. These numbers are indeed achieved within the parameter space scanned in our study. \end{itemize} \par The previous examples are defective in some regards. In order for the quoted numbers to be taken at face value the material synthesised in the hot torus and expelled must be assumed to efficiently mix in the interstellar medium. This might be the case of primordial star-forming haloes -- where extremely efficient internal mixing is expected \cite{Scannapieco:2003rd} --, but not of the Milky Way, which raises the issue of even higher concentrations of lithium isotopes locally, around the microquasars themselves and in regions where microquasars are more frequent. Also, although it is not unreasonable that a significant part of the material gets expelled from the torus as argued above, presumably some of the expelled material would cross cool regions where significant spallation may occur. Finally, light element spallation within the torus can be important if a nearby, intense external source of photons is present. With these caveats in mind, and the need to explore further the physics of this ``aftermath'' part in a self-consistent way, it is clear however that the mechanism described has the potential to produce amounts of lithium comparable to the primordial values as well as to stellar nucleosynthesis and cosmic-ray synthesis, see discussion in e.g.~\cite{Fields:2004ug}. We point out that future population studies should take this mechanism into account, addressing especially the open issues discussed in this Letter. It is also worth remarking that microquasars are indeed observed in the X-ray bands in our Galaxy, and that in principle their optical and infrared counterparts are observable. This should give rise to the possibility of observing the amount of lithium (whose observable feature lies at 670.8 nm), thus checking the validity of the mechanism described so far or, alternatively, permitting to set constraints on the parameters and nature of the accretion onto stellar mass black holes. Interestingly, anomalously high lithium abundances have been observed in late type stars, companion of black holes or neutron stars (see \cite{Mukhopadhyay:1999ut} and references therein), thus suggesting another observational strategy to constrain the mechanism we have studied. \par We have shown that nucleosynthesis of light elements taking place in the hot torus of accreting stellar mass black holes can produce sizable amounts of $\lisix$ and $\liseven$ for a wide range of parameters of the black hole and companion star system. Future studies concerning the ``lithium problem'' should take this mechanism into account, especially since its actual magnitude and impact can in principle be tested through observations. \vspace{0.5cm} {\it Acknowledgements } The authors would like to thank P.~D.~Serpico for useful comments. F.~I. is grateful to F.~Mirabel for having introduced him to the subject of microquasars, and thanks S.~P\'erez for useful references.
| 12 | 6 |
1206.0736
|
1206
|
1206.5113_arXiv.txt
|
We conducted a spectropolarimetic survey of 58 high proper-motion white dwarfs which achieved uncertainties of $\ga 2$ kG in the H$\alpha$ line and $\ga 5$ kG in the upper Balmer line series. The survey aimed at detecting low magnetic fields ($\la 100$ kG) and helped identify the new magnetic white dwarfs NLTT~2219, with a longitudinal field $B_{\rm l} = -97$ kG, and NLTT~10480 ($B_{\rm l}=-212$ kG). Also, we report the possible identification of a very low-field white dwarf with $B_{\rm l} = -4.6$ kG. The observations show that $\approx5$\% of white dwarfs harbour low fields ($\sim10$ to $\sim10^2$~kG) and that increased survey sensitivity may help uncover several new magnetic white dwarfs with fields below $\sim$1 kG. A series of observations of the high field white dwarf NLTT~12758 revealed changes in polarity occurring within an hour possibly associated to an inclined, fast rotating dipole. Also, the relative strength of the $\pi$ and $\sigma$ components in NLTT~12758 possibly revealed the effect of a field concentration (``spot''), or, most likely, the presence of a non-magnetic white dwarf companion. Similar observations of NLTT~13015 also showed possible polarity variations, but without a clear indication of the timescale. The survey data also proved useful in constraining the chemical composition, age and kinematics of a sample of cool white dwarfs as well as in constraining the incidence of double degenerates.
|
\begin{figure*} \centering \includegraphics[width=1.0\columnwidth]{fig1a.eps}% \includegraphics[width=1.0\columnwidth]{fig1b.eps}% \caption{VLT/FORS spectra of DA white dwarfs ordered by increasing temperatures (bottom to top and right to left): 20 spectra were obtained (left panel) using grism 600B and covering the upper Balmer lines, and (right panel) 39 spectra were obtained using grism 1200R+93 and covering H$\alpha$. Several objects show Ca~K (NLTT~888, 6390, 7547, 10480, 11393, and 25792) in their spectra with a few more showing Ca{\sc i}$\lambda$4226 (NLTT~7547, 10480, and 25792) and are classified as DAZ white dwarfs. Zeeman line splitting is immediately apparent in the H$\alpha$ spectra of NLTT~12758 and 13015.} \label{fig_DA} \end{figure*} Magnetic fields in white dwarfs show great diversity in strength and structure. Field strengths from a few kilogauss \citep[e.g., 40 Eri B or LTT~9857,][]{fab2000,azn2004} to nearly 10$^9$ G \citep[e.g., J0317$-$855,][]{bar1995,fer1997} delineate the current range of detection, although higher and lower fields cannot, in principle, be ruled out. Low-dispersion spectropolarimetric surveys successfully achieved detection limits below a kilogauss \citep{azn2004} or of the order of a few kG \citep{sch1994,kaw2007}, while echelle spectroscopy achieved limits of several kilogauss with Zeeman splitting measurements in line cores \citep{koe1998}. The spectra of high-field white dwarfs are very complex and detailed modelling requires application of model atoms in high-fields \citep{mar1984,jor1992}. Hydrogen and helium atomic data are available for such studies \citep{kem1974,gar1974}. Stellar rotation, by exposing a variable line-of-sight projection of the field vector, often reveals a more complex field structure than a simple dipole \citep{mar1984} as found in the cases of the fast-rotating ($P\approx12$ min) white dwarf J0317$-$855 \citep[see][]{bur1999,ven2003x} or the ``spotted'' magnetic white dwarf WD~1953$-$011 with a rotation period of 1.4 day \citep{max2000,bri2005,val2008}. Apart from the common hypothesis of a fossil origin, magnetic fields may be generated in later stages as first proposed by \citet{tou2008}, first, during a common-envelope (CE) phase of binary evolution \citep[see also][]{pot2010,nor2011} or in a double degenerate merger \citep[see also][]{gar2012}. \citet{kaw2004x} examined the distribution of field strength in the Ap star population and concluded that a direct link between Ap stars and high field magnetic white dwarfs ($B\ga 10^7$ G) may exist assuming magnetic flux conservation, but that low-field white dwarfs are without known progenitors. However, \citet{wic2005} found a progenitor deficit for high-field white dwarfs and postulated that a large fraction of massive main-sequence stars ($\ga 4.5\,M_\odot$) may harbour weak fields (10-100~G). We present a survey of 58 high proper-motion white dwarfs conducted with the FOcal Reducer and low dispersion Spectrograph (FORS) at the European Southern Observatory (ESO). The observations, presented in Section 2, provided us with intensity and circular polarization spectra enabling high-sensitivity measurements of the surface-averaged ($B_{\rm S}$) and longitudinal ($B_{\rm l}$) magnetic fields (Section 3). In particular, we examine the sample properties (Section 3.1), our new low-field detections (Section 3.2) and instances of variable high-fields (Section 3.3), and the sample kinematical properties (Section 3.4) as well as other interesting aspects of this survey (Section 3.5). We summarize and discuss some implications of our results in Section 4.
|
We have conducted a spectropolarimetric survey of 58 DA white dwarfs. We report the discovery of the low-field magnetic white dwarf NLTT~2219 ($B_l=-97$ kG) and of the likely extremely low-field white dwarf NLTT~347. Our survey also led to the identification of the magnetic DAZ white dwarf NLTT~10480 \citep{kaw2011}. Spectropolarimetric series of the high-field white dwarf NLTT~12758 revealed short-period ($\la 1$~hr) polarity variations characteristic of a rotating dipole. We also noted radial velocity variations and a strong contrast in the strengths of the $\pi$ and $\sigma$ components suggesting that NLTT~12758 is a spectroscopic binary. Further work on this object is awaiting detailed Zeeman modelling and additional spectroscopic data to establish the periodicity of the radial velocity and field variations. The time series of NLTT~13015 also showed possible variations and the surface-averaged field spread from 6 to 7.5 MG. The precision of H$\alpha$ velocity measurements also allowed us to identify potential close double degenerate stars such as the DA+DC NLTT~21913 and the single-lined DA white dwarfs NLTT~6559 and NLTT~31473. Incidentally, NLTT~31473 is also a member of the Galactic halo. \citet{max1999} used their radial velocity survey to determine the fraction of double degenerate systems among white dwarfs to be between $\sim 2\%$ and 19\%. Including the likely double-degenerate NLTT~12758, we estimate the fraction of close double degenerates at $7\pm3$\%. We exploited the present data to infer stellar (mass, age) and kinematical properties of this sample of relatively old high-proper motion white dwarfs. For instance, we identified two new halo white dwarf candidates (NLTT~31473 and NLTT~33503) among a sample of thin- or thick-disc white dwarfs. The atmospheric parameters (\teff\ and $\log{g}$) obtained using spectroscopic and photometric data are in good agreement. The SDSS $ugriz$ photometry allowed us for the first time to assess the effect of Ly$\alpha$ extended-wing opacities \citep{kow2006} on the SDSS $u-g$ colour index of cool DA white dwarfs. \begin{figure} \centering \includegraphics[width=1.0\columnwidth]{fig9.eps} \caption{Cumulative distribution of low-field measurements ($B_{\rm S} \la 1$MG) in white dwarfs, where $N_>$ is the number objects with a field larger than a surface average field $B_{\rm S}$. Notable objects from Table~\ref{tbl_low} are marked. With the exception of a slight enhancement near 10 kG, the observed distribution is nearly linear implying a constant incidence of magnetic field per decade.} \label{fig_cum} \end{figure} \begin{figure} \centering \includegraphics[width=1.0\columnwidth]{fig10.eps} \caption{Magnetic field strength versus cooling age for low-field white dwarfs (Table~\ref{tbl_low}).} \label{fig_mag_age} \end{figure} The incidence of magnetism in white dwarfs has been reported to be as low as 4\% \citep{sch1995} when taking into account all magnetic field strengths, or $\sim 1$\% per decade interval. However, it was reported to be as high as 25\% when considering only the very low-field white dwarfs \citep{azn2004}. \citet{azn2004} detected kG fields in three white dwarfs out of total 12, and when they extended their survey to an additional 10 objects they only reported one possible candidate \citep{jor2007}. The combined survey hence reduced the incidence of kG fields in white dwarfs to 11 - 15\%. \citet{kaw2007} studied the incidence of magnetism in the Solar neighbourhood and found that $21\%\pm8\%$ of white dwarfs are magnetic. In the present survey of nearly 60 objects we uncovered three new low-field white dwarfs with strengths of the order of $\sim10$ to $\sim10^2$ kG implying a field incidence of $5\pm2$\%, or $\sim 1-2$\% per decade interval. The incidence observed in the present sample is similar to that observed by \citet{sch1995}. The exact fraction remains uncertain because of inhomogeneous sampling and methodology. Figure~\ref{fig_cum} shows the cumulative distribution of low-field white dwarfs as a function of the field logarithm. The linear relation corresponds to a nearly flat distribution and is evidence that fields are distributed randomly rather than following a distribution pattern as found in Ap stars \citep{aur2007}. Fields generated by a dynamo involving a common-envelope phase \citep[see][]{tou2008,pot2010,nor2011} with a body varying in size, hence disposable energy, such as an asteroid, a planet, a brown dwarf, or a low-mass star are likely to vary in intensity as well. The random nature of the size of the body involved in the common-envelope phase should also result in random field intensity. Once the field is frozen into the stellar body, the decay time-scale is of the order of $10^9 - 10^{10}$ years \citep{mus1995}, i.e., comparable to the white dwarf cooling age. On the other hand, the Ap stars are still likely progenitors of high-field ($\ga 10^7$ G) white dwarfs. Are two independent formation channels possible? \citet{tou2008} argues that the absence of magnetic white dwarfs in non-interacting pairs implies that all magnetic white dwarfs are the products of interaction or merger. This syllogism does not exclude other possible channels if it can be shown that the failure to identify magnetic white dwarfs in non-interacting binaries is the result of a selection effect for this particular channel. For example, \citet{car2002} found that $\sim 40$\% of Ap stars are in binaries. The inferred distribution of mass ratios implies that close to half of the progeny of Ap stars, i.e., the high-field magnetic white dwarfs, would be paired with luminous companions (G- to A-type) hence escaping detection, although the remainder would be paired with M- to K-type stars and should be detectable, at least during the early cooling stages. As noted by \citet{tou2008}, late-type companions remain elusive, but it remains to be shown that early-type companions are missing as well. The stellar ages in this sample vary from 20 Myr to 5 Gyr. The distribution of field strengths as a function of temperatures possibly reveals strong selections effects in the sample. Figure~\ref{fig_mag_age} shows that all stars from Table~\ref{tbl_low} and with a field $\le 50$ kG are relatively young stars with cooling ages $\la 10^9$ years. Conversely, all stars save two with a field stronger than 50 kG are older stars with cooling ages in excess of $\sim 10^9$ years. Deep, narrow spectral lines are reliable field tracers but are also lacking in cool white dwarfs unless heavy element lines are present such as in the magnetic DAZ NLTT~43806 \citep{zuc2011} or NLTT~10480 \citep{kaw2011}. On the other hand, an explanation for the paucity of intermediate fields (100 kG$-$1 MG) in younger white dwarfs is not readily available. Although these are the field and temperature ranges targeted in most spectropolarimetric surveys \citep[see, e.g.,][]{azn2004}, a larger survey may yet uncover the missing objects. \begin{table} \centering \begin{minipage}{\columnwidth} \caption{Low-field ($B_{\rm S} \la 1$ MG) white dwarfs. \label{tbl_low}} \renewcommand{\footnoterule}{\vspace*{-15pt}} \centering \begin{tabular}{lrcccc} \hline\hline Name & \teff\ & Age \footnote{Calculated assuming $\log{g}=8$.} & $B_{\rm S}$ & Method \footnote{Original measurement from spectropolarimetry ($B_{\rm l}$) or spectroscopy ($B_{\rm S}$). The equivalent $B_{\rm S}$ is estimated at $i=57^\circ$, i.e., $B_{\rm S}\approx 3.16\times B_{\rm l}$.} & Ref. \footnote{ References: 1 - \citet{fab2000}; 2 - \citet{azn2004}; 3 - \citet{koe1998}; 4 - \citet{zuc2011}; 5 - \citet{ber1997}; 6 - \citet{far2011}; 7 - \citet{put1997}; 8 - \citet{sch1994}; 9 - this work; 10 - \citet{max2000}; 11 - \citet{kaw2011}; 12 - \citet{duf2006}; 13 - \citet{wes2001}.} \\ & (K) & (Gyr)& (kG) & & \\ \hline 40~Eri~B & 16500 & 0.15 & 7.3 & $B_{\rm l}$ & 1 \\ LTT~9857 & 8660 & 0.91 & 9.8 & $B_{\rm l}$ & 2 \\ LTT~4099 & 15280 & 0.19 & 12.3 & $B_{\rm l}$ & 2 \\ BPM~3523 & 23450 & 0.03 & 13.5 & $B_{\rm l}$ & 2 \\ 2329$-$291 & 24000 & 0.03 & 31. & $B_{\rm S}$ & 3 \\ 1531$-$022 & 18850 & 0.09 & 35. & $B_{\rm S}$ & 3 \\ 2105$-$820 & 10760 & 0.52 & 43. & $B_{\rm S}$ & 3 \\ 2039$-$682 & 16050 & 0.16 & 50. & $B_{\rm S}$ & 3 \\ NLTT~43806 & 5900 & 2.55 & 70. & $B_{\rm S}$ & 4 \\ LHS~5064 & 6680 & 1.79 & 100. & $B_{\rm S}$ & 5 \\ G~77-50 & 5310 & 3.76 & 120. & $B_{\rm S}$ & 6 \\ G~234-4 & $\sim$4500 & 6.21 & 125. & $B_{\rm l}$ & 7 \\ LP~907-37 & $\sim$9500 & 0.71 & 268. & $B_{\rm l}$ & 8 \\ NLTT~2219 & 5980 & 2.45 & 307. & $B_{\rm l}$ & 9 \\ G~217-37 & $\sim$6400 & 2.03 & 316. & $B_{\rm l}$ & 8 \\ 1953$-$011 & $\sim$7900 & 1.15 & 500.\footnote{Highest of the two components.} & $B_{\rm S}$ & 10 \\ NLTT~10480 & $\sim$5250 & 3.94 & 500. & $B_{\rm S}$ & 11 \\ G~165-7 & 6440 & 1.99 & 650. & $B_{\rm S}$ & 12 \\ LB~8915 & $\sim$24500 & 0.03 & 750. & $B_{\rm S}$ & 13 \\ \hline \end{tabular} \end{minipage} \end{table}
| 12 | 6 |
1206.5113
|
1206
|
1206.2396_arXiv.txt
|
{ Thirty years after the first observation of the $^7{\rm Li}$ isotope in the atmosphere of metal-poor halo stars, the puzzle about its origin persists. Do current observations still support the existence of a ``plateau'': a single value of lithium abundance, constant over several orders of magnitude in the metallicity of the target star? If this plateau exists, is it universal in terms of observational {\it loci} of target stars? Is it possible to explain such observations with known astrophysical processes? Can yet poorly explored astrophysical mechanisms explain the observations or do we need to invoke physics beyond the standard model of Cosmology and/or the standard model of Particle Physics to explain them? Is there a $^6{\rm Li}$ problem, and is it connected to the $^7{\rm Li}$ one? These questions have been discussed at the Paris workshop ``Lithium in the Cosmos'', and I summarize here its contents, providing an overview from the perspective of a phenomenologist.
|
The seminal observation of the $^7{\rm Li}$ isotope in low-mass turn-off stars of our galactic halo, returned a surprising result: the lithium abundance observed in the atmosphere of the target stars -whose metallicity spanned more than one order of magnitude in [Fe/H]- exhibited a constant behavior, \citet{spite82}. This permitted the identification of a ``plateau'' of $^7{\rm Li}$ in turn-off, metal-poor stars of our halo, given the very little dispersion of observations around a single value, an observational evidence that was puzzling for reasons that can be summarized by the following questions. If the observed $^7{\rm Li}$ has been processed by the host stars, how is it possible that it exhibits such a regular behavior over such a large interval in metallicity of the host star? If it has not been processed by the star, the $^7{\rm Li}$ we observe is the same that was in the atmosphere from the very beginning of the stellar formation process. If depletion from intervening chemical evolution is negligible (as it safely turns out to be) the latter must be identified with what is leftover from Primordial Nucleosynthesis, but then, why is it the only element not to match the standard Primordial Nucleosynthesis predictions made using the latest (independent) cosmological data on the baryon density? Thirty years later, the puzzle about the origin of the $^7{\rm Li}$ observed in the atmosphere of such stars is far from being solved. In spite of the bigger sample of stars, better quality spectra and amazing progress in the determination of stellar atmospheres, we still struggle to understand the origin of the observed $^7{\rm Li}$. In these proceedings, I summarize the view that a phenomenologist (not an observer, not an hard-core cosmologist, not a stellar theorist) has on the problem, in light of the latest findings as discussed in the Paris workshop. Observations are summarized in the first section, and the leading stellar theory arguments invoked to explain the observations are shortly summarized in the second section. In the third, current issues regarding Primordial (or Big-Bang) Nucleosynthesis (BBN) are briefly exposed. A very short update on observations of $^6{\rm Li}$ is provided before finally reporting the biggest open questions to date in the Conclusions section. Throughout these proceedings the references to the original literature must be limited and therefore utterly incomplete; for each topic, I also address to the material presented at \href{http://www.iap.fr/lithiuminthecosmos2012}{this workshop} with the name of the author presenting such results: a more complete list of references for each topic, as well as more quantitative details can be found in their proceedings.
|
`What is the ``Lithium Problem'' today?' is the relevant question to be asked before looking for its solution. Namely, what is it about lithium that state-of-the-art observations and theory fail to explain, and must therefore be regarded as a ``problem''? Until very few years ago the ``Lithium Problem'' could have been phrased this way: ``Observations of $^7{\rm Li}$ in the atmosphere of field halo, turn-off stars ---spanning almost two orders of magnitude in metallicity--- exhibit a single value abundance, with virtually zero dispersion around the central (only) value. Such value is a factor 3 to 5 smaller than what is expected to be leftover by SBBN, and no known astrophysical mechanism is able to deplete the lithium with such a fine---tuned accuracy.'' Such formulation, would hint toward a solution in terms of either: {\it i)} an unknown, fine tuned astrophysical mechanism, at work with same strength in the atmospheres of very different stars, capable to level the lithium abundance starting from the SBBN value or {\it ii)} a modification of SBBN, which would be accurate in predicting all other light elements but $^7{\rm Li}$, by virtue of wither unknown nuclear processes, or exotic processes involving non---standard model particles of modifications of the constants of nature. For both of these explanations, viable physical models existed, however yet unfalsified in their predictions of other systems. The observations and analysis of the last years, discussed at this workshop, display a somewhat more complicated observational evidence than only few years ago: {\it i)} the abundance of $^7{\rm Li}$ in turn-off stars in the halo of the Milky Way and in Globular clusters exhibit a ``roof value'' of ${\rm A(Li)}$=2.4 throughout the range of metallicities [Fe/H]$\leq$-2.0. Very few outliers can be found above such value, and their number is statistically irrelevant; {\it ii)} below such envelope value, the observed abundances show:\\ {\it iia)} moderate dispersion of $\sim$0.2 dex in the metallicity range -2.8$\leq$[Fe/H]$\leq$-2.0\\ {\it iib)} very big dispersion ---down to vanishing abundances--- in the metallicity range [Fe/H]$\leq$-2.8. In light of this, the ``Lithium Problem'' today may be rephrased in the following way: ``Observations of $^7{\rm Li}$ in the atmosphere of turn off stars spanning more than two orders of magnitude in metallicity, do not pass a roof/envelope abundance a factor $\sim$3 smaller than what predicted from SBBN. Little, yet non-zero, dispersion is seen below such value at intermediate metallicities, and much more consistent dispersion -down to vanishing abundances- is seen from the lowest metallicities.'' This is clearly a much more complicated scenario to be solved with a single answer. If the explanation is astrophysical, one shall envision a mechanism that from the SBBN value depletes the lithium of {\it at least} a factor 3 in the atmosphere of metal-poor stars, with little dispersion (with similar efficiency of the mechanism) at intermediate metallicities, and with very different efficiency at the lowest metallicities. On the other hand, if one assumes that some exotic mechanism is at work during BBN, such to modify the abundance of the $^7{\rm Li}$ isotope down to the plateau envelope value, additional problems would still to be faced. An astrophysical mechanism able to cause strong depletion at low metallicities, shall be invoked, yet capable of limiting such depletion at the observed level at higher metallicities, in a mechanism much resembling those that were so fine tuned, and be argued against when invoked as solution of the old formulation of the ``Lithium Problem''. Yet, it seems clear that in both scenarios astrophysical processes are at work, even if at low metallicities only, on the top of an unknown astrophysical, cosmological or particle process, and that the use of the plateau roof for cosmological use and constraints on non-standard processes seems riskier today than it was in the past. A specular discussion of these arguments can be found in the proceedings of Sbordone et al. and of Spite et al., and examples of composite explanations have been discussed at the meeting, see e.g. P.~Molaro's proceedings. In spite ---or maybe because of--- all the novelties and elements discussed at the Paris workshop, I find impossible to write down any Conclusion about the Lithium Problem, and I prefer to end these proceedings with a somewhat pedantic, yet not inappropriate semantic thought.\\ Is the Lithium Problem Primordial, Cosmological, Cosmic or Astrophysical: which of the several adjectives that have been imposed to the problem is the most fitting to its nature? In light of the previous considerations, I suggest that either Astrophysical, Cosmological or Primordial would impose on the problem a shade of pre-concept solution, and that perhaps ``Cosmic'' is the least unfitting definition, given the universality of the problem itself with respect to galactic observation loci. {\it Note added---} It is with much relief that ---after completing this text--- I read the proceedings of M.~Spite, F.~Spite, and P.~Bonifacio in this volume, and I realize that a phenomenologist's perspective is after all not that different from an observer's one. We leave it to the reader to investigate the consequences of this worrisome finding.
| 12 | 6 |
1206.2396
|
1206
|
1206.5749_arXiv.txt
|
We explore a set of single-point chemical models to study the fundamental chemical aspects of episodic accretion in low-mass embedded protostars. Our goal is twofold: (1) to understand how the repeated heating and cooling of the envelope affects the abundances of CO and related species; and (2) to identify chemical tracers that can be used as a novel probe of the timescales and other physical aspects of episodic accretion. We develop a set of single-point models that serve as a general prescription for how the chemical composition of a protostellar envelope is altered by episodic accretion. The main effect of each accretion burst is to drive CO ice off the grains in part of the envelope. The duration of the subsequent quiescent stage (before the next burst hits) is similar to or shorter than the freeze-out timescale of CO, allowing the chemical effects of a burst to linger long after the burst has ended. We predict that the resulting excess of gas-phase CO can be observed with single-dish or interferometer facilities as evidence of an accretion burst in the past \ten{3}--\ten{4} yr.
|
\label{sec:intro} The wide spread in bolometric luminosities observed among low-mass embedded protostars is at odds with a constant mass accretion rate onto the central source \citep{kenyon90a,kenyon94a,dunham08a,enoch09b,evans09a}. Several explanations have been put forward for this ``luminosity problem,'' the most common of which is episodic accretion: protostars accrete most of their mass in short bursts, while spending most of their time in a low-luminosity quiescent state \citep{kenyon90a}. The hypothesis of episodic accretion is supported by a suite of models \citep{young05a,vorobyov05b,vorobyov10b,zhu09a,zhu10b,dunham10a,dunham12a}, but many key questions remain unanswered. How intense are the accretion bursts? How many bursts does a given protostar experience, and on what timescales do they occur? How does episodic accretion affect the chemical evolution from a molecular cloud to a circumstellar disk? This Letter focuses on the question of episodic accretion chemistry and explores how one might use certain chemical tracers to help answer the questions outlined above. The lack of constraints on most aspects of episodic accretion in embedded Class 0 and I protostars comes from the difficulty of observing the accretion bursts directly. In more evolved Class II sources, accretion bursts show up as FU Ori and EX Ori events \citep{herbig77a,hartmann96a}. Luminosity flares of factors of 2--10 have been observed for a few late Class I sources \citep{kospal07a,caratti11a}. Other evidence for variable accretion in embedded sources is all indirect, such as the luminosity problem \citep{kenyon90a} or the presence of periodic shocks along protostellar jets \citep{reipurth89a}. Additional probes are needed, and chemical signatures may be one. To date, only two studies have addressed the topic of episodic accretion chemistry in embedded protostars. \citet{lee07a} showed that repeated burst--quiescent cycles lead to repeated freeze-out--evaporation cycles of CO and other species. The freeze-out timescale is longer than the duration of a burst, so the chemical effects of the burst can remain visible through part or all of the subsequent quiescent stage. \citet{kim11a} hypothesized that every time CO freezes out, a fraction is converted into \cdo{} ice. They found a better fit to the 15.2 \micron{} \cdo{} ice feature in the low-luminosity source CB130-1 -- presumed to be in a quiescent stage -- if 80\% of CO is converted into \cdo. It is unclear, however, why the conversion would have to happen in between accretion bursts rather than before the onset of collapse. \citet{lee07a} and \citet{kim11a} used a full envelope model with fixed timescales for the burst and quiescent stages. In this Letter, we explore episodic accretion chemistry at an even more fundamental level by way of single-point models at various densities and timescales (Sects.\ \ref{sec:model} and \ref{sec:res}). We identify the key chemical processes affected by episodic accretion and illustrate how the physical and chemical timescales play against each other. We also offer some suggestions on how the chemical effects of episodic accretion may be observed with single-dish and interferometer facilities (\sect{disc}).
|
\label{sec:conc} Low-mass protostars appear to accrete most of their mass in a series of bursts interspersed with relatively long phases of very little accretion. If this hypothesis of episodic accretion is indeed true, the protostellar envelope is exposed to multiple heating and cooling events over the course of its existence. This Letter presents a fundamental theoretical investigation into how this would affect the chemical composition and evolution of the gas and dust in the envelope. Based on simple single-point models, we conclude that the effects of episodic accretion chemistry depend strongly on the relative physical and chemical timescales. The abundances of common species like CO, \mn, \hcop, and \nnhp{} show strong time variability if the duration between subsequent accretion bursts is comparable to or longer than the dominant chemical timescale. For typical cold envelope conditions, the dominant chemical timescale is the freeze-out timescale of CO and \mn. Regardless of the exact timescales, the chemical effects of an accretion burst should remain visible for \ten{3}--\ten{4} yr after the burst has passed. In particular, we predict excess amounts of CO gas to be observable with either single-dish or interferometer facilities as chemical signposts of episodic accretion.
| 12 | 6 |
1206.5749
|
1206
|
1206.2169_arXiv.txt
|
s{Dark matter detectors using the liquid noble gases xenon and argon as WIMP targets have evolved rapidly in the last decade and will continue to play a major role in the field. Due to the possibility to scale these detectors to larger masses relatively easily, noble liquids will likely be the first technology realizing a detector with a ton-scale target mass. In this article, we summarize the basic concepts of liquid noble gas dark matter detectors and review the current experimental status.}
|
There is plenty of indirect cosmological evidence~\cite{ref::wimpcosmology} that the vast majority of the Universe's energy content is dark, with about 25\% being in the form of dark matter which builds large scale structures. Another 70\% is the mysterious dark energy, responsible for the accelerated expansion of the Universe and only about 5\% is ``ordinary'', baryonic matter which forms stars, planets, and eventually us. There is no known particle in the Standard Model of Particle Physics which could be the dark matter particle, neutrinos for example are too light and fast, hence the dark matter particle must be from new physics and is yet unknown. One of the most favorite candidates is the weakly interacting massive particle (WIMP)~\cite{ref::wimps}, which arises naturally in several extensions of the Standard Model, such as Supersymmetry, Universal Extra Dimensions, and little Higgs models. Many experiments aim at the direct detection of these particles by measuring nuclear recoils of target nuclei after they interact with a WIMP~\cite{ref::directdetect}. Sensitive detectors are placed in deep underground laboratories in order to fight backgrounds induced by cosmic rays and their daughter particles. The expected WIMP interaction rate is less than 1~event per kg of target material and year, and the featureless recoil spectrum is exponentially falling with typical energies of tens of~keV only. These experiments use different targets and detection methods, which all have different pros and cons. Liquid noble gases such as xenon and argon, but possibly also neon, have started to play an important role in the field since about a decade and are currently placing the most stringent limits on spin-independent WIMP-nucleon cross-sections over a large range of WIMP masses~\cite{ref::xe100run08,ref::xe10s2only}. This article gives a brief review on these detectors.
|
Many experiments aim to directly detect WIMP dark matter by searching for nuclear recoils from elastic WIMP collisions inside very sensitive detectors with ultra-low backgrounds. A large number of projects employs the noble gases xenon or argon, cooled down and liquefied in order to obtain high-density targets. We have detailed why these elements are excellent WIMP targets and have explained the most common detector concepts. These are either single phase detectors measuring the scintillation light signal only, or double-phase detectors measuring the light and the charge signal (from ionization) in a TPC setup. At the time of writing, the most stringent exclusion limits for all WIMP masses are from LXe based detectors. We have presented the current status of more than 10~experiments using noble liquids which are all aiming to reach even higher sensitivities. Their goal is to explore new regions in the cross section vs.~mass parameter space (see Fig.~\ref{fig::limits}) and to finally detect the dark matter particle with detectors of 100-1000~kg target mass or even beyond.
| 12 | 6 |
1206.2169
|
1206
|
1206.6056_arXiv.txt
|
We present follow-up observations\footnote{Based on observations obtained with the Apache Point Observatory 3.5-meter telescope, which is owned and operated by the Astrophysical Research Consortium. This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile. Support for the design and construction of the Magellan Echellette Spectrograph was received from the Observatories of the Carnegie Institution of Washington, the School of Science of the Massachusetts Institute of Technology, and the National Science Foundation in the form of a collaborative Major Research Instrument grant to Carnegie and MIT (AST0215989). } and analysis of the recently discovered short period low-mass eclipsing binary, SDSS J001641-000925. With an orbital period of 0.19856 days, this system has one of the shortest known periods for an M dwarf binary system. Medium-resolution spectroscopy and multi-band photometry for the system are presented. Markov chain Monte Carlo modeling of the light curves and radial velocities yields estimated masses for the stars of M$_{1} =0.54\pm0.07$ M$_\odot$ and M$_2 = 0.34 \pm0.04$ M$_\odot$, and radii of R$_1 =0.68\pm.03$ R$_\odot$ and R$_2 = 0.58\pm0.03$ R$_\odot$ respectively. This solution places both components above the critical Roche overfill limit, providing strong evidence that SDSS J001641-000925 is the first verified M-dwarf contact binary system. Within the follow-up spectroscopy we find signatures of non-solid body rotation velocities, which we interpret as evidence for mass transfer or loss within the system. In addition, our photometry samples the system over 9 years, and we find strong evidence for period decay at the rate of $\dot{P}\sim$8 s yr$^{-1}$. Both of these signatures raise the intriguing possibility that the system is in over-contact, and actively losing angular momentum, likely through mass loss. This places SDSS J001641-000925 as not just the first M-dwarf over-contact binary, but one of the few systems of any spectral type known to be actively undergoing coalescence. Further study SDSS J001641-000925 is on-going to verify the nature of the system, which may prove to be a unique astrophysical laboratory.
|
M dwarfs, with masses between $\sim$0.08 and 0.6 M$_\odot$, are the most numerous and faintest main sequence stars in the Galaxy. The high number density and very long main sequence lifetimes of M dwarfs allow them to be used as detailed tracers of the nearby galactic stellar population \citep{bochanski_gal,bochanski2010}. These stars are also well known for their high magnetic activity levels, characterized by frequent violent flaring outbursts \citep[e.g.][]{k09,davenport2012}, and H$\alpha$ emission \citep{west2008,westdr7,hilton10}. Eclipsing binary systems provide us with the valuable ability to directly measure the masses and radii of the two component stars. As discussed in \cite{becker2011}, the sample of known binary systems composed of two M dwarfs is very small. Their intrinsically low luminosity and small radii conspire to make M dwarf binaries difficult to detect in variability surveys. The fraction of M dwarfs in binary systems is also much lower than for higher mass stars. \citet{2006ApJ...640L..63L} has estimated that as few as $\sim$10\% of M dwarfs in the Galactic field may be in binary (or higher number) configurations. The M dwarf binary and single-star systems that are well studied indicate that stellar structure models do not accurately predict the observed radii \citep{ribas2006,morales2010}. Radii are often observed to be $\sim$10--20\% larger than predicted for a given mass. This may be due to limitations of the stellar models used, or to a fundamental difference in the interior structure of M dwarfs. Magnetic activity is frequently identified as a potential culprit, causing the radii to be enlarged due to the inhibition of convection or decreased heat flux from magnetic spots \citep[e.g.][]{chabrier2007,bochanski2011}. Long period M dwarf binaries ($P\gtrsim10$ days) are ideal systems for radii determinations, as they are not influenced by spin--orbit coupling or tidal distortion \citep{mazeh2008}. The above discrepancies will only be resolved by the addition of many accurately measured radii to the known sample over a wide range in mass and period. There also appears to be an absolute lower-limit on the orbital period for contact binary star systems, though no consensus about its origin has been reached. This short period limit at $\sim$0.22 days may be due to both components being fully convective \citep{rucinski1992}. At shorter periods, these stars cannot adhere to their mass-radius relationship while simultaneously staying within the Roche equipotential geometry. However, as \citet{rucinski1992} points out, this does not appear to be the primary effect at work in creating the sharp 0.22 day period limit. Alternatively, \citet{jiang2012} have shown that unstable mass transfer for low mass contact binaries may result in rapid coalescence. The observed period limit would thus be a result of the very short lifetimes for such systems. Models of angular momentum loss in binary systems, however, indicate that even given favorable mass ratios and initial orbital periods, 6-13 Gyr timescales are typically required for low mass binaries to obtain periods as short as 0.22 days \citep{stepien2006b}. The observed period limit would then be a consequence of the finite age of the binary population. Until recently, the shortest known M dwarf binary system period in the literature was BW3 V38 \citep{maceroni1997,maceroni2004}, a detached binary composed of two main sequence M3 dwarfs with an orbital period of 0.1984 days. \cite{rucinski2008} found a similarly short period system, GSC 01387--00475, with a period of 0.2178 days, but composed of higher mass K3 and K5 stars and in a contact configuration. \begin{figure}[t] \centering \includegraphics[width=3.5in]{fig1} \caption{Phased light curves in the five SDSS filter bandpasses for SDSS J001641-000925. Photometric errors are shown for all data. Blue points are from the Stripe 82 catalog, black are follow-up data from the NMSU 1-m in $griz$ bands. Red data in the $i$-band were obtained with the Agile camera at the APO 3.5-m.} \label{lc} \end{figure} \cite{dimitrov2010} reported the shortest period M dwarf binary yet characterized, GSC 2314--0530 with a 0.192636 day period, and stellar masses of 0.51 M$_\odot$ and 0.26 M$_\odot$. This system has an orbital period only $\sim$8 minutes shorter than that of our target, SDSS J001641-000925. \cite{nefs2012} have recently discovered four binary systems with M dwarf colors that have periods significantly below the $\sim0.22$ day period limit, providing a major challenge to our understanding of the formation and lifetimes of such systems. The rarity of short period M dwarf binaries, and the lack of known contact M dwarf binary systems, indicates that they are difficult to produce, are so unstable that they are rapidly destroyed, or are still very difficult to detect. A recent study of photometric variability by \citet[][hereafter B11]{becker2011} using the Sloan Digital Sky Survey \citep[SDSS,][]{york2000} revealed several new candidate M dwarf -- M dwarf eclipsing binary systems. B11 analyzed $\sim$4.8 million light curves and found 207 periodically variable objects, and a sharp drop in the number of systems with periods less than 0.22 days. Of these, two candidate eclipsing binary systems with sinusoidal light curves and M dwarf $ugriz$ colors were found to have very short periods: SDSS J200011.19+003806.5 at 0.14552 days, and SDSS J001641.03--000925.2 at 0.198561 days. Both of these objects warranted spectroscopic and photometric follow up to determine their fundamental parameters, and to confirm their status as short period eclipsing binaries. In this paper we describe our detailed photometric and spectroscopic investigation of the brighter of these two objects, the 0.198561 day periodic variable SDSS J001641-000925. In \S2 we describe the photometric and spectroscopic data used in this study. We model basic parameters in \S3, and analyze the peculiarities of the binary system in \S4. We discuss the context of this over-contact binary in \S5.
|
We have presented follow up spectroscopic and photometric observations of a low-mass binary, SDSS J001641-000925, whose orbital period is below the theoretical short period limit \citep{rucinski1992}. The components of this short period system have masses typical of spectral types of M1 and M3, and are in an over-contact configuration. Both stars have radii much larger than predicted by stellar isochrone models. These stars are the most ``oversized'' of any yet determined at this mass due to the over-contact configuration. The strength of the H$\alpha$ line at $\sim$1\AA\ was not particularly high with respect to active stars of this spectral type. Higher H$\alpha$ flux is typically accompanied by strong magnetic activity and flaring for early type M dwarfs; these are features that diminish as the stars age and lose angular momentum \citep{west2008}. The SDSS spectroscopic M dwarf sample, containing $\sim$70,000 spectroscopically confirmed M dwarfs \citep{westdr7} shows approximately half of stars with spectral types M0--M3 that are classified as ``active'' have EW(H$\alpha)\ge1.25$\AA. Thus the H$\alpha$ EW for this system is not usually high, nor does it appear particularly active. In fact, no signs of flaring were detected in more than 20 nights of observing. This is in strong contrast to the similar mass semi-detached binary system observed by \cite{dimitrov2010}, which showed six flares in a comparable amount of observing time. \citet{davenport2012} found that field stars in this spectral type range displayed photometric flares with amplitudes of $\Delta u\ge 1$ mag once every $\sim$2 days on average. However, the slight increase in H$\alpha$ EW during eclipse, as well as the broadened H$\alpha$ line profile with possibly non-solid body rotation velocities, together suggest that the emission feature may be the result of material being expelled from the outer Lagrange points. This would result in a complex H$\alpha$ line, with phase-dependent emission lines contributed from both stars, as well as possible P Cygni-like profiles from the outflowing material. Additional medium to high resolution spectroscopic monitoring will allow us to differentiate H$\alpha$ emission due to active surface regions from that of any nebular emission surrounding the system, as in RY Scuti \citep{grundstrom2007}. Dynamical interactions between a binary system and other stars can decrease the binary orbital period through angular momentum transfer, or through three-body interactions \citep{kozai1962}. Indeed the incidence of contact binary systems is higher in stellar clusters than in the field \citep{1998AJ....116.2998R}, due to the more frequent three-body interactions. Recent models predict a timescale of 6-13 Gyr for an isolated low-mass binary system to undergo enough angular momentum loss to evolve from a stable orbital period of $\sim$1-2 days to below 0.22 days \citep{stepien2006a,stepien2006b}. Estimates of angular momentum loss from single stars, applied to short period binary systems, show that magnetic braking takes on the order of a Hubble time to compress these periods from 1--2 days to below the theoretical limit \citep[e.g.][]{maceroni2004}. With their discovery of several low mass systems below the predicted 0.22 day limit, \cite{nefs2012} demonstrated that initial orbital periods must have been $\sim$1 day in order for magnetic braking schemes to explain the short period systems. \cite{nefs2012} also show that the orbital evolutionary timescales and initial conditions for these rare short period binaries are still largely unconstrained, and that many possible mechanisms may be at work in forming such systems. Once the stars reach a contact scenario, unstable mass transfer via the filled Roche lobes, and mass loss through the outer Lagrange points, predicts a rapid evolution towards coalescence \citep{jiang2011}. This type of over-contact evolution \citep{ibvs4460} is thought to be a formation path for blue straggler stars in stellar clusters \citep{bradstreet1994,mateo1990}, and signatures include mass loss, changes in luminosity, and orbital decay. Our measured period decay of approximately $|\dot{P}|\sim 8$ sec each year is larger than found for typical W UMa binary systems. The largest amplitude period decay measured for a contact binary is that of V1309 Sco, a merger system with an exponentially decreasing period with an amplitude of $|\dot{P}|\sim$300 sec year$^{-1}$ \citep{tylenda2011}. This system exhibited an extreme nova-like outburst, similar to V838 Mon, as it underwent a catastrophic merging event in 2008. Assuming a linear period decay of $|\dot{P}|\sim8$ seconds per year, we would expect SDSS J001641-000925 to have a lifetime of $\sim$10$^3$ years. However, if the period evolution follows an exponential decay as in the higher mass V1309 Sco system, the binary merger timescale may be as short as $\sim10^2$ years. This amplitude of angular momentum loss required by the observed period decay can't be explained solely by magnetic braking, and the stars are too widely separated for gravitational waves to expel significant energy \citep{chau1978}. The angular momentum loss is likely due to the system being in an over-contact configuration and having filled its critical Roche surface, with mass being expelled from the outer Lagrangian points. This would carry much more angular momentum from the system than magnetic breaking or winds alone, and would lead to a rapid coalescence into a single star \citep{li2004}. However, we cannot exclude the possibility of mass transfer from the primary to the secondary star with little to no loss of angular momentum to the system. This mass redistribution could instead lead to a binary evolution as described by \citet{stepien2006a}, with the orbital period increasing, and binary coalescence proceeding on a much more gradual nuclear or thermal timescale \citep{li2004}. Our follow up study of the period evolution will help discern between these two possibilities. We emphasize the rarity of this system, as SDSS J001641-000925 is the first true over-contact M dwarf binary known. The critical question remaining for the system is whether it is evolving rapidly towards coalescence due to the over-contact configuration. Additional high precision follow-up photometry, as well as searching existing time domain surveys, is underway to conclusively determine whether the period is decaying at an exponential rate, as was the case for V1309 Sco before its dramatic merger.
| 12 | 6 |
1206.6056
|
1206
|
1206.2337.txt
|
% context heading (optional) % {} leave it empty if necessary {Abundances of galaxies at redshifts $z>4$ are difficult to obtain from damped Ly $\alpha$ (DLA) systems in the sightlines of quasars (QSOs) due to the Ly $\alpha$ forest blanketing and the low number of high-redshift quasars detected. Gamma-ray bursts (GRBs) with their higher luminosity are well suited to study galaxies out to the formation of the first stars at $z>10$. Its large wavelength coverage makes the X-shooter spectrograph an excellent tool to study the interstellar medium (ISM) of high redshift galaxies, in particular if the redshift is not known beforehand.} % aims heading (mandatory) {We want to determine the properties of a GRB host at $z=4.66723$ from absorption lines. This is one of the highest redshifts where a detailed analysis with medium-resolution data is possible. Furthermore, we determine the dust extinction using the spectral energy distribution from X-rays to near infrared. Finally, we put the results in context to other GRBs at $z>4$ and properties of (high redshift) QSO absorbers.} % methods heading (mandatory) {The velocity components of the resonant and fine-structure absorption lines are fitted with Voigt-profiles and the metallicity determined from S, Si, Fe and O. \ion{Si}{II*} together with the energy released in the UV restframe as determined from GROND photometric data gives us the distance of the absorbing material from the GRB. The extinction is determined from the spectral slope using X-ray spectral information and the flux calibrated X-shooter spectrum, cross calibrated with photometric data from GROND. We also collect information on all GRB hosts with $z>4$.} % results heading (mandatory) {We measure a relatively high metallicity of $\textnormal{[M/H]}=-1.0\pm0.1$ from S, the distance of the material showing fine-structure lines is 0.3 to 1.0\,kpc. The extinction is moderate with $\textnormal{A}_V=0.24\pm0.06$\,mag. Low- and high ionization as well as fine-structure lines show a complicated kinematic structure probably pointing to a merger in progress. We detect one intervening system at $z=2.18$. } % conclusions heading (optional), leave it empty if necessary {GRB-DLAs have a shallower evolution of metallicity with redshift than QSO absorbers and no evolution in their HI column density or ionization fraction. GRB hosts at high redshift seem to continue the trend of the metallicity-luminosity relation towards lower metallicities but the sample is still too small to draw a definite conclusion. While the detection of GRBs at z $>$ 4 with current satellites is still difficult, they are very important for our understanding of the early epochs of star- and galaxy-formation in the Universe.}
|
Determining the properties of the interstellar medium (ISM) in high redshift galaxies is difficult due to their extreme faintness. Detailed and resolved studies using emission lines in the optical/near-IR range is restricted to redshifts up to $z\sim3$ with current facilities (see, e.g., \citealt{FoersterSchreiber, Maiolino08}) and only with the help of gravitational lensing beyond this redshift (see, e.g., \citealt{Swinbank07} for resolved studies of a gravitationally lensed galaxy at $z=4.9$). The use of GRBs as lighthouses, similar to what has been done since many years with intervening absorption systems towards QSOs, is a promising way to study the properties of galaxies $z > 4$. In contrast to QSOs, GRBs with their higher luminosities can probe more central and denser regions of those galaxies. Long GRBs are connected to massive star-formation (see, e.g., \citealt{WoosleyBloom} for a review of the GRB-supernova connection), hence GRBs probe star-forming places across cosmic history (e.g., \citealt{Fruchter}). GRB afterglows constitute a powerful source for absorption line studies as they have smooth, featureless intrinsic spectra on which the intervening ISM in the host imprints absorption lines from different metals. Optical spectroscopy allows the determination of metallicities from $z\sim1.7$ to $\sim6$ when those metal absorption lines get redshifted into the near-infrared (NIR). X-shooter at the ESO Very Large Telescope (VLT) \citep{DOdorico, Vernet11} with its wavelength coverage from 3,000 to 24,800 {\AA} facilitates detailed investigations of galaxies up to redshifts of $z\sim11-13$, provided GRBs exist at such high redshifts. The broad wavelength coverage of X-shooter also allows to fit an extinction curve and to derive the reddening from the shape of the continuum, assuming an intrinsic powerlaw for the continuum. In most cases, its medium resolution is also good enough to allow the fitting of the absorption lines with Voigt profiles, allowing a more accurate determination of the column density compared to low resolution methods. Previous studies have revealed a diverse picture of GRB host metallicities but they suffer from a small sample size, with currently about 20 metallicities published in the literature (for the largest samples see, e.g., \citealt{Fynbo06, Prochaska07,Savaglio09}). Metallicities of GRB hosts seem to be on average higher than those obtained from QSO-DLAs, in particular at higher redshifts (e.g. \citealt{Fynbo06}). GRB host metallicities also seem to show a slower evolution with redshift, albeit with a large scatter at any given redshift. Both GRB and QSO samples, however, show subsolar metallicities, in some cases down to 1/100 solar or less (e.g., GRB 050730, \citealt{DElia07}, and GRB 090926A, \citealt{Rau090926A, DElia10}). The difference between the two samples can be explained by QSO absorbers probing the outer, less metal-rich regions of galaxies due to their lower luminosity and the sight-lines being selected according to the cross-section, and by GRB hosts being larger than QSO-DLA galaxies \citep{Fynbo08}. The gas observed in GRB absorption-line studies is mostly in a low ionization state (see, e.g., \citealt{Fynbo09}) which makes it a good representation of the cold gas in the host galaxy, mostly unaffected by the GRB itself. The same is the case for the material observed in QSO absorbers; however, one has to consider that QSO and GRB-DLAs are likely probing different regions in the galaxy. Exceptions of highly ionized material in GRB afterglow spectra might point to a special environment of material from the vicinity of the GRB itself (e.g., GRB 090426, \citealt{Thoene10}) and hence are not representative for the metallicity of GRB hosts in general. Extinction in GRB hosts is usually low, although somewhat higher than in QSO-DLAs. For a sample of 41 {\it Swift} GRB afterglow spectra, \cite{Zafar11} found that 90\% have $\textnormal{A}_V<0.65$ mag with an average of 0.24 mag and an SMC extinction law. A similar result was found from photometric data of {\it Swift} GRBs by \cite{Kann10}. However, high extinction makes the detection of the afterglow at optical wavelengths difficult and hence this result are somewhat biased (e.g., \citealt{Greinerdarkgrbs, KruehlerDusty}). The extinction in GRB hosts also seems to decrease with redshift \citep{Kann10, Zafar11}. Again, we might miss more highly extinguished high-redshift bursts, due to the shape of the extinction curve which particularly affects optical observations, as these probe the rest-frame UV at those redshifts. Furthermore, dust is produced by AGB stars and SNe which, in a young star-forming region at high redshifts, might not be present or not have produced enough dust yet (see e.g. \citealt{Gall11rev}). GRB 100219A was discovered in an image trigger by the {\it Swift} satellite \citep{Gehrels04} on 2010 Feb. 19, 15:15:46 UT \citep{RowlinsonGCN} and had a duration of T$_{90}=$ 18.8 $\pm$ 5.0 s \citep{BaumgartnerGCN}. An X-ray as well as an optical afterglow \citep{JakobssonGCN} was found. A nearby galaxy detected in the SDSS was first assumed to be the host galaxy \citep{BloomGCN}, implying a low redshift for this GRB. However, GROND (Gamma-Ray burst Optical/Near-Infrared Detector) reported a $g^\prime$-band dropout and suggested a redshift of $z\sim4.5$ \citep{KruehlerGCN}. We took spectra with the second-generation instrument X-shooter at the VLT, revealing a DLA system and a number of absorption lines at a common redshift of $z=4.6667$ \citep{GrootGCN,AntonioGCN}. This redshift was later confirmed by GMOS-N/Gemini-N \citep{CenkoGCN}. In the following we present the observations and data reduction of the X-shooter spectra (Sect. 2), the analysis of the absorption lines in the host as well as the metallicities and abundances derived from fitting the column densities of the absorption lines (Sect. 3), a broad-band fit to the spectral energy distribution (SED) from X-ray to NIR (Sect. 4) and a description of the intervening system at $z=2.18$ (Sect. 5). Finally, we place the metallicity of GRB 100219A in the context of other GRB host metallicities and high-redshift galaxies in general (Sect. 6). For all calculations we use a cosmology with $\Omega_\mathrm{M}=0.27$, $\Omega_\Lambda=0.73$ and H$_0=71$ km s$^{-1}$Mpc$^{-1}$. The flux of a GRB is defined to behave as $F_{\nu} \propto t^{-\alpha} \nu^{-\beta}$
|
In this paper we presented X-shooter spectra of GRB 100219A at $z=4.667$ which is the highest redshift at which a high-resolution spectrum has been available until now, allowing a detailed analysis of the abundances in a high-redshift (star-forming) galaxy. The metallicity as determined from S is moderately high with $\textnormal{[M/H]}=-1.0$ or 0.1 Z$_\odot$, similar to the value found for other GRBs between redshift $3-4$, but 10 times higher than the average metallicity of galaxies found in the sightlines of QSOs at this redshift. There is little evidence for extinction from the afterglow SED and the relative abundances of the detected metal absorption species indicate only a mild dust depletion. This suggests that the $\alpha$-element enhancement of [$\alpha$/Fe]$=$0.3--0.7 we find from Si and S is likely real. The kinematics of low-, high-ionization and fine-structure lines is rather complicated, probably showing an early galaxy in the process of formation or merging with another galaxy. We also detect one intervening system at $z=2.181$, consistent with the detection rate of intervening absorbers in GRB sightlines. Studying galaxies and their abundances in the high-redshift Universe is of great importance to our understanding of the cosmic chemical evolution, in particular at redshifts where galaxies were still in the process of formation. Over the last years it has become evident that galaxies probed by QSOs and GRBs show somewhat different properties. While GRB hosts have a very shallow metallicity evolution, QSO-DLAs have on average a factor of 10 times less in metallicity at $z\sim4$ and show a steep increase up to $z\sim2$, where the metallicities of both samples become similar. GRBs also show no evolution in ionization rate (though this is likely also the case for QSO-DLAs) and in the HI average column density and distribution. Probably, GRBs select similar types of galaxies across the history of the Universe, highly star-forming and metal-poor, while QSO-DLAs probe the average galaxy population. It has been suggested that both QSO- and GRB-DLAs might come from the same population of galaxies and the metallicity distribution can be explained by a sightline effect (GRBs probe the dense regions of the galaxy while QSO-DLAs probe the more metal-poor outskirts) combined with a slightly higher average mass for GRB-DLA galaxies. This seems likely since GRB-DLAs also have much stronger lines, hence probing denser regions, and a higher velocity width than QSO-DLAs. It is still unclear into what type of galaxies in the present Universe high-redshift QSO-DLAs develop into, though they are likely not dwarf galaxies \citep{Prochaska05}. GRB hosts at low redshifts are a diverse mix of star-forming galaxies, from blue compact dwarfs to spiral galaxies. The picture is somewhat inverted for the mass-metallicity relation of GRB hosts compared to field galaxies. At low redshifts, GRBs select galaxies more metal-poor for their mass than average, even after accounting for a possible bias from star-forming galaxies (that have shown to be on average more metal-poor). The comparison at higher redshifts is still unclear but the difference might be less pronounced than in the local Universe. It will be an important task to develop a common picture for the galaxy populations probed by different methods in order to get the global picture of galactic chemical evolution. The evolution beyond redshift $\sim5$ is still largely unknown since the current detection rate of such high-redshift GRBs is still low. At redshifts approaching the reionization epoch and the formation of the first stars and galaxies, the determination of metallicities and relative abundances are crucial to test the models for high-redshift star-formation and the formation and evolution of galaxies.
| 12 | 6 |
1206.2337
|
1206
|
1206.1676_arXiv.txt
|
Star formation in galaxies is observed to be associated with gamma-ray emission, presumably from non-thermal processes connected to the acceleration of cosmic-ray nuclei and electrons. The detection of gamma rays from starburst galaxies by the \textit{Fermi} Large Area Telescope (LAT) has allowed the determination of a functional relationship between star formation rate and gamma-ray luminosity \citep{Bechtol2011}. Since star formation is known to scale with total infrared ($8-1000$ $\mu$m) and radio ($1.4$ GHz) luminosity, the observed infrared and radio emission from a star-forming galaxy can be used to quantitatively infer the galaxy's gamma-ray luminosity. Similarly, star forming galaxies within galaxy clusters allow us to derive lower limits on the gamma-ray emission from clusters, which have not yet been conclusively detected in gamma rays. In this study we apply the functional relationships between gamma-ray luminosity and radio and IR luminosities derived in \citet{Bechtol2011} to a sample of the best candidate galaxy clusters for detection in gamma rays from \citet{Ackermann2010c} in order to place lower limits on the gamma-ray emission associated with star formation alone in galaxy clusters. We find that several clusters have predicted gamma-ray emission from star formation that are within an order of magnitude of the upper limits derived in \citet{Ackermann2010c} based on non-detection by \textit{Fermi}-LAT. Given the current gamma-ray limits, star formation likely plays a significant role in the gamma-ray emission in some clusters, especially those with cool cores. We predict that both \textit{Fermi}-LAT over the course of its lifetime and the future Cherenkov Telescope Array will be able to detect gamma-ray emission from star-forming galaxies in clusters.
|
Galaxy clusters are the most massive gravitationally bound objects in the universe, and contain a dense population of galaxies surrounded by gas distributed throughout the intracluster medium (ICM). The complex environment of galaxy clusters is bound to host, at some luminosity level, processes that lead to the production of gamma rays. In particular, a significant fraction of the gamma-ray emission is thought to be associated with the ICM, and more specifically with cosmic ray (CR) populations accelerated by shocks and turbulence within the ICM, as well as, possibly, with dark matter annihilation and decay (first suggested in \citealt{Totani2004}). In the ICM, CR protons and other nuclei collide with dust and gas particles and decay to charged and neutral pions, which in turn decay into leptons and gamma rays, respectively. CR electrons, if sufficiently energetic, can inverse-Compton scatter photons from the Cosmic Microwave Background up to gamma-ray energies (see e.g., \citealt{Rephaeli2008} for a general description of nonthermal activity in the ICM of clusters of galaxies). Clusters have not, however, been detected yet as gamma-ray sources. The Large Area Telescope (LAT), the primary instrument aboard the \textit{Fermi} Gamma-ray Space Telescope, has placed upper limits on the flux from the best candidate clusters and used these upper limits to place constraints on the cosmic ray populations in clusters \citep{Ackermann2010c}. Atmospheric Cherenkov telescopes such as H.E.S.S. and MAGIC have also reported null results from observations of selected clusters of galaxies, such as Perseus \citep{Aleksic2012}, Coma \citep{Aharonian2009}, and A0085 and A0496 \citep{Aharonian2009a}. In addition to the gamma rays produced by the ICM, the cluster member-galaxies themselves are at some level a source of gamma rays. Ordinary galaxies such as our own Milky Way, its satellite galaxies the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC), and the nearby Andromeda Galaxy (M31) have all been detected in gamma rays (MW: \citealt{Abdo2009}, LMC: \citealt{Abdo2010h}, SMC: \citealt{Abdo2010g}, M31: \citealt{Abdo2010i}). In addition, the recent detection by the \textit{Fermi}-LAT of four star-forming galaxies, M82, NGC 253 \citep{Abdo2010c} and NGC 1068 and NGC 4945 \citep{Lenain2010}, allowed for the determination of a quantitative functional relationship between the star formation rate and the gamma-ray luminosity \citep{Bechtol2011}. While gamma-ray emission has not yet been detected from galaxy clusters, some minimum gamma-ray emission resulting from star formation activity in cluster members must exist. Lower limits on the gamma-ray flux from clusters of galaxies can therefore be determined by considering only the emission from cluster members with ongoing star formation, and can also provide insight into the star-forming population of galaxies within clusters, as compared to the field. This is the scope of the present study. The relations derived in \citet{Bechtol2011} are used to predict lower limits on the gamma-ray luminosity coming from star formation within cluster members alone, provided total IR and/or radio luminosity measurements for a sample of clusters. We then compare these estimates to the \textit{Fermi} upper limits on the gamma-ray luminosity from the same clusters \citep{Ackermann2010c}, and assess the potential of the \textit{Fermi}-LAT over its lifetime as well as of the future Cherenkov Telescope Array for detection of gamma-rays from star-forming galaxies in clusters. In the following section, we review the sources of multiwavelength emission resulting from star formation in galaxies and clusters. In section 3, we describe our cluster sample selection and the available IR and radio data. In section 4 we describe our results and present lower limits on the gamma-ray emission from a selection of clusters. We use the lower limits to explore the possibility of detection by various gamma-ray telescopes in section 5, and conclude in section 6.
|
We calculated lower limits on the gamma-ray emission from galaxy clusters considering only cluster member galaxies with active star formation using observed IR and radio luminosities for selected, nearby massive clusters. Employing the relationships derived in \citet{Bechtol2011} for \textit{Fermi}-LAT detected galaxies, we converted IR and radio cluster luminosities into gamma-ray luminosities. Several clusters have lower limits on their gamma-ray emission that are within about an order of magnitude of the upper limits based on the \textit{Fermi}-LAT non-detections from \citet{Ackermann2010c}, implying that star formation could contribute at the level of 10\% or more to cluster gamma-ray emission. Several clusters also have lower limits that are within a factor of a few of the 10-year sensitivity limits of the \textit{Fermi}-LAT; the best candidate clusters for detection by \textit{Fermi}-LAT based on these lower limits are A2029, Virgo, Coma, A1367, and Hydra. CTA will also likely be able to detect clusters such as A2029, Virgo and Coma for anticipated instrumental performance and design. Star formation may thus be a significant source of gamma-ray emission for some galaxy clusters.
| 12 | 6 |
1206.1676
|
1206
|
1206.4115_arXiv.txt
|
We update our prior work on the case B collisional-recombination spectrum of He~I to incorporate \textit{ab initio} photoionisation cross-sections. This large set of accurate, self-consistent cross-sections represents a significant improvement in He~I emissivity calculations because it largely obviates the piecemeal nature that has marked all modern works. A second, more recent set of \textit{ab initio} cross-sections is also available, but we show that those are less consistent with bound-bound transition probabilities than our adopted set. We compare our new effective recombination coefficients with our prior work and our new emissivities with those by other researchers, and we conclude with brief remarks on the effects of the present work on the He~I error budget. Our calculations cover temperatures $5000 \le T_e \le 25000$~K and densities $10^1 \le n_e \le 10^{14}$~cm$^{-3}$. Full results are available online.
|
\label{intro} The high precision required to make a significant measurement of the primordial helium abundance presents challenges that are unique in nebular astrophysics. The recombination rate coefficients, needed to convert emission line intensities into ionic abundance ratios, must have an accuracy better than the precision expected for the derived abundance. Usually we hope to measure abundances of most elements to an accuracy of 20 - 30\%. The primordial helium problem requires recombination rates accurate to better than a percent, presenting unprecedented challenges to the atomic physics of the line formation. See Brocklehurst (1972) and references therein for early seminal work in the field of theoretical He~I emissivities. We need four types of atomic data to calculate the case B recombination spectrum: level energies, transition probabilities, photoionization cross-sections, and collision rates. Porter et al (2009) summarize the contributors to the error budget. Energy uncertainties have always been negligible compared to other sources, and accurate transition probabilities have been available since Kono \& Hattori (1984). Drake (1996) and Drake \& Morton (2007) improved upon the latter still further. Photoionisation cross-sections and collision rates represent the greatest sources of uncertainties in current standard calculations of He~I emissivities (Benjamin, Skillman, \& Smits 1999, hereafter BSS99; Porter et al. 2005, 2007). For the low-density, extragalactic observations used in primordial helium analyses (Peimbert, Luridiana, \& Peimbert 2007; Izotov, Thuan, \& Stasi\'nska 2007; Aver, Olive, \& Skillman 2010), photoionisation cross-sections (and, by extension, recombination coefficients) are the greatest source of uncertainty (Porter et al. 2009). See Ferland et al. (2010) for a recent review of the errors in He~I emissivities and in primordial helium abundances. In this Letter we update our earlier calculations of case B, He~I emissivities (Bauman et al. 2005; Porter et al. 2005, 2007) to include a large set of self-consistent, \textit{ab initio} photoionisation cross-sections. We compare our present results with our previous work, with those by BSS99, and with those by Almog \& Netzer (1989). We present here a subset of our present results that is most applicable to primordial helium research. A much larger set is available in the electronic edition.
|
\begin{figure} \protect\resizebox{\columnwidth}{!} {\includegraphics{alpha.eps}} \caption{Ratio of present to PFM07 effective recombination coefficients in the low-density limit at $10,000$K. The three levels with the largest changes are $3d\,^1\!D$, $3d\,^3\!D$, and $5s\,^1\!S$. See text. The differences will generally be smaller at finite densities.} \label{fig:alpha} \end{figure} We compare effective recombination coefficients in our new treatment with those of Porter et al. (2007) in Figure~\ref{fig:alpha}. For the majority of levels the change is $\lesssim1\%$. There are two clear exceptions, corresponding to $3d\,^1\!D$ and $3d\,^3\!D$. The cause is a programming error in our earlier renormalisation of Peach (1967) cross-sections. There are only two levels affected. Unfortunately, these are the upper levels of two of the most important lines in primordial helium abundance works: $\lambda\lambda5876$ and $6678$. The new results yield stronger emissivities for both lines. The next largest differences in Figure~\ref{fig:alpha} correspond to levels with only weak optical lines. \begin{figure} \protect\resizebox{\columnwidth}{!} {\includegraphics{lines.eps}} \caption{Ratio of BSS99 and present emissivities for several strong lines as a function of temperature with $n_e = 100$~cm$^{-3}$. This figure should be compared with figure 5 of Aver, Olive, \& Skillman (2010). The principal effect is that for both $\lambda\lambda 5876$ and $6678$, the present results are greater than the earlier Porter et al. works and are roughly the average of the BSS99 results and our earlier work. Our $\lambda\lambda 3889$ and $7065$ results have also changed considerably, and (within the plotted temperature range) the ratios no longer cross the ``zero deviation line'' discussed by Aver, Olive, \& Skillman (2010).} \label{fig:BSS99} \end{figure} We compare our new emissivities with BSS99 for several strong lines in Figure~\ref{fig:BSS99}. This figure is directly comparable to figure 5 of Aver, Olive, \& Skillman (2010). Consistent with the discussion above, $j_{5876}$ and $j_{6678}$ are now in better agreement with BSS99, though important differences clearly remain. Our calculations cover $5000 \le T \le 25000$~K (in $1000$~K steps) and $10^1 \le n_e \le 10^{14}$~cm$^{-3}$ (in 1 dex steps). In addition to the lines published in our prior work, we have also included several weak infrared lines. Table~\ref{table:lineID} lists the wavelength and upper and lower level designations of all reported lines. Table~\ref{table:emis} contains a small subset of the full results that is most applicable to primordial helium abundance calculations. \begin{table} \centering \caption{Wavelengths and upper and lower levels of reported lines.} \begin{tabular}{rcc} \hline Wavelength (\AA, Air) & Upper level & Lower level \\ \hline 2945 & $5p\,{}^{3}\!P$ & $2s\,{}^{3}\!S$ \\ 3188 & $4p\,{}^{3}\!P$ & $2s\,{}^{3}\!S$ \\ 3614 & $5p\,{}^{1}\!P$ & $2s\,{}^{1}\!S$ \\ 3889 & $3p\,{}^{3}\!P$ & $2s\,{}^{3}\!S$ \\ 3965 & $4p\,{}^{1}\!P$ & $2s\,{}^{1}\!S$ \\ 4026 & $5d\,{}^{3}\!D$ & $2p\,{}^{3}\!P$ \\ 4121 & $5s\,{}^{3}\!S$ & $2p\,{}^{3}\!P$ \\ 4388 & $5d\,{}^{1}\!D$ & $2p\,{}^{1}\!P$ \\ 4438 & $5s\,{}^{1}\!S$ & $2p\,{}^{1}\!P$ \\ 4471 & $4d\,{}^{3}\!D$ & $2p\,{}^{3}\!P$ \\ 4713 & $4s\,{}^{3}\!S$ & $2p\,{}^{3}\!P$ \\ 4922 & $4d\,{}^{1}\!D$ & $2p\,{}^{1}\!P$ \\ 5016 & $3p\,{}^{1}\!P$ & $2s\,{}^{1}\!S$ \\ 5048 & $4s\,{}^{1}\!S$ & $2p\,{}^{1}\!P$ \\ 5876 & $3d\,{}^{3}\!D$ & $2p\,{}^{3}\!P$ \\ 6678 & $3d\,{}^{1}\!D$ & $2p\,{}^{1}\!P$ \\ 7065 & $3s\,{}^{3}\!S$ & $2p\,{}^{3}\!P$ \\ 7281 & $3s\,{}^{1}\!S$ & $2p\,{}^{1}\!P$ \\ 9464 & $5p\,{}^{3}\!P$ & $3s\,{}^{3}\!S$ \\ 10830 & $2p\,{}^{3}\!P$ & $2s\,{}^{3}\!S$ \\ 11013 & $5p\,{}^{1}\!P$ & $3s\,{}^{1}\!S$ \\ 11969 & $5d\,{}^{3}\!D$ & $3p\,{}^{3}\!P$ \\ 12527 & $4p\,{}^{3}\!P$ & $3s\,{}^{3}\!S$ \\ 12756 & $5p\,{}^{1}\!P$ & $3d\,{}^{1}\!D$ \\ 12785 & $5f\,{}^{3}\!F$ & $3d\,{}^{3}\!D$ \\ 12790 & $5f\,{}^{1}\!F$ & $3d\,{}^{1}\!D$ \\ 12846 & $5s\,{}^{3}\!S$ & $3p\,{}^{3}\!P$ \\ 12968 & $5d\,{}^{1}\!D$ & $3p\,{}^{1}\!P$ \\ 12985 & $5p\,{}^{3}\!P$ & $3d\,{}^{3}\!D$ \\ 13412 & $5s\,{}^{1}\!S$ & $3p\,{}^{1}\!P$ \\ 15084 & $4p\,{}^{1}\!P$ & $3s\,{}^{1}\!S$ \\ 17003 & $4d\,{}^{3}\!D$ & $3p\,{}^{3}\!P$ \\ 18556 & $4p\,{}^{1}\!P$ & $3d\,{}^{1}\!D$ \\ 18685 & $4f\,{}^{3}\!F$ & $3d\,{}^{3}\!D$ \\ 18697 & $4f\,{}^{1}\!F$ & $3d\,{}^{1}\!D$ \\ 19089 & $4d\,{}^{1}\!D$ & $3p\,{}^{1}\!P$ \\ 19543 & $4p\,{}^{3}\!P$ & $3d\,{}^{3}\!D$ \\ 20427 & $6p\,{}^{3}\!P$ & $4s\,{}^{3}\!S$ \\ 20581 & $2p\,{}^{1}\!P$ & $2s\,{}^{1}\!S$ \\ 20602 & $7d\,{}^{3}\!D$ & $4p\,{}^{3}\!P$ \\ 21118 & $4s\,{}^{3}\!S$ & $3p\,{}^{3}\!P$ \\ 21130 & $4s\,{}^{1}\!S$ & $3p\,{}^{1}\!P$ \\ 21608 & $7f\,{}^{3}\!F$ & $4d\,{}^{3}\!D$ \\ 21617 & $7f\,{}^{1}\!F$ & $4d\,{}^{1}\!D$ \\ \hline \end{tabular} \label{table:lineID} \end{table} Almog \& Netzer (1989, hereafter AN89) also presented He~I emissivities for electron densities up to $10^{14}$~cm$^{-3}$. In Figure~\ref{fig:AN89} we compare present emissivities in $\lambda\lambda 4471$, $5876$ and $7065$ to the AN89 results (with $\tau_{3889} = 0$). The calculations generally agree for $n_e \lesssim 10^{8}$~cm$^{-3}$ (where collisions do not dominate over radiative processes) and for $n_e \sim 10^{14}$~cm$^{-3}$ (where collisions are so dominant that levels are approaching local thermodynamic equilibrium). Critical densities for levels with $n\sim3$ or $4$ fall between these regions. Collisions are dominated by excitations from the metastable $2s\,^3\!S$, which is treated in both the present work and AN89. Our work clearly has enhanced collisional excitation relative to AN89, and differences between the two calculations are strongly correlated with the relative collisional contributions given in table 5 of Porter et al. (2007). Note, however, that those collisional contributions should not be added to the present tabulations; they are already included. \begin{figure} \protect\resizebox{\columnwidth}{!} {\includegraphics{an89_compare.eps}} \caption{Comparison of present emissivity calculations to those by AN89 as a function of density at $10,000$K.} \label{fig:AN89} \end{figure} A recalculation of the Monte Carlo error analyses performed in Porter et al. (2009) is beyond the scope of this paper. We expect that our analysis of the relatively high-density `Galactic' model would be largely unchanged, as collisional uncertainties should dominate both before and after the present work. In the low-density `Extragalactic' model, however, our `optimistic' uncertainties now seem somewhat more \emph{realistic}. Total uncertainties are largely due to uncertainties in threshold photoionisation cross-sections. One measure of those uncertainties (used by Porter et al. 2009) is the difference ($\lesssim0.7\%$) between the extrapolated threshold cross-sections and the HS98 \textit{ab initio} results. Goodness of the fits used to extrapolate threshold cross-sections, including sensitivity of the fits to the number of terms used in the fitting procedure, is another measure, and we obtain $\lesssim0.2\%$ for all levels with $n\le5$. \begin{table*} \centering \caption{Emissivities of several He~I lines at conditions important for primordial abundance analyses. This table is a small subset of the full results. Values are $4\pi j/n_e n_{\mathrm{He+}}$ in units $10^{-25}$~erg~cm$^{3}$~s$^{-1}$.} \begin{tabular}{rrrrrrrr} \hline $T_e$~(K)& $n_e$ (cm$^{-3}$)& 3889\AA & 4026\AA & 4471\AA & 5876\AA & 6678\AA & 7065\AA \\ \hline 10000 & 10 & 1.3889 & 0.2902 & 0.6098 & 1.6782 & 0.4706 & 0.2875 \\ 11000 & 10 & 1.2980 & 0.2652 & 0.5549 & 1.5112 & 0.4229 & 0.2727 \\ 12000 & 10 & 1.2194 & 0.2440 & 0.5086 & 1.3721 & 0.3833 & 0.2600 \\ 13000 & 10 & 1.1507 & 0.2257 & 0.4690 & 1.2546 & 0.3498 & 0.2487 \\ 14000 & 10 & 1.0901 & 0.2098 & 0.4347 & 1.1542 & 0.3213 & 0.2388 \\ 15000 & 10 & 1.0360 & 0.1959 & 0.4047 & 1.0674 & 0.2966 & 0.2299 \\ 16000 & 10 & 0.9875 & 0.1835 & 0.3783 & 0.9917 & 0.2751 & 0.2218 \\ 17000 & 10 & 0.9437 & 0.1726 & 0.3549 & 0.9252 & 0.2562 & 0.2145 \\ 18000 & 10 & 0.9039 & 0.1627 & 0.3340 & 0.8663 & 0.2395 & 0.2078 \\ 19000 & 10 & 0.8676 & 0.1539 & 0.3153 & 0.8138 & 0.2247 & 0.2017 \\ 20000 & 10 & 0.8343 & 0.1459 & 0.2983 & 0.7668 & 0.2113 & 0.1960 \\ 10000 & 100 & 1.3989 & 0.2904 & 0.6101 & 1.6768 & 0.4692 & 0.2975 \\ 11000 & 100 & 1.3100 & 0.2655 & 0.5557 & 1.5138 & 0.4224 & 0.2848 \\ 12000 & 100 & 1.2334 & 0.2444 & 0.5099 & 1.3787 & 0.3836 & 0.2738 \\ 13000 & 100 & 1.1666 & 0.2263 & 0.4708 & 1.2650 & 0.3509 & 0.2642 \\ 14000 & 100 & 1.1077 & 0.2105 & 0.4370 & 1.1682 & 0.3230 & 0.2557 \\ 15000 & 100 & 1.0553 & 0.1968 & 0.4075 & 1.0848 & 0.2990 & 0.2480 \\ 16000 & 100 & 1.0082 & 0.1846 & 0.3817 & 1.0123 & 0.2782 & 0.2409 \\ 17000 & 100 & 0.9657 & 0.1738 & 0.3587 & 0.9487 & 0.2598 & 0.2345 \\ 18000 & 100 & 0.9270 & 0.1641 & 0.3383 & 0.8926 & 0.2437 & 0.2285 \\ 19000 & 100 & 0.8917 & 0.1554 & 0.3200 & 0.8428 & 0.2293 & 0.2231 \\ 20000 & 100 & 0.8592 & 0.1475 & 0.3036 & 0.7984 & 0.2164 & 0.2181 \\ 10000 & 1000 & 1.4701 & 0.2928 & 0.6175 & 1.7310 & 0.4780 & 0.3754 \\ 11000 & 1000 & 1.3969 & 0.2687 & 0.5661 & 1.5893 & 0.4350 & 0.3771 \\ 12000 & 1000 & 1.3353 & 0.2486 & 0.5235 & 1.4761 & 0.4000 & 0.3790 \\ 13000 & 1000 & 1.2823 & 0.2315 & 0.4877 & 1.3842 & 0.3712 & 0.3807 \\ 14000 & 1000 & 1.2359 & 0.2168 & 0.4574 & 1.3084 & 0.3470 & 0.3816 \\ 15000 & 1000 & 1.1945 & 0.2040 & 0.4313 & 1.2449 & 0.3266 & 0.3818 \\ 16000 & 1000 & 1.1571 & 0.1929 & 0.4087 & 1.1910 & 0.3090 & 0.3811 \\ 17000 & 1000 & 1.1227 & 0.1830 & 0.3888 & 1.1444 & 0.2937 & 0.3797 \\ 18000 & 1000 & 1.0910 & 0.1743 & 0.3714 & 1.1041 & 0.2803 & 0.3778 \\ 19000 & 1000 & 1.0618 & 0.1666 & 0.3561 & 1.0706 & 0.2683 & 0.3765 \\ 20000 & 1000 & 1.0344 & 0.1596 & 0.3424 & 1.0408 & 0.2577 & 0.3746 \\ \hline \end{tabular} \label{table:emis} \end{table*}
| 12 | 6 |
1206.4115
|
1206
|
1206.2922_arXiv.txt
|
Sun-like stars are thought to be regularly disrupted by supermassive black holes (SMBHs) within galactic nuclei. Yet, as stars evolve off the main sequence their vulnerability to tidal disruption increases drastically as they develop a bifurcated structure consisting of a dense core and a tenuous envelope. Here we present the first hydrodynamic simulations of the tidal disruption of giant stars and show that the core has a substantial influence on the star's ability to survive the encounter. Stars with more massive cores retain large fractions of their envelope mass, even in deep encounters. Accretion flares resulting from the disruption of giant stars should last for tens to hundreds of years. Their characteristic signature in transient searches would not be the $t^{-5/3}$ decay typically associated with tidal disruption events, but a correlated rise over many orders of magnitude in brightness on months to years timescales. We calculate the relative disruption rates of stars of varying evolutionary stages in typical galactic centers, then use our results to produce Monte Carlo realizations of the expected flaring event populations. We find that the demographics of tidal disruption flares are strongly dependent on both stellar and black hole mass, especially near the limiting SMBH mass scale of $\sim 10^8 M_\odot$. At this black hole mass, we predict a sharp transition in the SMBH flaring diet beyond which all observable disruptions arise from evolved stars, accompanied by a dramatic cutoff in the overall tidal disruption flaring rate. Black holes less massive than this limiting mass scale will show observable flares from both main sequence and evolved stars, with giants contributing up to 10\% of the event rate. The relative fractions of stars disrupted at different evolutionary states can constrain the properties and distributions of stars in galactic nuclei other than our own.
|
Quasars are rapidly growing black holes lit up by the gas they accrete. They are the most dramatic manifestation of the more general phenomenon of active galactic nuclei (AGN) and they are among the most energetic objects in the universe. Several billion years after the Big Bang, the universe went through a quasar era when highly-luminous AGN were a standard feature of most massive galaxies \citep{Kormendy:1995hc,Richstone:1998wk}. Since that time, AGN have been dying out and the only activity that still occurs in many nearby galactic nuclei is weak \citep{Schawinski:2010bl}. All that should remain in the centers of local galaxies are the remnants of quasar-era exponential growth: quiescent SMBHs, now dim and starved of fuel \citep{Ho:2008kz}. It is, therefore, not surprising that definitive conclusions about the presence of local SMBHs are typically drawn from very nearby galaxies with little to no AGN activity \citep{Gebhardt2000,Ferrarese2000}. The centers of these galaxies are well resolved, revealing the region where the black hole dominates the stellar dynamics. The question then arises of whether the postulated presence of SMBHs lurking in the centers of most galaxies is consistent with the apparent quiescence of their nuclei. Quiescent black holes are, in fact, nearly black; they may only be lit up by the luminance of accreting matter. We do not directly know how much gas there is near most SMBHs, and there is no a priori reason why nuclear regions should be swept completely clean of gas. The distribution of stars in dense clusters that surround SMBHs, on the other hand, is much better constrained. These densely packed stars trace complicated and wandering orbits under the combined influence of all the other stars and the black hole itself. If a star wanders too close to the black hole it is violently ripped apart by the hole's tidal field \citep[eg,][]{Hills:1975kh,Frank:1978wx,Rees1988}. About half of the debris of tidal disruption eventually falls back and accretes onto the SMBH. This accretion powers a flare which is a definitive sign of the presence of an otherwise quiescent SMBH and a powerful diagnostic of its properties \citep{Rees1988}. Tidal disruption events are expected to be relatively rare, on the order of one per $\sim10^4$ years per galaxy \citep[e.g.][]{Magorrian:1999fd,Wang:2004jy}. Depending primarily on the structural properties of the disrupted star, an ultra-luminous transient signal could persist steadily for months to at most tens of years; thereafter the flare would rapidly fade. In a given galaxy, this luminous flaring activity would then have a short duty cycle. Quiescent SMBHs should greatly outnumber active ones. Observational constraints would not, therefore, be stringent until we had observed enough candidates to constitute a proper ensemble average. However, the long decay tails of these flares may account for an appreciable fraction of the total low-luminosity AGN activity in the local universe \citep{Milosavljevic:2006jj}. The critical pericenter distance for tidal disruption is the tidal radius, \beq\label{rt} \rt \equiv \left( \frac{M_{\rm bh}}{M_\ast}\right)^{1/3} R_\ast, \eeq where $M_\ast$ and $R_\ast$ are the stellar mass and radius, and $M_{\rm bh}$ is the black hole mass \citep{Hills:1975kh}. The tidal radius is larger than the black hole's horizon, $\rs = 2 G M_{\rm bh} /c^2$, for solar type stars as long as the black hole is less massive than about $10^8$ solar masses. In encounters with more massive black holes, solar type stars may pass the horizon undisrupted and are effectively swallowed whole. Such events would leave little electromagnetic signature \citep[although a portion of the gravitational wave signature would remain,][]{Kobayashi:2004kq}. However, for a given stellar and black hole mass, evolved stars have larger tidal radii than main sequence (MS) stars and are therefore more vulnerable to tidal disruption. Furthermore, giant branch stars are the only stars that can produce observable tidal disruption flares in encounters with the most massive black holes $\gtrsim 10^8 M_\odot$. Motivated by these facts, we examine the importance of stellar evolution in the context of tidal disruption. A sun-like star spends the majority of its lifetime on the MS, $\tau_{\rm ms}\sim 10^{10} $ years, followed by a relatively brief period of post-MS (giant branch) evolution, $\tau_{\rm g} \sim 10^8$ years, once its central supply of hydrogen fuel is exhausted. As nuclear reactions slow, the stellar core loses pressure support, and, in approximately a thermal diffusion time, the star ascends the giant branch as its outer layers expand in response to the core's collapse. Giant-branch stars are much less common than MS stars in a typical stellar population due to the ratio of their lifetimes, which for a solar mass star is $\tau_{\rm g}/\tau_{\rm ms} \sim 10^{-2}$. However, their large radii imply that they are exceptionally vulnerable to tidal disruption during these brief periods. The contribution of giant stars to the tidal disruption event rate and the luminosity function of AGN will depend on the competing effects of their enhanced cross-section and their relative rarity. Understanding the details of giant star disruption events and their contribution to the SMBH flaring population is the focus of this work. We use several methods to study this problem. In Section \ref{sec:SEandTD}, we discuss the calculation of detailed stellar evolution models and outline the importance of stellar evolution in the context of tidal disruption. The non-linear dynamics of the encounters themselves must be understood through hydrodynamic simulations; this is particularly true for post-MS stars which are not well described by a simple single-polytrope model. In Section \ref{sec:hydro}, we describe how we derive giant star initial models from our stellar evolution calculations, our methods of hydrodynamic simulation, and the results of our simulations of close encounters between giant-branch stars and SMBHs. In Section \ref{sec:lc}, we calculate the rates of tidal disruption that result from the two-body relaxation driven random walk of nuclear cluster stars in angular momentum space. We focus on the relative rates of disruption of stars in different evolutionary states. In Section \ref{sec:disc}, we combine our stellar evolution, hydrodynamic, and rate calculations of Sections \ref{sec:SEandTD} - \ref{sec:lc} and present Monte Carlo realizations of flaring events. We discuss the demographics of tidal disruption-powered flaring events as a function of black hole mass, the contribution of giant stars to the luminosity function of local AGN, and the detection of flares due to the disruption of giant stars.
| 12 | 6 |
1206.2922
|
|
1206
|
1206.5958_arXiv.txt
|
We present preliminary results of a pulsar population synthesis of normal pulsars from the Galactic disk using a Markov Chain Monte Carlo method to better understand the parameter space of the assumed model. We use the Kuiper test, similar to the Kolmogorov-Smirnov test, to compare the cumulative distributions of chosen observables of detected radio pulsars with those simulated for various parameters. Our code simulates pulsars at birth using Monte Carlo techniques and evolves them to the present assuming initial spatial, kick velocity, magnetic field, and period distributions. Pulsars are spun down to the present, given radio and gamma-ray emission characteristics, filtered through ten selected radio surveys, and a {\it Fermi} all-sky threshold map. Each chain begins with a different random seed and searches a ten-dimensional parameter space for regions of high probability for a total of one thousand different simulations before ending. The code investigates both the``large world" as well as the ``small world" of the parameter space. We apply the K-means clustering algorithm to verify if the chains reveal a single or multiple regions of significance. The outcome of the combined set of chains is the weighted average and deviation of each of the ten parameters describing the model. While the model reproduces reasonably well the detected distributions of normal radio pulsars, it does not replicate the predicted detected $\dot P - P$ distribution of {\it Fermi} pulsars. The simulations do not produce sufficient numbers of young, high-$\dot E$ pulsars in the Galactic plane.
| 12 | 6 |
1206.5958
|
||
1206
|
1206.5443_arXiv.txt
|
Massive stars are essential to understand a variety of branches of astronomy including galaxy and star cluster evolution, nucleosynthesis and supernovae, pulsars and black holes. It has become evident that massive star evolution is very diverse, being sensitive to metallicity, binarity, rotation, and possibly magnetic fields. While the problem to obtain a good statistical observational database is alleviated by current large spectroscopic surveys, it remains a challenge to model these diverse paths of massive stars towards their violent end stage. We show that the main sequence stage offers the best opportunity to gauge the relevance of the various possible evolutionary scenarios. This also allows to sketch the post-main sequence evolution of massive stars, for which observations of Wolf-Rayet stars give essential clues. Recent supernova discoveries due to the current boost in transient searches allow tentative mappings of progenitor models with supernova types, including pair instability supernovae and gamma-ray bursts.
| 12 | 6 |
1206.5443
|
||
1206
|
1206.1056_arXiv.txt
|
We have investigated the relationship between the kinematics and mass of young ($<3\times10^8$ years) white dwarfs using proper motions. Our sample is taken from the colour selected catalogues of SDSS \citep{Eisenstein:2006} and the Palomar-Green Survey \citep{Liebert:2005}, both of which have spectroscopic temperature and gravity determinations. We find that the dispersion decreases with increasing white dwarf mass. This can be explained as a result of less scattering by objects in the Galactic disk during the shorter lifetime of their more massive progenitors. A direct result of this is that white dwarfs with high mass have a reduced scale height, and hence their local density is enhanced over their less massive counterparts. In addition, we have investigated whether the kinematics of the highest mass white dwarfs ($>0.95\msunm$) are consistent with the expected relative contributions of single star evolution and mergers. We find that the kinematics are consistent with the majority of high-mass white dwarfs being formed through single star evolution.
|
\label{sec:intro} Despite the significant work on both the kinematics and mass distribution of white dwarfs, very little work has addressed their connection. The kinematics of galactic white dwarfs have been studied on numerous occasions with several motivations. They have proven useful in attempts to unravel the evolutionary history and progenitors of the various classes of white dwarfs \citep{Sion:1988,Anselowitz:1999}. Interest in white dwarf kinematics was also prompted by the suggestion that halo white dwarfs could provide a significant contribution to Galactic dark matter \citep{Oppenheimer:2001, Reid:2005}. This effort has concentrated on the identification of halo white dwarfs and estimating the resultant density, which now appears to be a small contribution to the Galactic dark matter budget \citep{Pauli:2006}. Moreover, the mass distribution of the most common hydrogen rich (DA) white dwarfs has also been extensively investigated, particularly for white dwarfs with $T\gtrsim10$,$000$\,K which are hot enough for their masses to be deduced spectroscopically from fits to their Balmer lines \citep{Liebert:2005,Kepler:2007,Vennes:1999}. The mass distribution shows a peak at $0.6 {\rm M}_\odot$ due to the relative abundance of their lower mass progenitors with a tail extending to higher masses formed from more massive progenitors. The connection between the galactic kinematics of a group of thin disk objects and their progenitors is largely due to the process of kinematic disk `heating' \citep{Wielen:1977,Nordstrom:2004}. The hot white dwarfs with short cooling ages we observe in the galactic neighbourhood today are formed from a wide range of progenitor masses ($\sim0.8$--$8\, \msun$) and hence have a wide range in age. We therefore expect high-mass disk white dwarfs to have a low velocity dispersion in comparison to low-mass disk white dwarfs whose progenitors formed earlier. This connection was suggested in \citet{Guseinov:1983} who performed an analysis suggesting that white dwarfs with larger masses have smaller dispersions, however this was reinvestigated by \citet{Sion:1988} with a larger sample of 78 DA white dwarfs where no evidence for any correlation was found. This paper readdresses the connection between mass and kinematics with a greatly increased sample size. The outline of the paper is as follows: In section \ref{sec:sample} we discuss the sample selection and the calculation of distances and proper motions. In section \ref{sec:kinomethod} we discuss how we estimate the kinematics of the sample without radial velocity information. We use two methods, that of \citet{Dehnen:1998} (section \ref{sec:dehnen}), and a Markov Chain Monte Carlo (MCMC) where we marginalise over the unknown radial velocity (section \ref{sec:mcmc}). In section \ref{sec:sse} we analyse whether the kinematics are consistent with single star evolution (SSE) both via analytic methods (section \ref{sec:sseanalytic}) and simulations (section \ref{sec:montesse}). In section \ref{sec:bse} we analyse whether the highest mass white dwarfs are largely formed through single star evolution or are the product of the merger of two lower mass white dwarfs. Finally, we discuss the implications of our findings on the scale height of white dwarfs in section \ref{sec:scaleh}. For the reader in a hurry, the primary result of this paper, the relationship between the mass of young white dwarfs and their velocity dispersion, is shown in figure \ref{fig:results} and discussed in section \ref{sec:kinomethod}. The implied scale heights, the second key result, are then discussed in section \ref{sec:scaleh}. These results have been checked using a Monte Carlo simulation of the formation and observation of an ensemble of white dwarfs, which is described by flowcharts in figures \ref{fig:sseflow}--\ref{fig:obsflow}: in figure \ref{fig:sseflow} the process of choosing stars is described, in figure \ref{fig:diskflow} the process of placing them in the disk is described, and in figure \ref{fig:obsflow} the process of determining the observability of the simulated white dwarf is described.
|
\label{sec:summary} We have analysed the kinematics of young ($<3\times 10^8~{\rm years}$) DA white dwarfs from both the PG and SDSS surveys and find a strong connection between their mass and kinematics: low-mass white dwarfs (\mrange[M_1+M_2]{0.45}{0.75}) display the kinematics of old stars, with higher velocity dispersion ($\sim 46\kms$) and asymmetric drift, while higher mass white dwarfs (\mrange[M_1+M_2]{0.75}{0.95}) display the kinematics of young stars with a velocity dispersion of only $\sim 19\kms$. We have shown in section \ref{sec:sse} that this is expected due to the shorter precursor lifetime of the more massive progenitors, and that there is agreement both on simple analytic grounds (section \ref{sec:sseanalytic}) and more quantitive Monte Carlo simulations of the PG and SDSS samples (section \ref{sec:montesse}). A further key conclusion is that the white dwarf scale height and its variation with age and mass is vitally important to consider when calculating birth rates based on local samples (section \ref{sec:scaleh}). In addition, we have separately analysed the highest mass white dwarfs (\mlim{0.95}, section \ref{sec:bse}), since it has been suggested that many of these formed as a result of the merger of two lower mass CO white dwarfs. We find at present a discrepancy in the SDSS velocity distribution where no high-mass white dwarfs with transverse velocity less than 14\kms~is detected. This results in a velocity distribution that within our statistical framework is inconsistent with purely single star evolution. We argue this is likely to an anomaly, either be a statistical, or a result of a number of these white dwarfs being members of moving groups. We find that, even under the most optimistic binary evolution models, we would only expect to find $3$ white dwarfs formed via white dwarf binary mergers and that the apparent excess of high mass white dwarfs found in PG is caused by their reduced scale height. In addition, we note the kinematic `smoking gun' of some fraction of high-mass white dwarfs coming from binary evolution would be high-mass white dwarfs traveling at $>50$\kms, of which none are found in PG or SDSS.
| 12 | 6 |
1206.1056
|
1206
|
1206.4997_arXiv.txt
|
We describe approximate axisymmetric computations of the dynamical evolution of material inside radio lobes and X-ray cluster gas cavities in Fanaroff-Riley II sources such as Cygnus A. All energy is delivered by a jet to the lobe/cavity via a moving hotspot where jet energy dissipates in a reverse shock. Our calculations describe the evolution of hot plasma, cosmic rays (CRs) and toroidal magnetic fields flowing from the hotspot into the cavity. Many observed features are explained. Gas, CRs and field flow back along the cavity surface in a ``boundary backflow'' consistent with detailed FRII observations. Computed ages of backflowing CRs are consistent with observed radio-synchrotron age variations only if shear instabilities in the boundary backflow are damped and we assume this is done with viscosity of unknown origin. A faint thermal jet along the symmetry axis may be responsible for redirecting the Cygnus A non-thermal jet. Magnetic fields estimated from synchrotron self-Compton (SSC) X-radiation observed near the hotspot evolve into radio lobe fields. Computed profiles of radio synchrotron lobe emission perpendicular to the jet are dramatically limb-brightened in excellent agreement with FRII observations although computed lobe fields exceed those observed. Strong winds flowing from hotspots naturally create kpc-sized spatial offsets between hotspot inverse Compton (IC-CMB) X-ray emission and radio synchrotron emission that peaks 1-2 kpc ahead where the field increases due to wind compression. In our computed version of Cygnus A, nonthermal X-ray emission increases from the hotspot (some IC-CMB, mostly SSC) toward the offset radio synchrotron peak (mostly SSC).
|
Iconic radio and X-ray images of Cygnus A (Figure 1) attest to the colossal energy attributed to cluster-centered massive black holes. Apparently in response to mass accretion, the massive black hole in Cygnus A ejects opposing non-thermal jets that form radio lobes and X-ray cavities. The jets in Cygnus A penetrate out through the cluster gas, driving strong bow-shocks that enclose the jet and its cavity like a cocoon. Since the velocity of the jet greatly exceeds that of the expanding shock, a second more powerful (reverse) shock must appear near the apexes of the cocoon where the energy of the jet is delivered to kpc-sized post-shock hotspots. The velocity of the hotspot is relatively modest, similar to that of the bow shock, but gas and relativistic particles flow through the hotspot with much higher velocities. Matter flowing from the high pressure hotspots inflates the entire radio lobe, displacing the cluster gas as it forms an X-ray cavity. Most, or perhaps all, of the contents of the radio lobes -- relativistic particles, magnetic field and plasma -- originated in the bright hotspots. As hotspots move out into the cluster gas, the energetic CRs produced there flow back (in a ``backflow'') toward the cluster center. Images as in Figure 1 have inspired many theoretical studies of FRII jets and their cocoons (e.g. Blandford \& Rees 1974; Scheuer 1974; Kaiser \& Alexander 1997; Clarke, Harris, \& Carilli 1997; Carvalho \& O'Dea 2002; Carvalho et al. 2005; Krause, 2005; Saxton et al. 2002; O'Neill \& Jones 2010; Huarte-Espinosa, Krause, \& Alexander 2011). Here we describe approximate calculations emphasizing the dynamical evolution of material inside the radio lobes. The approximate evolution and current morphology of Cygnus A can be produced by cosmic rays flowing away from the hotspot as it moves out into the cluster gas (Mathews \& Guo 2010, hereafter MG10). The powerful jet compresses the hotspot in the reverse shock at its inner surface, but most of the energy inside hotspots is contained in cosmic rays transported from the jet and/or accelerated in the strong reverse shock. Jet transport of CRs may be more likely since normal diffusive shock acceleration is suppressed by the magnetic field orientation perpendicular to the jet (Sironi \& Spitkovsky 2009) as observed by Carilli et al. (1999). In the discussion below, as in MG10, we regard the hotspot as the primary energy source in the cocoon. With this assumption we avoid direct computation of the jet itself which occupies a very small volume (Fig. 1) and which is much more difficult to observe and interpret than the bright hotspots, visible in both radio and X-rays (Fig. 1). Multiple pairs of discrete hotspots (as in Figure 1) are common in FRII sources (Black et al. 1992; Hardcastle, Croston, \& Kraft 2007), indicating that the direction of opposing jets changes rather abruptly from time to time. These changes can create a new hotspot before the previously activated hotspot has decayed and are sufficiently abrupt not to produce visible cometary smears where moving jets impact on the relatively denser outer wall of the radio cavity. Here we describe calculations similar to those in MG10 but with an emphasis on the detailed flow of post-hotspot gas and cosmic rays inside the radio cavity. In particular, we address two of the difficulties encountered in the MG10 computations: (1) large scale irregularities in the radio lobe boundaries (Figs. 3, 9 \& 11 in MG10) that have no observed counterparts and (2) chaotic, high velocity plasma flows inside the radio lobes that are inconsistent with the regular, radially ordered age-related variation of synchrotron spectra observed in Cygnus A (Fig. 1) and in FRII sources in general (Alexander \& Leahy, 1987). The orderly variation of observed radio spectra along the radio lobes reveals an evolutionary aging as cosmic ray (CR) electrons lose energy by synchrotron emission. Associated with this is a well-ordered internal flow pattern. Evidently CRs and the magnetic field necessary for synchrotron emission both advect along with low density gas as it backflows from the hotspot toward the cluster center. As a result, the oldest CR electrons are found closer to the center of Cygnus A, furthest from their hotspot origin. The monotonic radial variation of synchrotron ages (e.g. Alexander \& Leahy 1987; Machalski et al. 2007) in FRII sources indicates that their advection must be spatially smooth, uninterrupted by turbulence or large scale non-laminar flows inside the radio cavity. Clearly, the vortical irregularities in the lobe boundary and the chaotic flows inside the radio lobe that appear in previous FRII computations must not occur. The surface vortices appear to be non-linear Kelvin-Helmholtz (KH) instabilities driven by shear between rapidly backflowing post-hotspot material and adjacent gas on both sides. KH irregularities also drive vortical and other large scale flows deep inside the radio cavities that spatially mix synchrotron emitting CR electrons of all ages, upsetting the highly stratified age variation observed. Disordered internal lobe velocities computed by MG10 are sufficiently large, $\gta 500$ km s$^{-1}$, to distort the fragile arrangement of radio-synchrotron ages created during the Cygnus A lifetime, about $10^7$ yrs. In MG10 we recognized that some damping mechanism must be invoked to reduce or remove these shear-generated disturbances. Our impression is that similar unobserved internal lobe velocities are common in all previous computational studies of FRII evolution. KH instabilities can be stabilized by strong magnetic fields along the lobe or by viscous damping. In view of the dynamical weakness of observed magnetic fields in Cygnus A, we explore here the possibility that the apparent absence of KH vortical activity is due to viscosity. We do not claim to understand the physical nature of viscosity in a collisionless relativistic fluid mixed with very low density plasma and weak fields. However, a similar viscous damping has a remarkably beneficial effect in removing unobserved surface irregularities in the gamma ray image of the Fermi bubbles in the Milky Way (Guo \& Mathews 2012; Guo et al. 2012). Viscosity in hot cluster gas has also been considered by Reynolds et al. (2005), Roediger \& Bruggen (2008) and Jones (2008). Our objective is to explore dynamical and physical features in Cygnus A created by hot gas, CRs, and magnetic fields using 2D axisymmetric computations and a variety of additional simplifying assumptions. While we adopt many parameters consistent with observations of Cygnus A and its surrounding cluster gas, we do not adjust parameters to achieve the best possible match to Cygnus A observations -- our results are intended to apply to FRII sources in general. We adopt a distance to Cygnus A of $\sim230$ Mpc so that 1$\arcsec$ corresponds to 1 kpc.
|
Our gas dynamical calculation is successful in matching many detailed observations of Cygnus A and other FRII sources: \noindent$\bullet$ We describe a ``boundary backflow'' from which most of the strongly limb-brightened radio synchrotron emission occurs in agreement with FRII observations. \noindent$\bullet$ The trend in ages of radio synchrotron electrons along and transverse to the boundary backflow are monotonically organized, resembling observations. \noindent$\bullet$ To achieve this smooth variation of apparent synchrotron ages and smooth radio lobe boundaries, it is necessary to damp Kelvin-Helmholtz shear instabilities. This can be done with a small viscosity of uncertain origin, which we propose here, or possibly with magnetic tension provided the plasma density inside the radio lobe is considerably smaller than expected. \noindent$\bullet$ Our approximate calculation of toroidal magnetic fields passively evolving from the hotspot into the radio lobe allows us to relate the observed field strength in these two regions. If radio cavity fields evolve from toroidal fields estimated in the Cygnus A hotspots, the fields in the radio-emitting backflow are about 10-20 times larger than those observed, $15-20\mu$G. The origin of this disparity is unclear. Perhaps the field in the physically complex hotspots is lower than expected. The CR energy density inside our computed hotspot, required to inflate the Cygnus A cavity, is about ten times larger than the total CR electron energy density previously estimated, suggesting an additional hotspot component of non-radiating particles. \noindent$\bullet$ Low surface brightness X-ray emission in Cygnus A along the symmetry axis of each radio lobe can be understood as a jet or filament of thermal gas flowing from the cluster core, an expected hydrodynamic feature that accompanies all rapidly formed axisymmetric cavities in cluster gas. We speculate that small asymmetries in the relatively dense innermost part of this thermal jet, perhaps as it falls back, are responsible for sudden changes in the direction of the non-thermal jet in Cygnus A, particularly since the non-thermal jet is likely to have a rather small inertia. \noindent$\bullet$ When viewed in projection, our computed FRII flows predict two spatially distinct regions of enhanced non-thermal emission associated with the hotspot and its wind. Enhanced CRs directly behind the hotspot shock cause this region to emit nonthermal IC-CMB X-rays. Radio synchrotron emission is strongest in a second, more extended arc-shaped region 1-2 kpc ahead in the decelerating hotspot wind where the magnetic field is increased by compression. Nonthermal SSC X-ray emission, expected to be somewhat more luminous than IC-CMB X-ray emission, peaks in the hotspot wind near the radio synchrotron offset. Nonthermal X-ray emission is expected throughout the hotspot-arc region. \noindent$\bullet$ A narrow layer of very hot gas appears to backflow along the cavity wall just outside the radio cavity, causing the X-ray cavity to appear slightly larger than the radio lobe. This ``thermal sheath'', marginally resolved in our calculation, may contain most of the thermal gas inside the X-ray cavity.
| 12 | 6 |
1206.4997
|
1206
|
1206.3579_arXiv.txt
|
Recent deep {\it Hubble Space Telescope} WFC3 imaging suggests that a majority of compact quiescent massive galaxies at $z \sim 2$ may contain disks. To investigate this claim, we have compared the ellipticity distribution of 31 carefully selected high-redshift massive quiescent compact galaxies to a set of mass-selected ellipticity and S\'ersic index distributions obtained from 2D structural fits to $\sim$$40,000$ nearby galaxies from the Sloan Digital Sky Survey. A Kolmogorov-Smirnov test shows that the distribution of ellipticities for the high-redshift galaxies is consistent with the ellipticity distribution of a similarly chosen sample of massive early-type galaxies. However the distribution of S\'ersic indices for the high-redshift sample is inconsistent with that of local early-type galaxies, and instead resembles that of local disk-dominated populations. The mismatch between the properties of high-redshift compact galaxies and those of both local early-type and disk-dominated systems leads us to conclude that the basic structures of high-redshift compact galaxies probably do not closely resemble those of any single local galaxy population. Any galaxy population analog to the high-redshift compact galaxies that exists at the current epoch is either a mix of different types of galaxies, or possibly a unique class of objects on their own. \\
|
With the discovery of very compact massive quiescent galaxies at redshifts $z\sim2$ \citep[e.g.][and references therein]{Daddi2005,Toft2007, Trujillo2007, Zirm2007,Buitrago2008,Cimatti2008,VanDokkum2008,Damjanov2009,Williams2010,Saracco2010,Szomoru2011}, galaxy formation and evolution models have been challenged to explain the increase in size of these systems with decreasing redshift and the fact that similarly compact massive galaxies are almost completely absent from the local Universe \citep{Trujillo2009,Taylor2010,Valentinuzzi2010a}. Compared to present-day galaxies of similar (stellar) mass ($M_* \simeq 10^{11}M_\odot$), these high-$z$ compact galaxies or 'red nuggets' are a factor of $\sim5$ smaller \citep[e.g.,][]{Damjanov2011} with half-light or effective radii $R_e\lesssim1$ kpc, while their stellar mass densities within the effective radius are on average an order of magnitude higher \citep[although this difference is smaller for the stellar mass densities within the central kiloparsec, see e.g.][]{Bezanson2009,Saracco2012}. Based on the low fraction of close pairs among quiescent galaxies observed at $0<z<2$ \citep{Bell2006a, Bundy2009, DePropris2010, Williams2011,Man2012} and the small number of near equal mass mergers produced in N-body simulations \citep[e.g.,][]{Shankar2010}, it seems that major mergers can only be partly responsible for the observed size growth. Additional secular processes, such as adiabatic expansion \citep{Fan2010, Damjanov2009} and/or a series of minor mergers \citep{Naab2009, Hopkins2010,Oser2012}, might be needed to expand these compact systems. Recent deep, high-resolution images taken with the Wide Field Camera (WFC3) and NIC2 camera on board the {\it Hubble Space Telescope} (HST) have shown that based on observed elliptiticies and S\'ersic profile fits, there may be indications that many of these compact high-redshift galaxies contain disks \citep{VanDokkum2008,VanderWel2011}. Indeed, \citet{VanderWel2011} claim based on their sample of 14 quiescent massive compact galaxies, that the majority of these systems are disk dominated. Based on the structural parameters derived from ground-based imaging, \citet{Whitaker2012} have recently reported a small decrease in the average axial ratio with redshift (i.e., mildly increased prominence of the disk component) for a sample of post-starburst galaxies found at $0<z<2$. These findings would have interesting consequences for the possible formation and evolution scenarios of these galaxies \citep[e.g.,][]{Weinzirl2011}. In the present paper we investigate the claim in \citet{VanderWel2011} by comparing the ellipticity and S\'ersic distributions of these objects to the corresponding distributions for nearby massive disk-dominated galaxies, as well as massive bulge-dominated early-type galaxies. To define our high-redshift sample we complement the \citet{VanderWel2011} sample with the \citet{Damjanov2011} synthesis of published structural data for high-$z$ compact galaxies with secure spectroscopic redshifts. At low redshift, we characterize the ellipticity and S\'ersic index distributions of nearby galaxies using the local morphology sample recently published by \citet{Simard2011}.
|
\label{Con} We have compared the observed ellipticity distribution of massive, compact, quiescent galaxies at high redshift ($1.5 < z < 2.5$) to those of local ($z < 0.1$) early-type galaxies, and conclude that the two distributions are statistically indistinguishable. In addition, we show that the ellipticity distribution of our high-$z$ sample is inconsistent with that of a local massive disk-dominated sample. On the other hand, the S\'ersic index distributions of compact high-$z$ galaxies and local early-type galaxies are not consistent, and the S\'ersic index distribution of local disk galaxy samples provides a better match to the high-$z$ data. We conclude that either (a) high-$z$ galaxies are a composite population of disks and bulges (which presents the troublesome possibility that galaxy sizes are growing for all structural types); or else, (b) that the shapes and light profiles of high-redshift massive compact galaxies are unlike those of any local galaxy sample, and their structure changes over time. In the latter case, these objects constitute a new class of galaxies on their own.
| 12 | 6 |
1206.3579
|
1206
|
1206.1867_arXiv.txt
|
Spectroscopic observations of \Ha and \Hb emission lines of 128 star-forming galaxies in the redshift range $0.75\le z \le 1.5$ are presented. These data were taken with slitless spectroscopy using the G102 and G141 grisms of the Wide-Field-Camera~3 (WFC3) on board the Hubble Space Telescope as part of the WFC3 Infrared Spectroscopic Parallel (WISP) survey. Interstellar dust extinction is measured from stacked spectra that cover the Balmer decrement (H$\alpha$/H$\beta$). We present dust extinction as a function of \Ha luminosity (down to $3\times 10^{41}$~erg~s$^{-1}$), galaxy stellar mass (reaching $4\times 10^{8}$~M$_{\odot}$), and rest-frame \Ha equivalent width. The faintest galaxies are two times fainter in \Ha luminosity than galaxies previously studied at $z\sim 1.5$. An evolution is observed where galaxies of the same \Ha luminosity have lower extinction at higher redshifts, whereas no evolution is found within our error bars with stellar mass. The lower \Ha luminosity galaxies in our sample are found to be consistent with no dust extinction. We find an anti-correlation of the [\ion{O}{3}]$\lambda 5007$/H$\alpha$ flux ratio as a function of luminosity where galaxies with $L_{H\alpha}<5\times 10^{41}$ erg~s$^{-1}$ are brighter in [\ion{O}{3}]$\lambda 5007$ than H$\alpha$. This trend is evident even after extinction correction, suggesting that the increased [\ion{O}{3}]$\lambda 5007$/H$\alpha$ ratio in low luminosity galaxies is likely due to lower metallicity and/or higher ionization parameters.
|
Star-forming galaxies are characterized by emission lines from gas heated by young stars in \HII regions. The luminosity of these \emph{nebular} emission lines such as \Ha or \OIII provides reliable information concerning galaxy star-formation rates (SFRs) and gas-phase metallicities. Yet the dust present in the interstellar medium strongly attenuates rest-frame ultraviolet and optical fluxes in a wavelength-dependent manner. Therefore, inferring physical properties (\eg SFRs) from emission-line luminosities requires accurate dust corrections. In practice, the most reliable technique to estimate interstellar extinction is to measure the flux ratio of two nebular Balmer emission lines such as \HaHb (\ie the Balmer decrement). Since the value of the Balmer decrement is set by quantum physics, any deviation from this expected value may be attributed to dust extinction (for a fixed electron temperature). Other emission-line ratios, such as H$\beta$/H$\delta$ are useful as well, but are generally more difficult to measure because the higher order lines are weaker and more affected by stellar absorption. The determination of dust extinction from the Balmer decrement has been shown to be a very successful technique in the local Universe since the first statistical work by \citet{kennicutt92}. These results have been improved upon by the large amount of optical spectra provided by the Sloan Digital Sky Survey (SDSS), which were analyzed in this context by \citet{brinchmann04}, \citet{moustakas06}, and \citet{garn10}. However, the simultaneous detection of H$\alpha$ and H$\beta$ in higher redshift galaxies, which are shifted to the near-infrared (IR), is a difficult task with current instrumentation on ground-based telescopes. Indeed, Balmer decrements in high-redshift galaxies have been spectroscopically measured only in a few individual cases (\eg \citealt{teplitz00,hainline09}). Other recent, although less robust, estimates of the Balmer decrement are available at $z\sim 0.5$ for larger galaxy samples based on a combination of spectroscopy and photometry (\citealt{ly12}). There are other dust-extinction estimates at $z\sim 1.47$ from narrow-band photometry of the \Ha and \OII emission lines (\citealt{sobral12b}), but these measurements are affected by the unknown metallicities of the galaxies. At high redshifts ($z>2$) the ultraviolet (UV) slope is typically used to determine dust extinction (\eg \citealt{stanway05,hathi08,reddy10,finkelstein11,wilkins11,bouwens12,hathi12}), where access to the Balmer lines is difficult. The relationship between UV slope and dust reddening depends both on the dust properties and distribution of the dust with respect to the stars. While the local correlation between UV slope and dust attenuation appears to hold for typical star-forming galaxies up to $z\sim 2$ (\eg \citealt{reddy10,reddy12}), the Balmer decrement offers a complementary method of deducing dust attenuation, and can illuminate any differences in the nebular versus stellar extinction in galaxies (\citealt{calzetti94,calzetti00}). Previous works on dust extinction have focused on a relatively narrow dynamical range of \Ha luminosity (\eg \citealt{sobral12b}). Furthermore, these works have been generally sensitive to the brightest star-forming galaxies, which tend to have larger reddening than fainter galaxies. As a result, the common procedure to correct for dust extinction in high-redshift galaxies is to assume an extinction of one magnitude at the wavelength of H$\alpha$ for all galaxy luminosities. This assumption is based on the mean extinction of local galaxies (\citealt{kennicutt92}). However, this local average has a significant scatter, which may potentially affect results derived from the dust correction. An additional issue is that dust extinction as a function of bolometric luminosity is observed to evolve with redshift such that galaxies of the same luminosity are more extinguished at lower redshift, due mainly to the metal enrichment of the interstellar medium (\eg \citealt{reddy06,buat07,burgarella07,bouwens09,reddy10,buat11,bouwens12}). The Wide Field Camera 3 (WFC3) of the Hubble Space Telescope (HST) has now made it possible to carry out a statistically significant analysis of the Balmer decrement in high-redshift galaxies. The grism spectroscopy mode of the WFC3 instrument offers several advantages over ground-based spectroscopy. First, grism spectroscopy is slitless, so there are no concerns of variable slit losses at H$\alpha$ and H$\beta$ due to varying seeing, alignment errors, and atmospheric refraction. Second, the WFC3 grisms provide a continuous wavelength coverage over $0.85\le \lambda \le 1.65$~$\mu$m, which is unaffected by hydroxyl (OH) airglow emission and the high opacity of the atmosphere at certain wavelengths (\ie line measurements are obtained regardless of whether they lie within atmospheric windows or between sky lines). Third, the flux calibration with WFC3 is more accurate than ground-based instruments, as it is unaffected by variable telluric absorption from Earth's atmosphere. Lastly, the WFC3 grisms obtain unbiased samples, whereas ground-based spectroscopy typically requires a preselection in order to assign slits. Furthermore, longslit followup at higher redshifts has mostly focused on brighter galaxies. In this paper, interstellar dust-extinction of star-forming galaxies is statistically investigated in the redshift range $0.75\le z \le 1.5$ over two orders of magnitude in \Ha luminosities. Balmer decrements are measured using spectroscopy and analyzed down to an \Ha flux limit of approximately $5\times 10^{-17}$~erg~s$^{-1}$~cm$^{-2}$. These are galaxies a factor of approximately two fainter than galaxies previously studied at $z\sim 1.5$ (\citealt{sobral12b}). The paper is organized as follows. In \S\ref{sec:data}, we present our galaxy sample and the emission-line extraction technique. Section~\ref{sec:theoretical} explains the necessary framework of dust extinction used in this analysis. The results are shown in \S\ref{sec:results}. Section~\ref{sec:discussion} provides a discussion of our results, their robustness, and a comparison with previous works. Finally, we summarize the main findings from our analysis in \S\ref{sec:summary}. Throughout this paper, a standard cold dark matter cosmology is assumed, with matter density $\Omega_{m}=0.3$, vacuum energy density $\Omega_{\Lambda}=0.7$ and Hubble constant $H_{0}=70$~km~s$^{-1}$~Mpc$^{-1}$.
|
\label{sec:discussion} \subsection{Balmer decrements at $0.75\le z \le 1.5$} We find from Figure~\ref{fig:3in1} (left panel) that the Balmer decrement, and therefore dust extinction, increases with observed \LHa in the luminosity range of our analysis. The increase of the Balmer decrement with observed \LHa was already established at lower redshifts by \citet{brinchmann04,garn10,ly12}. This trend was also found recently by \citet{sobral12b} at $z\sim 1.5$ using less robust dust indicators than the Balmer decrement. \citet{sobral12b} used the ratio H$\alpha$/[\ion{O}{2}] (taken with narrow-band photometry), which is dependent on the unknown galaxy metallicity. We also note that the high star-forming galaxies represented in our sample are found rarely in the local Universe. On the other hand, galaxies with the lowest observed \LHa ($10^{41}{\rm~erg~s}^{-1}\lesssim L_{\rm H\alpha} \lesssim 10^{42}$~erg~s$^{-1}$) were found in \S\ref{sec:results} to have Balmer decrements compatible with dust-free galaxies. Our data are not enough to characterize the dependence of the Balmer decrement with galaxy stellar mass but it is consistent with no evolution of the local relation (Figure~\ref{fig:3in1}, middle panel). A trend of the Balmer decrement with EW$_{\rm H\alpha}$ (which traces \emph{specific} star formation) is also not evident from the right panel of Figure~\ref{fig:3in1}. \subsection{Evolution of the Balmer decrement with redshift} There is a redshift evolution in dust properties as a function of observed \LHa from the local Universe to higher redshifts. This result remains valid even without applying the \NII corrections. Our results are compatible with the claims by \citet{sobral12b} that an $L_{*}$ galaxy\footnote{According to a \citet{schechter76} parameterization.} at $z\sim 1$ (between $10^{42.25}$ and $10^{42.50}$~erg~s$^{-1}$, \citealt{sobral12b}) has the same dust extinction as an $L_{*}$ galaxy today (approximately $10^{41.20}$~erg~s$^{-1}$, \citealt{ly07}). This result comes from the fact that the evolution in the dust-extinction dependence with \LHa is similar to the evolution from the local Universe to $z\sim 1$ of $L_{*}$ in the luminosity function. On the other hand, looking at the middle panel of Figure~\ref{fig:3in1}, we see that our galaxies span the same stellar mass range as the galaxies studied in the local Universe by the SDSS. The dependence of the Balmer decrement with stellar masses does not seem to evolve with time, which is in agreement with results by \citet{sobral12b} utilizing photometry and a different tracer of extinction. These results are consistent with the following picture of galaxy evolution. Young star-forming galaxies have typically low content of dust and metals. Significantly older galaxies that built many stars in the past will be dustier and metal rich. When observing younger galaxies at earlier cosmic times, we see less dust in the interstellar medium even at fixed SFR (see \eg \citealt{reddy06,reddy10}). Nevertheless, the galaxy stellar mass is correlated with the production of dust and metals in such a way that the same amount of dust is produced per unit of formed stellar mass regardless of which redshift it was formed. Typically the dust is mainly produced by asymptotic giant branch (AGB) stars, which are formed when the galaxy is several 100~Myr old. Therefore, we expect that the correlation of dust extinction with stellar mass will be similar at any epoch except at higher redshifts, when most stars have not had time to enter the AGB phase. Not surprisingly, we find that this issue is not significant at the epoch around $z\sim 1$, when the universe was nearly half its present age. However, there is one caveat (which is still controversial) that we do not consider in this picture: dust may be destroyed and/or expelled from the galaxy by outflows. A possible redshift evolution in the Balmer decrements within our sample is investigated by means of binning in two different redshifts ranges but no conclusion can be drawn from our sample due to large uncertainties. We note that estimating dust extinction from the Balmer decrement is based on the assumption that the \Ha extinction is constant across all \Ha emitting region. As with any measure of extinction derived from unextinguished light, the Balmer decrement can not account for optically thick regions of the galaxies. This may result in an underestimate of the total extinction (\eg \citealt{meurer02}). However, because the extinction is higher in the ultraviolet and because the intrinsic ratios are known, we believe that our Balmer line-derived estimates of the extinction are more robust than those derived with ultraviolet colors. Also, when comparing to other epochs to determine an evolution in extinction, we use the same extinction metrics for consistency (the Balmer decrement). Ideally, we would like to also measure the infrared luminosities of these galaxies to fully account for obscured star formation, but that is not possible given the resolution and confusion limits of existing infrared telescopes. Statistical interstellar-dust properties of star-forming galaxies were analyzed in this work as a function of $L_{\rm H\alpha}$, galaxy stellar mass, and rest-frame \Ha equivalent width. These properties were derived by stacking the spectroscopic observations of Balmer decrements of 128 star-forming galaxies from the WISP survey. Evolution in dust-extinction properties from the local Universe up to $z=1.5$ as a function of \LHa is found as already suggested by other more model-dependent (\eg \citealt{buat07,burgarella07}) or less robust dust-extinction indicators (\eg \citealt{sobral12b}). Our data suggest that galaxies of the same luminosity are more attenuated in the local Universe than at $z\sim 1$ by a factor that is dependent on luminosity. However, the Balmer decrement as a function of galaxy stellar mass does not seem to evolve with redshift (as suggested by \citealt{sobral12b}). We show that the fainter star-forming galaxies have brighter \OIII than \Ha emission lines. Future galaxy surveys of faint star-forming galaxies may take advantage of the fact that \OIII is typically brighter than \Ha at $L_{\rm H\alpha}<5\times10^{41}$~erg~s$^{-1}$ as it will allow for detection of fainter galaxies and/or higher redshifts than H$\alpha$-targeted surveys. The number of sources in the WISP catalog will increase considerably before its completion and will benefit from ongoing ground-based observations. Our dust extinction results will be updated when these observations are available. The WISP team will soon present further results on the \Ha luminosity function (Colbert et al., in preparation), massive galaxies (Bedregal et al., in preparation), mass-metallicity relation (Henry et al., in preparation) and star-forming main sequence (Dom\'inguez et al., in preparation). These results will allow us to present a comprehensive picture of the Universe at $z\sim 1$ and beyond.
| 12 | 6 |
1206.1867
|
1206
|
1206.2109.txt
|
According to the CMB observations, Mielczarek (\cite{Mielczarek}) evaluated the reheating temperature, which could help to determine the history of the Universe. In this paper, we recalculate the reheating temperature using the new data from WMAP 7 observations. Based on that, we list the approximate solutions of relic gravitational waves (RGWs) for various frequency bands. With the combination of the quantum normalization of RGWs when they are produced and the CMB observations, we obtain the relation between the tensor-to-scalar ratio $r$ and the inflation index $\beta$ for a given scalar spectral index $n_s$. As a comparison, the diagram $r-\beta$ in the slow-roll inflation model is also given. Thus, the observational limits of $r$ from CMB lead to the constraints on the value of $\beta$. Then, we illustrate the energy density spectrum of RGWs with the quantum normalization for different values of $r$ and the corresponding $\beta$. For comparison, the energy density spectra of RGWs with parameters based on slow-roll inflation are also discussed. We find that the values of $n_s$ affect the spectra of RGWs sensitively in the very high frequencies. Based on the current and planed gravitational wave detectors, we discuss the detectabilities of RGWs. \ \noindent PACS number: 04.30.-w, 98.80.Es, 98.80.Cq
|
General relativity and quantum mechanics predict a stochastic background of relic gravitational waves (RGWs) \cite{grishchuk1,grishchuk,grishchuk3,starobinsky,Maggiore,Giovannini}, generated during the early inflationary stage. The primordial amplitudes could be determined by the quantum normalization at the time of the wave modes crossing the horizon during the inflation. After that, the evolution of RGWs are mainly determined by a sequence of stages of cosmic expansion including the current acceleration \cite{zhang2,Zhang4}, since the interaction of RGWs with other cosmic components is typically very weak. Therefore, RGWs carry a unique information of the early Universe, and serve as a probe into the Universe much earlier than the recombination stage. As an interesting source for gravitational wave (GW) detectors, RGWs exist everywhere and anytime unlike GWs radiated by usual astrophysical process. Moreover, RGWs spread a very broad range of frequency, $10^{-18}-10^{10}$ Hz, making themselves become one of the major scientific goals of various GW detectors with different response frequency bands. The current and planed GW detectors contain the ground-based interferometers, such as LIGO \cite{ ligo1}, Advanced LIGO \cite{ligo2,advligo}, VIRGO \cite{virgo,virgocurve}, GEO \cite{geo}, AIGO \cite{Degallaix}, LCGT \cite{lcgt} and ET \cite{Punturo,Hild} aiming at the frequency range $10^2-10^3$ Hz; the space interferometers, such as the future LISA \cite{lisa0,lisa} which is sensitive in the frequency range $10^{-4}-10^{-1}$ Hz, BBO \cite{Crowder,Cutler} and DECIGO \cite{Kawamura} which both are sensitive in the frequency range $0.1-10$ Hz; and the pulsar timing array, such as PPTA \cite{PPTA,Jenet} and the planned SKA \cite{Kramer} with the frequency window $10^{-9}-10^{-6}$ Hz. Besides, there some potential very-high-frequency GW detectors, such as the waveguide detector \cite{cruise}, the proposed gaussian maser beam detector around GHz \cite{fangyu}, and the 100 MHz detector with a pair of 75-cm baseline synchronous recycling interferometers \cite{Akutsu}. Furthermore, the very low frequency portion of RGWs also contribute to the anisotropies and polarizations of cosmic microwave background (CMB) \cite{basko}, yielding a magnetic type polarization of CMB as a distinguished signal of RGWs. WMAP \cite{Peiris,Spergel,Hinshaw,Komatsu}, Planck \cite{Planck}, the ground-based ACTPol \cite{Niemack} and the proposed CMBpol \cite{CMBpol} are of this type. The reheating temperature, $T_{\rm{RH}}$, carries rich information of the early Universe, and relates to the decay rate of the inflation as $T_{\rm{RH}}\propto \sqrt{\Gamma}$ \cite{Kolb,Nakayama} Recently, the reheating temperature was evaluated \cite{Mielczarek} according to the CMB observations by WMAP 7 in the frame of the slow-roll inflation \cite{Komatsu}. Then, the expansion histories of different stages could be determined subsequently. In this paper, we reevaluate the reheating temperature using the latest observational data from CMB, and adopt the resulting expansion periods of different phases of the Universe as references. The referenced reheating temperature can help us to divide the phases of the Universe definitely. The evolutions of the RGWs at various phases can be determined subsequently, and the primordial amplitude was normalized due to the quantum condition during inflation \cite{grishchuk,grishchuk3}. For the present time, the solutions of RGWs can be obtained for different frequency bands corresponding to the modes re-entered the horizon at different phases. Note that, this model of RGWs is free from the slow-roll inflation. Therefore, the above reheating temperature based on the slow-roll inflation just serves as a reference. On the other hand, the anisotropies due to the tensor metric perturbations (gravitational waves) can be scaled to those due to the observations of the scalar perturbations by introducing a parameter $r$ called tensor-to-scalar ratio. Combining the observations of the CMB and the quantum normalization of RGWs when they are generated, a constraint condition is arrived between the ratio $r$, the inflation index $\beta$, and the index $\beta_s$ describing the expansion behavior of the Universe from the end of inflation to the reheating process. For the chaotic inflation with a quadratic potential $V=\frac{1}{2}m^2\phi^2$, which means $\beta_s=1$, the diagram $r-\beta$ will be illustrated for given values of the scalar spectral index $n_s$. The resulting spectra of RGWs for different values of $r$ the corresponding $\beta$ will be demonstrated. For comparison, we will also discuss the spectra of RGWs with the values of $r$ and $\beta$ predicted by the slow-roll inflation itself. To this end, the spectra of RGWs given by different models and different parameters will confront the various current and planed GW detectors. The outline of this paper is as follows. In Sec. II, we recalculate the reheating temperature using the latest data from CMB and plot it as a function of the scalar spectral index. Based on that, the scale factor $a(\tau)$ is specified for consecutive stages of cosmic expansion. In section III, we present the resulting approximate solutions of the spectrum of RGWs for various frequency bands. In section IV, the spectra of RGWs for different values of parameters are shown and some comparisons between the spectra based on quantum normalization and those based on slow-roll inflation will be given. Some discussions are summarized in Sec. V. Throughout this paper, we use the units $c=\hbar=k_B=1$. Indices $\lambda$, $\mu$, $\nu$,... run from 0 to 3, and $i$, $j$, $k$,... run from 1 to 3.
|
~We determined the expansion histories of the preheating stage and the radiation-dominated stage due to the the reheating temperature which is recalculated using the latest observations of WAMP 7-year. Based on that, we illustrated the approximate solutions of RGWs in the current accelerating stage for various frequency bands. We found that the frequency $f_s$, describing that the mode re-entered the horizon at the moment of the reheating, is dependent on $n_s$ sensitively, however, the upper limit frequency of RGWs depends on the value of $n_s$ much less sensitively. Combing the quantum normalization of RGWs with the CMB observations, we obtained a relation between the tensor-to-scalar ratio $r$ and the inflation index $\beta$ for the fixed preheating index $\beta_s=1$. According to the relation between $r$ and $\beta$ with a fixed $n_s=0.966$, we find that a relatively tight constraint $0.01<r<0.24$ leads to $\beta$ localizing in a range of $-2.032<\beta<-2.005$ based on quantum normalization and in a more narrow range of $-2.015<\beta<-2.001$ based on slow-roll inflation, respectively. We plotted the spectrum and the energy density spectrum of the RGWs for three cases of $r=0.49(\beta=-2.038)$, $r=0.01(\beta=-2.005)$, and $r=0.001(\beta=-1.985)$, respectively. It was found that a lager $r$, i.e., a smaller $\beta$ leads to a larger spectrum of RGWs especially at lower frequencies. For comparison, we also illustrated the spectra of RGWs with the parameters of $r$ and $\beta$ given by the slow-roll inflation. Concretely, for $n_s=0.966$, one has $r=0.136$ and $\beta=-2.009$, and for $n_s=0.967$, one has $r=0.132$ and $\beta=-2.008$. It was found that, for the same value of $r$, the discrepancy of the energy spectra based on quantum normalization and those based on slow-roll inflation is larger and larger with the increasing frequency. However, our analysis above does not not apply, in general, to less conventional models of inflation where the RGW spectrum and the observed spectrum of scalar perturbations are produced with different primordial mechanisms \cite{Bozza,Gasperini}, and, as a consequence, they are in principle completely decoupled. Among the current and planed GW detectors, only the planed SKA using the pulsar timing technique, and the planed space-based interferometers BBO and DECIGO are promising to detect RGWs. However, these results are based on the referenced values of $\zeta_1$ and $\zeta_s$ which are obtained from the combination of CMB observations and the slow-roll inflation with a concrete potential $V(\phi)= \frac{1}{2}m^2\phi^2$. Note that, the values of $\zeta_1$ and $\zeta_s$ depend sensitively on the reheating temperature $T_{\rm{RH}}$ which is dependent on $n_s$ sensitively. However, the $r-\beta$ relation is nearly not dependent on $n_s$ once the form of the potential $V(\phi)= \frac{1}{2}m^2\phi^2$ is given. Hence, for the same value of $r$, different $n_s$ only affects the very high frequency RGWs that re-entered the horizon before the radiation-dominant stage. Therefore, to a certain extant, our analysis of the detection in the frequency range $f\leq10^3$ Hz is general, even though the determination of the reheating temperature from CMB has very large uncertainties. As forecasted in Ref. \cite{Mielczarek}, the future CMB experiments such as the Plank satellite \cite{Planck}, the ground-based ACTPol \cite{Niemack} and the planned CMBPol \cite{CMBpol} will provide significant reductions of the uncertainties of the reheating temperature $T_{\rm{RH}}$. Therefore, one expect accordingly that the expansion histories of the very early universe would be known better. On the other hand, the values of $\zeta_1$ and $\zeta_s$ could be chosen independently on the slow-roll inflation scenario, which would be studied in the future work. \ {ACKNOWLEDGMENT}: This work is supported by the National Science Foundation of China under Grant No. 11103024, and has been supported in part by the Fundamental Research Fund of Korea Astronomy and Space Science Institute. \small
| 12 | 6 |
1206.2109
|
1206
|
1206.4735_arXiv.txt
|
A significant fraction of the total photospheric light in nearby galaxy clusters is thought to be contained within the diffuse intracluster light (ICL), which extends 100s of kpc from cluster cores. The study of the ICL can reveal details of the evolutionary histories and processes occurring within galaxy clusters, however since it has a very low surface brightness it is often difficult to detect. We present here the first measurements of the ICL as a fraction of total cluster light at $z\sim1$ using deep {\it J}-band (1.2 $\micron$) imaging from HAWK-I on the VLT. We investigate the ICL in 6 X-ray selected galaxy clusters at 0.8$\le z \le$1.2 and find that the ICL below isophotes $\mu_{J}$ = 22 mag/arcsec$^{2}$ constitutes 1--4\% of the total cluster light within a radius $R_{500}$. This is broadly consistent with simulations of the ICL at a similar redshift and when compared to nearby observations suggests that the fraction of the total cluster light that is in the ICL has increased by a factor 2 -- 4 since z$\sim$1. We also find the fraction of the total cluster light contained within the Brightest Cluster Galaxy (BCG) to be 2.0--6.3\% at these redshifts, which in 5 out of 6 cases is larger than the fraction of the ICL component, in contrast to results from nearby clusters. This suggests that the evolution in cluster cores involves substantial stripping activity at late times, in addition to the early build up of the BCG stellar mass through merging. The presence of significant amounts of stellar light at large radii from these BCGs may help towards solving the recent disagreement between the semi-analytic model predictions of BCG mass growth (e.g. De Lucia \& Blaziot, 2007) and the observed large masses and scale sizes reported for BCGs at high redshift.
|
Dominated by dark matter and with masses rising above $10^{15}\,$M$_{\odot}$, galaxy clusters are ideal regions for testing our understanding of astrophysical processes and revealing insights into the formation and evolution of structure in the Universe. The ubiquitous presence of hot gas and hundreds of galaxies means they can be studied out to high redshift in optical, X-ray and now SZ surveys, and used, not only as probes of the hierarchical evolution process, but also to measure cosmological parameters - for a recent review see Allen et al. (2011). In most clusters the brightest cluster galaxy (BCG) dominates the photospheric stellar light in the cluster core, with the BCG located close to the peak of the X-ray emission. For example, Stott et al. (2012) find that the average BCG offset from the cluster X-ray centroid is only 0.03R$_{500}$, a result consistent with Lin \& Mohr (2004), who find that for local massive clusters the BCG lies at an average distance of only $\simeq$ 15 kpc from the cluster centroid - a figure which may rise to more like 50 kpc at $z\geq1$ (Fassbender et al., 2011). Recent work on the mass and size evolution of BCGs has provided a challenge for current cosmological models and simulations. BCGs have been found to have significantly larger masses (Whiley et al., 2008; Collins et al., 2009; Stott et al., 2010) at high redshift than is predicted by semi-analytic models (e.g., De Lucia and Blaizot, 2007). These observations have demonstrated that BCGs have already undergone the majority of their mass evolution by $z$=1, contrary to the predictions of simulations which suggest a tripling in mass since this time. It has also recently been observed that the scale sizes of BCGs show very little increase since z$\geq$1 (see Stott et al., 2011), contrary to observations of passively evolving massive galaxies in the field which are observed to increase in scale size by 2--5 times since z$\sim$2 without showing any significant mass increase. Whilst simulations of massive ellipticals show that this increase could be caused by minor mergers (e.g., Naab et al., 2009), there is no need for as many interactions in BCGs since z$\sim$1 to explain their modest size increase. The notion of the intracluster light (ICL) first arose from observational results that showed the surface brightness profiles of BCGs were extended, in excess of the predicted `classic' DeVaucouleurs (r$^{1/4}$) surface brightness radial profile for elliptical galaxies (Matthews et al., 1967; Sersic, 1968; Shombert, 1988). Estimates of the fraction of cluster light contained in the ICL in nearby clusters range from 10--50\%, with the upper end set by the observations in the core of Coma (Bernstein et al., 1995). With the growing realisation of the ICL's potential importance there have been concerted efforts on both the observational and theoretical front; new deep observations of ICL have been made in clusters now covering a range of redshifts out to $z$=0.8 (Gonzalez et al., 2005, 2007; Rudick et al., 2006; Krick et al., 2006, 2007; Guennou et al., 2011; Toledo et al., 2011). In addition, recent simulations of the ICL evolution with cluster evolution (e.g., Conroy et al., 2007; Murante et al., 2007; Puchwein et al., 2010; Rudick et al., 2011) open up the potential of new constraints on the assembly history in rich clusters. The wide range of measured ICL fractions is at least in part due to the numerous methods used to treat the BCG extended halo and the ICL as separate components (e.g. Gonzalez et al., 2005; Lauer et al., 2007). Although some authors fit BCGs with a double surface brightness profile (e.g. Gonzalez et al., 2005; Ascaso et al., 2011) and often find an extended outer component many times larger than the inner component, these fits are often degenerate making these composite analyses difficult to interpret without dynamical information (Dolag et al., 2010). Furthermore the different definitions, assumptions and fitting procedures make literature estimates of characteristic scale-sizes of BCGs difficult to compare. In our recent paper (Stott et al., 2011) we examine the surface brightness profiles of BCGs at $z\sim1$ using {\it HST} data and see tantalising hints of an extended surface brightness profile (beyond a DeVaucouleurs r$^{1/4}$ profile). This has motivated us to acquire deep {\it J}-band observations with HAWK-I on the VLT to examine the diffuse ICL component in six $z$=0.8--1.22 clusters. We present here the first search for the ICL in galaxy clusters at these redshifts and compare our results with the cosmological simulations of the ICL by Ruddick et al. (2011) who use surface brightness thresholding to distinguish the ICL from other galaxy components, thereby circumventing some of the complexities resulting from the different parameterisations of the extended light components discussed above. The structure of this paper is as follows: in \S~\ref{data} we describe our data, observations and reduction; in \S~\ref{method} we describe the methods used in our measurements; in \S~\ref{results} we present our results and discuss possible sources of systematic error; and \S s~\ref{discussion} and~\ref{conclusions} contain the discussion of the results and the conclusions drawn respectively. All magnitudes described in this paper are in the Vega magnitude system unless otherwise stated. Throughout this paper we adopt a $\Lambda$CDM cosmology with $H_0$ = 70 km s$^{-1}$Mpc$^{-1}$, $\Omega_M$ = 0.3, $\Omega_{\Lambda}$ = 0.7.
|
We have detected and measured the fraction of cluster light that is in the ICL for 6 galaxies at $z\sim$1 using a simple definition of surface brightness threshold. We find that an extended component is detectable down to surface brightness levels of $\mu_{J}\sim$22 mag/arcsec$^2$ measured within a radius R$_{500}$. At this level, the fraction of total measured cluster light in the ICL for our 6 clusters ranges between 1\% and 4\%, which is smaller than observations at lower redshift and similar or slightly below the predicted values at fainter isophotes, based on a similar ICL definition from the simulations of R11. This indicates that the ICL may have grown by a factor of 2 -- 4 since $z\sim$1, a scenario which is consistent with the idea of material being stripped from galaxies through mergers and close galaxy encounters. In the context of the cosmological mass assembly problem of BCGs reported in the literature, the quantity of extended light is comparable to the centrally concentrated light from the BCGs. Taking into account both components is likely to ease the current discrepancy between the observed and predicted timescales of BCG assembly.
| 12 | 6 |
1206.4735
|
1206
|
1206.3834_arXiv.txt
|
The energy spectrum of cosmic rays between $10^{16}\,$eV and $10^{18}\,$eV, derived from measurements of the shower size (total number of charged particles) and the total muon number of extensive air showers by the KASCADE-Grande experiment, is described. The resulting all-particle energy spectrum exhibits strong hints for a hardening of the spectrum at approximately $2\cdot10^{16}\,$eV and a significant steepening at $\approx 8\cdot10^{16}\,$eV. These observations challenge the view that the spectrum is a single power law between knee and ankle. Possible scenarios generating such features are discussed in terms of astrophysical processes that may explain the transition region from galactic to extragalactic origin of cosmic rays.
|
The main goals of experimental cosmic ray research are the determination of the arrival direction distribution, the primary energy spectrum, and the elemental composition. Those measurements comprise important hints to understand the origin, acceleration and propagation of energetic cosmic particles. The needed measurements can be done directly or indirectly, depending on the energy of the primary particle. At energies above $10^{15}\,$eV, the energy spectrum must be determined indirectly from the measured properties of extensive air showers (EAS) that cosmic rays induce in the Earth's atmosphere~\cite{Wat}. The determination of the primary energy and elemental composition in the energy range from $10^{15}\,$eV up to above $10^{20}\,$eV is subject of earth-bound experiments since more than five decades. It has been shown that the all-particle spectrum has a power-law like behavior ($\propto\,E^{-\gamma}$, with $\gamma\,\approx\,2.7$) with features, which are known as `knee' and `ankle' at $3$-$5\cdot10^{15}\,$eV and $4$-$10\cdot10^{18}\,$eV, respectively. Whereas at the knee the spectrum steepens, the ankle is characterized by a flattening of the spectrum by roughly the same change of the spectral index of $\Delta \gamma = \pm 0.3$-$0.4$. Cosmic rays above the ankle are most probable of extragalactic origin~\cite{auger-eg}, i.e.~ somewhere in the energy range from $10^{16}\,$eV to a few $10^{18}\,$eV a break-off of the heavy component and the transition of cosmic rays of galactic to extragalactic origin is expected. As the measured position of the knee is roughly in agreement with the energy where supernova remnants (SNR) become inefficient accelerating particles~\cite{hillas}, various theories with different assumptions were developed to explain the behavior of the spectrum between the knee and ankle features. \\ The basic idea of the `dip model'~\cite{berezinsky} is that the ankle is a propagation feature of extragalactic protons (energy loss by electron pair production). Consequently, in that model the composition at the ankle is to a large extent proton-dominant and the transition from galactic to extragalactic origin of cosmic rays occurs already at energies well below $10^{18}\,$eV. In the scenario of the dip model, at energies around $10^{17}\,$eV a pure galactic iron component should be left and a small kink in the spectrum at around $5$-$7\cdot10^{17}\,$eV, as indicated by observations by the AKENO~\cite{akeno} and HiRes~\cite{hires} experiments and named as `second knee'~\cite{second}, would be assigned to the transition. This is in agreement with the SNR theory, where the knee positions of individual primary masses are proportional to the charge of the nuclei starting with the proton knee at around $E_{knee}^p = 3$-$5\cdot10^{15}\,$eV and $E_{knee}^A = Z\cdot E_{knee}^p$ (rigidity dependence of knee positions for galactic cosmic rays). \\ On the other hand, to avoid an early appearance of the extragalactic cosmic ray component, Hillas~\cite{hillas} proposed in addition to the standard SNR component, a `component B' of cosmic rays of galactic origin. This component would also experience a charge dependence of break-offs, but now shifted to approximately ten times higher energy. As a result, the transition occurs here at the ankle and for the entire energy range from $10^{15}\,$eV to $10^{18}\,$eV a mixed elemental composition is expected. In this scenario, the second knee, if it exists, would be a feature of the component B. The KASCADE experiment and its extension, KASCADE-Grande, aim to provide high quality air-shower data in the energy range of $10^{14}\,$eV to $10^{18}\,$eV to evaluate the validity of these models and to distinguish between them. The KASCADE experiment has shown that the knee is due to a distinct break in the proton intensity despite protons are not the most abundant primary in this energy range. The break is followed by a kink in the spectrum of Helium nuclei~\cite{kas-unf}, i.e.~the knee in the all-particle spectrum is a feature of the light nuclei (Z$<6$), only, where the difference in the energies of the knee features of primary protons and Helium facilitates the assumption of a charge dependence of the break-off. First analyses of KASCADE-Grande data~\cite{kg-letter} resulted in a knee-like feature at around $8\cdot10^{16}\,$eV caused by a steepening in the spectrum of heavy primary cosmic rays. In the present analysis, the reconstruction of the all-particle energy spectrum of cosmic rays in the range from $10^{16}$ to $10^{18}\,$eV is described in detail. Depending on the experimental apparatus and the detection technique of ground-based air-shower experiments, different sets of EAS observables are available to estimate the energy of the primary cosmic ray~\cite{Haungs}. In case of ground arrays the total number of charged particles (often called shower size) in the shower and the corresponding particle density at observation level are commonly employed. The muon content of EAS plays an important role, too. In the atmosphere the muon component suffers less attenuation than electromagnetic or hadronic components and exhibits less fluctuations compared to the more abundant electromagnetic component. In KASCADE-Grande both components, the muon and the electromagnetic ones, are measured with independently operating detectors. Both, together with the information of their correlation on a single-event-basis, are used to derive the spectrum. After a short description of the apparatus and the reconstruction procedures of the EAS parameters, we will describe the method developed to determine the all-particle energy spectrum including studies of systematic uncertainties. We conclude this paper with a discussion of the results.
|
The main air-shower observables of KASCADE-Grande, shower size and total number of muons, are reconstructed with high precision and low systematic uncertainties. Applying various reconstruction methods to the KASCADE-Grande data the obtained all-particle energy spectra are compared as a way to cross-check the reconstruction, to study systematic uncertainties and to test the validity of the underlying hadronic interaction models. By combining both observables, the all-particle energy spectrum of cosmic rays is reconstructed in the energy range of $10^{16}\,$eV to $10^{18}\,$eV within an uncertainty in intensity of 10-15\%, based on the hadronic interaction model QGSJet-II. Correcting the spectra for reconstruction uncertainties and taking into account the systematic uncertainties for all methods, the underlying hadronic interaction models (QGSJet-II/FLUKA) result in a consistent solution, independent on the observable used, i.e.~the single shower sizes or the correlation between the different observables. Tests with the hadronic interaction model EPOS 1.99 have shown that there is a shift in the absolute energy scale when interpreting the data with this model, but the shape of the spectrum with its structures stays preserved. Progress in improving the interaction models is expected in the near future by detailed analyses of the now available data of the Large Hadron Collider, LHC (see, e.g.~\cite{pierog}). The resulting spectrum is consistent, and in the overlapping energy range in a very good agreement, with results of the KASCADE, EAS-TOP, and other experiments (Fig.~\ref{spectrum}). The all-particle energy spectrum in the range from $10^{16}\,$eV to $10^{18}\,$eV is found to exhibit some smaller structures: In particular, a hardening of the spectrum is observed at $2\cdot10^{16}\,$eV and a small break-off at around $8\cdot10^{16}\,$eV. These features are used to discuss the astrophysics in the transition region from galactic to extragalactic origin of cosmic rays, where a final conclusion is not possible without detailed knowledge of the elemental composition in this energy range. However, amongst others, the model proposed by Hillas~\cite{hillas}, e.g., which assumes a second component of galactic cosmic rays in addition to the standard SNR component, can explain the observed features of the measured all-particle energy spectrum. A wealth of information on individual showers is available with KASCADE-Grande. This makes it possible to reconstruct the all-particle energy spectrum with high precision, as well as to investigate the elemental composition, to test hadronic interaction models, and to study cosmic ray anisotropies. All these studies are under way and further results are expected in the near future. \begin{ack} KASCADE-Grande is supported by the BMBF of Germany, the MIUR and INAF of Italy, the Polish Ministry of Science and Higher Education (this work partly by grant for 2009-2011). This work was partially supported by the Romanian Authority for Scientific Research CNCSIS-UEFISCSU grant PNII-IDEI no.461/2009, code 1442/2008 and project PN 09 37 01 05, and the German-Mexican bilateral collaboration grant (DAAD-Proalmex 2009-2012). J.C.A. acknowledges the partial support of CONACyT and the Coordinaci\'on de la Investigaci\'on Cient\'\i fica de la Universidad Michoacana. \end{ack} \begin{appendix}
| 12 | 6 |
1206.3834
|
1206
|
1206.1831_arXiv.txt
|
{Classifier combination methods need to make best use of the outputs of multiple, imperfect classifiers to enable higher accuracy classifications. In many situations, such as when human decisions need to be combined, the base decisions can vary enormously in reliability. A Bayesian approach to such uncertain combination allows us to infer the differences in performance between individuals and to incorporate any available prior knowledge about their abilities when training data is sparse. In this paper we explore Bayesian classifier combination, using the computationally efficient framework of variational Bayesian inference. We apply the approach to real data from a large citizen science project, Galaxy Zoo Supernovae, and show that our method far outperforms other established approaches to imperfect decision combination. We go on to analyse the putative community structure of the decision makers, based on their inferred decision making strategies, and show that natural groupings are formed. Finally we present a dynamic Bayesian classifier combination approach and investigate the changes in base classifier performance over time.}
|
In many real-world scenarios we are faced with the need to aggregate information from cohorts of imperfect decision making agents (\emph{base classifiers}), be they computational or human. Particularly in the case of human agents, we rarely have available to us an indication of how decisions were arrived at or a realistic measure of agent confidence in the various decisions. Fusing multiple sources of information in the presence of uncertainty is optimally achieved using Bayesian inference, which elegantly provides a principled mathematical framework for such knowledge aggregation. In this paper we provide a Bayesian framework for imperfect decision combination, where the base classifications we receive are greedy preferences (i.e. labels with no indication of confidence or uncertainty). The classifier combination method we develop aggregates the decisions of multiple agents, improving overall performance. We present a principled framework in which the use of weak decision makers can be mitigated and in which multiple agents, with very different observations, knowledge or training sets, can be combined to provide complementary information. The preliminary application we focus on in this paper is a distributed \emph{citizen science} project, in which human agents carry out classification tasks, in this case identifying transient objects from images as corresponding to potential supernovae or not. This application, \emph{Galaxy Zoo Supernovae} \cite{smith_galaxy_2010}, is part of the highly successful \emph{Zooniverse} family of citizen science projects. In this application the ability of our base classifiers can be very varied and there is no guarantee over any individual's performance, as each user can have radically different levels of domain experience and have different background knowledge. As individual users are not overloaded with decision requests by the system, we often have little performance data for individual users (base classifiers). The methodology we advocate provides a scalable, computationally efficient, Bayesian approach to learning base classifier performance thus enabling optimal decision combinations. The approach is robust in the presence of uncertainties at all levels and naturally handles missing observations, i.e. in cases where agents do not provide any base classifications. We develop extensions to allow for dynamic, sequential inference, through which we track information regarding the base classifiers. Through the application of social network analysis we can also observe behavioural patterns in the cohort of base classifiers. The rest of this paper is organised as follows. In the remainder of the Introduction we briefly describe related work. In Section \ref{sec:IBCCmodel} we present a probabilistic model for independent Bayesian classifier combination, IBCC. Section \ref{sec:VB} introduces the approximate inference method, variational Bayes, and details its application to IBCC. Section \ref{sec:galaxyzooresults} shows an example application for classifier combination, Galaxy Zoo Supernovae, and compares results using different classifier combination methods, including IBCC. In Sections \ref{sec:picomms} and \ref{sec:taskcomms} we investigate how communities of decision makers with similar characteristics can be found using data inferred from Bayesian classifier combination. Section \ref{sec:dynibcc} presents an extension to independent Bayesian classifier combination that models the changing performance of individual decision makers. Using this extension, Section \ref{sec:ContributorDynamics} examines the dynamics of individuals from our example application, while Sections \ref{sec:picommsDynamics} and \ref{sec:taskcommsDynamics} show how communities of decision makers change over time. Finally, Section \ref{sec:discussion} discusses future directions for this work. \subsection{Related Work} Previous work has often focused on aggregating expert decisions in fields such as medical diagnosis \cite{dawid_maximum_1979}. In contrast, \emph{crowdsourcing} uses novice human agents to perform tasks that would be too difficult or expensive to process computationally or using experts \cite{bloodgood_using_2010,quinn_crowdflow:_2010}. The underlying problem of fusing labels from multiple classifications has been dealt with in various ways and a review of the common methods is given by \cite{tulyakov_review_2008}. The choice of method typically depends on the type of labels we can obtain from agents (e.g. binary, continuous), whether we can manipulate agent performance, and whether we can also access input features. Weighted majority and weighted sum algorithms are popular methods that account for differing reliability in the base classifiers; an analysis of their performance is given by \cite{littlestone_weighted_2002}. Bayesian model combination \cite{monteith_turning_2011} provides a theoretical basis for soft-selecting from a space of combination functions. In most cases it outperforms Bayesian model averaging, which relies on one base classifier matching the data generating model. A well-founded model that learns the combination function directly was defined by \cite{ghahramani_bayesian_2003}, giving a Bayesian treatment to a model first presented in \cite{dawid_maximum_1979}. A similar model was also investigated by \cite{raykar_learning_2010} with extensions to learn a classifier from expert labels rather than known ground truth labels. Both papers assume that base classifiers have constant performance, a problem that we address later in this paper.
|
\label{sec:discussion} In this paper we present a very computationally efficient, variational Bayesian, approach to imperfect multiple classifier combination. We evaluated the method using real data from the Galaxy Zoo Supernovae citizen science project, with 963 classification tasks, 1705 base classifiers and 26,558 observations. In our experiments, our method far outperformed all other methods, including weighted sum and weighted majority, both of which are often advocated as they also learn weightings for the base classifiers. For our variational Bayes method the required computational overheads were far lower than those of Gibbs sampling approaches, giving much shorter compute time, which is particularly important for applications that need to make regular updates as new data is observed, such as our application here. Furthermore, on this data set at least, the accuracy of predictions was also better than the slower sampling-based method. We have shown that social network analysis can be used to extract sensible structure from the pool of decision makers using information inferred by Bayesian classifier combination or task co-occurrence networks. This structure provides a useful grouping of individuals and gives valuable information about their decision-making behaviour. We extended our model to allow for on-line dynamic analysis and showed how this enables us to track the changes in time associated with individual base classifiers. We also demonstrated how the community structures change over time, showing the use of the dynamic model to update information about group members. Our current work considers how the rich information learned using our models can be exploited to improve the base classifiers, namely the human volunteer users. For example, we can use the confusion matrices, $\boldsymbol{\Pi}$, and the community structure to identify users who would benefit from more training. This could take place through interaction with user groups who perform more accurate decision making, for example via extensions of \emph{apprenticeship learning} \cite{abbeel_apprenticeship_2004}. We also consider ways of producing user specialisation via selective object presentation such that the overall performance of the human-agent collective is maximised. We note that this latter concept bears the hallmarks of \emph{computational mechanism design} \cite{dash_computational-mechanism_2003} and the incorporation of incentive engineering and coordination mechanisms into the model is one of our present challenges. Future work will also investigate selecting individuals for a task to maximise both our knowledge of the true labels and of the confusion matrices, for example, by looking at the effects of previous tasks on the confusion matrices. To bring these different aspects together, we consider a global utility function for a set of classification and training tasks indexed $i=1,...,N$ assigned to a set of base classifiers $k=1,...,K$. Classifiers assigned to object $i$ are part of coalition $\mathbf{C}_i$ to maximise the total expected value of these assignments: \begin{equation} V(\mathbf{C}_1,...,\mathbf{C}_N) = \sum_{i=1}^N V_{object}(\mathbf{C}_i) + V_{dm}(\mathbf{C}_i) + V_{cost}(\mathbf{C}_i) \label{eq:weakcontrolvalues} \end{equation} where $V_{object}(\mathbf{C}_i)$ is the expected information gain about the true class of object $i$ from the classifiers in $\mathbf{C}_i$, $V_{dm}(\mathbf{C}_i)$ is the improvement to the decision makers through this assignment and $V_{cost}(k,i)$ captures other costs, such as payments to a decision maker. The value $V_{object}(\mathbf{C}_i)$ should be higher for classifiers in $\mathbf{C}_i$ that are independent, so coalitions of decision makers from different communities may be favoured as different experience and confusion matrices may indicate correlation is less likely. $V_{object}(\mathbf{C}_i)$ should also account for specialisations, for example, by members of the same common task community. $V_{dm}(\mathbf{C}_i)$, captures expected changes to confusion matrices that result from the combiner learning more about base classifiers and from base classifiers improving through training or experience. In Galaxy Zoo Supernovae, for example, the contributors are attempting to identify objects visually from a textual description. The description may leave some ambiguity, e.g. ``is the candidate roughly centred''. Seeing a range of images may alter how ``roughly'' the candidate can be centred before the contributor answers ``yes''. Thus the value $V_{dm}(k,i)$ will depend on the objects previously classified by classifier $k$. A key direction for future work is defining these values so that systems such as Galaxy Zoo Supernovae can feed back information from confusion matrices and community structure to improve the overall performance and efficiency of the pool of decision makers. Common task communities and $\boldsymbol{\pi}$ communities may play a central role in estimating the effects of task assignments and training on related individuals. The could also be exploited to reduce the size of the task assignment problem to one of choosing classifiers from a small number of groups rather than evaluating each classifier individually.
| 12 | 6 |
1206.1831
|
1206
|
1206.6620_arXiv.txt
|
In order to put MIDI/VLTI observations of AGNs on a significant statistical basis, the number of objects had to be increased dramatically from the few prominent bright cases to over 20. For this, correlated fluxes as faint as $\approx$ 150 mJy need to be observed, calibrated and their errors be estimated reliably. We have developed new data reduction methods for the coherent estimation of correlated fluxes with the {\em Expert Work Station} (EWS). They increase the signal/noise of the reduced correlated fluxes by decreasing the jitter in the group delay estimation. While correlation losses cannot be fully avoided for the weakest objects even with the improved routines, we have developed a method to simulate observations of weak targets and can now detect --- and correct for --- such losses. We have analyzed all sources of error that are relevant for the observations of weak targets. Apart from the photon-noise error, that is usually quoted, there is an additional error from the uncertainty in the calibration (i.e.\ the conversion factor). With the improved data reduction, calibration and error estimation, we can consistently and reproducibly observe fluxes as weak as $\approx$ 150 mJy with an uncertainty of $\approx$ 15 \% under average conditions.
|
There is little doubt that the energy-releasing central engine of an Active Galactic Nucleus (AGN) consists of a black hole surrounded by an accretion disk that produces copious amounts of radiation from infrared to X-Rays. At a distance of several milli parsec, gas clouds get irradiated by this light and show Doppler-broadened broad emission lines that are observed in the direct light in so called ``type 1'' AGNs. In others, called ``type 2'', only narrow emission lines are observed in the direct light but the broad lines are weakly detectable in polarized, i.e.\ scattered, light. Unified schemes of AGNs \cite{antonucci1993} ascribe this difference in the optical spectra of AGNs to different lines of sight towards the symmetry axis of the system and require a toroidal dusty structure -- the so called ``torus'' -- that intercepts the radiation from the accretion disk and reprocesses it in the infrared. In observations with a single 8m telescope (``single-dish observations''), the torus is unresolved. While single-dish spectra\cite{hoenig2010, ramosalmeida2011} are able to constrain a number of parameters for models of clumpy tori\cite{nenkova2002,hoenig2006,nenkova2008,schartmann2008,hoenig2010}, it is challenging to isolate the torus emission from the emission of a nuclear starburst and from synchrotron radiation of a nuclear jet in unresolved observations. In order to resolve the torus emission, spatial resolutions of better than 100 milli arcseconds (mas) are needed. The MID-infrared Interferometric instrument (MIDI) at the Very Large Telescope Interferometer (VLTI) on Cerro Paranal, Chile, is worldwide unique to observe at such high resolutions in the atmospheric $N$ band ($\lambda \approx$ 8 -- 13 $\um\!$) where the torus SED peaks. The MIDI AGN programme has found parsec-scale dust structures that can be associated with the ``torus'' from the unified model \cite{jaffe2004,tristram2007b,raban2009,burtscher2009,tristram2012}. A study using GTO time \cite{tristram2009} showed that objects fainter than the two brightest targets can still be observed and resolved with MIDI and a recent study of six type 1 objects \cite{kishimoto2011b} hinted at more compact dust structures for higher AGN luminosities. However, only few sources have been studied initially and the implications on the prevalent astrophysical questions -- e.g.\ are ``type 1'' and ``type 2'' tori different? Is there a connection between torus properties and AGN activity? How does the torus size vary with AGN luminosity? -- were limited by the low number of sources. It was clear that a large and systematic observational campaign was needed to collect the basic observational information necessary to understand dusty tori on a statistical basis. This is the aim of the MIDI AGN Large Programme (LP). It was also clear, however, that the sample size can only be increased by observing targets that are fainter than ESO's official limiting magnitude for visibility observations with MIDI on the UTs ($N=4^{\rm mag}$ or $F_{\nu}$ = 1 Jy for an unresolved object). The data and first scientific results of the MIDI AGN LP will be presented elsewhere (L. Burtscher et al., in preparation). The topics of this proceedings article are the observing strategy and data reduction method necessary to successfully observe and calibrate faint (100 mJy $< F_{\nu} <$ 1 Jy for an unresolved source) objects with MIDI. This paper is structured as follows: First we describe what an observer can do at the telescope to ensure that faint targets can be optimally calibrated. Next, an outline of the data reduction method is given and the modifications and specific problems for weak targets are described. Lastly, we discuss an improved error estimation for weak sources and summarize.
|
The weakest objects that are observable with MIDI at the VLTI require special observing and data reduction methods in order to limit and reliably estimate the otherwise large errors. The largest improvement is achieved by calibrating correlated fluxes directly (instead of visibilities). In order to limit the uncertainty due to the sometimes very variable transfer function, the target and calibrator observations should be taken as close in time as possible which is achievable by concentrating on only taking correlated fluxes. In the data reduction, the biggest challenge for weak sources is an accurate estimation of the group delay. Progress has been made by implementing an iterative approach for the group delay estimation and especially by simulating OPD changes during each smoothing interval. A method has been developed to robustly test the data reduction method for weak sources by generating artificially diluted data of a real observation and comparing its reduction with the one using the original data. This way, significant correlation losses have been uncovered for fluxes lower than 300 mJy. They can be corrected for by applying a decorrelation correction factor that depends both on the observing conditions and the data reduction parameters. After both photon noise and conversion factor errors have been taken into account and after correction of correlation losses, consistent results are achieved for weak targets. Using the methods described here we can reproducibly observe objects as faint as $\approx$ 150 mJy with an uncertainty of $\approx$ 15 \% under average conditions. Some of the methods presented here are a part of EWS and are available from the previously quoted web page; the higher level methods, that require a knowledge of all observations of a night, such as the determination of conversion factor variations and decorrelation correction factors have not (yet) been implemented in EWS. They are available as a Google code project and can be downloaded from \href{http://code.google.com/p/miditools/}{http://code.google.com/p/miditools/}. Interaction with the authors is highly encouraged if you plan to use these scripts. The observing and data reduction method as well as the error estimation are not specific to observations of weak AGNs but may be applied for MIDI observations of any weak target. With PRIMA becoming available as an external fringe tracker for MIDI observations\cite{mueller2010}, weak targets will be observed more frequently with MIDI and a precise estimation of the measurement uncertainties is needed.
| 12 | 6 |
1206.6620
|
1206
|
1206.6882_arXiv.txt
|
The high energy activity in the inner few degrees of the Galactic center is traced by diffuse radio, X-ray and $\gamma$-ray emission. The physical relationship between different components of diffuse gas emitting at multiple wavelengths is a focus of this work. We first present radio continuum observations using Green Bank Telescope and model the nonthermal spectrum in terms of a broken power-law distribution of $\sim$GeV electrons emitting synchrotron radiation. We show that the emission detected by Fermi is primarily due to nonthermal bremsstrahlung produced by the population of synchrotron emitting electrons in the GeV energy range interacting with neutral gas. The extrapolation of the electron population measured from radio data to low and high energies can also explain the origin of FeI 6.4 keV line and diffuse TeV emission, as observed with Suzaku, XMM-Newton, Chandra and the H.E.S.S. observatories. The inferred physical quantities from modeling multiwavelength emission in the context of bremsstrahlung emission from the inner $\sim300\times120$ parsecs of the Galactic center are constrained to have the cosmic ray ionization rate $\sim1-10\times10^{-15}$ s$^{-1}$, molecular gas heating rate elevating the gas temperature to 75-200K, fractional ionization of molecular gas $10^{-6}$ to $10^{-5}$, large scale magnetic field $10-20\mu$G, the density of diffuse and dense molecular gas $\sim100$ and $\sim10^3$ cm$^{-3}$ over 300pc and 50pc pathlengths, and the variability of FeI K$\alpha$ 6.4 keV line emission on yearly time scales. Important implications of our study are that GeV electrons emitting in radio can explain the GeV $\gamma$-rays detected by Fermi and that the cosmic ray irradiation model, like the model of the X-ray irradiation triggered by past activity of Sgr A*, can also explain the origin of the variable 6.4 keV emission from Galactic center molecular clouds.
|
The Galactic center hosts several sources of energetic activity: X-ray flare activity from Sgr~A*, nonthermal linear filaments, supernova remnants interacting with molecular clouds, colliding winds of massive stars, pulsars, transient radio and X-ray sources and a population of hard X-ray sources (Muno et al. 2006, 2009; Koyama et al. 1996; Tsuboi, Ukita \& Handa 1997; Baganoff et al. 2001; Murakami et al. 2001; Deneva, Cordes, and Lazio 2009). This region also hosts massive molecular clouds containing pockets of current and past massive star formation (see Jones et al. 2011 and references therein). The most prominent clouds are associated with Sgr B2 and Sgr C, the 50, 40, 20 and --30 \kms\, complexes as well as the cloud G0.11-0.11 adjacent to the radio continuum Arc near $l \sim$ 0.2$^\circ$. Molecular clouds are traditionally studied by molecular line observations at millimeter wavelengths. However, diffuse high energy emission has also been detected from Galactic center molecular clouds. These unique Galactic center molecular clouds that emit the 6.4\, keV X-ray line, GeV and TeV radiation as well as rotationally excited millimeter lines help to bridge a gap in understanding the radiation processes that operate at low and high energies. The Galactic center region hosts warm molecular gas as well as a number of synchrotron emitting radio sources. A high cosmic ray ionization rate is estimated from H$_3^+$ measurements of this region (Oka et al. 2005). It is then natural to consider the interaction of cosmic ray electrons that produce radio emission with ambient gas in the context of nonthermal bremsstrahlung. We study this interaction in detail and investigate the origin of the high cosmic ray ionization rate and high molecular gas temperature (Oka et al. 2005; H\"uttemeister et al. 1993). We show the distribution of GeV $\gamma$-ray emission observed by $Fermi$ and model the emission by studying the population of nonthermal electrons using radio data. Furthermore, the extrapolation of the radio spectrum of the GeV population to 10 keV as well as a young population of electrons extrapolated to TeV energies can also explain the observed emission at X-ray and TeV energy range, respectively. In particular, the fluorescent FeI K$\alpha$ line emission at 6.4 keV and diffuse TeV emission are recognized to trace the molecular clouds of the Galactic center. It has been suggested that the fluorescent 6.4 keV emission results from X-ray irradiation (Sunyaev, Markovitch \& Pavlinsky 1993). The source of the emission is considered to be a hypothetical transient source associated with the massive black hole at the Galactic center, Sgr A*, and that we are now seeing its echo in the 6.4 keV line emission (Koyama et al. 1996; Murakami et al. 2001; Ponti et al. 2010). This event requires a hard X-ray luminosity of $\sim$10$^{39}$ erg s$^{-1}$ from Sgr A*. The year-to-year time variability of 6.4 keV line emission has also been used as a strong support for the irradiation scenario. In this picture, the yearly variability is due to X-ray fronts from multiple outbursts from Sgr A* which occurred in the last few hundred years. The origin of the 6.4 keV line emission from neutral iron due to low-energy cosmic ray electrons and protons of neutral gas has also been considered (Yusef-Zadeh, Wardle \& Roy 2007a; Chernyshov et al. 2011). More recently, the origin of the 6.4 keV line emission from the Arches cluster has also been explained in terms of cosmic-ray ion bombardment of molecular gas surrounding the cluster (Tatischeff, Decourchelle \& Maurin 2012). Here, we reinvestigate the cosmic ray irradiation picture in the context of nonthermal bremsstrahlung. It is important to determine the 6.4 keV emission contributed by each of these two models as they provide evidence for the past activity of Sgr A* or for a large population of low energy cosmic rays (LECR) in the Galactic center region. We begin by describing radio observations using Green Bank Telescope (GBT), $\gamma$-ray observations with the $Fermi$ Large Area Telescope (LAT), and X-ray line observations in $\S2$. In $\S$2.1, the spectrum of radio emission between 325 MHz and 8.5 GHz is modeled in order to separate thermal and nonthermal radio components. In $\S$3 we estimate the cosmic ray ionization rate and compare it with that measured from H$_3^+$ absorption lines (Oka et al. 2005; Goto et al. 2011). We also account for the warm molecular gas as observed throughout the Galactic center and the origin of 6.4 keV emission from Galactic center molecular clouds. Sections 2 and 3 discuss the interaction of low energy cosmic ray particles with molecular gas, whereas $\S4$ discusses the high energy tail of cosmic rays interacting with molecular gas to produce $\gamma$-ray emission detected by $Fermi$ and the H.E.S.S. telescopes. \section {Nonthermal Radiation from Diffuse Gas} Nonthermal radio continuum emission is used to probe the population of cosmic ray electrons. These cosmic ray electrons may interact with the reservoir of molecular gas distributed in the Galactic center. An accurate measure of the cosmic ray flux traced at radio wavelengths is critical to investigate the origin of $\gamma$-ray and X-ray emission in the context of bremsstrahlung emission. We first discuss radio measurements of the Galactic center to estimate the total nonthermal radio flux, followed by the analysis of $\gamma$-ray data from $Fermi$. \subsection{The Separation of Thermal and Nonthermal Radio Emission} The distribution of relativistic electrons is traced by synchrotron continuum emission at low radio frequencies. However, the large scale study of radio continuum emission from the inner two hundred parsecs of the Galaxy shows that the diffuse component is due to a mixture of thermal and nonthermal emission (e.g., Law et al. 2008). Thus, it is difficult to separate these two components spatially as their emission overlaps at radio wavelengths. Even more challenging is that some of the diffuse and extended sources have a spectral index, $\alpha$, where the flux density F$_{\nu} \propto \nu^{-\alpha}$, that is flatter or harder than $\alpha$=0.5 (p=$2\alpha$+1=2 corresponding to energy spectrum E$^{-p}$). Apart from the large-scale diffuse nonthermal emission on a scale of several degrees (LaRosa et al. 2005; Crocker et al. 2010), there are several discrete sources of nonthermal emission. One is the population of nonthermal filamentary structures found throughout this region. These synchrotron filaments can be as long as $>15'$ (or 36 parsecs at the 8 kpc distance to the Galactic center), and narrow ($\approx5-10''$ corresponding to 0.2-0.4 pc). Polarization studies of the filaments trace an organized magnetic field which runs perpendicular to the Galactic plane (Yusef-Zadeh, Morris and Chance 1984; Lang, Goss \& Morris 2002; Nord et al. 2004). Nonthermal emission also arises from supernova remnants in the Galactic center, some of which are interacting with molecular clouds, such as Sgr A East (SNR G0.0-0.0, e.g. Tsuboi et al. 2011). Another source of nonthermal emission is the population of pulsars that could contribute to nonthermal emission from this region (Johnston et al. 2006; Deneva, Cordes and Lazio 2009; Wharton et al. 2011). Lastly, populations of compact stellar sources could produce nonthermal radiation from colliding winds in massive binary systems; two such examples have been detected in the Arches cluster and Sgr B2 (Yusef-Zadeh et al. 2003; Yusef-Zadeh, Wardle \& Roy 2007a). A quantitative estimate of the relative amount of thermal and nonthermal emission from the Galactic center was made by Law et al. (2008) based on radio continuum data at 5 and 8.5 GHz taken with the GBT over the region between 357.5\deg\ $ < l < $1.2\deg\, and --0.6\deg $< b < $0.4\deg\,. These authors assumed that thermal and nonthermal sources are separated from each other and identified them from the spectral index $\alpha$ values measured between 5 and 8 GHz. It was concluded that 85\% and 76\% of continuum radio flux from individual sources is due to nonthermal processes at 5 and 8 GHz, respectively. Earlier studies claimed that $\sim$50\% of the continuum emission at 5 GHz is due to nonthermal emission (Schmidt et al. 1980; Mezger and Pauls 1979). The discrepancy in the ratio of nonthermal to thermal emission could be due to the flat spectrum of some of the nonthermal sources, thus complicating the identification of thermal and nonthermal sources. LaRosa et al. (2005) studied diffuse radio continuum emission from the inner 6\degree$\times$2\degree of the Galactic center at 75 and 327 MHz. They found a strong diffuse nonthermal structure with integrated flux density of 7000 Jy at 330 MHz. The spectral index value between 330 and 74 MHz gave $\alpha > 0.7$ which is a lower limit due to thermal absorption at 74 MHz. In another study, Crocker et al. (2010) investigated the spectrum of nonthermal emission from the inner 3\degree$\times$2\degree and found a spectral break of 0.6 at 1.7 GHz. To measure the distribution of radio flux from the inner 2\deg$\times1$\deg\ of the Galactic center region, we integrated the total continuum flux at 0.325, 1.40, 8.5 and 5 GHz based on GBT observations described by Law et al. (2008) who focused only on 8.5 and 5 GHz data. A region away from the Galactic plane was selected having minimum contamination by Galactic center sources. To construct a background subtracted image, a noise map was first constructed from the region that has been mapped by GBT. The noise map and a DC offset were then subtracted from the entire image. Figure 1a shows a continuum subtracted image at 1.415 GHz from the inner $\sim5$\deg$\times$5\deg\ of the Galactic center. Prominent radio continuum sources along the Galactic equator such as Sgr A near l$\sim0$\deg\,, radio continuum Arc near l$\sim0.2$\deg\,, Sgr B near l$\sim0.7$\deg\,, Sgr C near l$\sim-0.6$\deg\,, Sgr D near l$\sim1.2$\deg\, and the bright nonthermal source the Tornado nebula near l $\sim -2.5$\deg\, show peaks in contours of 1.415 GHz emission (Yusef-Zadeh, Hewitt and Cotton 2004). The grayscale image in Figure 1b shows weak extended structures distributed away from the Galactic ridge. Extended features distributed at positive-latitudes are known as Galactic center radio lobes (e.g., Law et al. 2008). There are also large-scale features at negative latitudes near l $=-0.9$\deg\, extending to b $\sim-1$\deg\, associated with two supernova remnants G359.1-0.5 and G359.0-0.9 (Reich 1982; Reich and Reich 1986). A new feature, G359.02+0.27, is a long vertical structure running perpendicular to the plane extending toward more negative latitudes near b$\sim-1.6$\deg\, between l $\sim-0.075$\deg\, and l$\sim$0.27\deg. We measured the flux from the brightest region of the maps at four different frequencies all based on GBT observations and presented the flux in Table 1. The first two columns of this table show the frequency and integrated flux from the inner 2\deg$\times$0.85\deg\ of the Galactic center. The DC offset and the RMS noise per beam, measured from blank regions of individual images of the survey, are listed in the last two columns, respectively. To illustrate the distribution of flux as a function of radius from the Galactic center, we made azimuthally averaged radial profiles of radio emission at all four frequencies, as shown in Figure 2a-d. We used MIRIAD task {\tt ellint} to integrate elliptical annuli with an aspect ratio of two centered on Sgr A*. The width of each annulus is one pixel corresponding to 20$''$, 30$''$, 30$''$ and 600$''$ at 8.5, 4.85, 1.415 and 0.325 GHz, respectively The RMS in Jy/beam was calculated and then scaled by the square root of the number of beams in each annulus. These plots show considerable flux variations as a function of frequency, suggesting that thermal and nonthermal features dominate the total observed flux at high and low frequencies, respectively. To estimate the contribution of thermal and nonthermal emission, we use the integrated flux to derive spectral index values $\alpha^{325\rm MHz}_{1.4 \rm GHz}=0.17\pm0.01$, $\alpha^{1.4\rm GHz}_{4.5\rm GHz}=0.58\pm0.01$, $\alpha^{4.5\rm GHz}_{8.5\rm GHz}=1.14\pm0.01$. The spectral index distribution is relatively flat at low frequencies whereas it becomes steeper at high frequencies. The variation of the spectral index is consistent with thermal emission from HII regions ($F_{\nu}\propto\nu^{-0.1}$) which becomes optically thick (F$_{\nu}\propto\nu^{2}$) at low frequencies. The flattening of the spectral index between 325 MHz and 1.415 GHz could result from the decrease of thermal flux due to free-free absorption of thermal gas that becomes opaque at low frequencies. The true percentage of thermal and nonthermal emission from the complex region of the inner 2\deg$\times$0.85\deg\, is very difficult to measure directly. In order to separate the intrinsic flux of thermal and nonthermal emission, we assumed that the two components are spatially mixed with or separate from each other following Gregory and Seaquist (1974). In this case, the observed flux in this model is given by $$ S_\nu = \Omega \left(S_{NT} \exp(-\tau_\nu) + B_\nu(T)\right)\times (1-\exp(-\tau_\nu)) $$ where $S_{NT}$ $\propto \nu^{-\alpha}$ is the nonthermal flux in the absence of free-free absorption, $\tau_\nu$ is the free-free optical depth at frequency $\nu$, $B_{\nu}$(T) is Planck's function at the temperature T, and $\Omega$ is the solid angle subtended by the source. These calculations account for the spectral turnover at low frequencies due to opacity of diffuse thermal emission. Figure 3 shows the flux from the inner 2\deg$\times$0.85\deg\ as a function of frequency. The solid black curve represents the $\chi^2$-fit to total flux which is itself decomposed into thermal and nonthermal components, shown as long and short dashed lines, respectively. We fix the thermal contribution at 4.85 GHz to be 25\% (Law et al. 2008) and assume a kinetic temperature of 5000K. We adopt a broken power-law for the unabsorbed nonthermal emission and assume that this component lies behind the thermal emission. With this model we find $\nu^{-0.25}$ below 3.3 GHz and $\nu^{-1.7}$ above 3.3 GHz, with an unabsorbed nonthermal flux of 2450 Jy at 325 MHz. Because the optical depth is only significant below 200 MHz, there is no difference between assuming that the thermal and nonthermal components are mixed in versus having the thermal emission be a foreground screen. Using a 25\% contribution from thermal emission at 8.5 GHz (Law et al. 2008) corresponds to an emission measure $E\sim$10$^{4}$ cm$^{-6}$ pc. This gives average electron density $n_e\sim$6 cm$^{-3}$ assuming that it is uniformly distributed over $L\sim$288 pc. The study of the cosmic rays in the Galactic disk has recently suggested a need for a low-energy break in the spectrum of cosmic ray electrons (Strong, Orlando and Jaffe 2011), This is not dissimilar to the spectral break that we infer from the cosmic ray electrons in the Galactic center. An unusual aspect of the spectrum of radio emission from the Galactic center is the large change in particle distribution index $\sim$1.7. The energy spectrum of electrons corresponding to a broken power-law is hard corresponding to $p$=1.5 at low energies whereas the spectrum is steep at high energies with $p$=3.2. A non-standard possibility that can account for such a large change in the spectral index value is the contribution of electrons and positrons produced as the byproduct of dark matter annihilation. In this picture, the electrons and positrons created through the annihilation of a relatively light ($\sim$5-10 GeV) dark matter particle can provide a new population of electrons at energies less than the annihilation energy of WIMPS. Although this picture is by no means unique in explaining the large change in the spectral index, spectral distribution of electrons and positrons which emit synchrotron radiation are consistent with the observed spectral shape of electrons for individual nonthermal radio filaments at high frequencies (Linden, Hooper and Yusef-Zadeh 2011). \subsection {Gamma-ray Emission from the Galactic Center} Extended $\gamma$-ray emission within the inner 2\degree\ has been detected at TeV energies by the H.E.S.S. atmospheric Cherenkov telescope. The Galactic center ridge of $\gamma$-ray emission (hereafter, Galactic ridge) appears well correlated with the molecular gas distribution in the inner region (Aharonian et al. 2006). The Galactic center is also a prominent sources of GeV $\gamma$-rays. The {\it Compton Gamma Ray Observatory} identified a source coincident with the Galactic center, 2EG J1746--2852, at energies of 0.2-10 GeV (Thompson et al. 1995). With greatly improved sensitivity and spatial resolution, the $Fermi$ LAT resolves multiple GeV sources in the inner 2\degree\ of the Galaxy. A bright point source coincident with the position of Sgr A is reported in the LAT First and Second Source Catalogs (Abdo et al. 2010a; Nolan et al. 2012, hereafter 1FGL and 2FGL). Emission from the central source, 2FGL J1745.6--2858, shows a peak at a few GeV. Several explanations have been proposed for the GeV emission in the Galactic center detected by $Fermi$. Chernyakova et al. (2011) propose that this central gamma-ray source is produced by the diffusion of cosmic ray protons into the surrounding dense molecular gas in the inner 10 pc. A separate analysis by Hooper \& Goodenough (2011) claims the existence of a diffuse $\gamma$-ray source in the inner degree of the Galactic center, on top the the Galactic diffuse background. This emission peaks at 2-4 GeV, which they interpret as the possible annihilation of dark matter. Alternatively this feature could arise from a population of millisecond pulsars in the region (Abazajian 2011) or may be due to improperly accounting for known point sources in the region (Boyarsky, Malyshev \& Ruchaysky 2011). Interestingly, the hard spectrum of the filaments of the Arc which emit radio synchrotron radiation could be a strong source of cosmic rays responsible for the excess $\gamma$-ray emission within the inner 30\arcmin\ of the Galactic center (Linden, Hooper \& Yusef-Zadeh 2011). The Galactic center nonthermal filaments of the radio Arc are unique in the Galaxy and have a harder spectrum compared to typical nonthermal radio sources. We will argue in \S4 that the interaction of relativistic electrons with molecular gas in the Galactic center produces significant bremsstrahlung radiation, and that the distribution of diffuse $\gamma$-ray emission correlates well with the distribution of both nonthermal radio continuum emission and the 6.4 keV K$\alpha$ line emission. Here, we analyze the $\gamma$-ray emission from the Galactic center using three years of $Fermi$ LAT data, in order to characterize emission from both the central $gamma$-ray source, as well as nonthermal emission from the Galactic ridge. \subsubsection {$Fermi$ LAT Observations} $Fermi$ LAT detects $\gamma$-rays between $\sim$20 MeV to $>$300 GeV in an all-sky scanning mode, observing the entire sky every $\sim$3 hours (Atwood et al. 2009). Events are detected by the LAT tracker in both the "front" and "back" sections, which are combined in this analysis. Events were selected within a radius of interest of 30 degrees from the Galactic center, and for times between 2008 August 4 and 2011 August 4, and at energies between 1 GeV and 100 GeV. The angular resolution (68\%\ containment angle for events at incident angle) is $\sim$0\ddeg9 at 1 GeV, increasing to 0\ddeg2 at the highest energies. The point spread function is detailed on the Fermi Science Support Center (FSSC) webpage\footnote{http://fermi.gsfc.nasa.gov/ssc/data/analysis/documentation/Cicerone/Cicerone\_LAT\_IRFs/IRF\_PSF.html}. The energy resolution of the LAT is 8--10\%\ between 100 MeV and 100 GeV. The systematic uncertainties in the IRF are energy dependent: 8\% at 100 MeV, 5\% at 560 MeV, 10\% at 10 GeV\footnote{http://fermi.gsfc.nasa.gov/ssc/data/analysis/LAT\_caveats.html}. Data is analyzed using the $Fermi$ Science Tools (v9r15p2) with the "P7SOURCE\_V6" instrument response functions. Only source class events with Earth zenith angles less than 100$\degree$ have been used to reduce contamination from the Earth limb. We use the standard maximum likelihood fitting, with photons binned in 0.05 degree pixels within a 10\deg$\times$10\deg\ region centered on Sgr A. Data is also binned spectrally with 4 log-normal bins per decade in energy between 1 and 100 GeV. We restrict our analysis only to these high energies at which the PSF of the LAT is sufficient to spatially resolve sources within the central 2$\times$1\degree\ region. For source modeling we include all sources in the 2FGL source catalog (Nolan et al. 2012). Additionally, we include the standard isotropic model which accounts for the extragalactic diffuse background and residual instrumental background ('iso\_p7v6source.txt') and Galactic diffuse model which accounts for interactions between cosmic rays and the Galactic interstellar medium and photon field ('gal\_2yearp7v6\_v0.fits'). The Galactic diffuse model\footnote{Details are available at the FSSC: http://fermi.gsfc.nasa.gov/ssc/data/access/lat/Model\_details/Pass7\_galactic.html} is derived from a fit to 2 years of LAT data using Galacto-centric rings derived from tracers of the interstellar gas distribution (HI and CO) and a model of inverse Compton emission calculated using GALPROP (Strong, Moskalenko \& Reimer 2004). To estimate the systematic uncertainty from the diffuse model, we change the best-fit normalization of the diffuse components by $\pm$6\%, following the method used for analysis of unresolved or small-scale sources, such as Galactic supernova remnants (Abdo et al. 2010b). This value was determined by using different versions of the Galactic diffuse emission generated by GALPROP (Strong et al. 2004) to compare the gamma-ray intensity of nearby source-free regions of the Galactic plane with that expected from the models (Abdo et al. 2010b). We note that use of the Galactic diffuse model is only appropriate for analysis of small diameter sources, and has been employed for other extended GeV sources as large as a few degrees in extension. An additional source of uncertainty arises as we must assume a morphology for GeV emission from the inner $\sim$2\degree\ of the Galaxy in our likelihood fit. Figure 4a shows a smoothed counts map at $\ge$1 GeV, after subtraction of the isotropic and Galactic diffuse templates. Prominent emission is seen from the vicinity of Sgr A, with fainter emission extending along the Galactic plane. Additionally, there are point sources which lie off the plane of the Galaxy, and a faint complex of emission coincident with TeV source H.E.S.S. J1745-303. For comparison with the distribution of nonthermal emission from the same region, Figure 4b shows the positions of 2FGL sources superimposed on 20cm radio continuum emission observed by the GBT. Ellipses indicate the 68\%\ error in the source localization. These sources are listed in Table 2, and are described in the following section. The 2FGL catalog decomposes emission above the Galactic diffuse model as individual point sources, however we also test the hypothesis that the emission arises from an extended component along the Galactic ridge. To obtain the best possible model of the emission, we relocalize the positions of all 2FGL point sources in the inner 2 degrees and refit their spectra using only $>$1 GeV data. We search for un-modeled point sources by creating test statistic maps of the residual emission. The test statistic is a measure of the significance of adding a source to a model, defined as TS = 2 log($\mathcal{L}_1$/$\mathcal{L}_0$) where $\mathcal{L}$ is the Poisson likelihood, and the subscripts 0 and 1 refer to the original model and a model with an additional source, respectively. Within 2\deg\ of the Galactic center, we find two significant sources with TS $>$ 25 that are not listed in 2FGL. A source is found near the location of Sgr C, $\alpha$,$\delta$(J2000) = 266.044,-29.323, previously identified as 1FGL J1744.0-2931c. Another source is found 0.5 degrees away from the Galactic ridge at positive latitudes, $\alpha$,$\delta$(J2000) = 265.005,-28.533, and has a very soft spectrum, $\Gamma$=2.9$\pm$0.2, above 1 GeV. Adding these two additional sources improved the model of GeV emission, as shown in Table 2. We refer to this model as the "2FGL refit" model, hereafter. Sources are initially assumed to have a power-law spectrum. For highly significant sources we attempted to replace a simple power-law spectral model with a broken power-law model of the form: \begin{equation} \frac{dN}{dE} = N_0 \times \left \{ \begin{array}{l l} (E/E_b)^{\Gamma_1} & if E < E_b \\ (E/E_b)^{\Gamma_2} & if E > E_b\end{array} \right \} \end{equation} For Sgr A* we find a broken power-law improves the fit. The best fit spectral parameters are $\Gamma_1$=1.9, $\Gamma_2$=3.0, and E$_b$=3 GeV. \subsubsection{Point Sources in the Inner Galaxy} We briefly summarize point sources detected in the inner 2\degree . Source 2FGL J1745.6-2858 corresponds to the position of Sgr A*. This source has been studied in detail by Chernyakova et al. (2011) and Linden, Lovegrove \& Profumo (2012). The $Fermi$ LAT spectrum connects to that of the detected H.E.S.S. TeV source at $\sim$100 GeV, with a softening of the spectrum between 1-100 GeV, and a hardening of the spectrum at $>$100 GeV to multi-TeV energies. In addition to emission from Sgr A*, there are two point sources corresponding to the locations of the Arc and Sgr B (sources 2FGL J1746.6-2851c and J1747.3-2825c, respectively). Faint emission was reported in the vicinity of Sgr C in 1FGL, but the source was not present in 2FGL. We note these three point sources closest to the Galactic center (corresponding with the Arc, Sgr B and Sgr C) appear coincident with the diffuse emission detected at TeV energies by H.E.S.S. We explore this further in the following section. Other sources are also present within the inner 2\deg\ that are not thought to be associated with the Galactic center region. The Mouse pulsar corresponds to source 2FGL J1747.1-3000, with detected $\gamma$-ray pulsations. However, this pulsar is known to lie at a distance of only 5 kpc (Camilo, et al. 2002). Two sources (2FGL J1743.9-3039c and J1745.5-3028c) appear to be counterparts to the extended TeV source H.E.S.S. J1745-303. These sources may be related to the SNR G359.1-0.5, known to be interacting with molecular clouds, or may be candidate pulsar wind nebulae (Aharonian et al. 2008). In either case these sources lie outside the Galactic ridge. There are also three sources detected more than half a degree off the Galactic plane, with no readily apparent counterparts (2FGL J1738.9-2908, J1748.6-2913, J1754.1-2930). Similarly, the newly detected source ``bkgA" also lies above the Galactic plane, and has no apparent multiwavelength counterpart. The off-plane GeV sources show no correlation with the diffuse background model, or large scale structures seen towards the Galactic center, and are therefore unlikely to have any relation to the Galactic ridge. \subsubsection{Emission from the Galactic Ridge} To probe whether GeV emission is present on extended spatial scales we replace the three point sources associated with the Arc, Sgr B and Sgr C, with an extended spatial template. We then maximize the likelihood using the extended spatial template plus a point source which accounts for emission from Sgr A. We separately apply four template models: 20cm radio continuum, X-ray FeI K$\alpha$ line emission, H.E.S.S. diffuse TeV emission, and CS 1--0 integrated line intensity representing the distribution of dense gas in the region. All templates span roughly the inner 2\deg$\times$1\deg . In the 20cm and H.E.S.S. templates, the central emission from Sgr A* is removed, as it is clearly detected as a point source with a unique spectrum. Fitting the spatial templates from other wavelengths gives a means of comparing them with the morphology of GeV emission from the Galactic ridge above the modeled Galactic diffuse. First, we add an extended spatial template using the CS 1--0 map (Tsuboi, Handa \& Ukita 1999). As CS is an optically thin tracer of dense gas, this model probes the distribution of dense clouds in the Galactic center region. However, we find replacing the three point sources with the CS template results in a significantly lower global likelihood than the point source model. This is likely due to the fact that CS emission is detected at Galactic longitudes$>$1\degree\ while TeV and GeV emission do not appear to extend this far from the Galactic center. We do find an improved fit when the point sources in the Galactic ridge are replaced by other spatial templates representing the distribution of X-ray FeI K$\alpha$ line, H.E.S.S. TeV and diffuse 20cm radio emission. The X-ray data that we used are based on Chandra observations (Yusef-Zadeh et al. 2007b). Table 3 presents the 6 models which we fit to the LAT data. The 2FGL point source models have 12 degrees of freedom (Sgr A with a broken power-law, three point sources with power-law spectra, and the isotropic and Galactic diffuse normalizations). The extended models require 4 fewer degrees of freedom since the three point sources are replaced by one source. We note that the TeV and radio templates provide a better fit to the data than the X-ray line template, though this may be due to non-uniform sensitivity of the X-ray observations. We conclude that the GeV emission from the Galactic ridge is well-correlated with the extended morphologies observed at radio, TeV and X-ray wavelengths. We note that the Galactic ridge emission has sufficient statistics to fit with a broken power-law spectral model. Using the TeV template, we find the best fit spectral parameters are $\Gamma_1$=1.8, $\Gamma_2$=3.0, and E$_b$=2.5 GeV. However, we caution that despite the improvement in the likelihood, the spatial template and point source models are not nested, so a significance of the improvement of the extended templates over the point source model cannot be stated. We also note that while simply increasing or decreasing the normalization of the diffuse Galactic model cannot fit the emission observed by the LAT in the Galactic ridge, we have not performed an in-depth study of the diffuse emission for the Galaxy. However, that the GeV emission is consistent with the morphology of extended nonthermal emission observed at other wavelengths is suggestive of a common origin. We discuss in detail a plausible model for nonthermal emission from the Galactic ridge in \S4. \begin{deluxetable}{lrrr} \tablewidth{0pt} \tablecaption{Integrated Radio Flux from the Inner 2\degree$\times$0.85\degree} \tablehead{ \colhead{Frequency (Hz)}& \colhead{Flux$\pm\sigma$ (Jy)} & \colhead{DC Offset (Jy)} & \colhead{RMS Noise (Jy/beam)} } \startdata 3.25$\times10^8$ & 3.57$\times10^3\pm10.1$ & 127 & 5.8\\ 1.41$\times10^9$ & 2.77$\times10^3\pm1.1$ & 8.1 & 1.3$\times10^{-1}$ \\ 4.85$\times10^9$ & 1.35$\times10^3\pm0.6$ & 1.44$\times10^{-2}$ & 2$\times10^{-2}$ \\ 8.5$\times10^9$ & 7.11$\times10^2\pm0.8$ & 1.2$\times10^{-2}$ & 1.5$\times10^{-2}$ \enddata \label{tab:fitparams} \end{deluxetable} \begin{deluxetable}{lllrrrl} \tablecaption{Detected $\gamma$-ray Sources in the Inner 2\degree\ of the Galaxy \label{tbl:2fgl}} \tabletypesize{\small} \tablewidth{0pt} \tablehead{ \colhead{Name} & \colhead{RA} & \colhead{Dec} & \colhead{Flux (1--100 GeV)} &\colhead{TS} &\colhead{Association} \\ &h\, m\, s & $^0\,\,\, '\,\,\, ''$ & \colhead{(10$^{-9}$ ph cm$^{-2}$ s$^{-1}$)} & } \startdata 2FGL J1745.6-2858& 17 45 41.6& -28 58 43& 77.3(2.0)& 1857& Sgr A \\ 2FGL J1746.6-2851c& 17 46 40.6& -28 51 31& 6.6(1.4)& 35 & the Arc \\ 2FGL J1747.3-2825c& 17 47 23.9& -28 25 53& 14.2(1.4)& 112 & Sgr B \\ 1FGL J1744.0-2931c& 17 44 01.0& -29 31 57& 10.0(1.4)& 79& Sgr C \\ 2FGL J1747.1-3000& 17 47 09.2& -30 00 50& 25.0(1.1)& 729& PSR J1747-2958 \\ 2FGL J1745.5-3028c& 17 45 32.4& -30 28 56& 4.3(0.9)& 26 & H.E.S.S. J1745-303\\ 2FGL J1743.9-3039c& 17 43 57.3& -30 39 13& 3.7(0.8)& 25 & H.E.S.S. J1745-303\\ 2FGL J1748.6-2913& 17 48 39.2& -29 13 53& 12.0(1.0) & 169& \\ 2FGL J1738.9-2908& 17 38 56.7& -29 08 25& 6.8(0.8)& 234& \\ 2FGL J1754.1-2930& 17 54 08.9& -29 30 33& 3.6(0.5)& 83 \\ bkgA & 17 40 01.2& -28 31 59& 3.6(0.7)& 45 & \enddata \end{deluxetable} \begin{deluxetable}{lrrrr} \tablecaption{Comparison of Spatial Template Fits to Fermi LAT Data $\ge$1 GeV \label{tbl:spatialmaps} } \tablewidth{0pt} \tablehead{ \colhead{Model} & \colhead{2 log($\mathcal{L}_1/\mathcal{L}_0$)} & \colhead{$d.o.f.$} & } \startdata 2FGL & 0 & 12 \\ % 2FGL refit & 51 & 12 \\ % X-ray Fe K$\alpha$ & 68 & 8 \\ % H.E.S.S. residual & 101 & 8 \\ % 20cm Radio big & 113 & 8 \\ % CS gas &--103 & 8 \\ % \enddata \end{deluxetable} \subsection {X-Ray Emission from the Galactic Center} \subsubsection{Chandra Data} The results of large-scale Chandra observations of the Galactic center focusing on the distribution of FeI K$\alpha$ line emission were described in Yusef-Zadeh et al. (2007b). Since the publication of these results in 2007, additional Chandra observations of this region have been carried out. Here, we use 15 additional pointings with exposure time of 40 ks each. These new observations are combined with additional archived data sets described in detail by Muno et al. (2009) who presented a catalog of X-ray sources in the inner 2\deg$\times0.8$\deg\ of the Galactic center. We reproduce below the description of data reductions that were given for earlier analysis of 6.4 keV line emission (Yusef-Zadeh et al. 2007b). Images of the equivalent widths of the low-ionization 6.4 keV line of FeI K$\alpha$ were constructed using the techniques described by Park et al. (2002, 2004). Adaptively-smoothed images of the diffuse line emission were generated in the same manner as the continuum image, using the 6.25--6.50 keV band for FeI K$\alpha$. The continuum under each line was computed based on adaptively-smoothed images of the flux in the 5.0--6.1 keV and 7.15--7.30 keV energy bands. We assumed that the flux in each continuum band ($F_{\rm band}$) could be described as a power-law, so that the normalization ($N$) and slope ($\Gamma$) of the power-law could be computed from \begin{equation} F_{\rm band} = {{NE_{\rm low}^{-\Gamma+1} - NE_{\rm high}^{-\Gamma+1}}\over{\Gamma - 1}}. \end{equation} Using the fluxes in both continuum bands, the above equation was solved for $N$ and $\Gamma$ using Newton's algorithm and the parameters were used to estimate the continuum contribution to the line emission images. To derive the equivalent width (EW) images we subtracted the estimated total continuum flux from the line image, and then divided the line image by the continuum flux density at the centroid of the line (6.4 keV). We caution that we have neglected the cosmic-ray background in generating these maps, which could account for as much as $\sim$40\% of the events in the 6--7 keV band and consequently biases any estimate of the EW. The assumption of a power-law spectrum, instead of multiple plasma temperatures especially corresponding to the He-like K$\alpha$ line at 6.7 keV also introduces a small systematic bias in these maps. From Figure 5 in Muno et al. (2004), the nonthermal X-ray flux is estimated to be about one-third of the continuum flux at the FeI K$\alpha$ line band. We have not attempted to correct these effects because they are only used to search for regions of enhanced iron emission. In order to confirm the properties suggested by Chandra images of the diffuse line and continuum emission, we compared the Chandra EW map with that constructed from Suzaku measurements. \subsubsection{Suzaku Data} To check the accuracy of the EW map measured from Chandra observations, we derived the distribution of Fe I K$\alpha$ line emission and EW map using the Suzaku data. The details of the Suzaku observations are shown in table 1 of Uchiyama et al. (2011), which partially covers the region between $-3^{\circ}<l<2^{\circ}$ and $-1^{\circ}<b<1^{\circ}$. We made X-ray images in the energy bands of 5--6 and 7--8 keV for continuum emissions and 6.3--6.5 keV for Fe I K$\alpha$. We sorted non X-ray background (NXB) data by the cut-off rigidity with {\tt xisnxbegen} (Tawa et al. 2008) and made NXB images in the foregoing energy ranges for the respective observations. The NXB images are subtracted from the X-ray images. Thus, in the case of the Suzaku image, the effects of the NXB are removed with an uncertainty of less than $\sim$4\% (Tawa et al. 2008). After the NXB subtraction, the vignetting effects of the X-ray images are corrected with {\tt xissim} (Ishisaki et al. 2007). Both of {\tt xisnxbegen} and {\tt xissim} are include in the HEASoft package\footnote{http://heasarc.nasa.gov/lheasoft/}. We calculated the continuum flux in the 6.3--6.5 keV band from the 5--6 and 7--8 keV band images, following a similar technique that was applied to Chandra data. We subtracted the calculated continuum image from the 6.3--6.5 keV band image and obtained the Fe I K$\alpha$ line emission map. The Fe I K$\alpha$ line emission map was divided by the continuum image before the EW map was constructed. Bright point sources, 2E 1743.1-2842, 2E 1742.9-2929 and 2E 1740.7-2943 are masked by circles with the radius of 3\ddeg5. We ignored the cosmic X-ray background (CXB) when we made the EW map. It is because that the interstellar absorption of the CXB is difficult to estimate. Assuming the CXB flux of Kushino et al. (2002), the systematic errors of the EW in Figure 9 are estimated to be less than 20\%.
|
We have explored different aspects of diffuse emission from the Galactic center in the context of cosmic ray electrons interaction with Galactic center clouds. We began by presenting $\gamma$-ray observations and data reductions using $Fermi$ LAT, followed studying the relativistic and the nonrelativistic components of nonthermal particles in the interstellar medium of the Galactic center. We presented nonthermal radio flux over the inner 2\degree$\times1$\degree of the Galactic center at four different radio frequencies. We used the reservoir of relativistic and non-relativistic cosmic rays electrons in the Galactic center region as seed particles interacting with neutral gas to determine cosmic ray ionization rate, molecular gas heating rate, the production of K$\alpha$ line and diffuse X-ray and $\gamma$-ray emission. The origin of high energy X-ray and $\gamma$-ray emission was explained in the context of bremsstrahlung mechanism, as had previously been used to explain the origin of 6.4 keV line emission from neutral iron. In addition, we investigated the time variability of low energy cosmic ray flux by discussing that the cosmic ray flux should vary on a short time scale because of ionization losses of electrons diffusing through a molecular cloud. The ionization losses of electrons are particularly dramatic at 100 keV which could diffuse for roughly ten years in a medium with molecular density of 100 cm$^{-3}$ before they lose most of their energy. Assuming that diffusion of low energy cosmic ray particles is not hindered by magnetic field fluctuations in molecular clouds, the fluorescent 6.4 keV line emission was predicted to vary on such a time scale unless there is constant acceleration of particles at these energies. Future studies will determine the importance of cosmic ray irradiation model for individual Galactic center molecular clouds when compared to that of the X-ray irradiation model. Another characteristic that can place constraints on the applicability of these two models is to study the chemistry of the cosmic ray dominated region of the central molecular zone. In summary, we explained the origin of $\gamma$-ray emission based on $Fermi$ and the H.E.S.S. observations. The mechanism for production of $\gamma$-ray emission is similar to that invoked to explain the production of K$\alpha$ line emission except that high energy particles are involved for production of bremsstrahlung $\gamma$-ray radiation. Another byproduct of the impact of cosmic rays with gas clouds is ionization losses suffered by interacting electrons with gas particles. The estimate of the ionization rate was compared with that measured from H$_3^+$ absorption lines. Lastly, cosmic rays heat molecular gas, increasing the temperature and ionization fraction of molecular gas. The required cosmic ray heating rate was estimated to explain an increasing molecular gas temperature in the Galactic center region. These physical processes placed constraints on the strength of the magnetic field, the cosmic ray ionization rate and cosmic ray heating rate of molecular gas in the inner region of the Galaxy. Observed synchrotron emission from the Galactic center at radio wavelengths indicated a magnetic field of $\sim15\mu$G and a large population of relativistic GeV electrons. The interaction of these electrons with neutral gas explained the GeV emission observed with $Fermi$. We were also able to explain the origin of the TeV emission and the FeI K$\alpha$ line emission at 6.4 keV which required high cosmic ray ionization rate with some uncertainties related to the extrapolation of the electron spectrum to 10 keV and TeV energies.
| 12 | 6 |
1206.6882
|
1206
|
1206.3469_arXiv.txt
|
{The presence of two stellar populations in the Milky Way bulge have been reported recently, based on observations of giant and dwarf stars in the inner an intermediate bulge.} {We aim at studying the abundances and kinematics of stars in the outer Galactic bulge, thereby providing additional constraints on formation models of the bulge.} {Spectra of 401 red giant stars in a field at $(l,b)=(0\degr,-10\degr)$ were obtained with the FLAMES-GIRAFFE spectrograph at the VLT. Stars of luminosities down to below the two bulge red clumps are included in the data set. From these spectra we measure general metallicities, abundances of iron and the $\alpha$-elements, and radial velocities of the stars. The abundances are derived from an interpolation and fitting procedure within a grid of COMARCS model atmospheres and spectra. These measurements as well as photometric data are compared to simulations with the Besan\c{c}on and TRILEGAL models of the Galaxy.} {We confirm the presence of two populations among our sample stars: i) a metal-rich one at $[{\rm M}/{\rm H}]\sim+0.3$, comprising about 30\% of the sample, with low velocity dispersion and low $\alpha$-abundance, and ii) a metal-poor population at $[{\rm M}/{\rm H}]\sim-0.6$ with high velocity dispersion and high $\alpha$-abundance. The metallicity difference between the two populations, a systematically and statistically robust figure, is ${\Delta}[{\rm M}/{\rm H}]=0.87\pm0.03$. The metal-rich population could be connected to the Galactic bar. We identify this population as the carrier of the double red clump feature. We do not find a significant difference in metallicity or radial velocity between the two red clumps, a small difference in metallicity being probably due to a selection effect and contamination by the metal-poor population. The velocity dispersion agrees well with predictions of the Besan\c{c}on Galaxy model, but the metallicity of the ``thick bulge'' model component should be shifted to lower metallicity by 0.2 to 0.3\,dex to well reproduce the observations. We present evidence that the metallicity distribution function depends on the evolutionary state of the sample stars, suggesting that enhanced mass loss preferentially removes metal-rich stars. We also confirm the decrease of $\alpha$-element over-abundance with increasing metallicity.} {Our sample is consistent with the existence of two populations, one being a metal-rich bar, the second one being more like a metal-poor classical bulge with larger velocity dispersion.}
|
The bulge of the Milky Way galaxy is such a complex system that its formation and evolution is still poorly understood. There exist two main scenarios for the \object{Galactic bulge} (GB) formation. The first one, called the ``classical'' scenario, describes the bulge formation through initial collapse of gas at early times \citep{Egg62} or through hierarchical merging of sub-clumps \citep{Nog99,Agu01}. In the monolithic collapse case the bulge formed {\em before} the disc and the star-formation time-scale was very short \citep[$\sim0.5$\,Gyr;][]{Tho05}. The resulting stars are old ($\gtrsim10$\,Gyr) and have enhancements of $\alpha$-elements relative to iron in a large range of Fe abundances, which are characteristic of classical bulges. This indicates a very fast bulge formation, where SNe\,Ia did not have time to pollute the gas with $\alpha$-element-free ejecta. In the hierarchical merging the bulge also formed before the disc but on a longer timescale \citep[of the order of a few Gyr;][]{Nog99} and therefore this approach predicts lower over-abundances of $\alpha$-elements. The second scenario, called the ``pseudo-bulge'' scenario, describes the bulge formation by the buckling of the disc, following a disc instability \citep[also called a bar;][]{Com90,Rah91,Nor96,KK04,Lia05}. In this case the bulge forms {\em after} the disc and on a much longer timescale than a classical bulge. After the bar formation the disc is heated in vertical direction \citep{CS81}, giving rise to the typical boxy/peanut shape. The bulge formed in this way will be a mixture of disc stars and stars formed in situ by gas which is likely to be well mixed by the action of the bar. In this scenario, the enhancement of the $\alpha$-elements in the bulge stars is predicted to be low, similar to that of the inner disc stars in the models. It should be noted that, in addition to the classical bulge and pseudo-bulge classifications, an alternative formation mechanism has been suggested, namely the ``clump-origin bulge''. In this scenario, first proposed by \citet{Nog98} and recently elaborated upon by \citet{IS11}, stellar clumps spontaneously form in high gas-density discy galaxies, as shown by N-body/SPH simulations, and dynamical friction drags these clumps to the centre of the galaxy where they aggregate into a bulge-like structure. The models of \citet{IS11} reproduce the observed boxy shape, rapid star formation, and vertical metallicity gradients observed in the bulge of the Milky Way. Clumpy galaxies that could be the analogues of the primordial Milky Way and that are consistent with these models have been observed in the high-redshift universe \citep{EE05,Genz11}, but also locally \citep{Elm12}. Each of these scenarios is supported by at least some of the observational constraints. The question of formation history is crucial and necessary to investigate because our Galaxy is a benchmark for understanding the formation of disc galaxies. Recently, \citet{Bab10} and \citet{Hill11} analysed large samples of red clump stars in Baade's window and three fields close to the minor axis, at $b\sim-4\degr$, $-6\degr$, and $-12\degr$, which revealed the presence of two distinct populations: a metal-poor component around $[{\rm Fe}/{\rm H}]\approx-0.3$\,dex with a broad distribution in [Fe/H], and metal-rich component centered around $[{\rm Fe}/{\rm H}]\approx+0.3$ with a small spread in metallicity. In addition, these two populations show kinematical differences: the metal-poor component is compatible with an old spheroid, whereas the metal-rich component is consistent with a bar population. Therefore, two different formation scenarios have been proposed: A rapid formation timescale for the metal-poor component, and a formation over a longer timescale driven by the evolution of the bar (pseudo-bulge) for the metal-rich component. Similarly, \citet{Bens11} find two populations in their sample of micro-lensed bulge dwarf and sub-giant stars, centred at $[{\rm Fe}/{\rm H}]\approx-0.6$ and $[{\rm Fe}/{\rm H}]\approx+0.3$, with a dearth of stars around $[{\rm Fe}/{\rm H}]=0.0$. Other observations favoured one or the other scenario, which prevented a clear picture of bulge formation to emerge. For example, \citet{Zoc08}, from the observed sample re-analysed later by \citet{Bab10}, found a clear metallicity gradient in the bulge; this was interpreted as a challenge to the scenario in which the bulge would result solely from the vertical heating of the bar. On the other hand, recent radial velocity studies \citep{How08,How09,Shen10,Kun12} find that the radial velocity dispersion ($\sigma_{\rm RV}$) of bright bulge giants is fully consistent with the pseudo-bulge scenario. In particular, \citet{Shen10} show that any classical bulge contribution cannot be larger than $\sim8$\% of the disc mass. Furthermore, recent spectroscopic studies of the abundances of the $\alpha$-elements as a function of [Fe/H] revealed that at least the metal-poor bulge stars are chemically similar to stars in the local thick disc \citep{Mel08,Alv10,Ryde10} and the inner disc at Galactocentric distances of 4 to 7\,kpc \citep{Bens10b}. A comprehensive summary of the current observational picture of the bulge structure, formation, and evolution cannot be given in this paper. Instead, we refer to the recent review by \citet{Rich11}. In any case, it is clear that the current observational evidence is not sufficient to conclusively constrain the structure and formation history of the Galactic bulge, and that more observations are required. In the past, most of the attention has been paid to the intermediate bulge, e.g.\ Baade's window toward $(l,b)=(+1\degr,-3.9\degr)$, while the outer bulge has been somewhat neglected. This may explain why an important feature such as the double red clump (RC), which becomes apparent only at $|b|\gtrsim5\degr$, was detected only recently \citep{Nat10,MZ10}. This feature is interpreted as two over-densities of bulge stars at different distances from the sun \citep{MZ10,Sai11}. It is suggested that the over-densities look like a three-dimensional X-structure \citep{MZ10}. A first spectroscopic study of stars located in the two RCs was performed by \citet{DePro10}. These authors could not discern any difference in kinematics and metal abundance between the two RCs, which is in agreement with the interpretation that the two RCs represent the same parent population at different distances from the sun. However, these studies were based on optical spectra with relatively low resolution and signal-to-noise ratio (S/N), from which only an abundance index could be measured. An investigation of the double RC at higher spectral resolution and S/N is desirable to foster these conclusions. In this Paper we present medium-resolution optical spectra of $\sim400$ bulge stars towards a field at $(l,b)=(0\degr,-10\degr)$, i.e.\ $\sim1.4$\,kpc south of the Galactic plane (assuming a bulge distance of 8.0\,kpc) in the outer part of the bulge. The spectra were obtained with the FLAMES spectrograph at the VLT in GIRAFFE multi-object mode. Our sample includes stars from the tip of the RGB to stars less luminous than the expected bump in the red giant branch (RGB) luminosity function (RGB bump), hence it also includes the two RCs. This is the first study of the two RCs with medium-resolution, high-S/N spectra. We measure from these spectra radial velocities, general metallicities, and abundances of iron and the $\alpha$-elements, and combine this information to obtain a clearer picture of the structure of the outer bulge. Furthermore, we extensively compare our results with predictions by models of the Galaxy and use these models to infer selection biases and the contamination by non-bulge stars. Recently, \citet{Rob12} presented a model where two populations co-exist in the bulge region: a bar or pseudo-bulge of high metallicity and small scale height, and a ``thick bulge'' or classical bulge with a higher scale height, lower metallicity, and higher velocity dispersion. This ``Besan\c{c}on model of the Galaxy'' (BGM) explains well the apparent gradient in metallicity that is observed along the minor axis, by a variable proportion of the two populations of different scale height. Here, we use our observed sample as a test case for the new version of the BGM. The paper is structured in the following way: The sample selection and the observations are presented in Sect.~\ref{SampleObs}; the analysis of the data with the help of COMARCS atmospheric models and spectral synthesis techniques, as well as with the Besan\c{c}on and TRILEGAL models of the Galaxy, is introduced in Sect.~\ref{analysis}; Sect.~\ref{results} presents and discusses our results on the radial velocities, metallicities, and $\alpha$-element abundances; in Sect.~\ref{compCMD}, a comparison of the Galaxy models with 2MASS photometry is done; finally, conclusions are drawn in Sect.~\ref{conclusio}.
|
We presented an analysis of spectra of $\sim400$ red giant stars towards a field at $(l,b)=(0\degr,-10\degr)$. From these spectra, we derive metallicities, iron and $\alpha$-element abundances, and radial velocities. It is the first study that presents a homogeneous analysis of stars on the upper and lower RGB of the Galactic bulge. These data, as well as photometric data from the 2MASS survey, are compared to predictions by the TRILEGAL \citep{Gir05} and Besan\c{c}on \citep{Rob12} models of the Galaxy. These models are also used extensively to interpret our observations. The mean metallicity of the whole sample is $[{\rm M}/{\rm H}]=-0.34$, and the radial velocity dispersion is $\sigma_{\rm RV}\sim76$\,km\,s$^{-1}$. In this study we confirm the presence of two sub-populations in the bulge at peak metallicities that differ by $\sim0.9$\,dex. The peak metallicities are found at $[{\rm M}/{\rm H}]\sim-0.6$ and $\sim+0.3$, with roughly equal dispersions. The sub-populations have significantly different kinematics and $\alpha$-element abundances: the metal-rich population has a narrow velocity distribution ($\sigma_{\rm RV}\sim50$\,km\,s$^{-1}$) and low $\alpha$-abundances, whereas the metal-poor one has a broad distribution in radial velocities ($\sigma_{\rm RV}\sim90$\,km\,s$^{-1}$) and high $\alpha$-abundances. The metal-rich population makes up $\sim30$\% of our sample. This confirms and fosters recent results by \citet{Bab10}, \citet{Bens11}, and \citet{Hill11} in most aspects. Also the kinematic models of \citet{Zhao96} and \citet{Fux99} are confronted with our data, and good agreement is found. Furthermore, we find support for the suggestion by \citet{Bab10} that the ratio in number of these two sub-populations is a function of angular distance from the Galactic plane, which explains the observed metallicity gradient. The new scheme in the Besan\c{c}on Galaxy model explains well the features seen in this sample, with two populations, a flaring metal-rich bar and a more metal-poor classical or thick bulge, even though the mean metallicity of this thick bulge should be adjusted downward by 0.2 to 0.3\,dex. The metallicity distribution simulated with the TRILEGAL model yields a clearly too high mean metallicity to fit our observations. This study also presents the first medium-resolution, high-S/N spectra of stars belonging to the two red clumps of the bulge. A small difference in mean metallicity between the two RCs is attributed to selection effects. We find that the double RC might be entirely due to the metal-rich sub-population. The kinematic difference between the two RCs when measured with radial velocities alone is at most very small. Some difference in the mean radial velocity of bright and faint metal-rich RC stars is found, although a still larger sample would be needed to confirm that stars on the far side preferentially move faster towards us than the ones on the near side. We also find indications that the metallicity distribution function of the bulge might depend on the evolutionary state of the considered sample stars. In particular, there are fewer metal-rich stars present among the brighter, more evolved stars in our sample. Although this result could be a consequence of selection bias or the still limited number of stars in our sample, we interpret this as the result of strong mass loss that causes the most metal-rich stars to terminate their evolution before the most advanced states. A very robust indication for that comes from the fact that AGB stars and PN in the outer bulge have a velocity dispersion that agrees with that of the metal-poor population identified here, but clearly disagrees with that of the metal-rich population. We conclude, hence, that metal-rich stars might lose so much mass that they skip phases of post-main-sequence stellar evolution. This means that the selection of M giants in the BRAVA survey could be biased towards metal-poor stars. We also confirm the trend of decreasing $\alpha$-element over-abundance with increasing iron abundance, as found in previous studies \citep[e.g.][]{Gon11a}. Our study also provides for an explanation how the existence of a dual bulge identified here and elsewhere can be reconciled with kinematic studies that conclude that the Milky Way bulge might be a pure pseudo-bulge \citep[e.g.][]{Shen10}. In our version of the Besan\c{c}on model, the (thick or classical) bulge population has only 4\% the mass of the bar, even when its contribution is significant when one moves away from the plane. Thus it is compatible with the result of \citet{Shen10}, which finds that the fraction of the classical bulge cannot be more than 8\% of the disk mass. The pseudo-bulge dominates, but there is some space for a classical bulge, which we see in the data.
| 12 | 6 |
1206.3469
|
1206
|
1206.3972_arXiv.txt
|
``Propellers'' are features in Saturn's A ring associated with moonlets that open partial gaps. They exhibit non-Keplerian motion \citep{tiscareno10}; the longitude residuals of the best-observed propeller, ``Bl\'{e}riot,'' appear consistent with a sinusoid of period $\sim$4~years. \cite{pan10} proposed that propeller moonlets librate in ``frog resonances'' with co-orbiting ring material. By analogy with the restricted three-body problem, they treated the co-orbital material as stationary in the rotating frame and neglected non-co-orbital material. Here we use simple numerical experiments to extend the frog model, including feedback due to the gap's motion, and drag associated with the Lindblad disk torques that cause Type I migration. Because the moonlet creates the gap, we expect the gap centroid to track the moonlet, but only after a time delay $\tdiff$, the time for a ring particle to travel from conjunction with the moonlet to the end of the gap. We find that frog librations can persist only if $\tdiff$ exceeds the frog libration period $\Plib$, and if damping from Lindblad torques balances driving from co-orbital torques. If $\tdiff \ll \Plib$, then the libration amplitude damps to zero. In the case of Bl\'{e}riot, the frog resonance model can reproduce the observed libration period $\Plib \simeq 4$ yr. However, our simple feedback prescription suggests that Bl\'{e}riot's $\tdiff \sim 0.01 \Plib$, which is inconsistent with the observed libration amplitude of 260~km. We urge more accurate treatments of feedback to test the assumptions of our toy models.
|
\label{sec:introduction} ``Propellers'' observed by the {\em Cassini} spacecraft in Saturn's A ring appear as S-like features superimposed on azimuthally long and radially narrow gaps \citep{tiscarenoetal06,srem07,tiscarenoetal08,tiscareno10}. Each propeller is believed to trace a moonlet several hundred meters in size which gravitationally repels nearby ring particles, creating an underdense gap in the moonlet's immediate vicinity, as well as overdensities at radii just outside the gap. Because of Keplerian shear, these density perturbations propagate toward greater longitudes inside the moonlet's orbit and smaller longitudes outside, producing two lobes separated by a few Hill spheres of the moonlet \citep{sei05,lewis09}. The gap's azimuthal length is set by the moonlet mass and the time for ring particles to diffuse back into the gap via particle-particle interactions \citep{spahn00,srem02,sei05,lewis09}. Propellers in the outer A ring exhibit non-Keplerian motion \citep{tiscareno10}. In particular, the longitude residuals of the propeller ``Bl\'{e}riot,'' observed 89 times over 4.2~years, show variations consistent with a sine wave of half-amplitude 260~km and period 3.68~years. The longitude residuals imply semimajor axis variations of order 100~m. These data constrain the underlying mechanism. The variations' smooth sinusoidal character suggests that this mechanism is not stochastic on timescales shorter than a few years. Secular interactions with the Saturnian moons, rings, or equatorial bulge have timescales typically much longer than a few years; in any case, secular interactions cannot induce semimajor axis changes. Finally, no other Saturnian moon appears to occupy a mean motion resonance with Bl\'{e}riot \citep{tiscareno10}. Pan \& Chiang (2010, hereafter PC) proposed that Bl\'eriot's non-Keplerian motion is caused by gravitational interactions between Bl\'{e}riot's moonlet and co-orbital ring material outside the moonlet's gap. The interaction is long-range: the co-orbital mass is located thousands of Hill sphere radii away from the moonlet. The propeller moonlet and the much more massive co-orbital material participate in a 1:1 resonance reminiscent of tadpole and horseshoe orbits in the conventional restricted three-body problem. The moonlet performs what PC called ``frog'' librations within the gap. To re-cap the main ideas behind PC's analysis we give the following order-of-magnitude description of frog librations. Because our goal here is to describe the physical processes clearly, we neglect factors of order unity; we refer readers to \S\ 2 of PC for an exact treatment. We use units where Saturn has mass $M_\mathrm{Saturn}=1$, the co-orbital mass's distance from Saturn is $r_\mathrm{coorb}=1$, and Newton's constant $G$ is 1. We work in the frame co-rotating with a test particle on a circular orbit of radius 1 and (as a consequence of our unit system) angular velocity 1. The moonlet of mass $\mumoon$ opens a gap of angular size $2\phi \ll\pi$ in the co-orbital material (Figure~\ref{fig:libschematic}). The co-orbital material outside the gap has mass $\muring$. Since the co-orbital material closest to the ends of the gap interacts most strongly with the moonlet, we model the co-orbital material as two point masses, each of mass $\muend=\muring\phi/2$, fixed at longitudes $\pm\phi$. We label the moonlet's polar coordinates $(r=1+\Delta,\theta)$ where $\Delta \ll 1$ and $|\theta|\ll\phi$. The moonlet librates about the equilibrium point% \footnote{This equilibrium point is a local maximum of the gravitational potential. The moonlet can librate about this potential maximum because the Coriolis force stabilizes its motion.} between the co-orbital masses, as shown in the right-hand side of Figure~\ref{fig:libschematic}. The moonlet's motion is governed by Keplerian shear and gravitational interactions with the co-orbital masses. We derive scaling relations for the frog libration's period and radial/azimuthal aspect ratio as follows. The azimuthal length $\theta_\mathrm{max}$ of one libration is of order the moonlet's azimuthal Keplerian drift in one libration period $\Plib$. If the libration radial width is $\Delta_\mathrm{max}$, then the moonlet's drift speed is of the same order, and \begin{equation} \theta_\mathrm{max} \sim \Plib\cdot\Delta_\mathrm{max} \;\;\; . \label{eqn:drift} \end{equation} Over the libration cycle, gravitational interactions with the co-orbital masses change the moonlet's semimajor axis from $1+\Delta_\mathrm{max}$ to $1-\Delta_\mathrm{max}$. The corresponding fractional change in the moonlet's specific angular momentum is $\sim$$\Delta_\mathrm{max}$. The angular momentum changes because the (azimuthal) gravitational forces $\sim$$\pm\muend/\phi^2$ exerted by the co-orbital masses do not cancel exactly; the residual is of order $\theta/\phi$: \begin{equation} \Delta_\mathrm{max} \sim \frac{\muend}{\phi^2}\frac{\theta_\mathrm{max}}{\phi}\cdot \Plib \;\;\; . \label{eqn:kick} \end{equation} Together, Eqs.~\ref{eqn:drift} and \ref{eqn:kick} imply \begin{equation} \Plib \sim \frac{\phi^{3/2}}{\muend^{1/2}} \;\;\; , \;\;\; \frac{\Delta_\mathrm{max}}{\theta_\mathrm{max}} \sim \frac{\muend^{1/2}}{\phi^{3/2}} \;\;\; . \label{eqn:plibsim} \end{equation} These scalings match those of the exact relations in Eqs.~10 and 11 of PC, which we repeat here for reference: \begin{equation} \Plib = \frac{\pi}{\sqrt{3}}\frac{\phi^{3/2}}{\muend^{1/2}} \;\;\; , \;\;\; \frac{\Delta_\mathrm{max}}{\theta_\mathrm{max}} = \frac{4}{\sqrt{3}} \frac{\muend^{1/2}}{\phi^{3/2}} \;\;\; . \label{eqn:plib} \end{equation} Note that the coorbital mass $\mu$ used by PC equals $2\muend$ as we define it here. In a more detailed calculation with the co-orbital mass spread uniformly over the entire co-orbital region outside the gap, PC confirmed the scalings of Eq.~\ref{eqn:plibsim} and found that for parameters characteristic of Bl\'{e}riot's environment, the frog librations should indeed have a period of $\sim$4~years. \begin{figure} \begin{center} \includegraphics[scale=1]{libschematic.eps} \caption{Schematic of frog librations. The left side shows the geometric configuration of the moonlet and its co-orbital material. We use units where Saturn's mass is unity and where the orbit radius of the co-orbital ring material (dashed circle arc) is unity. The moonlet of mass $\mumoon$ located at polar coordinates $(r=1+\Delta,\theta)$ moves in its gap of angular size $2\phi$ in the co-orbital material. The portions of the co-orbital mass $\muring$ that interact most strongly with the moonlet are those within azimuth $\sim$$\phi$ of the ends of the moonlet's gap. For simplicity, we model the entire co-orbital mass as two identical point masses of mass $\muend =\muring\phi/2$ located at the gap ends. The dashed oval curve on the right represents a frog libration trajectory. \label{fig:libschematic}} \end{center} \end{figure} While the agreement between the period of the frog resonance as estimated by PC, and the period of Bl\'{e}riot's longitude variations as observed by \citet{tiscareno10} is promising, PC's treatment is incomplete. In particular, PC treated the co-orbital masses as stationary (in the co-rotating frame). This is a severe simplification. Because the moonlet creates and maintains its gap, the co-orbital material must, to some degree, follow the moonlet's position. If it follows too closely, the frog libration amplitude ($\theta$) may be unobservably small. On the other hand, if the gap ends are far enough away from the moonlet, the mass there will respond sluggishly to the moonlet's motion because of the finite time needed for particles to drift from conjunction with the moonlet to the gap ends. In this case, large-amplitude frog librations should be permitted. A self-consistent understanding of the moonlet's motion must account for how the non-Keplerian motions of the moonlet feed back into the non-Keplerian motions of the co-orbital masses. Here we investigate the behavior of frog orbits when the co-orbital masses move in response to the moonlet, and when Lindblad torques due to close encounters between the moonlet and ring particles are present. Our focus here is on conceptual clarity; from a technical standpoint, our models are, by design, crude. Many of our calculations are accurate to order-of-magnitude at best. In our equations we use ``$\sim$'' to denote a relation in which order-unity factors are ignored; ``$\simeq$'' to denote a relation in which order-unity factors are retained but some quantities remain approximate or not precisely defined; and ``='' to denote an exact relation. In Section~\ref{sec:feedback} we present a simple toy model for feedback and examine its implications for frog librations. In Section~\ref{sec:damping} we add Lindblad torques. In Section~\ref{sec:discussion} we summarize and comment on the results of our experiments.
|
\label{sec:discussion} As a step toward a self-consistent model for propellers' non-Keplerian motions, we added to the frog libration model of PC new terms representing co-orbital mass motion and Lindblad torques. In numerical experiments with this `extended' frog model, we found that allowing the co-orbital mass at the ends of the gap to move in response to the moonlet's non-Keplerian motions can either damp the frog librations completely or drive the librations resonantly. In other words, in our simple model for co-orbital feedback, the feedback is either strongly negative or strongly positive. We found further that the strong positive feedback could be limited, and the motion stabilized, by Lindblad torques. Our numerical experiments emphasize simplicity over realism. Although they clarify the conditions necessary for stable frog librations, they offer no explanation for why these conditions should be met. That is, we leave unanswered the question of why $\tdiff$, $\Plib$, $\mumoon$, and $\muring$ of real propeller systems should occur in the right proportions for stable frog librations to exist. Still, our extended frog model makes observationally testable predictions: if propeller moonlets are performing frog librations, we expect that 1) the properties of Bl\'eriot's gap (its azimuthal and radial dimensions, and the co-orbital surface density outside the gap) are such that its frog libration period $\Plib \simeq 4$ yr; 2) Bl\'{e}riot's and other propellers' longitude residuals will continue to vary sinusoidally in time; 3) at any given time, propeller positions will be typically offset from the centers of their gaps by azimuthal distances of order the observed rms longitude residuals; and 4) the properties of propeller gaps are such that gap drift (equivalently, gap closing) timescales $\tdiff$ (Eq.~\ref{eqn:tdiff}) are comparable to or longer than frog libration periods $\Plib$. Of these four predictions, the first three are retained from PC's original frog model, while the fourth is new from the extended frog model. Unfortunately, we cannot seem to satisfy both predictions 1 and 4 for Bl\'{e}riot. If we take the azimuthal length of Bl\'eriot's gap to be $\phi \approx 0.004$ and its radial width $x_{\rm gap}$ to be a few km (a few moonlet Hill radii), we can indeed reproduce $\Plib \simeq 4$ yr, in accord with the {\it Cassini} observations (PC, see the discussion following their Eq.~12). But a gap of such dimensions would close in a time $\tdiff \sim 0.01 \Plib$ (Eq.~\ref{eqn:tdiff}) and would lead to a libration amplitude much smaller than the 260-km amplitude that is observed. For the gap drift time $\tdiff$ to be longer than the frog libration time $\Plib$, the radial width of the gap may need to be unrealistically small --- comparable to the ring particle size. This conclusion is tentative because our treatment of feedback is primitive and possibly oversimplified. We state this shortcoming of our model in the hope that more accurate studies---e.g., numerical simulations designed to explore long-range interactions between the moonlet and the entire gap---may either confirm that the frog resonance is not responsible for the observed non-Keplerian motions, or reveal that feedback works in a way different from what we have imagined in this paper.
| 12 | 6 |
1206.3972
|
1206
|
1206.4887_arXiv.txt
|
Backreaction effects of the large scale structure on the background dynamics have been claimed to lead to a renormalization of the background dynamics that may account for the late time acceleration of the cosmic expansion. This article emphasizes that generically the averaged flow is locally anisotropic, a property that can be related to observation. Focusing on perturbation theory, the spatially averaged shear, that characterizes the anisotropy of the flow, is computed. It is shown that this shear arising from backreaction differs from a homogeneous shear: its time evolution is different and its amplitude is completely determined by the cosmological parameters and the matter power spectrum. It ranges within (2-37)\% at a redshift of order 0.5 so that the isotropy of the Hubble flow may allow to constrain the backreaction approach to dark energy.
|
In the standard cosmological framework~\cite{pubook}, one assumes that on large scales, the universe is well described by a spatially homogeneous and isotropic spacetime, at least at the background level, so that its dynamics is obtained from the Einstein equations for a Friedmann-Lema\^{\i}tre (FL) metric. Structure formation is then described using perturbation theory, which has proven to be successful to understand the existing observations from cosmic microwave background anisotropies to the growth rate of the large scale structure. While most of the observations are compatible with the assumption of a spatially homogeneous and isotropic universe on large scales, they exhibit a clumpy distribution of matter on small scales and at late time. This is at the heart of a lively debate concerning the magnitude of the backreaction of the large scale structure on the background dynamics. While its magnitude depends on the averaging procedure~\cite{Buchert,Zalaletdinov} (see also Ref.~\cite{PS}) and on the actual small scale geometry of the universe, it has been mostly estimated using perturbation theory at linear and second order either in synchronous gauge~\cite{LS,rasanen1,Kolb:2004am} or in Newtonian gauge~\cite{Kolb:2004am,rasanen2,behrend,brown,kasai,CAN} (see e.g. Ref.~\cite{bura} for reviews). One important conclusion is the existence of ultraviolet divergences (see, for example, Refs.~\cite{Kolblast,CU}) when particular observables are calculated, with no convincing regularization schemes proposed so far. This lets open the question of the magnitude of the backreaction and its ability to explain the late time acceleration of the cosmic expansion. This is a rather controversial subject and, according to some authors \cite{rasanen1,rasanen2,AutPro} the backreaction of present inhomogeneities might explain, by itself, cosmic acceleration while, according to others \cite{AutAga}, the effect of inhomogeneities is totally negligible. This article lies on a very simple, and almost trivial, remark: the spatially averaged flow has no reason to be isotropic. While obvious, this fact has been hidden in the generally adopted backreaction procedure~\cite{Buchert}, in which the averaged dynamics is presented in a form mimicking the Friedmann dynamics so that attention has been focused on the volume averaged expansion factor and on the backreaction terms (see below for definitions). Late time growth of a spatial anisotropy may thus be a specific signature of backreaction. The goal of this work is thus to estimate the level of anisotropy of the averaged flow and address the following questions: (1) Is the shear, which is related to the anisotropy of the Hubble flow (and thus observable), divergent in the ultraviolet? (2) How is the shear magnitude related to the backreaction magnitude? (3) Can a bound on the shear on cosmological scales allow us to set a bound on the backreaction? To that purpose, we start by recalling the averaging procedure in \S~\ref{II} and propose to split the kinematical backreaction term into a term describing the anisotropy of the flow and a genuine backreaction term. Under that form the averaged dynamics of any spatially homogeneous (but not necessarily isotropic) flow on a surface of homogeneity remains unchanged and the genuine backreaction term strictly vanishes. Using perturbation theory, the shear is computed at lowest order in perturbation theory in \S~\ref{III} and then computed explicitly in \S~\ref{V} after having discussed the choice of the matter power spectrum in \S~\ref{IV}. We have actually used two power spectra, one motivated by observations (with a simple analytical form allowing for an exact integration) and another motivated by theory, relying on the initial conditions from inflation and the transfer function of the standard $\Lambda$CDM model, but which requires numerical integration. As we shall show the scalar shear is divergent in the ultraviolet, which raises several questions that are summarized in \S~\ref{VI}. Appendix A summarizes the main results of linear perturbation theory around a spatially Euclidean homogeneous background spacetime. A detailed description of how to implement the shear average is given in Appendix B, and the normalization of the power spectra is described in Appendix C.
|
\label{VI} This article relies on the simple remark that generically a spatially averaged flow has no reason to be isotropic. We have thus focused our analysis of the shear in order to quantify the expected deviation from isotropy that arises from the backreaction of large scale structure. For that purpose, we have used the averaging procedure designed in Ref.~\cite{Buchert} but rewritten in a way that makes explicit the anisotropy of the averaged flow. Under this new form the kinematical backreaction term arises only from inhomogeneities and, e.g., the spatial average of a Bianchi dynamics remains unchanged, so that it is physically more sound (in particular, one can think of comparing the backreaction that arises from similar inhomogeneities with respect to different background homogeneous flows). In order to evaluate the order of magnitude of the scalar anisotropy $\Sigma$, it is sufficient to work at first order in perturbation theory.\\ Concerning the questions that were raised in the introduction, we can give the following answers. First, $\overline{\langle \sigma^2 \rangle}$ diverges in the ultraviolet and it must be regularized by the introduction of a UV cut-off $k_{\rm UV}$; see Eqs.~(\ref{shearv1}) and~(\ref{shearv2}) or Eqs.~(\ref{Sigma2_k_general2_with_Cutoff}) and~(\ref{Sigma2_k_general2_with_window}). Such UV divergence has a large impact on the final result and the same problem of UV divergent terms is also found in other approaches (e.g. the one based on the all-sky average (monopole) of the redshift-distance relation, obtained from the Kristan and Sachs approach \cite{KS}, as clearly shown in Ref.~\cite{CU}).\footnote{However, note that the use of a well-defined procedure to average over the light-cone~\cite{GMNV}, applied to the perturbative expansion up to the second order of the exact redshift-distance relation, gives a well-defined result with no ultraviolet divergences \cite{BGMNV}.} The question regarding this cut-off is central in the backreaction debate. Indeed, since we have used linear perturbation theory, it is probably not safe to extrapolate at scales larger than $k\sim1 \,{\rm Mpc}^{-1}$ without taking into account the non-linear effects which turn on beyond such scales. This divergence is particulary problematic for the shear, since this is related to an anisotropy of the Hubble flow and can thus, in principle, be observed. We see that its amplitude can shift from 2\% to 37\% when $k_{\rm UV}$ varies from $0.1$ to $1\,{\rm Mpc}^{-1}$ for the standard $\Lambda$CDM model (see Fig. 3), and it varies with the value of the cosmological constant (see Fig. 6). Since the amplitude of some backreaction effects can also depend on $k_{\rm UV}$ (see Ref.~\cite{CU}), a constraint of the scalar shear can be translated into a constraint on the backreaction, hence possibly resolving the debate of the ability for these effects to explain the late time acceleration of the universe. The average Friedmann equation~(\ref{e.backreac1bis}) can be rewritten as $1=\Omega_{\rm m} + \Omega_\Lambda + \Omega_\sigma + \Omega_K + \tilde\Omega_Q$. It is well-known (see, for example, Refs.~\cite{LS,CAN}) that $\Omega_Q=\Omega_\sigma + \tilde\Omega_Q$, which usually characterizes the backreaction, is not UV divergent, while both $\Omega_\sigma$ and $\tilde\Omega_Q$ are. This arises from the fact that the divergence does not appear in $\average{\Theta}$ while it does in both $\average{\sigma}$ and $\average{\Theta^2}$. This shows trivially that $\Omega_\sigma\sim- \tilde\Omega_Q$ for large $k_{\rm UV}$ so that the amplitude of the anisotropy and kinematical backreaction are related in this regime. Let us stress that there is no total agreement about the physical meaning of the Buchert procedure and its connection to observable quantities. For example, quantities connected to spatial averages are not, strictly speaking, observable because we only have observational access to our past light-cone (see, for example, Ref.~\cite{CU}). On the other hand, if we take seriously these equations we have an important observational impact via the averaged shear. It is then important to realize that the anisotropy arising from the averaged flow, as a specific signature of backreaction, may allow us to discriminate with dark energy models~\cite{jpude} (unless dark energy has an anisotropic stress, as e.g. in Ref.~\cite{anisoDE}) or modification of general relativity. We argue that this is a key quantity to discriminate these models as a possible explanation of the late time acceleration of the cosmic expansion. We have shown that its amplitude is fixed by the cosmological parameters and the matter power spectrum, and not as an initial condition as e.g. for Bianchi universes. Its time evolution is also different from the homogeneous shear of a Bianchi universe since it increases with time to eventually reach a maximum. In an effective way, this can indeed be rephrased as a dark energy anisotropic stress, the time evolution of which is determined by the growth of the structures. We have shown that for a standard $\Lambda$CDM background dynamics, $\Sigma$ peaks between 2 and 37\% at a redshift of order 0.5. Any bound on the anisotropy of the Hubble flow can probably set constraints on backreaction effects. In particular, it shows explicitly that a cut-off scales larger than or of the order of $1~{\rm Mpc}^{-1}$ induces too strong an anisotropy. Indeed, it does not make sense to derive the value of a cut-off from observation, but it emphasizes, again, the necessity to design a proper regularization scheme for this mechanism to be fully predictive. An anisotropy with that amplitude can potentially be observable, in particular with weak lensing experiment such as Euclid~\cite{euclid} via the $B$-modes~\cite{pup}. From a technical point of view, we have used two matter power spectra. One is more realistic while the second has a more simple form. Interestingly, we have shown that they give similar results as long as $k_{\rm UV}$ remains small. This is thus a excellent tool that allows us to make analytical estimates and, for instance, to derive scalings and order of magnitude without numerical integrations of the spectrum. Our analysis, while restricted to simple power spectra and linear perturbation theory, points toward a specific signature of backreaction. This may offer the possibility to constrain this class of explanations for the dark energy. \vskip0.5cm {\bf Acknowledgements:} We thank Chris Clarkson, Obinnah Umeh and Carlo Schimd for discussions and the Action Sp\'ecifique GRAM for its financial support. We also thank Thomas Buchert for his comments and insights. \appendix
| 12 | 6 |
1206.4887
|
1206
|
1206.1370_arXiv.txt
|
We present the latest improvements in the Center for Radiative Shock Hydrodynamics (CRASH) code, a parallel block-adaptive-mesh Eulerian code for simulating high-energy-density plasmas. The implementation can solve for radiation models with either a gray or a multigroup method in the flux-limited-diffusion approximation. The electrons and ions are allowed to be out of temperature equilibrium and flux-limited electron thermal heat conduction is included. We have recently implemented a CRASH laser package with 3-D ray tracing, resulting in improved energy deposition evaluation. New, more accurate opacity models are available which significantly improve radiation transport in materials like xenon. In addition, the HYPRE preconditioner has been added to improve the radiation implicit solver. With this updated version of the CRASH code we study radiative shock tube problems. In our set-up, a $1\,$ns, $3.8\,$kJ laser pulse irradiates a $20\,$micron beryllium disk, driving a shock into a xenon-filled plastic tube. The electrons emit radiation behind the shock. This radiation from the shocked xenon preheats the unshocked xenon. Photons traveling ahead of the shock will also interact with the plastic tube, heat it, and in turn this can drive another shock off the wall into the xenon. We are now able to simulate the long term evolution of radiative shocks.
|
Radiative shocks are important in many astrophysical environments like for instance supernova explosions, supernova remnants, and shocked molecular clouds. With the emergence of high-energy-density (HED) facilities, such flows can now be studied in detail in laboratory experiments. Laser-driven experiments revealed many properties of radiative shocks. Ionizing radiative precursors can appear ahead of strong shocks, see e.g. Refs. \cite{keiter2002,bouquet2004,koenig2006}. A radiative cooling layer was discussed for a system that is optically thick in the shocked plasma, while optically thin in the unshocked material \cite{reighard2007}. More recently, magnetic fields were shown to be important in laser-produced shock waves. Magnetic fields can for instance be generated by shock waves by means of the Biermann battery process\cite{gregori2012}. Experiments are proposed to produce collisionless shocks via counterstreaming plasmas \cite{park2012}. These laser-driven shock experiments do not only provide insight in the underlying physical mechanism related to radiative shocks and the connections to astrophysics. They are also useful for validating numerical simulation codes that are used for the HED experiments and in the astrophysical context. In recent radiative shock tube experiments \cite{doss2009,doss2010} it was demonstrated that sufficiently fast shocks can produce wall shocks ahead of the primary shock. These experiments were performed at the Omega high-energy-density laser facility \cite{boehly1995} using ten laser beams delivering a total energy of $3.8\,$kJ to a beryllium target. The ablated beryllium drives like a piston a primary shock through a xenon-filled plastic tube. This shock is sufficiently fast that it produces a radiative precursor in the unshocked xenon, which will also heat the plastic tube and subsequently can launch wall shocks. This compound shock is a challenging problem for numerical simulation codes as it involves hydrodynamics and radiation transport at different spatial and temporal scales. The center for radiative shock hydrodynamics (CRASH) project aims to improve our understanding of radiative shocks through experiments and simulations, and to be able to predict radiative shock properties with a validated simulation code. In previous modeling of radiative shock tubes with the CRASH code \cite{vanderholst2011,vanderholst2012} we used the H2D simulation code, the 2D version of Hyades \cite{larsen1994} to evaluate the laser energy deposition during the first $1\,$ns. H2D is Lagrangian radiation-hydrodynamics code with multigroup radiation diffusion capability. After $1\,$ns we remapped the H2D output to the CRASH code for further simulation. The latter code is also a radiation-hydrodynamics code and uses the block adaptive tree library (BATL) \cite{toth2012} to solve the equations on dynamically adaptive Eulerian meshes. It currently includes flux-limited multigroup radiation diffusion, flux-limited electron heat conduction, multi-material treatment with equation-of-state and opacity solvers. While this suite of codes was able to solve for the radiative shock structures in xenon-filled nozzles \cite{vanderholst2012}, the more basic radiative shocks in xenon-filled straight plastic tubes turned out to be problematic \cite{drake2011}. In this paper, we describe several new improvements to the CRASH code. First of all we have implemented a new parallel laser energy deposition library as an integral part of our code. This allows the code to simulate the laser heating and the subsequent radiation-hydrodynamic response in a self-consistent and efficient way with one single model. Another improvement was needed for the xenon opacities, since the atomic data provided to our opacity solver were inaccurate. We now use high quality xenon opacities calculated with the super-transition-arrays (STA) model \cite{barshalom1989} as an alternative. Both the introduction of the laser package and improved xenon opacities turned out to make the radiation transport much stiffer in some regions. The algebraic multigrid preconditioner using the BoomerAMG solver from the HYPRE library \cite{falgout2002} resulted in more accurate solutions. It is the purpose of this paper to demonstrate that these code changes result in improvement in the fidelity of the simulation results. The reported distortion of the compressed xenon layer on axis \cite{drake2011} is now significiantly reduced and the wall shock is now more realistic. The overarching goal of the CRASH project is to assess and improve the predictive capability and uncertainty quantification of a simulation code, using experimental data and statistical analysis \cite{holloway2011}. The specific focus in this project is radiative shock hydrodynamics. The aim is to predict the experimental radiative shock structure in elliptical nozzles with our simulation code. To achieve this we first calibrate our code with experimental results obtained for straight shock tubes and circular nozzles. It is the purpose of this paper to demonstrate that we can now also model the straight shock tube problem with sufficient fidelity that we can aim to reproduce the experimental data. The outline of this paper is as follows: Section \ref{sec:setup} describes how we setup the shock tube and laser pulse with our new laser package that is consistent with the experiments performed with the Omega laser facility. This is followed in Section \ref{sec:results} by a discussion of the simulation results. We conclude the paper in Section \ref{sec:conclusions}.
|
\label{sec:conclusions} In this paper we discussed laser-driven radiative shocks in xenon-filled straight plastic tubes. The simulations capture the shock properties seen in the laser-driven experiments and radiation-hydrodynamic theories. The laser heating ablates the beryllium target, which subsequently drives a shock through a xenon-filled tube. For laser energies of $3.8\,$kJ, scaled down to $2.7\,$kJ, beryllium disk thickness of $20\,\mu$m and initial xenon gas pressure of $1.2\,$atm we obtain initial shock velocities of $200\,$km/s. These shocks are fast enough to produce a radiative cooling layer in the shocked xenon. The photons can propagate ahead of the primary shock and produce a radiatively heated precursor in the unshocked xenon. The radiation also expands sideways and heats the plastic wall ahead of the primary shock. This produces an inward moving wall shock. The numerical modeling was performed with the CRASH simulation code that solves the radiation-hydrodynamic equations on a block adaptive Eulerian grid. The hydrodynamic equations are solved explicitly, while the radiation diffusion, electron heat conduction and energy exchanges are treated implicitly. This code also includes equation-of-state and opacity solvers to enable multi-material simulations. Several code improvements have been implemented that enabled the improved quality of straight shock tube simulations. A new laser package with 3-D ray tracing has been added to CRASH so that the simulations can be performed self-consistently in one single model instead initializing the simulation runs with an external lagrangian code to evaluate the laser-energy deposition. We also incorporated highly accurate xenon opacities calculated with the super-transition-arrays (STA) model. Finally, we improved the robustness of the implicit radiation solvers with the HYPRE preconditioner instead of the original Block Incomplete Lower-Upper decomposition preconditioner. These developments greatly improved the fidelity of the radiative shock tube results. From both the experimental and simulated X-ray radiographs, we can deduce quantities like primary shock position, wall shock position, and compressed xenon layer thickness. In future work, we will employ these type of metrics for code validation. The goal of our project is to use the validated CRASH code to perform predictive studies of three-dimemsional radiation-hydrodynamic flows, such as radiative shocks in elliptical nozzles.
| 12 | 6 |
1206.1370
|
1206
|
1206.2659_arXiv.txt
|
{Host galaxies are an excellent means of probing the natal environments that generate gamma-ray bursts (GRBs). Surveys of long-duration GRB (LGRB) host environments and their ISM properties have produced intriguing new results with important implications for LGRB progenitor models. These host studies are also critical in evaluating the utility of LGRBs as potential tracers of star formation and metallicity at high redshifts, particularly when considering the implications for properties of host galaxies above z $\sim$ 6. I will summarize our group's latest research on LGRB host galaxies, and discuss the resulting impact on our understanding of these events' progenitors, energetics, afterglow properties, and cosmological applications. } \FullConference{Gamma-Ray Bursts 2012 Conference -GRB2012,\\ May 07-11, 2012\\ Munich, Germany} \begin{document}
|
Long-duration gamma-ray bursts (LGRBs), some of the most energetic events observed in our universe, are associated with the core-collapse deaths of young massive stars. As a result of this connection, they are widely cited as powerful and potentially unbiased tracers of the star formation and metallicity history of the universe out to $z \sim 8$ [1,2,3,4]. In recent years, however, potential biases in the star-forming galaxy population sampled by LGRBs have become a matter of debate. Recent work on a small number of nearby LGRBs suggested a connection between LGRBs and low-metallicity environments [5,6]. Nearby host galaxies appeared to fall below the luminosity-metallicity and mass-metallicity relations for star-forming galaxies out to $z \sim 1$ [7,8,9,10]. These results could potentially introduce key biases that would impact the use of LGRBs as effective cosmic probes of galaxy formation and evolution. A metallicity bias, or some correlation between metallicity and the properties of LGRBs, is predicted by the most commonly-cited progenitor model for LGRBs, the collapsar model [11]. Under the classical assumptions of stellar evolutionary theory, the progenitor is a single rapidly-rotating massive star which maintains a high enough angular momentum over its lifetime to generate an LGRB from core-collapse to an accreting black hole. In addition, LGRBs have been observationally associated with broad-lined Type Ic supernovae [12,13,14,15,16], requiring the progenitors to have shed mass, and therefore angular momentum, as a means of stripping away their outer H and He shells. Mass loss rates for these evolved massive stars are dependent on stellar winds [17], which in turn are dependent on the stars' metallicity [18,19]. For young massive stars, the metallicities of their natal environments can be adopted as the metallicities of the stars themselves. This therefore implies that the wind-driven mass loss rates in high-metallicity environments would rob the stars of too much angular momentum, preventing them from rotating rapidly enough to produce a LGRB and suggesting that LGRBs should either be restricted to low-metallicity environments [20,21,22], or produce weaker explosions at higher metallicities [23].
| 12 | 6 |
1206.2659
|
|
1206
|
1206.5309_arXiv.txt
|
We use the joint measurement of geometry and growth from anisotropic galaxy clustering in the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) CMASS sample reported by \citeauthor{Reid12} to constrain dark energy (DE) properties and possible deviations from the General Relativity (GR). Assuming GR and taking a prior on the linear matter power spectrum at high redshift from the cosmic microwave background (CMB), anisotropic clustering of the CMASS DR9 galaxies alone constrains $\Omega_{\rm m} = 0.308 \pm 0.022$ and $100\Omega_{\rm k} = 5.9 \pm 4.8$ for $w = -1$, or $w = -0.91 \pm 0.12$ for $\Omega_k = 0$. When combined with the full CMB likelihood, the addition of the anisotropic clustering measurements to the spherically-averaged BAO location increases the constraining power on dark energy by a factor of 4 in a flat CDM cosmology with constant dark energy equation of state $w$ (giving $w = -0.87 \pm 0.05$). This impressive gain depends on our measurement of both the growth of structure and Alcock-Paczynski effect, and is not realised when marginalising over the amplitude of redshift space distortions. Combining with both the CMB and Supernovae Type Ia (SNeIa), we find $\Omega_{\rm m} = 0.281 \pm 0.014$ and $1000\Omega_{\rm k}=-9.2\pm5.0$ for $w = -1$, or $w_0 = -1.13 \pm 0.12$ and $w_{\rm a}=0.65 \pm 0.36$ assuming $\Omega_k = 0$. Finally, when a $\Lambda$CDM background expansion is assumed, the combination of our estimate of the growth rate with previous growth measurements provides tight constraints on the parameters describing possible deviations from GR giving $\gamma = 0.64 \pm 0.05$. For one parameter extensions of the flat $\Lambda$CDM model, we find a $\sim 2\sigma$ preference either for $w > -1$ or slower growth than in GR. However, the data is fully consistent with the concordance model, and the evidence for these additional parameters is weaker than $2\sigma$.
|
All currently available cosmological observations, including the latest datasets of CMB temperature and polarisation anisotropies \citep{Komatsu2011}, Supernovae Type Ia (SNeIa) magnitudes \citep{Suzuki2011} and the distance ladder mapped by Baryon Acoustic Oscillation (BAO) peak signature in the clustering of galaxies \citep{Aadvark:2012} are consistent with a simple cosmological model in which general relativity (GR) describes gravitational interactions on all scales and times, about 70 per cent of the Universe's current energy density is in form of a Cosmological Constant as originally described by Einstein, and most of the remaining 30 per cent is in form of nonrelativistic ``dark matter'' \citep[For a detailed review see e.g.,][]{Peebles2003,Weinberg2012}. Ongoing and future observations have been designed to test if the cosmological constant needs to be replaced by a dynamical Dark Energy (DE), and if so, to measure the properties of this DE fluid. We should also be able to tell if GR describes the properties of gravity on cosmological scales or if it must be replaced by a yet unknown modified theory of gravity (MG) \citep[see e.g.,][]{Albrecht2009,Zhao2009,Samushia11,Wang2010}. Observational effects of dynamic DE and MG are partially degenerate and careful data analysis should take into account both possibilities \citep{Ishak:2006,Shapiro:2010}. The clustering of galaxies provides a very powerful and robust test of both the nature of DE and MG. The shape of the measured correlation function \citep{Rei10} or the power-spectrum \citep{Montesano2011}, analogously to the shape of the measured CMB power-spectrum \citep{WMAP7}, can be used to constrain basic cosmological parameters. Features within the clustering signal, particularly the BAO, allow the clustering to be used as a standard ruler. Additionally, although the statistical properties of galaxy clustering are expected to be isotropic, the measured clustering can be highly anisotropic, depending on how redshifts are translated to distances. The two main sources of this apparent anisotropy are redshift-space distortions \citep[RSD;][]{Kai87} and the Alcock-Paczynski \citep[AP;][]{AP} effect. RSD arise because peculiar velocities contribute to observed galaxies redshifts, but can not be corrected for when computing line-of-sight separations. On quasi-linear scales, the average pairwise galaxy peculiar velocity is negative, meaning that galaxies are on average falling towards the mass over-densities traced by neighbouring galaxies. These coherent motions appear as a ``squashing'' of the correlation function along the line-of-sight. The amplitude of the observed anisotropy can be used to infer the strength of the gravitational interaction at different scales and redshifts. \citep[For a detailed review of RSD see][]{HamiltonReview}. RSD allow measurements of the amplitude of fluctuations in the velocity field, which in linear theory give a dependence on \begin{equation} f(z)\sigma_8(z)=\frac{d\sigma_8(z)}{d\ln a}, \label{eq:fs8} \end{equation} \noindent where $\sigma_8(z)$ is the overall normalisation of the matter density fluctuations. The AP effect results from the fact that, to convert observed angular positions and redshifts of galaxies into physical positions, we must use a cosmological model on the observed lightcone. If the wrong model is used when computing the correlation function, the initial isotropy of the clustering signal will be distorted. The measured anisotropy of clustering can be used to infer the proper geometry and hence the true values of cosmological parameters. If we have a prior on the shape of the correlation function, the dilation of scales between the spherically averaged observed and model clustering statistics allows a measurement of \begin{equation} D_V(z) = \left[(1+z)^2D_A^2(z)\frac{cz}{H(z)}\right]^{1/3}, \label{eq:Dv} \end{equation} \noindent where $D_{\rm A}(z)$ is the physical angular diameter distance and $H(z)$ is the Hubble expansion rate \citep{Eis05}. Applying the AP test to the measured direction dependent clustering additionally allows the measurement of \begin{equation} F(z) = \frac{1+z}{c}D_{\rm A}(z)H(z). \label{eq:F} \end{equation} \noindent This allows the degeneracy between radial and angular distances in BAO measurements to be broken and an accurate estimate of Hubble expansion rate at different redshifts to be derived. Many RSD measurements have been made from a variety of galaxy surveys, including most recently the 2dFGRS \citep{Per04}, the VVDS \citep{Guz08}, the 2SLAQ \citep{Ang08}, the SDSS-II \citep{Cabre:2009,Song:2011,SamPerRac11}, the WiggleZ \citep{Bla11a}, and the 6dFGRS \citep{Beutler12} surveys. These measurements have in turn been used to set constraints on the cosmological growth rate. Thus far geometric constraints from galaxy clustering have focused predominantly on spherically averaged power spectra or correlation functions. From such measurements, the BAO feature allows few percent-level distance measurements \citep[for the latest constraints, see][]{Per10,Bla11b,Beutler11,Padmanabhan2012,Aadvark:2012}. By contrast, the AP test has received less attention, since better signal-to-noise data is needed to disentangle RSD and AP effects, and more careful modelling of anisotropic correlation function is required. The AP effect has been recently used to jointly measure $D_A$, $H$ and $f\sigma_8$ in three redshift bins from WiggleZ survey \citep{Blake2012} and using the SDSS-II LRG sample \citep{Chuang2012}. The Sloan Digital Sky Survey \citep[SDSS;][]{York:2000} has mapped over one third of the sky using the dedicated 2.5-m Sloan telescope \citep{Gunn:2006}. A drift-scanning mosaic CCD camera \citep{Gunn:1998} imaged sky in five photometric bandpasses \citep{Fukugita:1996} to a limiting magnitude of $r \simeq 22.5$. The ongoing Baryon Oscillation Spectroscopic Survey \citep[BOSS;][]{BOSS}, which is a part of SDSS-III \citep{Eis11}, is measuring spectra of 1.5 million galaxies and 150,000 quasars selected from the multicolor SDSS imaging. The CMASS sample in the BOSS Data Release 9 (DR9) contains a catalog of $264\,283$ highly biased ($b \sim 2$) galaxies sampling an effective volume of about $0.77\ h^{-3}\ {\rm Gpc}^3$ with mean redshift of $z\sim 0.57$, allowing for best-to-date statistical uncertainty in the measurement of galaxy clustering \citep[see][for detailed description of early data]{Whi11}. This work is part of series of papers providing a comprehensive description of the galaxy clustering in the CMASS DR9 sample. \citet{Nuza:2012} compared the clustering of CMASS DR9 galaxies to state of the art dark matter simulations and showed that they are compatible with $\Lambda$CDM model and GR. \citet{Ross:2011} provided an up-to-date description of the CMASS DR9 data, a study of possible observational systematic effects and the methods to remove known systematics. \citet{Manera:2012a} presented 600 mock catalogs that match the observed volume of CMASS DR9 sample and are essential for determining the covariance matrix associated with the measured correlation functions and power spectra. \citet{Aadvark:2012} used these data to measure the BAO peak position to 1.7 per cent precision. \citet{Sanchez:2012} derived cosmological constraints using the full shape of the measured spherically-averaged correlation function, while \citet{Reid12} studied the anisotropic clustering of CMASS DR9 galaxies using the measured monopole and quadrupole moments of the correlation function (henceforth we shall simply refer to these as the monopole and quadrupole). By adopting a sophisticated model for galaxy clustering in the quasi-linear regime, \citet{Reid12} made accurate RSD and AP measurements from the direction-dependent clustering of CMASS DR9 galaxies to simultaneously measure growth and geometry at a redshift of $z = 0.57$. We now extend this work to investigate the cosmological implications of these measurements. We show that information provided by the RSD-derived growth rate significantly enhances constraints on basic cosmological parameters compared to the case where only geometric measurements are used. We combine measurements of the growth rate, angular diameter distance and expansion rate with previous measurements to constrain properties of DE and gravity. In combination with CMB, $H_0$ and SNeIa data we are able to estimate values of basic cosmological parameters to very high precision and tightly constrain possible deviations from $\Lambda$CDM and GR (henceforth we will refer to the model in which the background expansion follows $\Lambda$CDM and the gravity is described by GR as $\Lambda$CDMGR). The paper is organised as follows: in Sec.~\ref{sec:measurements} we describe the CMASS DR9 AP and RSD measurements, in Sec.~\ref{sec:previous} we briefly review previous similar measurements, in Sec.~\ref{sec:theory} we describe different ways of looking for deviations from $\Lambda$CDMGR, and in Sec.~\ref{sec:constraints} we present constraints on deviations form $\Lambda$CDMGR. We conclude and discuss our results in Sec.~\ref{sec:conclusion}.
|
\label{sec:conclusion} We have used the \citet{Reid12} measurements of angular distance, Hubble expansion rate and growth rate derived from the anisotropic clustering of BOSS CMASS DR9 galaxies to place constraints on deviations from the standard cosmological model that assumes a $\Lambda$CDM background with structure formation driven by GR. The geometric measurements of $D_{\rm V}$ and $F$ are complementary to similar measurements from the BAO peak position \citep{Aadvark:2012} and the full shape of the correlation function \citep{Sanchez:2012} and strengthen existing constraints on parameters describing the time-dependence of DE energy density. The RSD measurement of $f\sigma_8$ was shown to provide an additional constraint on the parameters describing deviations from GR and helped to significantly tighten DE constraints derived from geometric measurements. We now highlight our findings by using them to answer fundamental questions about our Universe.\\ \noindent{\it How much do RSD measurements enhance the geometric measurements?}\\ When GR is assumed the RSD measurements of growth break parameter degeneracies present when using purely geometric measurements, and consequently significantly tighten constraints on basic cosmological parameters. The addition of growth rate information improves constraints on $\Omega_{\rm m}$ by 18 per cent relative to the case where only BAO peak position data is used. The improvement is most dramatic for the $w_0$ parameter constraints, which improve by a factor of four compared to BAO only results (see Table~\ref{table:all}).\\ \noindent{\it Does GR provide a good description of data?}\\ When $\Lambda$CDM is assumed our measurements of growth and geometry show a $2\sigma$ preference for models in which the growth of structure is weaker compared to GR. Adding previous RSD measurements at other redshifts brings the best-fit closer to GR value but still prefers somewhat weaker growth. This results from the fact that most RSD measurements of $f(z)\sigma_8(z)$ with high signal-to-noise are below GR predictions (see Fig.~\ref{fig:fs8}).\\ \noindent{\it Does the Cosmological Constant provide a good description of data?}\\ Assuming GR, our measurements of growth and geometry show a $2\sigma$ preference for $w>-1$. When combined with SNeIa data, the best-fit is closer to the cosmological constant model and the discrepancy is lowered to about $1\sigma$. It should be noted that, for DE as well as GR, the $2\sigma$ preference means a preference in terms of relative Bayesian likelihood.\\ \noindent{\it How well can the DE scalar field potential be constrained?}\\ We demonstrated that our measurements of growth and geometry, when combined with CMB information, provide strong constraints on scalar field DE model parameters. The constraints obtained are better than previously reported from different combinations of data sets. The flat potential (Cosmological Constant) provides a good fit to data.\\ \noindent{\it Has the expansion of the Universe accelerated recently?}\\ We employed a model-independent approach that relies on very few general assumptions to reconstruct the ``deceleration parameter'' at low redshifts. We showed that current AP measurements provide $2$ to $3\sigma$ evidence for the accelerated Universe at low redshifts. Much stronger measurements of $q(z)$ exist in the literature, but they depend on additional assumptions about the nature of DE.\\ \noindent{\it Did DE emerge as a dominant component only very recently?}\\ Our estimate of $H(z=0.57)$ combined with an estimate of $H_0$ suggest that energy density of DE relative to nonrelativistic matter was about 4.5 times lower at $z=0.57$.\\ \noindent{\it Is the standard $\Lambda$CDMGR model still valid?}\\ Measurements of growth and geometry from CMASS DR9 sample allow for a very strong test of MG and DE. When combined with WMAP7 data they show a $2\sigma$ preference for either weaker gravity or $w>-1$. However, in terms of absolute $\chi^2/{\rm dof}$, the simple $\Lambda$CDMGR model still provides a good fit to the data.
| 12 | 6 |
1206.5309
|
1206
|
1206.2832_arXiv.txt
|
Some inflationary models predict the existence of isocurvature primordial fluctuations, in addition to the well known adiabatic perturbation. Such mixed models are not yet ruled out by available data sets. In this paper we explore the possibility of obtaining better constraints on the isocurvature contribution from future astronomical data. We consider the axion and curvaton inflationary scenarios, and use Planck satellite experimental specifications together with SDSS galaxy survey to forecast for the best parameter error estimation by means of the Fisher information matrix formalism. In particular, we consider how CMB lensing information can improve this forecast. We found substantial improvements for all the considered cosmological parameters. In the case of isocurvature amplitude this improvement is strongly model dependent, varying between less than 1\% and above 20\% around its fiducial value. Furthermore, CMB lensing enables the degeneracy break between the isocurvature amplitude and correlation phase in one of the models. In this sense, CMB lensing information will be crucial in the analysis of future data.
|
} Since the early measurement of the first acoustic peak in the Cosmic Microwave Background (CMB) angular power spectrum \citep{2000debernardis, hanany2000}, a pure isocurvature model of primordial fluctuations was ruled out \citep{2000enqvist}. In addition, recent CMB data from the WMAP satellite found no evidence for non-adiabatic primordial fluctuations \citep{2011komatsu}. These results are consistent with a single scalar field inflationary model prediction of perfectly adiabatic density perturbations. However, small contributions from isocurvature primordial fluctuations (in mixed models) cannot be excluded by the current data. The standard inflationary scenario driven by a single field cannot account for isocurvature fluctuations. If we want to take into account isocurvature fluctuations, a multiple-field inflation has to be considered (for a general formalism, see \citet{2001gordon} for example). We consider the alternative scenario where perturbations to a light field different from the inflaton (the curvaton) are responsible for curvature perturbations and may also generate isocurvature fluctuations \citep{2002lyth, 2002moroi, 2003lyth}. In this case, the isocurvature component is completely correlated or anti-correlated with the adiabatic component. A second scenario is also taken into account in this work, where quantum fluctuations in a light axion field generate isocurvature fluctuations. Unlike the first scenario, this isocurvature component is fully uncorrelated with the adiabatic one. It is important to point out that axion particles can be produced in this scenario, which can contribute to the present dark matter in the universe (see \citet{2007beltran, 2002bozza, 2008hertzberg} and references therein). There are already many studies in the literature constraining the isocurvature contribution using different data sets (CMB, large-scale structure (LSS), type Ia supernovae (SN), Lyman-$\alpha$ forest and baryon acoustic oscillations (BAO)) (see, for example, \citet{2011li, 2011carbone, 2011larson, 2011komatsu, 2010mangilli, 2006bean, 2005beltran, 2003crotty}). We intend to use the well-known Fisher information matrix formalism (for a short guide see \citet{2009coe}) to estimate whether better constrains to the isocurvature contribution can be obtained in the near future using measurements of the CMB temperature and polarization power spectrum from the Planck satellite, as well as the large-scale matter distribution observed by the Sloan Digital Sky Survey (SDSS), using CMB lensing information. We will see how this new information could improve the error prediction for some cosmological parameters, especially those related to the isocurvature mode. The paper is organized as follows: in Section \ref{Isocurvature notation} we describe briefly the isocurvature models and the notation that will be used throughout the paper. We give a small introduction on CMB lensing in Section \ref{CMB lensing}. In Section \ref{Method}, we briefly review the Fisher information matrix formalism for the CMB (with and without lensing information) and for a galaxy survey. Finally, we present our results in Section \ref{Results}, followed by our discussion and conclusions in Section \ref{Discussion and conclusions}.
|
} In this paper we studied a possible contribution of isocurvature initial perturbations in the pure adiabatic fluctuations scenario from the well tested $\Lambda$CDM model. Using the fisher formalism we obtained the best constraints possible for the isocurvature parameters using CMB and galaxy distribution information. The main goal of this work has been to quantify how CMB lensing information can provide better constraints in the cosmological parameters, specially in the ones related to the isocurvature contribution. Moreover, we saw that CMB lensing information broke the parameter degeneracie between the isocurvature parameters $\alpha$ and $\beta$ for one of the three studied scenarios. In all tested inflationary scenarios, the CMB lensing information improves the constraints of all chosen parameters, including the ones related to the isocurvature mode. If we consider Planck information alone (with $\beta$ not allowed to vary) the smallest improvement obtained on $\alpha$ standard deviation is in the axion type inflation for $n_{ad}\neq n_{iso}$ with a difference of 0.17\% of its fiducial value between the lensed and unlensed analysis. This improvement gets bigger for the scenarios considered by WMAP reaching almost 9\% (axion type with $n_{ad} = n_{iso}$) and 25\% (curvaton type) (see the lower part where $\beta$ is kept fixed inTables \ref{tbl-modelo1_sem_beta}, \ref{tbl-modelo3_sem_beta} and \ref{tbl-modelo2_sem_beta}). Moreover, if CMB lensing can be measured, it would be possible to distinguish between the axion models with $n_{iso}= 0.982$ and $n_{iso}= 2.7$ for instance. The effect of CMB lensing is bigger for higher $n_{iso}$ values as can be seen in the comparison of Figures \ref{fisher_modelo1} and \ref{fisher_modelo3}. We can visualize better this lensing effect on $n_{iso}$ by analyzing the power spectra derivatives in respect to $\alpha$ and $\beta$ in Figure \ref{der1}. \begin{figure*} [h] \includegraphics[scale=0.6]{./figures/Fig4a.eps} \includegraphics[scale=0.6]{./figures/Fig4b.eps} \\ \includegraphics[scale=0.6]{./figures/Fig4c.eps} \includegraphics[scale=0.6]{./figures/Fig4d.eps} \\ \includegraphics[scale=0.6]{./figures/Fig4e.eps} \includegraphics[scale=0.6]{./figures/Fig4f.eps} \caption{ CMB power spectra derivatives in respect to the isocurvature parameters $\alpha$ (purple) and $\beta$(red). The dashed darker lines are related to the unlensed power spectra's derivative and the solid lighter ones are related to the lensed power spectra's derivative for the axion scenario of $\alpha = 0.06$, $\beta = 0$. On the left column the scalar spectral index is $n_{iso} = 2.7$ and on the right column the scalar spectral index is $n_{iso} = 0.982$ } \label{der1} \end{figure*} When the combined Planck + SDSS forecast is done, the improvement with the use of lensing information is not so significant for any of the scenarios. This is due to the poor ability of SDSS to constrain the parameters compared to Planck, especially when CMB lensing information is included. For a CMB experiment alone, or combined with any other precise experiments on galaxies distribution, lensing is an important extra information in the attempt to know how well observations can constrain the presence of isocurvature contribution to the primordial fluctuations. An interesting forecast would include future galaxy surveys, such as EUCLID, combined with planck CMB information including the lensing effects. \appendix
| 12 | 6 |
1206.2832
|
1206
|
1206.3413_arXiv.txt
|
{We observed a sample of 20 representative Herbig Ae/Be stars and five A-type debris discs with PACS onboard of {\em Herschel}. The observations were done in spectroscopic mode, and cover far-IR lines of [O\,{\sc i}], \CII, CO, CH$^+$, \water \ and OH. We have a \Odrie \ \mic \ detection rate of 100\% for the Herbig Ae/Be and 0\% for the debris discs. \Ohon \ \mic \ is only detected in 25 \%, CO $J$=18-17 in 45 \% (and less for higher $J$ transitions) of the Herbig Ae/Be stars and for \CII \ 157 \ \mic, we often found spatially variable background contamination. We show the first detection of water in a Herbig Ae disc, HD 163296, which has a settled disc. Hydroxyl is detected as well in this disc. CH$^+$, first seen in HD 100546, is now detected for the second time in a Herbig Ae star, HD 97048. We report fluxes for each line and use the observations as line diagnostics of the gas properties. Furthermore, we look for correlations between the strength of the emission lines and stellar or disc parameters, such as stellar luminosity, UV and X-ray flux, accretion rate, PAH band strength, and flaring. We find that the stellar UV flux is the dominant excitation mechanism of \Odrie, with the highest line fluxes found in those objects with a large amount of flaring and greatest PAH strength. Neither the amount of accretion nor the X-ray luminosity has an influence on the line strength. We find correlations between the line flux of \Odrie \ and \Ohon, CO $J$ = 18-17 and \Oopt, and between the continuum flux at 63 \mic \ and at 1.3 mm, while we find weak correlations between the line flux of \Odrie \ and the PAH luminosity, the line flux of CO $J$ = 3-2, the continuum flux at 63 \mic, the stellar effective temperature and the Br$\gamma$ luminosity. Finally, we use a combination of the \Odrie \ and $^{12}$CO $J$ = 2-1 line fluxes to obtain order of magnitude estimates of the disc gas masses, in agreement of the values we found from detailed modelling of 2 HAEBEs, HD 163296 and HD 169142. }
|
\label{s_intro} Circumstellar discs around young stars are the sites of planet formation (e.g. Pollack et al. \cite{pollack1996}, Alibert et al. \cite{alibert2005}). During the first 10 Myr, the initially gas-rich disc will evolve into first a transitional and then a debris disc, while dispersing its gas content. The understanding of this dispersal process and what favours/hinders it is a crucial part of the planet formation puzzle, as the amount of gas present in a disc is crucial to determine whether gas giant planets can still be formed. Furthermore, the disc mass controls the migration of planetary bodies of all sizes, from gas giants to meter-sized planetesimals. Three components need to be characterised well: the disc geometry, the dust, and the gas content. The disc geometry of young intermediate-mass stars, the Herbig Ae/Be stars (HAEBEs), is constrained through multi-wavelength imaging, interferometry, and radiative transfer modelling (e.g. Benisty et al. \cite{benisty2010}). Meeus et al. (\cite{meeus2001}) empirically divided the HAEBE discs into group I (flared) and group II (flat). A general consensus exists that discs become flatter as dust grains grow and settle towards the midplane (Dullemond \& Dominik \cite{dullemond2004}). Lately, several of the group I sources have been found to have an inner opacity hole in the disc (e.g. Grady et al. \cite{grady2007}, \cite{grady2009}), possibly due to a lack of small dust grains in the inner disc. In HD 100546, the gap may be caused by a planet (e.g. Bouwman et al. \cite{bouwman2003}, Tatulli et al. \cite{tatulli2011}). In a study of 53 HAEBEs, 85\% show a silicate emission feature at 10 \mic \, with a variety in grain size and crystallinity, proving the presence of {\em warm} small grains in these discs (Juh\'asz et al. \cite{juhasz2010}). Polycyclic Aromatic Hydrocarbons (PAH) features were clearly detected in 70\% of the sample, with a clear preference towards flared discs (Acke et al. \cite{acke2010}). PAHs located in the disc atmosphere are transiently excited by UV photons and are an important heating source for the gas in the disc surface through the photo-electric effect. The study of gas properties is difficult as, in general, emission lines are rather weak. Different gas species and transitions probe different regions in the disc: lines in the near- and mid-IR generally trace the inner disc ($<$10-20 AU), while lines in the far-IR and mm mainly trace the outer disc. We refer to Carmona et al. (\cite{carmona2010}) for a discussion of different gas tracers, their location in the disc and observational characteristics. To understand the disc radial and vertical structure, it is necessary to observe several transitions of different species, as they arise under different conditions (density, temperature, radiation field). \hh \, and CO lines are most often used, since they are the most abundant species present, with the canonical \hh \ to CO number ratio in the ISM being 10$^4$. However, the detection of \hh \ in the IR has proven to be difficult because of its weak rotational and ro-vibrational transitions - it has only been detected in 3 HAEBEs. In a survey of 15 Herbig Ae/Be stars with CRIRES, Carmona et al.\ (\cite{carmona2011}) detected ro-vibrational transitions of \hh \ at 2.1218 \mic \ in only two objects: HD 97048 and HD 100546. Earlier, Bitner et al.\ (\cite{bitner2008}), Carmona et al.\ (\cite{carmona2008}), Martin-Za\"idi et al.\ (\cite{claire2009,claire2010}) searched for mid-IR pure rotational lines of \hh \ at 17.035~\mic \ in a sample of in total 20 HAEBEs; only two detections were made, in AB Aur and HD 97048. In sharp contrast, the detection of CO, although much less abundant, is easier as its rotational/ro-vibrational lines are much stronger. CO is routinely detected in HAEBEs (e.g. Thi et al. \cite{thi2001}, Dent et al. \cite{dent2005}). Lorenzetti et al. (\cite{lorenzetti2002}) showed {\em ISO}/LWS observations of atomic and molecular lines in the far-IR for a sample of HAEBEs. They detected the fine-structure lines of \Odrie \ \& 145.5~\mic \ and \CII \ at 157.7~\mic. Despite the wealth of observations, it is still not clear how HAEBE discs dissipate with time. In the less massive T Tauri stars, disc dispersal is thought to be initiated by photo-evaporation, mainly due to ionising EUV ($h \nu >$ 13.6 eV) photons that first create a gap in the inner disc, which is subsequently rapidly viscously accreted. In a next step, the outer disc is efficiently removed through a photo-evaporative disc wind (Alexander et al. \cite{alexander2006}). However, Gorti et al. (\cite{gorti2009}) showed that UV can rapidly disperse the outer disc, where the bulk of the disc mass is located, thus setting the disc lifetime. Also X-rays are thought to play an important role in those discs (e.g. Ercolano et al. \cite{ercolana2008}, Owen et al., \cite{owen2012}). And finally, also the accretion of a planet with a mass of a few Jupiter can play an important role in the dissipation of the disc. Which mechanism is ultimately dominating the dispersion process is not yet determined. We present ESA {\it Herschel} Space Observatory (Pilbratt et al. \cite{pilbratt2010}) spectroscopy of 20 HAEBEs and 5 A-type debris discs, covering several transitions of abundant atoms and molecules that can be used as crucial tests of our understanding of disc physics and chemistry in the upper layers of the disc. The observations cover a significant part of the disc surface that was not accessible before. Our observations are part of the {\it Herschel} Open Time Key Programme (OTKP) "GAS in Protoplanetary Systems" (GASPS; P.I. Dent; see Dent et al. \cite{dent2012}). With this paper, we want to obtain a better understanding of HAEBE discs by relating several gas tracers and excitation mechanisms with stellar and disc properties. What gas species are present in a HAEBE disc and at what temperatures? What is the physical and chemical structure of the disc chemistry? What is the dominant excitation mechanism of gas in HAEBE discs? In Sect.\,\ref{s_targets}, we describe the sample and our methods to derive the stellar and disc parameters. In Sect.\,\ref{s_spec} we present the spectroscopy and the line detections. We discuss gas lines as a diagnostic tool in Sect.\,\ref{s_conditions} and look for correlations between the observed line fluxes. We relate our detections and upper limits to stellar and disc parameters in Sect.\,\ref{s_ana}. Finally, we round off with conclusions in Sect.\,\ref{s_conc}. \begin{table*} \caption{Main stellar parameters of the sample.} \begin{tabular}{lllrlllllll} \hline\hline Star &\multicolumn{1}{c}{ Alternative}& Sp. Type & $T_{\rm eff}$ & $\log g_*$ & [M/H] & Refs. &\multicolumn{1}{c}{$d$} & $L_*/L_\odot$ &A$_{V}$&\multicolumn{1}{c}{Age} \\ &\multicolumn{1}{c}{Name}& & (K) & & & &\multicolumn{1}{c}{(pc)} & &&\multicolumn{1}{c}{(Myr)} \\ \hline AB Aur & HD 31293 & A0 Ve & 9280 & 4.00 & {\it 0.00} & 1 & $139.3\pm 19.0$ & $33.0\pm 9.2$ &0.25& $5.0\pm 1.0$ \\ HD 31648 & MWC 480 & A3-5 Ve & 8250 & 4.00 & 0.00 & 2 & $137.0\pm 26.2$ & $13.7\pm 5.5$ &0.16& $8.5\pm 2.0$ \\ HD 35187 & & A2 Ve & 8915 & {\it 4.00} & {\it 0.00} & 3 & $114.2\pm 32.4$ & $17.4\pm 10.6$ &0.78& $9.0\pm 2.0$ \\ HD 36112 & MWC 758 & A5 IVe & 7750 & 3.50 & --0.08$^a$ & 4 & $279.3\pm 75.0$ & $33.7\pm 19.3$ &0.16& $3.7\pm 2.0$ \\ & & & & & --0.14$^b$ & 4 & & && $3.5\pm 2.0$ \\ CQ Tau &HD 36910 & F3 Ve & 6900 & {\it 4.35} & {\it 0.00} & 5 & $113.0\pm 24.0$ & $3.4\pm 1.5$ &1.40& $4.0\pm 2.0$ \\ HD 97048 & CU Cha & A0 Ve & 10000 & 4.00 & --0.05$^a$ & 4 & $158.5\pm 15.7$ & $30.7\pm 6.1$ &1.15& $6.5\pm 1.0$ \\ & & & & &--0.75$^c$ & 4 & & && $4.0\pm 0.5$ \\ HD 100453 & & A9 Ve & 7400 & 4.20 & +0.30 & 6 & $121.5\pm 9.7$ & $8.8\pm1.4$ &0.00& $>10$ \\ & & & & & --0.02$^a$ & 4 & & && $10.0\pm 2.0$ \\ & & & & & --0.09$^b$ & 4 & & && $9.0\pm 2.0$ \\ HD 100546 & & B9 Ve & 10470 & 3.50 & --0.08$^a$ &3, 4, 7& $96.9\pm 4.0$ & $22.7\pm 1.9$ &0.09& -- \\ & & & & & --1.30$^d$& 4 & & && $3.8\pm 0.5$ \\ HD 104237 & DX Cha & A4-5 Ve & 8550 & 3.90 & +0.16 & 8 & $114.7\pm 4.7$ & $28.8\pm 2.4$ &0.16& $5.5\pm 0.5$ \\ HD 135344 B &SAO 206462& F3-4 Ve & 6810 & 4.40 & +0.14$^a$ & 10, 4 & $142.0\pm 27.0$ & $8.1\pm 3.1$ &0.37& $10.0\pm 2.0$ \\ & & & & & --0.08$^b$ & 4 & & && $9.5\pm 2.0$ \\ HD 139614 & & A7 Ve & 7400 & 4.00 & --0.50 & 6 & $140\pm 42$ & $7.6\pm 4.6$ &0.00& $9.2\pm 2.0$ \\ & & & & & --0.19$^a$ & 4 & & && $11.5\pm 2.0$ \\ & & & & & --0.27$^b$ & 4 & & && $10.5\pm 2.0$ \\ HD 141569 A & & B9.5 Ve & 10000 & 4.28 & --0.50 & 11 & $116.1\pm 8.1$ & $29.6\pm 4.2$ &0.37& $4.7\pm 0.3$ \\ HD 142527 & & F6 IIIe & 6250 & 3.62 & {\it 0.00} & 12 & $233.1\pm 56.2$ & $33.2\pm 16.9$ &0.59& $2.0\pm 0.5$ \\ HD 142666 & & A8 Ve & 7500 & 4.30 & +0.20 & 6 & $145\pm 43$ & $13.5\pm 8.0$ &0.93& $9.0\pm 2.0$ \\ HD 144668 & HR 5999 & A7 IVe & 7925 & {\it 4.00} & {\it 0.00} & 13 & $162.9\pm 15.3$ & $50.8\pm 9.5$ &0.47& $2.8\pm 1.0$ \\ HD 150193 & MWC 863 & A2 IVe & 8970 & 3.99 & {\it 0.00} & 2 & $216.5\pm 76.0$ & $48.7\pm 38.0$ &1.55& $3.8\pm 2.0$ \\ KK Oph A & & A6 Ve & 8000 & {\it 4.00} & {\it 0.00} & 16 & {\it 260} & 13.7 &1.60& $8.0\pm 2.0$ \\ KK Oph B & & G5 Ve & 5750 & {\it 4.50} & {\it 0.00} & 17 & {\it 260} & 2.1 &2.80& $8.0\pm 2.0$ \\ 51 Oph &HD 158643 & B9.5 IIIe & 10250 & 3.57 & +0.10 & 2 & $124.4\pm 3.7$ & $285.0\pm 17.0$ &0.37& $0.7\pm 0.5$ \\ HD 163296 & MWC 275 & A1 Ve & 9250 & 4.07 & +0.20 & 14 & $118.6\pm 11.1$ & $33.1\pm 6.2$ &0.47& $5.5\pm 0.5$ \\ HD 169142 & MWC 925 & A7-8 Ve & 7500 & 4.00 & --0.50 & 15 & $145\pm 43$ & $9.4\pm 5.6$ &0.00& $7.7\pm 2.0$ \\ \hline 49 Cet & HD 9672 & A4 V & 9500 & 4.30 & +0.10 & 2 & $59.4\pm 1.0$ & $21.0\pm 0.7$ &0.22&$8.9_{-2.4}^{+6.1}$, $61_{-46}^{+119}$ \\ HD 32297 & & A0 V & 9520 & {\it 4.15} & {\it 0.00} & 18 & $112.4\pm 10.8$ & $10.9\pm 2.1$ &0.62& -- \\ HR 1998 &HD 38678, $\zeta$ Lep& A2 IV-V & 8500 & 4.27 & --0.76 & 9, 19 & $21.6\pm 0.1$ & $14.0\pm 0.1$ &0.00& $1250\pm250$ \\ HR 4796 A &HD 109573 A & A0 Ve & 9750 & 4.32 & {\it 0.00} & 9 & $72.8\pm 1.8$ & $23.4\pm1.1$ &0.00& $10.0\pm2.0$ \\ HD 158352 & HR 6507 & A7 V & 7500 & 3.85 & {\it 0.00} & 9 & $59.6\pm 0.9$ & $17.7\pm 0.6$ &0.00& $1000\pm200$ \\ \hline \end{tabular} \label{t_para} {\bf Notes}: Quantities in {\it italics} are assigned. ($a$) These metallicities are weighted averages of all the elemental abundances listed in Tables 2, 3 and 4 of Acke \& Waelkens (2004), see Appendix A of Montesinos et al. (2009) for details; ($b/c/d$) Metallicities assumed to be in the same proportion as the species [Fe {\sc i}]/([Si {\sc ii}])/[Fe {\sc ii}], respectively (see Table 3 of Acke \& Waelkens, 2004). Refs.: (1) Woitke et al. (GASPS) (in prep), (2) Montesinos et al. (2009), (3) Manoj et al. (2006), (4) Acke \& Waelkens (2004), (5) Testi et al. (2003), (6) Guimar\~aes et al (2006), (7) Levenhagen et al. (2006), (8) Fumel \& B\"ohm (2011), (9) Allende-Prieto et al. (1999), (10) M\"uller et al. (2011), (11) Mer\'{\i}n et al. (2004), (12) Verhoeff et al. (2011), (13) van Boekel et al. (2005), (14) Tilling et al. (GASPS) (2012), (15) Meeus et al. (GASPS) (2010), (16) Herbig (2005), (17) Carmona et al. (2007), (18) Torres et al. (2006), (19) Gray (2006). Distances are from the revised parallaxes by van Leeuwen (2007) except for HD 135344 B (M\"uller et al. 2011) and HD 139614, HD 142666 and HD 169142 (van Boekel et al. 2005). \end{table*}
|
\label{s_conc} In this paper, we studied the gas content with {\em Herschel} PACS spectroscopy for a sample of 20 Herbig Ae stars and five A-type debris discs, that can be summarised as follows: \begin{enumerate} \item{We detect the \Odrie \ \mic \ line in all the Herbig Ae stars of our sample, while it is absent in the debris discs, confirming the lack of a large amount of gas in these discs. The \Odrie \ line is by far the strongest line observed in our spectra, next in strength (if detected) are \Ohon \ and \CII; they are only detected in 5 (25\%) and 6 (30\%) sources, respectively. } \item{The CO mid to high $J$ transitions (18-17 and 29-28) are only detected in 9 (45\%) and 2 (10\%) objects, respectively. % The highest $J$ (33-32 and 36-35) CO lines covered in our spectra are not seen at all in our sample. The three detections of CO $J$=29-28 are in the three strongest UV emitting objects, AB Aur, HD 97048 and HD 100546, revealing the need for a large amount of UV photons for this line to become visible. Interesting in this respect is the transitional disc of HD 141569A, where we did not detect CO $J$=18-17, but did detect a strong line of \Ohon. This cannot be attributed to a difference in UV luminosity but rather to significant inner disc clearing, and to a more tenous disc.} \item{We detect two lines of CH$^+$ in HD100546, and also detect CH$^+$ for the first time in HD 97048, only the second Herbig Ae star in which it is detected.} \item{Hydroxyl and \water \ are important ingredients of the disc chemistry. However, we found water and OH in only one object, HD 163296, which has a settled disc. The previous detection of \water, announced by Sturm et al. (\cite{sturm2010}) in HD 100546 cannot be confirmed. The misidentification was caused by a blend with the CH$^+$ line, often present at the same wavelength as \water. The non-detection of \water \ in most sources is in agreement with findings of Pontoppidan et al. (\cite{pontoppidan2010}) and Fedele et al. (\cite{fedele2011}), who also did not detect water at IR wavelengths, despite dedicated surveys.} \end{enumerate} We correlated the strength of the \Odrie \,\mic \,\ line with stellar parameters, as well as disc properties. We can summarise our findings as follows: \begin{enumerate} \item{The \Odrie \ line flux correlates weakly with the continuum flux at 63 \,\mic. The line flux ratios of \Odrie / \Ohon \ and \Odrie / \CII \ are between 10 and 30.} \item{We found that three of our sources, AB Aur, HD 97048 and HD 100546, have very strong \Odrie \ line fluxes, when compared to the rest of the sample. These three sources have group I discs and have the highest \teff \ values in the sample, and thus have more stellar UV flux. Indeed, we see a correlation between the {\em total} (stellar + accretion) UV luminosity and the strength of the \Odrie \ line. We do not see a correlation with the X-ray luminosity, which is rather low in our sample of HAEBE stars. } \item{We did not find a correlation between the accretion rate estimated from the Balmer discontinuity, and a tentative one with the Br$\gamma$ line. This shows that accretion is not the main driver of the \Odrie \ excitation in HAEBEs. The bulk of the UV luminosity is photospheric rather than from accretion.} \item{Sources with high \Odrie \ fluxes also have high PAH luminosity, which can both be related to their high UV fluxes. We also see a correlation with the luminosity of the \Oopt \ line. } \item{The disc geometry (flat versus flared) does not uniquely determine the strength of the \Odrie \,\ line flux. The three strongest lines are observed in flared discs, but once these sources are excluded, there is no significant difference in line strength observed between the group I and II discs.} \item{We found a strong correlation between the continuum at 63\,\mic \ and at 1.3\,mm. There is no correlation between the \Odrie \,\ line strength and the strength of the dust continuum at 1.3\,mm. We also did not find a correlation with the slope of the far-IR to mm SED, nor with the IR excess. } \item{We see a weak correlation with the strength of $^{12}$CO $J$ = 3-2 line. Based on the line ratio \Odrie /$^{12}$CO $J$=2-1, we can derive an estimate of the gas mass present in the disc. We found M$_{\rm{gas}}$ between 0.25 and 25 $\times \ 10^{-3}$ \Msun, consistent with the estimates derived from a detailed modelling of HD 163296 (M$_{\mathrm{gas}} \sim 15-120 \times 10^{-3}$ \Msun; Tilling et al. \cite{tilling2012}) and HD 169142 (M$_{\mathrm{gas}} \sim 3-6.5 \times 10^{-3}$ \Msun; Meeus et al. \cite{meeus2010}).} \end{enumerate} A picture emerges for the protoplanetary discs around Herbig Ae/Be stars where the stellar UV flux is the main parameter controlling the strength of the \Odrie \ line, which is formed just below the disc surface. An increased amount of settling can enhance the line flux for those species (such as water or OH) that are formed deeper in the disc, where the density is higher. We plan to follow-up on this study with detailed modelling of a few key objects: AB Aur \& HD 97048 and HD 135344 B \& HD 142527 (group I, high and low UV, respectively), HD163296 (group II), HD141569 A (transitional disc), and finally the enigmatic compact disc of 51 Oph. Our modelling results will further aid in the understanding of the chemistry and physical processes present in Herbig Ae/Be discs. \begin{acknowledgement} We would like to thank the PACS instrument team for their dedicated support and A. Carmona for discussions about gas line diagnostics. G. Meeus, C. Eiroa, I. Mendigut\'ia and B. Montesinos are partly supported by AYA-2008-01727 and AYA-2011-26202. G. Meeus is supported by RYC-2011-07920. CAG and SDB acknowledge NASA/JPL for funding support. WFT thanks CNES for financial support. FM thanks the Millennium Science Initiative (ICM) of the Chilean ministry of Economy (Nucleus P10-022-F). FM, IK and WFT acknowledge support from the EU FP7-2011 under Grant Agreement No. 284405. CP acknowledges funding from the EU FP7 under contract PERG06-GA-2009-256513 and from ANR of France under contract ANR-2010-JCJC-0504-01. PACS has been developed by a consortium of institutes led by MPE (Germany) and including UVIE (Austria); KUL, CSL, IMEC (Belgium); CEA, OAMP (France); MPIA (Germany); IFSI, OAP/AOT, OAA/CAISMI, LENS, SISSA (Italy); IAC (Spain). This development has been supported by the funding agencies BMVIT (Austria), ESA-PRODEX (Belgium), CEA/CNES (France), DLR (Germany), ASI (Italy), and CICT/MCT (Spain). This research has made use of the SIMBAD database, operated at CDS , Strasbourg, France. \end{acknowledgement}
| 12 | 6 |
1206.3413
|
1206
|
1206.4005_arXiv.txt
|
We present \textit{Spitzer Space Telescope} mid-infrared IRS spectra, supplemented by ground-based optical observations, of the classical novae V1974 Cyg, V382 Vel, and V1494 Aql more than 11, 8, and 4 years after outburst respectively. The spectra are dominated by forbidden emission from neon and oxygen, though in some cases, there are weak signatures of magnesium, sulfur, and argon. We investigate the geometry and distribution of the late time ejecta by examination of the emission line profiles. Using nebular analysis in the low density regime, we estimate lower limits on the abundances in these novae. In V1974 Cyg and V382 Vel, our observations confirm the abundance estimates presented by other authors and support the claims that these eruptions occurred on ONe white dwarfs. We report the first detection of neon emission in V1494 Aql and show that the system most likely contains a CO white dwarf. %
|
\label{sec:intro} A classical nova (CN) explosion results from a thermonuclear runaway (TNR) on the surface of a white dwarf (WD) that has accreted matter from a dwarf secondary star in a close binary system. The elemental composition of the ejected material depends both on the degree of thermonuclear processing during the TNR and the amount and composition of the material dredged up from the underlying WD. CO-type nova eruptions are thought to arise on the surface of relatively low-mass (M$_{\mathrm{WD}} < 1.2$ M$_{\odot}$) WDs composed primarily of carbon and oxygen, whereas evidence suggests that ONe-type (or simply ``neon'') novae arise from TNRs on high-mass (M$_{\mathrm{WD}} > 1.2$ M$_{\odot}$) oxygen, neon, and magnesium-rich WDs \citep{Gehrz08b}. Infrared (IR) observations are critical for accurately constraining photoionization models of CN ejecta \citep[e.g.][]{Helton10a} since diagnostics derived from only the optical or UV fail to sample a broad enough range of ionization and excitation levels in the emission lines. IR observations may also allow the determination of abundances in systems that are subject to such a high degree of extinction that few emission features are detected in the UV or optical \citep[e.g., V1721 Aql;][]{Hounsell11}. In addition, late-epoch IR observations of CNe are particularly valuable for revealing metals in the ejecta through emission lines with very low critical densities. In some cases, these may arise from elemental species with few or weak transitions at ultraviolet or optical wavelengths. Ideally, the abundances of metals are determined by comparing the flux of the forbidden metal lines to hydrogen recombination lines present at the same time. However, at late epochs ($\gtsimeq 1000$ days post-outburst), the infrared spectra are devoid of hydrogen recombination line emission, and thus, we are limited to estimates of relative abundances, unless a proxy for the hydrogen number density, $n_{H}$, is available. In these cases one may use early post-eruption measurements to constrain the total mass of the hydrogen expelled by the nova allowing the calculation of the metal abundances relative to hydrogen. In this paper, we report on mid-infrared observations CNe in their late nebular stages ($>4$ years post-outburst), including V1974 Cyg, V382 Vel, and V1494 Aql. Table \ref{tab:properties} lists the targets with some of their basic observational characteristics. In \S\ref{sec:OldNovae_Obs}, we detail the \textit{Spitzer} and supporting optical observations. This is followed by an overview of the abundance determination methods and parameter selection in \S\ref{sec:Abundances}. Section \ref{sec:Analysis} then presents a detailed analysis of each of the targets, which includes examination of the emission lines to characterize the nebular environment as well as abundance calculations. In \S\ref{sec:Discussion}, we place the derived abundances in context with results for other systems of both the CO and ONe classes. Finally, we present our conclusions in \S\ref{sec:Conclusions}. \begin{deluxetable*}{lccccccccc} \tabletypesize{\scriptsize} \setlength{\tabcolsep}{0.05in} \tablewidth{0pt} \tablecaption{Fundamental Properties \label{tab:properties}} \tablehead{ \colhead{Target}& \colhead{RA (J2000.0)}& \colhead{Dec (J2000.0)}& \colhead{t$_{max}$ (UT)}& \colhead{m$_{V,max}$}& \colhead{t$_{2}$\tablenotemark{a}}& \colhead{t$_{3}$\tablenotemark{b}}& \colhead{Speed Class}& \colhead{Type\tablenotemark{c}}& \colhead{Dust?} } \startdata V1500 Cyg& 21$^{h}$11$^{m}$36\fs61& +48\degr09'01\farcs9& 1975 Aug. 29.5& 1.8& 2.9& 3.6& Very Fast& Hybrid\tablenotemark{d}; ONe?& No\\ NQ Vul& 19$^{h}$29$^{m}$14\fs68& +20\degr27'59\farcs7& 1976 Oct. 21.8& 6.5& 23& 53& Fast&\ion{Fe}{2}; ONe?& Yes\\ V1668 Cyg& 21$^{h}$42$^{m}$35\fs31& +44\degr01'55\farcs0& 1978 Sep. 12.2& 6.0& 12.2& 24.3& Fast& \ion{Fe}{2}; CO& Yes\\ V1974 Cyg& 20$^{h}$30$^{m}$31\fs66& +52\degr37'51\farcs3& 1992 Feb. 20.8& 4.2& 16-24& 47& Fast& \ion{Fe}{2}; ONe& No\\ V382 Vel& 10$^{h}$44$^{m}$48\fs37& -52\degr25'30\farcs6& 1999 May 22.4& 2.3& 4.5-6& 9-12.5& Very Fast& \ion{Fe}{2}; ONe& No\\ V1494 Aql& 19$^{h}$23$^{m}$05\fs28& +04\degr57'21\farcs6& 1999 Dec. 03.4& 4.0& 6.6& 16& Very Fast& \ion{Fe}{2}; CO?& No\\[-2.5ex] \enddata \tablenotetext{a}{t$_{2}$ is the time (in days) it takes for the nova to decline 2 visual magnitudes from its maximum.} \tablenotetext{b}{t$_{3}$ is the time (in days) it takes for the nova to decline 3 visual magnitudes from its maximum.} \tablenotetext{c}{The first entry is for the classification of the spectrum as presented by \citet{Williams92}. The second entry identifies the system based on the underlying WD composition.} \tablenotetext{d}{``Hybrid'' novae exhibit spectra that transition from \ion{Fe}{2}-type to He/N-type.} \end{deluxetable*}
|
\label{sec:Conclusions} We have presented IR and optical observations of three CNe in their late nebular stages ($> 4$ years post-outburst). We derived lower limits to abundances by number, relative to hydrogen using ejecta masses obtained during earlier stages of the outbursts. In the case of V1494 Aql, we used nearly contemporaneous optical spectra to obtain an independent estimate of the O abundance through direct comparison to H$\beta$. We placed lower limits on the abundances of oxygen and neon (9 and 35 times solar, respectively) in the ejecta of V1974 Cygni and found that the high abundances of these elements is consistent with earlier studies. Our derived abundances support the conclusion that the system contains an ONe WD. Although the emission lines of neon were weak relative to the [\ion{O}{4}] line at 25.91 \micron, the profiles suggested that the oxygen and neon emission may arise in different regions of the ejecta. Further, the stability of the oxygen line profile implied that the ejecta were still expanding ballistically and had not undergone substantial deceleration by the surrounding ambient medium. The late time spectra of V382 Vel revealed emission lines from oxygen, neon, argon and sulfur, allowing us to estimate lower limits to the abundances of each of these elements. In particular, we found that the neon abundance was at least 18 times solar, with respect to hydrogen, oxygen was at least 1.7 times solar, and argon and sulfur were at least 0.1 times solar. The neon and oxygen abundances were consistent with results from previous studies. Our values represent the first abundance estimates for argon or sulfur in the ejecta of V382 Vel, but unfortunately they do not significantly constrain the abundances of these species. Examination of the emission line structure during this late optically thin stage demonstrated that the various emitting species had different spatial distributions in the ejecta and indicate the possible presence of ionization gradients. Our optical and \textit{Spitzer} IR observations of V1494 Aql provided the first detection of neon in this object. Based upon these data, we derived a minimum abundance of neon relative to hydrogen, relative to solar of about 5. This neon abundance is not high enough to confirm an ONe progenitor WD and, taken in concert with the high oxygen abundance ($\gtsimeq 14$ times solar), more strongly suggests a CO WD. The late time observation of neon in the ejecta of V1494 Aql reveals the importance of high sensitivity observations in the IR and near-UV regimes as well as the value of late time observations for characterizing the physical conditions and geometry of the nebular environment. Lower limits to the abundance of magnesium and sulfur were found to be 3.4 and 0.5 times solar, respectively.
| 12 | 6 |
1206.4005
|
1206
|
1206.1882_arXiv.txt
|
Results of speckle observations at the 4.1-m SOAR telescope in 2012 (158 measures of 121 systems, 27 non-resolutions) are reported. The aim is to follow fast orbital motion of recently discovered or neglected close binaries and sub-systems. Here 8 previously known orbits are defined better, two more are completely revised, and five orbits are computed for the first time. Using differential photometry from {\it Hipparcos} or speckle and the standard relation between mass and absolute magnitude, the component's masses and dynamical parallaxes are estimated for all 15 systems with new or updated orbits. Two astrometric binaries HIP 54214 and 56245 are resolved here for the first time, another 8 are measured. We highlight several unresolved pairs that may actually be single despite multiple historic measures, such as 104~Tau and f~Pup AB. Continued monitoring is needed to understand those enigmatic cases.
|
Close binaries with fast orbital motion resolved by speckle interferometry and adaptive optics require frequent measures to compute their orbits. This shifts the main problem of visual orbits from insufficiently long time coverage, as typical for binaries studied in the past two centuries, to sparse time sampling. Many close pairs discovered by W.~S.~Finsen in the 1960s have completed several revolutions, but their orbits still remain undetermined for the lack of data. This is also true for speckle and {\it Hipparcos} binaries discovered in the 1980s and 1990s but not followed further. We try to address this issue here by re-visiting close pairs resolved recently and other binaries in need of follow-up. Knowledge of binary-star orbits is of fundamental value to many areas of astronomy. They provide direct measurements of stellar masses and distances, inform us on the processes of star formation through statistics of orbital elements, and allow dynamical studies of multiple stellar systems, circumstellar matter \citep{Kennedy2012}, and planets \citep{Roberts2011}. A large fraction of visual binaries are late-type stars within 100\,pc amenable to search of exo-planets. The current orbit catalog contains some poor or wrong orbital solutions based on insufficient data. The only way to improve the situation is by getting new measures and revising those orbits. Data on binary-star measures and orbits are collected by the Washington Double Star Catalog, WDS \citep{WDS}\footnote{See current version at \url{http://ad.usno.navy.mil/wds/}} and associated archives such as the {\em 4-th Catalog of Interferometric Measurements of Binary Stars}, INT4\footnote{\url{http://ad.usno.navy.mil/wds/int4.html}}, and the {\it 6$^{th}$ Orbit Catalog of Orbits of Visual Binary Stars}, VB6 \citep{VB6}.\footnote{\url{http://ad.usno.navy.mil/wds/orb6.html}} These resources are extensively used here. This paper continues series of speckle interfero\-metry observations published by \citet[][hereafter TMH10]{TMH10}, \citet[][hereafter SAM09]{SAM09}, and \citet[][HTM12]{HTM12}. We used same equipment and data reduction methods. Section~\ref{sec:data} recalls the observing technique and presents new measures and non-resolutions. Updated and new orbits for 15 systems are given in Section~\ref{sec:orb}, with estimates of masses and dynamical parallaxes and brief comments on each system. In Section~\ref{sec:other} we draw attention to two particular groups: resolved pairs with astrometric accelerations and unresolved binaries which are either false discoveries or enigmatic. Section~\ref{sec:concl} summarizes the results.
|
\label{sec:concl} This work provides follow-up measures of close binary stars to be used in calculation or refinement of their orbits. Fifteen orbits are contributed to the VB6 catalog. Speckle interferometry is very efficient. Only a modest investment of telescope time (few nights per year at 4-m telescopes) is needed to supply good-quality speckle measures for calculating orbits of fast binaries and making the existing orbits accurate and definitive. Bright stars can be observed in twilight or through transparent clouds. One class of objects to benefit from the speckle follow-up are {\it Hipparcos} astrometric binaries, mostly nearby low-mass dwarfs. Two such stars are resolved here for the first time, few more are measured. Astrometry of these and other binaries requires knowledge of their orbits to disentangle them from parallax and PM. Future space astrometric missions like {\it Gaia} will be too short to do this and will rely heavily on the VB6 catalog. This is one more reason to follow the motion of fast binaries with speckle interferometry {\em now}. Determination of a large number of orbits is a routine task. However, any large sample contains unusual or particularly interesting objects. This might be the case of ``ghost'' binary companions that have been resolved several times, yet seem non-existent. Here we attract attention to two such cases, 104~Tau and f~Pup, and to some other visual companions with seemingly erratic motion and frequent disappearances. It is difficult to accept that these resolutions, some by very accomplished observers, are all spurious. Continued monitoring of such ``ghosts'' is needed in hope of collecting crucial observations and eventually explaining this phenomenon.
| 12 | 6 |
1206.1882
|
1206
|
1206.6977_arXiv.txt
|
{Subluminous B stars (sdBs) form the extremely hot end of the horizontal branch and are therefore related to the blue horizontal branch (BHB) stars. While the rotational properties of BHB stars have been investigated extensively, studies of sdB stars have concentrated on close binaries that are influenced by tidal interactions between their components. Here we present a study of 105 sdB stars, which are either single stars or in wide binaries where tidal effects become negligible. The projected rotational velocities have been determined by measuring the broadening of metal lines using high-resolution optical spectra. All stars in our sample are slow rotators (${v_{\rm rot}\sin{i}}<10\,{\rm km\,s^{-1}}$). Furthermore, the $v_{\rm rot}\sin{i}$-distributions of single sdBs are similar to those of hot subdwarfs in wide binaries with main-sequence companions as well as close binary systems with unseen companions and periods exceeding $\simeq1.2\,{\rm d}$. We show that blue horizontal and extreme horizontal branch stars are also related in terms of surface rotation and angular momentum. Hot blue horizontal branch stars ($T_{\rm eff}>11\,500\,{\rm K}$) with diffusion-dominated atmospheres are slow rotators like the hot subdwarf stars located on the extreme horizontal branch, which lost more envelope and therefore angular momentum in the red-giant phase. The uniform rotation distributions of single and wide binary sdBs pose a challenge to our understanding of hot subdwarf formation. Especially the high fraction of helium white dwarf mergers predicted by theory seems to be inconsistent with the results presented here.
|
} Subluminous B stars (sdBs) show similar colours and spectral characteristics to main sequence stars of spectral type B, but are less luminous. Compared to main sequence B stars, the hydrogen Balmer lines in the spectra of sdBs are stronger while the helium lines are much weaker. The strong line broadening and the early confluence of the Balmer series is caused by the high surface gravities ($\log\,g\simeq5.0-6.0$) of these compact stars ($R_{\rm sdB}\simeq0.1-0.3\,R_{\rm \odot}$). Subluminous B stars are considered to be core helium-burning stars with very thin hydrogen envelopes and masses of about half a solar mass (Heber \cite{heber86}) located at the extreme end of the horizontal branch (EHB). \subsection{Hot subdwarf formation \label{sec:formation}} The origin of EHB stars is still unknown (see Heber \cite{heber09} for a review). The key question is how all but a tiny fraction of the red-giant progenitor's hydrogen envelope was removed at the same time at which the helium core has attained the mass ($\simeq0.5\,M_{\rm \odot}$) to ignite the helium flash. The reason for this high mass loss at the tip of the red giant branch (RGB) is unclear. Several single-star scenarios are under discussion (D'Cruz et al. \cite{dcruz96}; Sweigart \cite{sweigart97}; De Marchi \& Paresce \cite{demarchi96}; Marietta et al. \cite{marietta00}), which require either a fine-tuning of parameters or extreme environmental conditions that are unlikely to be met for the bulk of the observed subdwarfs in the field. According to Mengel et al. (\cite{mengel76}), the required strong mass loss can occur in a close-binary system. The progenitor of the sdB star has to fill its Roche lobe near the tip of the red-giant branch (RGB) to lose a large part of its hydrogen envelope. The merger of close binary white dwarfs was investigated by Webbink (\cite{webbink84}) and Iben \& Tutukov (\cite{iben84}), who showed that an EHB star can form when two helium core white dwarfs (WDs) merge and the product is sufficiently massive to ignite helium. Politano et al. (\cite{politano08}) proposed that the merger of a red giant and a low-mass main-sequence star during a common envelope (CE) phase may lead to the formation of a rapidly rotating single hot subdwarf star. Maxted et al. (\cite{maxted01}) determined a very high fraction of radial velocity variable sdB stars, indicating that about two thirds of the sdB stars in the field are in close binaries with periods of less than 30 days (see also Morales-Rueda et al. \cite{morales03}; Napiwotzki et al. \cite{napiwotzki04a}; Copperwheat et al. \cite{copperwheat11}). Han et al. (\cite{han02,han03}) used binary population synthesis models to study the stable Roche lobe overflow (RLOF) channel, the common envelope ejection channel, where the mass transfer to the companion is dynamically unstable, and the He-WD merger channel. The companions are mostly main sequence stars or white dwarfs. If the white dwarf companion is sufficiently massive, the merger of the binary system might exceed the Chandrasekhar mass and explode as a type Ia supernova. Indeed, Maxted et al. (\cite{maxted00}) found the sdB+WD binary KPD\,1930$+$2752 to be a system that might qualify as a supernova Ia progenitor (see also Geier et al. \cite{geier07}). In Paper~I of this series (Geier et al. \cite{geier10b}) more candidate systems with massive compact companions, either massive white dwarfs or even neutron stars and black holes, have been found. Furthermore, Geier et al. (\cite{geier11c}) reported the discovery of an eclipsing sdB binary with a brown dwarf companion. \begin{figure}[t!] \begin{center} \resizebox{\hsize}{!}{\includegraphics{tefflogg_vsini.eps}} \caption{$T_{\rm eff}-\log{g}$-diagram for the entire sample (not RV-variable) under study. The helium main sequence (HeMS) and the EHB band (limited by the zero-age EHB, ZAEHB, and the terminal-age EHB, TAEHB) are superimposed with EHB evolutionary tracks for solar metallicity taken from Dorman et al. (\cite{dorman93}) labelled with their masses. Open circles mark objects where only upper limits could be derived for $v_{\rm rot}\sin{i}$, filled circles objects with significant $v_{\rm rot}\sin{i}$. The size of the symbols scales with the value of $v_{\rm rot}\sin{i}$.} \label{fig:tefflogg} \end{center} \end{figure} \subsection{Rotation on the horizontal branch \label{sec:rotation}} The rotational properties of horizontal branch (HB) stars both in globular clusters and in the field all the way from the red to the blue end have been studied extensively in the last decades (Peterson \cite{peterson83b}, \cite{peterson85}; Peterson et al. \cite{peterson83a}, \cite{peterson95}; Behr et al. \cite{behr00a}, \cite{behr00b}; Kinman et al. \cite{kinman00}; Recio-Blanco et al. \cite{recio02}, \cite{recio04}; Behr \cite{behr03a}, \cite{behr03b}; Carney et al. \cite{carney03}, \cite{carney08}). Most of these investigations were motivated by the puzzling horizontal branch morphologies in some globular clusters and the search for second or third parameters responsible for this phenomenon. The most interesting result of these studies is the discovery of a significant change in the rotational velocities of blue horizontal branch (BHB) stars when their effective temperatures exceed $\simeq11\,500\,{\rm K}$. HB stars cooler than this threshold value show ${v_{\rm rot}\sin\,i}$ values up to $40\,{\rm km\,s^{-1}}$, while the hotter stars rotate with velocities lower than $\simeq10\,{\rm km\,s^{-1}}$. The transition in rotational velocity is accompanied by a jump towards brighter magnitudes in the colour-magnitude diagram (Grundahl et al. \cite{grundahl99}) and a change in the atmospheric abundance pattern. Stars cooler than $\simeq11\,500\,{\rm K}$ show the typi\-cal abundances of their parent population (e.g. For \& Sneden \cite{for10}), while stars hotter than that are in general depleted in helium and strongly enriched in iron and other heavy elements such as titanium or chromium. Lighter elements such as magnesium and silicon on the other hand have normal abundances (Behr et al. \cite{behr03a,behr03b}; Fabbian et al. \cite{fabbian05}; Pace et al. \cite{pace06}). Diffusion processes in the stellar atmosphere are most likely responsible for this effect. Michaud et al. (\cite{michaud83}) predicted such abundance patterns before the anomalies were observed (see also Michaud et al. \cite{michaud08}). Caloi (\cite{caloi99}) explained the sharp transition between the two abundance patterns as the disappearance of subsurface convection layers at a critical temperature. Sweigart (\cite{sweigart02}) indeed found that thin convective layers below the surface driven by hydrogen ionization should exist and shift closer to the surface when the effective temperature increases. At about $12\,000\,{\rm K}$ the convection zone reaches the surface and the outer layer of the star becomes fully radiative. Since convection is very efficient in mixing the envelope, diffusion processes do not operate in HB star atmospheres of less than $12\,000\,{\rm K}$. Slow rotation is considered as a prerequisite for diffusion. Michaud (\cite{michaud83}) was the first to show that meridional circulation stops the diffusion process as soon as the rotational velocity reaches a critical value and could explain the chemical peculiarity of HgMn stars in this way. Quievy et al. (\cite{quievy09}) performed similar calculations for BHB stars and showed that the critical rotational velocity is somewhere near $\simeq20\,{\rm km\,s^{-1}}$ at the transition temperature of $11\,500\,{\rm K}$. This means that the atmospheric abundances of stars with lower ${v_{\rm rot}\sin\,i}$ should be affected by diffusion processes. What causes the slow rotation that allows diffusion to happen, is still unclear. Sills \& Pinsonneault (\cite{sills00}) used a standard stellar evolution code and modelled the distribution of rotational velocities on the BHB. In order to reproduce the two populations of fast and slow rotators they assumed two distinct main sequence progenitor populations with different rotational veloci\-ties. In their picture the slowly rotating BHBs originate from slowly rotating main sequence stars. Another possible explanation is the spin-down of the surface layers by diffusion itself. Sweigart (\cite{sweigart02}) argued that the radiative levitation of iron triggers a weak stellar wind that carries away angular momentum. Vink \& Cassisi (\cite{vink02}) showed that such winds are radiatively driven. Brown (\cite{brown07}) used a stellar evolution code including rotation and modelled the distribution of rotational velocities on the BHB. This code allows one to follow the evolution of the progenitor star through the He-flash. Brown (\cite{brown07}) argues that no signifi\-cant angular momentum is exchanged between the stellar core and stellar envelope during the flash. The surface rotation of their models highly depends on the rotation of the surface convection zone, which contains most of the outer envelope's angular momentum. Hot BHB stars without surface convection zone rotate slower than the cooler ones with convection zone. This approach allows one to reproduce the observed ${v_{\rm rot}\sin\,i}$-distribution of BHB stars without assuming bimodal stellar po\-pulations (Brown et al. \cite{brown08}). While the rotational properties of horizontal branch stars both in globular clusters and in the field are thoroughly examined, the investigation of EHB stars has mostly been restricted to close binary systems, where tidal interaction plays a major role (Geier et al. \cite{geier10b}). Very few apparently single EHB stars have been studied so far, all of which are slow rotators ($<10\,{\rm km\,s^{-1}}$, e.g. Heber et al. \cite{heber00}; Edelmann \cite{edelmann01}). In this paper we determine the projected rotational velocities of more than a hundred sdB stars by measuring the broadening of metal lines. In Paper~I (Geier et al. \cite{geier10b}) the rotational properties of sdBs in close binary system were derived and used to clarify the nature of their unseen companions. Here we focus on the rotational properties of apparently single sdBs and wide binary systems, for which tidal interactions become negligible. In Sect.~\ref{sec:obs} we give an overview of the observations of high-resolution spectra and the atmospheric parameters of our sample. The determination of the rotational properties of 105 sdB stars are described in Sect.~\ref{sec:rotlow}, the results are interpreted in Sect.~\ref{sec:distrib} and compared to the corresponding results for BHB stars in Sect.~\ref{sec:bhb}. The implications for the sdB formation scenarios and the further evolution to the white dwarf cooling tracks are discussed in Sect.~\ref{sec:implications} and Sect.~\ref{sec:wd}, respectively. Finally, a summary is given in Sect.~\ref{sec:summary}.
|
} We extended a project to derive the rotational properties of sdB stars and determined the projected rotational velocities of 105 sdB stars by measuring the broadening of metal lines using high-resolution spectra. All stars in our sample have low ${v_{\rm rot}\sin{i}}<10\,{\rm km\,s^{-1}}$. For $\simeq75\%$ of the sample we were able to determine significant rotation. The distribution of projected rotational velocities is consistent with an average rotation of $\simeq8\,{\rm km\,s^{-1}}$ for the sample. Furthermore, the $v_{\rm rot}\sin{i}$-distributions of single sdBs, hot subdwarfs with main sequence companions vi\-sible in the spectra and close binary systems with periods exceeding $1.2\,{\rm d}$ are similar. The BHB and EHB stars are related in terms of surface rotation and angular momentum. Hot BHBs with diffusion-dominated atmospheres are slow rotators like the EHB stars, which lost more envelope and therefore angular momentum on the RGB. The uniform rotation distributions of single and wide binary sdBs pose a challenge to our understanding of hot subdwarf formation. Especially the high fraction of He-WD mergers predicted by theory seems to be inconsistent with our results. We predict that the evolutionary channel of single sdB stars gives birth to a small population of rapidly rotating WDs with masses lower than average. \begin{table*}[t!] \caption{Projected rotational velocities of single sdBs and sdBs with visible companions.} \label{tab:vrot} \begin{center} \begin{tabular}{llllllll} \hline \noalign{\smallskip} System & $T_{\rm eff}$ & $m_{B/V}$ & S/N & seeing & $N_{\rm lines}$ & ${v_{\rm rot}\,\sin\,i}$ & Instrument \\ & [K] & [mag] & & [arcsec] & & [${\rm km\,s^{-1}}$] \\ \noalign{\smallskip} \hline \noalign{\smallskip} HE\,0151$-$3919 & 20\,800 & 14.3$^{\rm B}$ & 66 & 1.06 & 27 & $<5.0$ & UVES \\ EC\,21494$-$7018 & 22\,400 & 11.2$^{\rm V}$ & 85 & & 16 & 8.6 $\pm$ 1.8 & FEROS \\ EC\,15103$-$1557 & 22\,600 & 12.9$^{\rm V}$ & 163 & & 8 & 6.5 $\pm$ 1.6 & FEROS \\ HD\,4539 & 23\,000 & 10.1$^{\rm B}$ & 112 & & 21 & 3.9 $\pm$ 1.0 & FEROS \\ EC\,11349$-$2753 & 23\,000 & 12.5$^{\rm B}$ & 185 & & 49 & 4.7 $\pm$ 1.0 & FEROS \\ EC\,14345$-$1729 & 23\,300 & 13.1$^{\rm V}$ & 117 & & 40 & 6.2 $\pm$ 1.0 & FEROS \\ HE\,0539$-$4246 & 23\,300 & 14.5$^{\rm B}$ & 40 & 0.87 & 19 & $<10.0$ & UVES \\ HE\,2307$-$0340$^{\rm no}$ & 23\,300 & 15.8$^{\rm B}$ & 61 & 0.89 & 17 & $<5.0$ & UVES \\ PG\,1432$+$004$^{\rm nr}$ & 23\,600 & 12.0$^{\rm B}$ & 170 & & 13 & 4.7 $\pm$ 1.0 & FEROS \\ EC\,19563$-$7205$^{\rm c}$ & 23\,900 & 12.8$^{\rm B}$ & 85 & & 34 & 9.8 $\pm$ 1.0 & FEROS \\ EC\,20106$-$5248 & 24\,500 & 12.6$^{\rm V}$ & 114 & & 47 & 7.8 $\pm$ 1.0 & FEROS \\ BD$+$48$^{\circ}$\,2721 & 24\,800 & 10.5$^{\rm B}$ & 326 & & 10 & 4.7 $\pm$ 1.4 & FOCES \\ HD\,205805 & 25\,000 & 9.9$^{\rm B}$ & 255 & & 20 & 4.5 $\pm$ 1.0 & FEROS \\ HE\,0321$-$0918$^{\rm no}$ & 25\,100 & 14.7$^{\rm B}$ & 37 & 1.22 & 7 & 5.6 $\pm$ 2.3 & UVES \\ PG\,1653$+$131 & 25\,400 & 14.1$^{\rm B}$ & 68 & & 32 & 8.3 $\pm$ 1.0 & FEROS \\ HE\,2237$+$0150 & 25\,600 & 15.8$^{\rm B}$ & 40 & 0.78 & 11 & 8.5 $\pm$ 1.8 & UVES \\ PG\,0342$+$026 & 26\,000 & 11.1$^{\rm B}$ & 190 & & 54 & 6.2 $\pm$ 1.0 & FEROS \\ PG\,2122$+$157$^{\rm c}$ & 26\,000 & 15.0$^{\rm B}$ & 67 & 0.78 & 13 & 7.9 $\pm$ 1.4 & UVES \\ GD\,108 & 26\,100 & 13.3$^{\rm B}$ & 97 & & 6 & 6.0 $\pm$ 1.8 & FEROS \\ Feige\,65 & 26\,200 & 11.8$^{\rm B}$ & 150 & & 18 & 7.2 $\pm$ 1.1 & FOCES \\ PHL\,44$^{\rm l}$ & 26\,600 & 13.0$^{\rm B}$ & 85 & & 31 & 8.4 $\pm$ 1.0 & FEROS \\ HE\,0513$-$2354 & 26\,800 & 15.8$^{\rm B}$ & 21 & 0.99 & 18 & $<10.0$ & UVES \\ HE\,0135$-$6150 & 27\,000 & 16.3$^{\rm B}$ & 37 & 0.71 & 13 & 5.5 $\pm$ 1.7 & UVES \\ SB\,815 & 27\,000 & 10.6$^{\rm B}$ & 85 & & 48 & 7.3 $\pm$ 1.0 & FEROS \\ HE\,2201$-$0001 & 27\,100 & 16.0$^{\rm B}$ & 35 & 1.10 & 28 & $<5.0$ & UVES \\ PG\,2205$+$023 & 27\,100 & 12.9$^{\rm B}$ & 36 & & 9 & $<10.0$ & FEROS \\ PG\,2314$+$076$^{\rm nb}$ & 27\,200 & 13.9$^{\rm B}$ & 71 & & 6 & 6.0 $\pm$ 2.2 & FEROS \\ SB\,485 & 27\,700 & 13.0$^{\rm B}$ & 112 & 0.71 & 24 & 7.2 $\pm$ 1.0 & UVES \\ KUV\,01542$-$0710$^{\rm c}$ & 27\,800 & 16.3$^{\rm B}$ & 58 & 0.92 & 8 & 7.2 $\pm$ 2.1 & UVES \\ HE\,2156$-$3927$^{\rm c}$ & 28\,000 & 14.1$^{\rm B}$ & 62 & 0.61 & 16 & 7.0 $\pm$ 1.2 & UVES \\ EC\,03591$-$3232 & 28\,000 & 11.2$^{\rm V}$ & 131 & & 34 & 4.8 $\pm$ 1.0 & FEROS \\ EC\,12234$-$2607 & 28\,000 & 13.8$^{\rm B}$ & 60 & & 19 & 6.8 $\pm$ 1.4 & FEROS \\ PG\,2349$+$002 & 28\,000 & 12.0$^{\rm B}$ & 68 & & 11 & 5.7 $\pm$ 1.5 & FEROS \\ HE\,2322$-$0617$^{\rm c,no}$ & 28\,100 & 15.7$^{\rm B}$ & 62 & 0.70 & 15 & 6.8 $\pm$ 1.3 & UVES \\ PG\,0258$+$184$^{\rm c,no}$ & 28\,100 & 15.2$^{\rm B}$ & 48 & 0.99 & 12 & 7.2 $\pm$ 1.7 & UVES \\ HE\,0136$-$2758$^{\rm no}$ & 28\,200 & 16.2$^{\rm B}$ & 29 & 1.20 & 27 & $<5.0$ & UVES \\ HE\,0016$+$0044$^{\rm no}$ & 28\,300 & 13.1$^{\rm B}$ & 58 & 0.67 & 14 & 6.5 $\pm$ 1.3 & UVES \\ PG\,1549$-$001$^{\rm no}$ & 28\,300 & 14.8$^{\rm B}$ & 45 & 1.16 & 20 & 5.6 $\pm$ 1.1 & UVES \\ HE\,2349$-$3135 & 28\,500 & 15.6$^{\rm B}$ & 53 & 1.13 & 13 & 10.0 $\pm$ 1.7 & UVES \\ EC\,01120$-$5259 & 28\,900 & 13.5$^{\rm V}$ & 73 & & 19 & 5.8 $\pm$ 1.2 & FEROS \\ HE\,0007$-$2212$^{\rm no}$ & 29\,000 & 14.8$^{\rm B}$ & 53 & 0.64 & 21 & 7.4 $\pm$ 1.0 & UVES \\ LB\,275$^{*}$ & 29\,300 & 14.9$^{\rm B}$ & 48 & 1.16 & 20 & 5.6 $\pm$ 1.1 & UVES \\ EC\,03263$-$6403 & 29\,300 & 13.2$^{\rm V}$ & 32 & & 40 & $<5.0$ & FEROS \\ HE\,1254$-$1540$^{\rm c,no}$ & 29\,700 & 15.2$^{\rm B}$ & 54 & 0.75 & 20 & 7.2 $\pm$ 1.3 & UVES \\ PG\,1303$+$097 & 29\,800 & 14.3$^{\rm B}$ & 51 & & 18 & 6.1 $\pm$ 1.5 & FEROS \\ HE\,2222$-$3738 & 30\,200 & 14.2$^{\rm B}$ & 61 & 0.83 & 28 & 8.7 $\pm$ 1.0 & UVES \\ HE\,2238$-$1455 & 30\,400 & 16.0$^{\rm B}$ & 48 & 0.80 & 14 & $<5.0$ & UVES \\ EC\,03470$-$5039 & 30\,500 & 13.6$^{\rm V}$ & 53 & & 9 & 7.3 $\pm$ 2.0 & FEROS \\ Feige\,38 & 30\,600 & 12.8$^{\rm B}$ & 148 & & 34 & 5.3 $\pm$ 1.0 & FEROS \\ HE\,1038$-$2326$^{\rm c}$ & 30\,600 & 15.8$^{\rm B}$ & 34 & 1.27 & 28 & $<5.0$ & UVES \\ PG\,1710$+$490 & 30\,600 & 12.1$^{\rm B}$ & 80 & & 11 & 7.1 $\pm$ 1.6 & FOCES \\ HE\,0447$-$3654 & 30\,700 & 14.6$^{\rm V}$ & 44 & & 11 & 7.3 $\pm$ 1.8 & FEROS \\ EC\,14248$-$2647 & 31\,400 & 12.0$^{\rm V}$ & 104 & & 14 & 7.0 $\pm$ 1.5 & FEROS \\ HE\,0207$+$0030$^{\rm no}$ & 31\,400 & 14.7$^{\rm B}$ & 27 & 1.30 & 7 & 5.1 $\pm$ 2.3 & UVES \\ KPD\,2109$+$4401$^{\rm s}$ & 31\,800 & 13.2$^{\rm B}$ & 136 & & 9 & 10.5 $\pm$ 1.6 & HIRES \\ EC\,02542$-$3019 & 31\,900 & 12.8$^{\rm B}$ & 65 & & 13 & 7.3 $\pm$ 1.5 & FEROS \\ $[$CW83$]$\,1758$+$36$^{\rm nb}$ & 32\,000 & 11.1$^{\rm B}$ & 110 & & 5 & 5.7 $\pm$ 1.4 & FOCES \\ TON\,S\,155$^{\rm c}$ & 32\,300 & 14.9$^{\rm B}$ & 35 & 0.85 & 14 & $<5.0$ & UVES \\ EC\,21043$-$4017 & 32\,400 & 13.1$^{\rm V}$ & 65 & & 8 & 5.6 $\pm$ 1.8 & FEROS \\ EC\,20229$-$3716 & 32\,500 & 11.4$^{\rm V}$ & 153 & & 29 & 4.5 $\pm$ 1.0 & FEROS \\ HS\,2125$+$1105$^{\rm c}$ & 32\,500 & 16.4$^{\rm B}$ & 29 & 0.80 & 8 & 6.0 $\pm$ 2.4 & UVES \\ HE\,1221$-$2618$^{\rm c}$ & 32\,600 & 14.9$^{\rm B}$ & 35 & 1.06 & 11 & 6.8 $\pm$ 1.6 & UVES \\ HS\,2033$+$0821$^{\rm no}$ & 32\,700 & 14.4$^{\rm B}$ & 43 & 1.14 & 37 & $<5.0$ & UVES \\ HE\,0415$-$2417$^{\rm no}$ & 32\,800 & 16.2$^{\rm B}$ & 34 & 0.83 & 10 & $<10.0$ & UVES \\ EC\,05479$-$5818 & 33\,000 & 13.1$^{\rm V}$ & 81 & & 20 & 5.8 $\pm$ 1.1 & FEROS \\ HE\,1200$-$0931$^{\rm c,no}$ & 33\,400 & 16.2$^{\rm B}$ & 30 & 0.86 & 12 & $<5.0$ & UVES \\ \hline \\ \end{tabular} \end{center} \end{table*} \begin{table*}[t!] \begin{center} \begin{tabular}{llllllll} \hline \noalign{\smallskip} System & $T_{\rm eff}$ & $m_{B}$ & S/N & seeing & $N_{\rm lines}$ & ${v_{\rm rot}\,\sin\,i}$ & Instrument \\ & [K] & [mag] & & [arcsec] & & [${\rm km\,s^{-1}}$] \\ \noalign{\smallskip} \hline \noalign{\smallskip} PHL\,932 & 33\,600 & 12.0$^{\rm B}$ & 102 & 1.10 & 12 & 9.0 $\pm$ 1.3 & UVES \\ HE\,1422$-$1851$^{\rm c,no}$ & 33\,900 & 16.3$^{\rm B}$ & 14 & 0.58 & 10 & $<10.0$ & UVES \\ PHL\,555 & 34\,100 & 13.8$^{\rm B}$ & 56 & 0.88 & 17 & 6.9 $\pm$ 1.2 & UVES \\ HE\,1419$-$1205$^{\rm c}$ & 34\,200 & 16.2$^{\rm B}$ & 28 & 0.69 & 16 & $<10.0$ & UVES \\ PG\,1219$+$534$^{\rm s}$ & 34\,300 & 12.4$^{\rm B}$ & 140 & & 11 & 5.7 $\pm$ 1.4 & HIRES \\ HS\,2216$+$1833$^{\rm c}$ & 34\,400 & 13.8$^{\rm B}$ & 54 & 0.90 & 11 & 5.3 $\pm$ 1.6 & UVES \\ HE\,1050$-$0630$^{\rm no}$ & 34\,500 & 14.0$^{\rm B}$ & 59 & 1.20 & 28 & 7.3 $\pm$ 1.4 & UVES \\ HE\,1519$-$0708$^{\rm no}$ & 34\,500 & 15.6$^{\rm B}$ & 20 & 0.84 & 8 & 9.0 $\pm$ 2.4 & UVES \\ HE\,1450$-$0957 & 34\,600 & 15.1$^{\rm B}$ & 32 & 0.71 & 6 & 9.0 $\pm$ 2.4 & UVES \\ EC\,13047$-$3049 & 34\,700 & 12.8$^{\rm V}$ & 68 & & 5 & 6.8 $\pm$ 3.6 & FEROS \\ HS\,1710$+$1614$^{\rm no}$ & 34\,800 & 15.7$^{\rm B}$ & 38 & 1.30 & 13 & $<5.0$ & UVES \\ PHL\,334 & 34\,800 & 12.5$^{\rm B}$ & 87 & & 13 & $<5.0$ & FEROS \\ Feige\,49 & 35\,000 & 13.2$^{\rm B}$ & 119 & & 40 & 6.2 $\pm$ 1.0 & FEROS \\ HE\,2151$-$1001$^{\rm s}$ & 35\,000 & 15.6$^{\rm B}$ & 42 & 0.66 & 6 & 6.7 $\pm$ 2.4 & UVES \\ PG\,0909$+$164$^{\rm s}$ & 35\,300 & 13.9$^{\rm B}$ & 52 & & 4 & $<10.0$ & FEROS \\ HE\,1021$-$0255$^{\rm no}$ & 35\,500 & 15.3$^{\rm B}$ & 40 & 1.61 & 11 & $<10.0$ & UVES \\ PG\,0909$+$276$^{\rm nb}$ & 35\,500 & 13.9$^{\rm B}$ & 82 & & 13 & 9.3 $\pm$ 1.4 & FOCES \\ HE\,0101$-$2707 & 35\,600 & 15.0$^{\rm B}$ & 67 & 0.85 & 12 & 8.1 $\pm$ 1.5 & UVES \\ EC\,03408$-$1315 & 35\,700 & 13.6$^{\rm V}$ & 66 & & 11 & 8.8 $\pm$ 1.8 & FEROS \\ HE\,1352$-$1827$^{\rm c}$ & 35\,700 & 16.2$^{\rm B}$ & 24 & 0.85 & 5 & 8.2 $\pm$ 2.7 & UVES \\ PG\,1207$-$032$^{\rm no}$ & 35\,700 & 13.1$^{\rm B}$ & 50 & 0.64 & 9 & 6.6 $\pm$ 1.6 & UVES \\ HE\,0019$-$5545 & 35\,700 & 15.8$^{\rm B}$ & 38 & 0.76 & 7 & 5.9 $\pm$ 2.3 & UVES \\ GD\,619 & 36\,100 & 13.9$^{\rm B}$ & 96 & 0.81 & 10 & 6.1 $\pm$ 1.5 & UVES \\ HE\,1441$-$0558$^{\rm c,no}$ & 36\,400 & 14.4$^{\rm B}$ & 30 & 0.70 & 8 & 6.9 $\pm$ 2.0 & UVES \\ HE\,0123$-$3330 & 36\,600 & 15.2$^{\rm B}$ & 48 & 0.66 & 8 & 6.9 $\pm$ 1.8 & UVES \\ PG\,1505$+$074 & 37\,100 & 12.2$^{\rm B}$ & 153 & & 4 & $<5.0$ & FEROS \\ HE\,1407$+$0033$^{\rm no}$ & 37\,300 & 15.5$^{\rm B}$ & 35 & 0.72 & 9 & $<10.0$ & UVES \\ PG\,1616$+$144$^{\rm nb}$ & 37\,300 & 13.5$^{\rm B}$ & 44 & & 4 & $<10.0$ & FEROS \\ EC\,00042$-$2737$^{\rm c}$ & 37\,500 & 13.9$^{\rm B}$ & 37 & & 9 & $<10.0$ & FEROS \\ PHL\,1548 & 37\,400 & 12.5$^{\rm B}$ & 90 & & 10 & 9.1 $\pm$ 1.6 & FEROS \\ PB\,5333$^{\rm nb}$ & 40\,600 & 12.5$^{\rm B}$ & 66 & & 2 & $<10.0$ & FEROS \\ $[$CW83$]$\,0512$-$08 & 38\,400 & 11.3$^{\rm B}$ & 124 & & 14 & 7.7 $\pm$ 1.1 & FEROS \\ \hline \\ \end{tabular} \tablefoot{The average seeing is only given if the spectra were obtained with a wide slit in the course of the SPY survey. In all other cases the seeing should not influence the measurements. $^{\rm c}$Main sequence companion visible in the spectrum (Lisker et al. \cite{lisker05}). $^{\rm s}$Pulsating subdwarf of V\,361\,Hya type. $^{\rm l}$Pulsating subdwarf of V\,1093\,Her type. No short-period pulsations have been detected either by $^{\rm nb}$Bill\`{e}res et al. (\cite{billeres02}), $^{\rm nr}$Randall et al. (\cite{randall06}) or $^{\rm no}$\O stensen et al. (\cite{oestensen10}). $^{*}$Misidentified as CBS\,275 in Lisker et al. (\cite{lisker05}).} \end{center} \end{table*} \begin{table*}[t!] \caption{Projected rotational velocities of radial velocity variable sdBs.} \label{tab:vrotrv} \begin{center} \begin{tabular}{lllllll} \hline \noalign{\smallskip} System & $T_{\rm eff}$ & $m_{B/V}$ & S/N & $N_{\rm lines}$ & ${v_{\rm rot}\,\sin\,i}$ & Instrument\\ & [K] & [mag] & & & [${\rm km\,s^{-1}}$] & \\ \noalign{\smallskip} \hline \noalign{\smallskip} TON\,S\,135 & 25\,000 & 13.1$^{\rm B}$ & 45 & 35 & 6.4 $\pm$ 1.0 & FEROS \\ LB\,1516$^{\rm l}$ & 25\,200 & 12.7$^{\rm B}$ & 58 & 23 & 6.0 $\pm$ 1.3 & FEROS \\ PHL\,457$^{\rm l}$ & 26\,500 & 13.0$^{\rm B}$ & 59 & 47 & 6.1 $\pm$ 1.0 & FEROS \\ EC\,14338$-$1445 & 27\,700 & 13.5$^{\rm V}$ & 71 & 39 & 8.9 $\pm$ 1.0 & FEROS \\ PG\,1725$+$252 & 28\,900 & 11.5$^{\rm B}$ & 45 & 11 & 7.4 $\pm$ 1.1 & HRS \\ PG\,1519$+$640 & 30\,300 & 12.1$^{\rm B}$ & 104 & 11 & 9.4 $\pm$ 1.4 & FOCES \\ PG\,2151$+$100 & 32\,700 & 12.9$^{\rm B}$ & 69 & 9 & 9.0 $\pm$ 1.7 & FEROS \\ \hline \\ \end{tabular} \tablefoot{$^{\rm l}$Pulsating subdwarf of V\,1093\,Her type.} \end{center} \end{table*} \begin{table*}[t!] \caption{Comparison with literature.} \label{tab:vrotlit} \begin{center} \begin{tabular}{lrrl} \hline \noalign{\smallskip} System & This work & Literature & Reference \\ & ${v_{\rm rot}\,\sin\,i}$ & ${v_{\rm rot}\,\sin\,i}$ & \\ & [${\rm km\,s^{-1}}$] & [${\rm km\,s^{-1}}$] & \\ \noalign{\smallskip} \hline \noalign{\smallskip} KPD\,2109$+$4401 & $10.5\pm1.6$ & $<10.0$ & Heber \\ PG\,1219$+$534 & $5.7\pm1.4$ & $<10.0$ & et al. (\cite{heber00}) \\ \noalign{\smallskip} \hline \noalign{\smallskip} BD$+$48$^{\circ}$\,2721 & $4.7\pm1.4$ & $<5.0$ & Edelmann \\ Feige\,65 & $7.2\pm1.1$ & $<5.0$ & et al. (\cite{edelmann01}) \\ HD\,205805 & $4.5\pm1.0$ & $<5.0$ & \\ HD\,4539 & $3.9\pm1.0$ & $<5.0$ & \\ LB\,1516 & $6.0\pm1.3$ & $<5.0$ & \\ PG\,0342$+$026 & $6.2\pm1.0$ & $<5.0$ & \\ PG\,0909$+$276 & $9.3\pm1.4$ & $<5.0$ & \\ PHL\,932 & $9.0\pm1.3$ & $<5.0$ & \\ \noalign{\smallskip} \hline \noalign{\smallskip} Feige\,49 & $6.2\pm1.0$ & $0.0^{*}$ & Przybilla \\ HD\,205805 & $4.5\pm1.0$ & $0.0^{*}$ & et al. (\cite{przybilla06}) \\ \noalign{\smallskip} \hline \noalign{\smallskip} \end{tabular} \tablefoot{$^{*}$Adopted value for line fits is below the detection limit.} \end{center} \end{table*}
| 12 | 6 |
1206.6977
|
1206
|
1206.2848_arXiv.txt
|
We present analytic flux prescriptions for broadband spectra of self-absorbed and optically thin synchrotron radiation from gamma-ray burst afterglows, based on one-dimensional relativistic hydrodynamic simulations. By treating the evolution of critical spectrum parameters as a power-law break between the ultrarelativistic and non-relativistic asymptotic solutions, we generalize the prescriptions to any observer time. Our aim is to provide a set of formulas that constitutes a useful tool for accurate fitting of model-parameters to observational data, regardless of the dynamical phase of the outflow. The applicability range is not confined to gamma-ray burst afterglows, but includes all spherical outflows (also jets before the jet-break) that produce synchrotron radiation as they adiabatically decelerate in a cold, power-law medium. We test the accuracy of the prescriptions and show that numerical evidence suggests that typical relative errors in the derivation of physical quantities are about 10 per cent. A software implementation of the presented flux prescriptions combined with a fitting code is freely available on request and on-line \footnotemark. Together they can be used in order to directly fit model parameters to data.
|
\let\thefootnote\relax\footnotetext{$\!\!\!\! \dag \,\,$ The URL is http://www.astro.uva.nl/research/cosmics/gamma-ray-bursts/software/.} Gamma-ray bursts (GRBs) are believed to be produced by powerful relativistic outflows resulting from the catastrophic death of massive stars (\citealt{Woosley1993}), or the merger of two compact objects (\citealt{Eichler1989}). The burst itself (prompt emission) likely arises from internal shocks occurring due to the variability of the central engine \citep{Rees1994,SariPiran1997}, while the \textit{afterglow} emission comes from the interaction of the same outflow with the medium surrounding the burster \citep{Rees1992,Paczynski1993}. Although the dominant radiation process behind the prompt emission is not yet clear, it is well established that the afterglow radiation is dominated by synchrotron emission from shock-accelerated electrons \citep{MeszarosRees1993,vanParadijs2000}. The prompt emission is typically very brief and concentrated at high energies. On the other hand, afterglows are often visible over many more orders of magnitude both in time- and frequency-space (see \citealt{Meszaros2006} for an extensive review of GRB research). Thus, studying the afterglow radiation allows us to put a multitude of constrains both on the microphysics (e.g. the fraction of internal energy going to the magnetic fields and the power-law accelerated electrons) governing the shocked plasma \citep{Spitkovsky2008,Sironi2009}, as well as on the basic physical parameters describing the phenomenon macroscopically, like blast-wave energy, density and structure of the surrounding medium. It is these macroscopic parameters that determine the dynamical evolution of the outflow. However, a full analytic description of the dynamics is only possible when the spatial component of the four-velocity of the outflow $\beta \gamma$ is either much greater \citep{Blandford1976} or much smaller \citep{Sedov1959} than $1$. Therefore, relativistic hydrodynamic (RHD) simulations \citep{Kobayashi1999,Meliani2007,Zhang2009,DeColle2012a} are the most accurate means of studying the intermediate dynamical regime linking the ultrarelativistic and Newtonian solutions (see however \citealt{Huang1999}). Van Eerten et al. (2010a) have numerically studied the lightcurves of outflows advancing through all three dynamical regimes and have shown that the transition is slow, i.e. deviations from the expected relativistic behaviour appear well before the Newtonian asymptotes are reached, mainly due to the changing adiabatic index of the shocked gas. For typical burst parameters (isotropic blast-wave energy $E_{\textrm{iso}}=10^{52}\, \textrm{ergs}$, ambient medium number density $n_{0}=1\, \textrm{cm}^{-3}$) the Sedov-Taylor scalings set in at a few thousand days, observer time, implying that an appreciable portion of the afterglow (typically around hundreds of days) emanates from outflows with dynamics that cannot be described analytically by either of the two asymptotic solutions. Soon after the discovery of the first afterglows \citep{Costa1997,Groot1997} efforts were made to calculate broadband synchrotron spectra and light curves as a function of burst parameters \citep{Wijers1997,Sari1998,Panaitescu2000}. The common way to do this is by tying the dynamical evolution of the blast-wave in regimes where this is feasible to radiation models that, according to the jump conditions at the shock front, calculate the resulting spectra. Despite the success of early efforts in capturing general features of the observed spectra, the progressive refinement of the used models has led to very different estimates of the physical parameters of individual bursts. For example \citet{Wijers1999} and \citet{Granot2002} have both fitted GRB 970508 and their derived values differ up to 3 orders of magnitude. Furthermore, the applicability of most of these models is restricted to a particular dynamical phase and only recently have there been a few attempts at addressing the entire evolution of spectra and light curves through the performance of simulations \citep{Zhang2009, vanEerten2012b,Wygoda2011, DeColle2012a}. Even so, these models do not contain a treatment of self-absorption (apart from \citealt{vanEerten2012b}), necessary to model low-frequency observations with e.g. the Expanded Very Large Array EVLA (\citealt{Perley2011}), the Low-Frequency Array LOFAR (\citealt{Morganti2011}) and the upcoming Karoo Array Telescope MeerKAT (\citealt{Booth2009}) and Square Kilometre Array SKA (\citealt{Carilli2004}), and do not provide flux-prescriptions. Van Eerten et al. (2012) do provide a broadband fit code, but it requires the use of a parallel computer network. The purpose of this work is to provide accurate analytic flux-prescriptions, based on one-dimensional RHD simulations, that are applicable to both the ultrarelativistic and Newtonian phase but also, and perhaps more importantly, to observer times when the outflow is transitioning from the former to the latter. Apart from the typical, initially ultrarelativistic outflows of GRBs, the formulas we present are applicable to Newtonian as well as relativistic (\citealt{Soderberg2010}) outflows from supernova explosions in the adiabatic phase \citep{Chevalier1977,Chevalier1982,Draine1993} and mildly relativistic outflows originating from binary neutron star (NS) mergers, expected to produce detectable electromagnetic (EM) counterparts to gravitational wave detections \citep{Nakar2011, Metzger2012b}. They can also be applied to relativistic outflows resulting from the tidal disruption of stars by a super-massive black hole \citep{Bloom2011,Metzger2012a}, under the limiting assumption of quasi-spherical outflow. The presented model naturally accounts for the exact shape of the synchrotron spectrum (including self-absorption, but ignoring cooling) and the structure of the blast-wave. Furthermore, it can be applied to a range of power-law density structures of the circumburst medium, a possibility previously studied by \citet{vanEerten2009} and \citet{DeColle2012b}. This allows for modelling of more complex environments, expected on a theoretical basis (\citealt{Ramirez-Ruiz2005}) and deduced observationally (\citealt{Curran2009}). With such a tool a light curve can be fitted without the need of costly simulations and the restrictions of models specialising in specific dynamical phases, or preset structures of the circumburst medium. In order to obtain the flux-prescriptions we combine three elements: (1) analytic formulas for flux-scalings during the Blandford-McKee and the Sedov-Taylor phases, (2) one-dimensional, hydrodynamic simulations, using the adaptive mesh refinement code \textsc{amrvac} \citep{Meliani2007,Keppens2012}, that span the whole range of the dynamics (from ultrarelativistic to Newtonian velocities) and (3) a radiative-transfer code that uses simulation snapshots and a parametrisation of the microphysics to calculate instantaneous spectra. This paper is organised as follows: in section \ref{numerics} we briefly describe the setup of the performed simulations and the subsequent calculations of spectra and light curves. In section \ref{flux-prescriptions} we present formulas that describe the flux as a function of physical parameters in both the relativistic and the Newtonian phase of the outflow. That includes specifying the flux at any given power-law segment, as well as a description of the sharpness of the spectral breaks that occur at critical frequencies. We then proceed in section \ref{transrel} to connect the two dynamical regimes (relativistic and Newtonian) by treating the transition from the former to the latter as a prolonged temporal \textit{break} the characteristics of which can be linked to the physical parameters of the burst and its environment. In section \ref{using} we describe how one can make use of the flux-prescriptions to obtain spectra at any given time. We also show comparisons between spectra based on simulations and spectra constructed using the provided prescriptions. Finally, we present an application of this model to mildly relativistic outflows from binary neutron star mergers in order to assess the recent predictions of \citet{Nakar2011} concerning the detectability of the produced radio signals. In section \ref{discuss} we discuss our results and the implications of this work for GRB afterglow models.
|
We have used high-resolution 1D hydrodynamic simulations to calibrate flux scalings of synchrotron, self-absorbed radiation for GRB afterglows in the relativistic and Newtonian dynamical phases (BM and ST, respectively). The transition from the former to the latter is well described by approximating the evolution of spectral parameters (maximum flux and positions of critical frequencies) by power-law breaks connecting the two asymptotic behaviours. The properties of these breaks have been modelled in terms of the values of the physical parameters describing the blast-wave. This way we have managed to encapsulate the precision of the performed simulations into a set of analytic formulas that trace the full evolution of GRB afterglows, from the ultrarelativistic to the Newtonian phase. Due to the general nature of the prescriptions, they are applicable to any source characterised by emission of synchrotron radiation from an adiabatic blast-wave. A numerical code containing a practical implementation of the results presented in this paper combined with a fitting code is freely available on request and on-line at http://www.astro.uva.nl/research/cosmics/gamma-ray-bursts/software/.
| 12 | 6 |
1206.2848
|
1206
|
1206.2309_arXiv.txt
|
Here we propose a mechanism for efficiently growing intermediate mass black holes (IMBH) in disks around supermassive black holes. Stellar mass objects can efficiently agglomerate when facilitated by the gas disk. Stars, compact objects and binaries can migrate, accrete and merge within disks around supermassive black holes. While dynamical heating by cusp stars excites the velocity dispersion of nuclear cluster objects (NCOs) in the disk, gas in the disk damps NCO orbits. If gas damping dominates, NCOs remain in the disk with circularized orbits and large collision cross-sections. IMBH seeds can grow extremely rapidly by collisions with disk NCOs at low relative velocities, allowing for super-Eddington growth rates. Once an IMBH seed has cleared out its feeding zone of disk NCOs, growth of IMBH seeds can become dominated by gas accretion from the AGN disk. However, the IMBH can migrate in the disk and expand its feeding zone, permitting a super-Eddington accretion rate to continue. Growth of IMBH seeds via NCO collisions is enhanced by a pile-up of migrators. We highlight the remarkable parallel between the growth of IMBH in AGN disks with models of giant planet growth in protoplanetary disks. If an IMBH becomes massive enough it can open a gap in the AGN disk. IMBH migration in AGN disks may stall, allowing them to survive the end of the AGN phase and remain in galactic nuclei. Our proposed mechanisms should be more efficient at growing IMBH in AGN disks than the standard model of IMBH growth in stellar clusters. Dynamical heating of disk NCOs by cusp stars is transferred to the gas in a AGN disk helping to maintain the outer disk against gravitational instability. Model predictions, observational constraints and implications are discussed in a companion paper (Paper II).
|
\label{sec:intro} Extensive evidence exists that supermassive black holes ($>10^{6}M_{\odot}$) are found in the centers of most galaxies \citep[e.g.][]{b5}. Extensive evidence also exists for stellar mass black holes in our own Galaxy \citep{b68}. Stellar mass black holes are expected to form as the end product of high-mass stars. Supermassive black holes, by contrast, have grown to their current size over cosmic time, from much smaller seeds \citep[e.g.][ \& references therein]{b18,b16,b15,b90}. Intermediate mass black holes (IMBH; $\sim 10^{2}-10^{4}M_{\odot}$) may have been the original seeds for supermassive black holes or, they may have contributed to fast early growth of such seeds via mergers \citep[e.g.][]{b86,b87}. Though we expect IMBH should exist, at least as an intermediate stage on the way to a supermassive black hole, observationally the evidence for their existence is scant and ambiguous, especially compared with evidence for supermassive and stellar mass black holes. The low mass end of the supermassive black hole distribution in galactic nuclei may extend down to $\sim 10^{5}M_{\odot}$ \citep{b73}, but below this mass the evidence becomes ambiguous. The ultra-luminous X-ray sources (ULXs) observed outside galactic nuclei \citep[e.g.][]{b54} may be powered by accretion onto IMBH \citep{b87}. However ULXs could also be a explained by beamed radiation from accreting stellar-mass black holes \citep{b82} and power-law dominated ULXs might be due to background AGN. IMBH have so far been hard to find and constrain in the local Universe, either in our own Galaxy or at low z. Active galactic nuclei (AGN) are believed to be powered by accretion onto a supermassive black hole. The accretion disk should contain a population of stars and compact objects (collectively nuclear cluster objects, NCOs) that can migrate within and accrete from the disk \citep[e.g.][]{b57,b58,b51,b44,b45,b35,b96,b99}. In \citet{b96} we speculated that IMBH seeds may form efficiently in AGN disks due to NCO collisions and mergers, which is quite different from the standard model of stellar mass black holes merging in stellar clusters \citep[e.g.][]{b81,b87}. Here we argue that IMBH production is in fact far more likely and more efficient in AGN disks, with implications for AGN observations, duty cycle and supermassive black hole accretion rates. In this paper (and its companion, Paper II, McKernan et al. 2012) we discuss semi-analytically the production of intermediate mass black holes in the environment of AGN disks. Discussion of observational predictions of this model of IMBH growth as well as consequences for AGN disks, duty cycles and the demographics of activity in galactic nuclei at low and high redshift will be left to Paper II. In section \S\ref{sec:collisions}, we discuss why we think IMBH can be built in AGN disks. In section \S\ref{sec:grow} we explore mechanisms that will be important in actually growing IMBH in AGN disks, including the competing forces of eccentricity damping and excitation in the disk. The importance of IMBH migration is outlined in section \S\ref{sec:mig}. Section~\S\ref{sec:model_growth} outlines a simple model of IMBH growth in AGN disks and we highlight the remarkable parallel between the growth of IMBH in AGN disks and the growth of giant planets in protoplanetary disks. Finally in section \S\ref{sec:conclusions}, we outline our conclusions and future work.
|
\label{sec:conclusions} We show that it is possible to efficiently grow intermediate mass black holes (IMBH) from stars and compact objects within an AGN disk. Nuclear cluster objects (NCOs) in the AGN disk are subject to two competing effects: orbital excitation due to cusp dynamical heating and orbital damping due to gas in the disk. For a simple, semi-analytic model we show that gas damping dominates such that equilibrium eccentricities of disk NCOs are $e \sim 0.01$. In this case IMBH seedling formation via NCO collision is more efficient in the AGN disk than in stellar clusters (the standard model for IMBH formation). If, as we expect, gas damping dominates then the dynamical heating of disk NCOs by cusp stars is transmitted to the gas disk. This is a new, additional source of heating of the outer disk that can help counter the well-known gravitational instability ($Q \leq 1$) of the outer disk. Stellar mass black holes and hard massive binaries are likely IMBH seeds. IMBH seedlings grow by collisions with disk NCOs within their feeding zone ($a \pm 4R_{H}$) at near Eddington rates, as well as via gas accretion. IMBH seedlings will migrate within the AGN disk and so continue to feed on disk NCOs as they accrete gas. If there are regions of modest over-density of NCOs in the disk, IMBH seedling growth via collisions can be super-Eddington and a $10M_{\odot}$ IMBH seed orbiting a $10^{8}M_{\odot}$ supermassive black hole can grow to $\sim 300 M_{\odot}$ in less than the fiducial AGN disk lifetime. An over-density of disk NCOs can occur in regions of the disk where e.g. outward torques and inward torques balance, or where the aspect ratio changes, or where IMBH migration stalls. The largest IMBH will open gaps in AGN disks, analagous to giant planets in protoplanetary disks. Gap-opening IMBH are more likely to arise if: gas damping is very efficient (equilibrium disk NCO eccentricity is $\overline{e}<0.01$), or if the disk is long-lived ($>50$Myrs), or disk NCO surface density is moderately high ($>15$g$\rm{cm}^{-2}$), or if there is an IMBH seedling which survived a previous AGN phase (analagous to the survival of planets in protoplanetary disks). Our model of IMBH growth in AGN disks strongly parallels the growth of giant planets in protoplanetary disks. We leave a discussion of model predictions, observational constraints and implications of efficient IMBH growth in AGN disks to Paper II.
| 12 | 6 |
1206.2309
|
1206
|
1206.5003_arXiv.txt
|
When transiting their host stars, hot Jupiters absorb about 10\% of the light in the wings of the stellar Lyman-alpha emission line. \revised{% The absorption occurs at wavelengths Doppler-shifted from line center by $\pm 100$ km/s --- larger than the thermal speeds with which partially neutral, $\sim$$10^4$ K hydrogen escapes from hot Jupiter atmospheres.} It has been proposed that the absorption arises from $\sim$$10^6$ K hydrogen from the host stellar wind, made momentarily neutral by charge exchange with planetary H I. \revised{% The $\pm$100 km/s velocities would then be attributed to the typical velocity dispersions of protons in the stellar wind --- as inferred from spacecraft measurements of the Solar wind. } To test this proposal, we perform 2D hydrodynamic simulations of colliding hot Jupiter and stellar winds, augmented by a chemistry module to compute the amount of hot neutral hydrogen produced by charge exchange. We observe the contact discontinuity where the two winds meet to be Kelvin-Helmholtz unstable. The Kelvin-Helmholtz instability mixes the two winds; in the mixing layer, charge exchange reactions establish, within tens of seconds, a chemical equilibrium in which the neutral fraction of hot stellar hydrogen equals the neutral fraction of cold planetary hydrogen (about 20\%). In our simulations, enough hot neutral hydrogen is generated to reproduce the transit observations, and the amount of absorption converges with both spatial resolution and time. Our calculations support the idea that charge transfer between colliding winds correctly explains the Lyman-alpha transit observations --- \revised{% modulo the effects of magnetic fields, which we do not model but which may suppress mixing. Other neglected effects include, in order of decreasing importance, rotational forces related to orbital motion, gravity, and stellar radiation pressure; we discuss quantitatively the errors introduced by our approximations.} How hot stellar hydrogen cools when it collides with cold planetary hydrogen is also considered; a more careful treatment of how the mixing layer thermally equilibrates might explain the recent detection of Balmer H$\alpha$ absorption in transiting hot Jupiters.
|
\label{sec:intro} Gas-laden planets lose mass to space when their upper atmospheres are heated by stellar ultraviolet (UV) radiation. Ubiquitous in the Solar System, thermally-driven outflows modify the compositions of their underlying atmospheres over geologic time (e.g., \citealt{weissman}). Thanks to the {\it Hubble Space Telescope (HST)}, escaping winds are now observed from extrasolar hot Jupiters: Jovian-sized planets orbiting at distances $\lesssim 0.05$ AU from their host stars and bathed in intense ionizing fields. Spectroscopy with {\it HST} reveals absorption depths of $\sim$2--10\% in various resonance transitions (H I, O I, C II, Si III and Mg II) when the planet transits the star, implying gas outflows that extend for at least several planetary radii (e.g., \citealt{Vidal-Madjar2003}, VM03; \citealt{Vidal-Madjar2004}; \citealt{Ben-Jaffel2007}; \citealt{Ben-Jaffel2008}; \citealt{Vidal-Madjar2008}; \citealt{Lecavelier2010}; \citealt{Fossati2010}; \citealt{Linsky2010}). \revised{% Recent observations of HD 189733b also indicate temporal variations in H I Lyman-$\alpha$ absorption, possibly correlated with stellar X-ray activity \citep[][]{LecavelierdesEtangs:2012jq}.} These data promise to constrain the compositions of hot Jupiter atmospheres and the degrees to which they are vertically mixed (\citealt{Liang2003}; \citealt{Moses2011}). The {\it HST} observations of hot Jupiter winds are accompanied by theoretical studies that model planetary outflows starting from first principles (e.g., \citealt{Yelle2004}; \revised{% \citealt{Yelle:2006fw}; } \citealt{Tian2005}; \citealt{GarciaMunoz2007}; Murray-Clay, Chiang, \& Murray~2009, M09). These 1D hydrodynamic models generally agree that hot Jupiters like HD 209458b and HD 189733b are emitting $\dot{M} \sim 10^{10}$--$10^{11}$ g/s in mostly hydrogen gas. \revised{% Three-dimensional models include \citet{LecavelierdesEtangs:2004jm} and \citet{Jaritz:2005kr}, who emphasize the importance of tidal forces. } Do the models agree with the observations? Linsky et al.~(2010) find that their observations of C II absorption in HD 209458b can be made consistent with modeled mass loss rates, assuming the carbon abundance of the wind is not too different from solar. More comparisons between observation and theory would be welcome---particularly for hydrogen, the dominant component of the wind. But the observations of H I absorption have proven surprisingly difficult to interpret. On the one hand, the original measurements by VM03 indicate substantial ($\sim$10\%) absorption at Doppler shifts of $\pm 100$ km/s from the center of the H I Lyman-$\alpha$ line. On the other hand, theory (e.g., M09) indicates that planetary outflows, heated by photoionization to temperatures $T \lesssim 10^4$ K, blow only at $\sim$10 km/s. How can such slow planetary winds produce significant absorption at $\pm 100$ km/s? \revised{% Measurements of blueshifted velocities as large as -230 km/s in the case of HD 189733b only accentuate this problem \citep{LecavelierdesEtangs:2012jq}. } \citet[][H08]{Holmstrom2008} propose that the observed energetic neutral H atoms arise from charge exchange between planetary H I and protons from the incident {\it stellar} wind. In this interpretation, the $\pm$100 km/s velocities correspond to the thermal velocities of $10^6$ K hydrogen from the star---hydrogen which is made neutral by electron-exchange with planetary H I. The situation is analogous to that of the colliding winds of O star binaries (\citealt{Stevens:1992gf}; \citealt{lamberts}, and references therein). The H I Lyman-$\alpha$ absorption arises from the contact discontinuity where the two winds meet, mix, and charge exchange to produce hot neutral hydrogen. The calculations of H08, and those of the follow-up study by \citet[][E10]{Ekenback2010}, are based on a Monte Carlo algorithm that tracks individual ``meta-particles'' of neutral hydrogen launched from the planet. The meta-particles collide and charge exchange with stellar wind protons outside a presumed planetary magnetosphere, which is modeled as an ``obstacle'' in the shape of a bow shock. Good agreement with the Ly-$\alpha$ observations is obtained for a range of stellar and planetary wind parameters, and for a range of assumed obstacle sizes. In this work we further test the hypothesis of charge exchange first explored by H08 and E10. Our methods are complementary: instead of adopting their kinetic approach, we solve the hydrodynamic equations. We do not prescribe any obstacle to deflect the stellar wind, but instead allow the planetary and stellar winds to meet and shape each other self-consistently via their ram and thermal pressures. Some aspects of our solution are not realistic---we ignore the Coriolis force, the centrifugal force, stellar tidal gravity, and magnetic fields.\footnote{ \revised{% For recent explorations of star-planet interactions including magnetic forces, see \citet{cohenetal11a,cohenetal11b}. These simulations do not resolve the mixing layer interface between the stellar and planetary winds.}} Our goal is to develop a first-cut hydrodynamic-chemical model of the contact discontinuity between the two winds where material mixes and charge exchanges. Simple and physically motivated scaling relations will be developed between the amount of H I absorption and the properties of the stellar and planetary winds. The plan of this paper is as follows. In \S\ref{sec:method} we describe our numerical methods, which involve augmenting our grid-based hydrodynamics code to solve the chemical reactions of charge exchange, and specifying special boundary conditions to launch the two winds. In \S\ref{sec:results} we present our results, including a direct comparison with the H I Ly$-\alpha$ transit spectra of VM03, and a parameter study to elucidate how the absorption depth varies with stellar and planetary wind properties. A summary is given in \S\ref{sec:summary}, together with an assessment of the shortcomings of our study and pointers toward future work.
|
\label{sec:summary} Using a 2D numerical hydrodynamics code, we simulated the collisional interaction between two winds, one emanating from a hot Jupiter and the other from its host star. The winds were assumed for simplicity to be unmagnetized. Properties of the stellar wind were drawn directly from observations of the equatorial slow Solar wind (Sheeley et al.~1997; Qu\'emerais et al.~2007; Lemaire 2011), while those of the planetary wind were taken from hydrodynamic models of outflows powered by photoionization heating (Garc\'ia-Mu\~noz 2007; Murray-Clay et al.~2009). For our standard parameters, the mass loss rate of the star is $\dot{M}_\ast = 2 \times 10^{-14} M_{\odot}$/yr $ = 10^{12}$ g/s and the mass loss rate of the planet is $\dot{M}_p = 1.6 \times 10^{11}$ g/s $= 2.7 \times 10^{-3} M_{\rm J}$/Gyr. At the relevant distances, each wind is marginally supersonic---the stellar wind blows at $\sim$130--170 km/s (sonic Mach number $M_\ast \lesssim 1.3$) and the planetary wind blows at $\sim$12--15 km/s (Mach number $M_p \lesssim 1.5$). Thus shock compression is modest, even without additional stiffening of the gas by magnetic fields. A strong shear flow exists at the contact discontinuity between the two winds. At sufficiently high spatial resolution, we observed the interfacial flow to be disrupted by the Kelvin-Helmholtz instability. The Kelvin-Helmholtz rolls mix cold, partially neutral planetary gas with hot, completely ionized stellar gas. Charge exchange in the mixing layer produces observable amounts of hot ($10^6$ K) neutral hydrogen. Upon impacting the planetary wind, the hot stellar wind acquires, within tens of seconds, a neutral component whose fractional density equals the neutral fraction of the planetary wind (about $1-f_p^+ = 20$\%). Seen transiting against the star, hot neutral hydrogen in the mixing layer absorbs $\sim$10\% of the light in the thermally broadened wings of the stellar Lyman-$\alpha$ emission line, at Doppler shifts of $\sim$100 km/s from line center. Just such a transit signal has been observed with the {\it Hubble Space Telescope} (Vidal-Madjar et al.~2003). \revised{% The $\pm$100 km/s velocities reflect the characteristic velocity dispersions of protons in the stellar wind --- as inferred from in-situ spacecraft observations of the Solar wind (e.g., Figure 3 of \citealt{Marsch06}).} Our work supports the proposal by Holmstr\"om et al.~(2008) and Ekenb\"ack et al.~(2010) that charge exchange between the stellar and planetary winds is responsible for the Ly-$\alpha$ absorption observed by {\it HST}. \revised{% This same conclusion is reached by \citet{LecavelierdesEtangs:2012jq} in the specific case of HD 189733b.} Our ability to reproduce the observations corroborates the first-principles calculations of hot Jupiter mass loss on which we have relied (e.g., Yelle 2004; Garc\'ia-Mu\~noz 2007; Murray-Clay et al.~2009, M09). Time variations in Ly-$\alpha$ absorption are expected both from the variable stellar wind --- the Solar wind is notoriously gusty --- and from the variable planetary wind, whose mass loss rate tracks the time-variable ultraviolet and X-ray stellar luminosity. \subsection{Neglected Effects and Directions for Future Research}\label{sec:future} Although the general idea of photoionization-powered planetary outflows exchanging charge with their host stellar winds seems correct, details remain uncertain. We list below some unresolved issues, and review the effects that our simulations have neglected, in order of decreasing concern. \begin{enumerate} \item {\it Thermal equilibration in the mixing layer.} Our calculations overestimate the amount of hot neutral hydrogen produced by charge exchange because they neglect thermal equilibration. A hot neutral hydrogen atom cools by colliding with cold gas, both ionized and neutral, from the planetary wind. The concern is that hot neutral gas cools before it transits off the face of the star. Starting from where the mixing layer is well-developed (say the lower red dashed line in Figure \ref{mixing_layer}), hot neutral gas is advected off the projected stellar limb in a time \begin{equation} t_{\rm adv} \sim 2 R_p / v_\ast \sim 2 \times 10^3 \, {\rm s} \,. \end{equation} By comparison, the cooling time is of order \begin{equation} \label{tcool} t_{\rm cool} \sim \frac{1}{n_c^+ \sigma v_{\rm rel}} \sim 500 \left( \frac{2 \times 10^6 \, {\rm cm}^{-3}}{n_c^+} \right) \left( \frac{ 10^{-16} \, {\rm cm}^2}{\sigma} \right) \left( \frac{100 \,{\rm km/s}}{v_{\rm rel}} \right) \, {\rm s} \end{equation} where $n_c^+$ is the density of cold ionized hydrogen in the mixing layer, $v_{\rm rel}$ is the relative speed between hot and cold hydrogen, and $\sigma$ is the H-H$^+$ cross section for slowing down fast hydrogen, here taken to be the ``viscosity'' cross section calculated by \citet{Schultz2008}.\footnote{For slowing down fast H in a sea of cold H$^+$, there may also be a contribution to $\sigma$ from ``momentum transfer'' in ``elastic'' (non-charge-exchange) collisions. This contribution increases $\sigma$ over the viscosity cross section by only $\sim$30\%; compare Figures 6 and 7 of \citet{Schultz2008}.} Our estimate of $t_{\rm cool}$ in (\ref{tcool}) neglects cooling by neutral-neutral collisions, but we estimate the correction to be small, as $n_c^0$ is lower than $n_c^+$ by a factor of $1/(1-f_p^+) \sim 5$, and the cross section for H-H collisions is generally not greater than for H-H$^+$ collisions (A.~Glassgold 2012, personal communication; see also \citealt{Swenson1985}; note that \citet{Ekenback2010} take the relevant H-H cross section to be $10^{-17}$ cm$^2$ but do not provide a reference). That $t_{\rm cool} \sim t_{\rm adv}$ indicates our simulated column densities of hot neutral hydrogen may be too large, but hopefully not by factors of more than a few. Keeping more careful track of the velocity distributions---and excitation states---of neutral hydrogen in the mixing layer would not only improve upon our calculations of Lyman-$\alpha$ absorption, but would also bear upon the recent detection of Balmer H$\alpha$ absorption in the hot Jupiters HD 209458b and HD 189733b (\citealt{jensen2012}). \revised{% \item {\it Magnetic fields.} Insofar as our results depend on Kelvin-Helmholtz mixing, our neglect of magnetic fields is worrisome because magnetic tension can suppress the Kelvin-Helmholtz instability (\citealt{frank1996}). For numerical simulations of magnetized planetary winds interacting with magnetized stellar winds, see \citet{cohenetal11a,cohenetal11b}. These magnetohydrodynamic simulations can track how planetary plasma is shaped by Lorentz forces, but as yet do not resolve how the planetary wind mixes and exchanges charge with the stellar wind. } \item {\it Dependence of Ly-$\alpha$ absorption $A$ on the planetary wind density $n_p$.} In the same vein as item (ii), we found empirically that $A\propto n_p^{1/2}$, and argued that this result arose from the Kelvin-Helmholtz growth timescale. Ekenb\"ack et al.~(2010) found a much weaker dependence: increasing $n_p$ by a factor of 100 only increases $A$ in their models by a factor of $\sim$2 at -100 km/s and even less at positive velocities---see their Figures 8 and 9. The true dependence of $A$ on $n_p$ remains unclear. \item {\it Rotational effects and gravity.} There are a few order-unity geometrical corrections that our study is missing. Our standard stellar wind velocity of $v_\ast = 130$ km/s is comparable to the planet's orbital velocity of $v_{\rm orb} = 150$ km/s, so that in reality the stellar wind strikes the planet at an angle of roughly 45 deg. The Coriolis force will also deflect the planetary wind by an order-unity angle after a dynamical time of $r/v_{\rm orb} \sim 5\times 10^4$ s, by which time the wind will have travelled $\sim$$5 R_p$ from the planet. These geometrical effects are potentially observable---see, e.g., \revised{% \citet{Schneiter:2007ju} and \citet{Ehrenreich:2008hj} for modeling of HD 209458b,} and \citet{Rappaport2012} for a real-life example of a transit light curve that reflects the trailing comet-tail-like shape of the occulting cloud. However, these geometrical effects seem unlikely to change the basic order of magnitude of the absorption $A \sim 10$\% that we have calculated. We have also neglected planetary gravity, stellar tidal gravity, and the centrifugal force, all of which can change the planetary wind velocity. But this omission seems minor, since we have drawn our input planetary wind velocities from calculations that do account for such forces (M09), at least along the substellar ray. According to Figure 9 of M09, the planetary wind accelerates from $v_p \approx 10$ km/s at a planetocentric distance $d = 4R_p$, to $v_p \approx 30$ km/s at $d = 10R_p$. This range of velocities and corresponding distances overlap reasonably well with the range of velocities and distances characterizing our simulations. \item {\it Hydrodynamic approximations for the stellar and planetary winds.} We have not formally justified our use of the hydrodynamic equations to describe the wind-wind interaction. The problem is that the collisional mean free path in the stellar wind is much longer than the lengthscales of the flow: $\lambda_{\rm Coulomb, \ast} = 1/(n_\ast\sigma_{\rm Coulomb}) \sim 10^{13} (10^4 \, {\rm cm}^{-3}/n_\ast) (10^{-17} \,{\rm cm}^{2} / \sigma_{\rm Coulomb}) \, {\rm cm}$, where $\sigma_{\rm Coulomb} \sim 10^{-17} (T_\ast / 10^6 \, {\rm K})^{-2} \, {\rm cm}^2$ is the cross section for protons scattering off protons. That the Solar wind is collisionless and does not necessarily admit a one-fluid treatment is well-known. Nevertheless, it is perhaps just as well-known that Parker's (\citeyear{Parker58}, \citeyear{Parker63}) use of the fluid equations to describe the collisionless Solar wind is surprisingly accurate, capturing the leading-order features of the actual Solar wind. The role of Coulomb collisions in relaxing the velocity distribution functions of protons and electrons is fulfilled instead by plasma instabilities and wave-particle interactions---see, e.g., reviews of Solar wind physics by \citet{Marsch03} and \citet{Marsch06}. The gross properties of collisionless shocks can still be modeled with the hydrodynamic equations insofar as those properties depend only on the macroscopic physics of mass, momentum, and energy conservation, and not on microphysics (e.g., \citealt{Shu92}). Note that the planetary wind is fully collisional because of its higher density and lower temperature, and modeling it as a single fluid appears justified: $\lambda_{{\rm Coulomb}, p} \sim 10^7 (10^6 \, {\rm cm}^{-3} / n_p) (T_p/10^4 \,{\rm K})^2 \, {\rm cm}$, which is smaller than any other length scale in the problem. \item {\it Non-Maxwellian behavior of the stellar proton velocity distribution.} Lyman-$\alpha$ absorption at the redshifted velocity of +100 km/s arises from charge-exchanged neutral hydrogen at the assumed stellar wind temperature of $10^6$ K. We have assumed a Maxwellian distribution function for hydrogen in the stellar wind, and have ignored non-Maxwellian features that have been observed in the actual Solar wind, including high-energy tails and temperature anisotropies. Accounting for non-Maxwellian behavior may introduce order-unity corrections to our results for the absorption. For the more polar fast Solar wind, proton temperatures parallel to and perpendicular to the Solar wind magnetic field differ by factors of a few at heliocentric distances of 5--10 Solar radii \citep{McKenzie97}. For the more equatorial slow Solar wind---which our simulations are modeled after---temperature anisotropies are more muted (\citealt{Marsch03}, page 391). \item {\it Stellar radiation pressure.} Stellar Lyman-$\alpha$ photons can radiatively accelerate neutral hydrogen away from the star (e.g., \citealt{Vidal-Madjar2003}; M09). Both the planetary wind, and the charge-exchanged stellar wind in the mixing layer, are subject to a radiation pressure force that exceeds the force of stellar gravity by a factor $\beta$ on the order of unity. Radiative repulsion of the charge-exchanged stellar wind in the mixing layer may not be observable, because once hot neutral hydrogen is created in the mixing layer, it is advected off the projected limb of the star before radiation pressure can produce a significant velocity: $\delta v_{\rm rad} \sim GM_\ast / r^2 \times \beta \times t_{\rm adv} \sim 6 \beta$ km/s, which does not exceed the hot neutral hydrogen's thermal velocity of $\sim$100 km/s. What about radiative acceleration of the planetary wind? The travel time of the planetary wind from the planet to the mixing layer is $\sim$$10 R_p / v_p \sim 10^5$ s, long enough for neutral hydrogen to attain radiative blow-out velocities in excess of 100 km/s. However, the amount of hydrogen that suffers radiative blow-out is limited to the column that presents optical depth unity to Lyman-$\alpha$ photons. This column is $1/\sigma_{\rm line-ctr} \sim 2 \times 10^{13} (T_p/10^4 \, {\rm K})^{1/2}$ cm$^{-2}$, and is much smaller than the typical column in the planetary wind, which is $(1-f_p^+) n_p R_p \sim 10^{16}$ cm$^{-2}$. Thus the bulk of the planetary wind is shielded from radiative blow-out, and our neglect of radiation pressure appears safe. \revised{ Note that \citet[][]{LecavelierdesEtangs:2012jq} find that radiation pressure cannot explain the largest blueshifted velocities observed for HD 189733b; like us, they favor charge exchange. } \end{enumerate}
| 12 | 6 |
1206.5003
|
1206
|
1206.5529_arXiv.txt
|
We use images taken with the infrared channel of the Wide Field Camera 3 on the {\it Hubble Space Telescope (HST)} to study the multiple main sequences (MSs) of NGC~2808. Below the turn off, the red, the middle, and the blue MS, previously detected from visual-band photometry, are visible over an interval of about 3.5 F160W magnitudes. The three MSs merge together at the level of the MS bend. At fainter magnitudes, the MS again splits into two components containing $\sim$65\% and $\sim$35\% of stars, with the most-populated MS being the bluest one. Theoretical isochrones suggest that the latter is connected to the red MS discovered in the optical color-magnitude diagram (CMD), and hence corresponds to the first stellar generation, having primordial helium and enhanced carbon and oxygen abundances. The less-populated MS in the faint part of the near-IR CMD is helium-rich and poor in carbon and oxygen, and it can be associated with the middle and the blue MS of the optical CMD. The finding that the photometric signature of abundance anticorrelation are also present in fully convective MS stars reinforces the inference that they have a primordial origin.
|
\label{introduction} In recent years, photometric studies have shown that the color-magnitude diagrams (CMDs) of globular clusters (GCs) can be very complex, with the presence of multiple main sequences (MSs, e.\ g.\ Anderson 1997, Bedin et al.\ 2004, Piotto et al.\ 2007, hereafter P07), multiple sub-giant branches (SGBs, e.\ g.\ Milone et al.\ 2008 and 2012a, Anderson et al.\ 2009, Piotto et al.\ 2012), and multiple or spread red-giant branches (RGBs, e.\ g.\ Yong et al.\ 2008, Marino et al.\ 2008, Lee et al.\ 2011). Photometric and spectroscopic investigations have revealed that the multiple sequences in the CMDs of many GCs are populated by stars with different helium and light-element abundances (e.\ g.\ Piotto et al.\ 2005, 2007, Yong et al.\ 2008, Marino et al.\ 2008, Sbordone et al.\ 2011, hereafter S11). Is some cases, the presence of stellar populations with different composition (in particular, Helium) has been associated with the presence of multimodal or extended horizontal-branches (HBs) (e.\ g.\ D'Antona et al.\ 2005, P07, D'Antona \& Caloi 2008, Marino et al.\ 2011). Among clusters with multiple stellar populations, NGC~2808 is certainly one of the most intriguing objects. Its CMD shows a multimodal MS (D'Antona et al.\ 2005) composed of three distinct components (P07, Milone et al.\ 2012b, hereafter M12), a multimodal HB, which is greatly extended blueward (Sosin et al.\ 1997, Bedin et al.\ 2000), and a spread RGB (Lee et al.\ 2011). Furthermore, spectroscopic studies of RGB, HB, and bright MS stars have revealed significant star-to-star variations in the light-element abundances, with three distinct groups of stars populating an extended Na-O anti-correlation (Carretta et al.\ 2006, Gratton et al.\ 2011, Bragaglia et al.\ 2010). Photometric studies, based on data collected with the Wide Field Channel of the Advanced Camera for Survey (WFC/ACS) on board {\it HST} have made it possible to detect and characterize the multiple MSs of NGC~2808 from the MSTO down to about 4 magnitudes below the MSTO (P07, M12): the stars all have almost the same age and [Fe/H] but different Helium and light-element abundances. The red MS (rMS) corresponds to a first generation and has primordial helium and light-element abundances (Y$\sim$0.25), while the blue (bMS) and the middle (mMS) include later generations of stars, and are both enhanced in helium, sodium, and nitrogen (Y$\sim$0.38 and Y$\sim$0.32, respectively) and depleted in oxygen and carbon (D'Antona et al.\ 2005, P07). Usually, photometry of GC sequences extends over a limited spectral region, from the ultra-violet ($\lambda \sim$ 2000\AA) to the near-infrared (NIR, $\lambda \sim$ 8000\AA). As such, multiple sequences are rarely detected along the lower part of the MS, because observational limits make it hard to get high-accuracy photometry of very faint and red stars in optical and UV colors. In this Letter we use {\it HST} to extend the study to the near-infrared passbands and complement the work by S11 who analysed the signatures of the anticorrelations in the visual and ultra-violect portion of the spectrum. We analyze the CMD of NGC~2808 through the F110W ($\sim${\it J}) and F160W ($\sim${\it H}) filters of the infra-red channel of the Wide Field Camera 3 (WFC3/IR) and follow, for the first time, the multiple sequences of this cluster over a wide interval of stellar masses, from the turn off down to very low-mass (VLM) MS stars ($\mathcal{M} \sim$0.2$\mathcal{M}_{\odot}$).
|
The near-IR/WFC3 CMD presented in this Letter allows us to examine, for the first time, the behavior of multiple MSs among VLM stars. As expected, in the near-IR, the MS stars less massive than $\sim$0.4$\mathcal\, M_{\odot}$ define a sequence with nearly-constant color (see e.g.\ Baraffe et al.\ 1997, Zoccali et al.\ 2000, Bono et al.\ 2010 and references therein). Theoretical models predict that this is due to two competing effects. On one hand, the increase of the radiative opacity, coupled with the decrease of the effective temperature shifts the stellar colors to the red. On the other hand, the increase of the collisional induced absorption (CIA) of the H$_{2}$ molecule in the infrared moves back the stellar flux to the blue. In a given range of stellar masses, the two effects compensate, and the MS locus runs almost vertical. Moving towards less massive stars the second effect becomes dominant, and the color of the MS becomes bluer and bluer with decreasing stellar mass. The CIA source is obviously related to the abundance of H$_2$ molecules. It also scales as the square of the density ($\rho$), as opposed to other opacity sources, which are proportional to $\rho$ (Cassisi 2011 and references therein). In order to compare empirical evidence with suitable evolutionary predictions, we have computed some grids of evolutionary models for both low- and very low-mass stars. For the low-mass structures (i.\ e.\ ${\rm \mathcal{M}>0.5\mathcal{M}_\odot}$) we adopt the physical scenario described in Pietrinferni et al.\ (2006), while in the VLM regime we use the same physical inputs adopted in Cassisi et al.\ (2000). We address the interested reader to the quoted references for details. The match between the more massive models and the VLM ones was made at a mass level where the transition in luminosity and effective temperature between the two regimes is smooth (usually ${\rm \sim 0.5\mathcal{M}_\odot}$). We computed stellar models for an iron content equal to ${\rm [Fe/H]=-1.3}$, and $\alpha-$elements enhancement equal to ${\rm [\alpha/Fe]=+0.4}$, and for three values for the initial He abundances: Y=0.248, 0.35 and 0.40, namely. These initial He abundances have been selected on the basis of the comparison between stellar models and the triple MS observed in the optical CMD of NGC~2808 performed by P07. The theoretical models have been transformed into the observational domain by integrating the synthetic spectra of the BT-Settl AGSS model atmosphere grid\footnote{These model atmospheres and colors tables are available via the Phoenix web simulator at the following URL site: http://phoenix.ens-lyon.fr/simulator.} (Allard et al.\ 2011, 2012) over the IR WFC3 bandpasses. We used the filter transmission tables provided by the System Throughputs web site for the WFC3. The upper-left panel of Fig.~\ref{fig4} shows the location in the selected near-IR CMD of 12-Gyr isochrones for the selected assumptions about the initial He abundances. Data in Fig.~\ref{fig4} show that for $m_{\rm F160W} \lesssim 21$ (i.\ e.\ $M_{\rm F160W}\lesssim6$, the He abundance plays a fundamental role in driving the MS location: when increasing the He abundance from Y=0.248 to 0.40 the MS locus becomes fainter by more than 0.5~mag at fixed color. This is consistent (and indeed explains) the separation of the three MSs observed in the upper part ($m_{\rm F160W}<20.5$) of the CMDs of Figs.~1 and 3. However, since helium-rich stars have lower hydrogen abundance, we would expect that, in the stellar mass regime where the two - previously quoted - physical processes are in competition, the He-rich VLM stars would appear redder than He-normal stars for their lower H$_{2}$ abundance, and consequent lower contribution coming from the H$_2$ CIA. Indeed, at fainter magnitudes, the He-normal (Y=0.248) MS sequence runs on the blue side of the more He-rich sequences, but the effect is very small, smaller than the observed one. We note that, below the faint limit of our photometry ($M_{\rm F160W}\lesssim10$), the He-normal sequence reaches fainter magnitudes and bluer colors than the He-rich counterpart. This is an important feature that could be tested with deeper CMDs, and may represent an independent observational confirmation of high-He enhancement. \begin{figure}[ht!] \centering \epsscale{.99} \plotone{f4.ps} \caption{\textit{Left panels}: theoretical isochrones for an age of 12~Gyr, a metallicity suitable for NGC~2808 and various assumptions about the initial He content (see labels). The upper-left panel shows the theoretical absolute magnitudes and colors. In the lower-left panel, we show -after applying a distance modulus $\rm (m-M)_{0}$=15.0 and a reddening E(B$-$V)=0.18, in order to make the comparison with the upper right panel of Fig.~3 easier- the location in the CMD of the stellar models with mass in the range from ${\rm 0.0894M_{\odot}}$ to ${\rm 0.65M_{\odot}}$. The arrow marks the approximate location along the MS loci of the VLM stellar model with effective temperature and gravity values consistent with those adopted for computing the model atmospheres. \textit{Right panels}: Comparison of the synthetic spectra of an bMS star (cyan) and an rMS star (red, see text for more details) difference between the synthetic spectrum of a bMS and a rMS star (middle). Normalized responses of the F110W and F160W WFC3/NIR {\it HST} filters (bottom). } \label{fig4} \end{figure} The bottom-left panel of Fig.~\ref{fig4} shows that the difference in the initial He abundances among the stars belonging to the distinct MS loci is not able to provide a complete explanation of the observed trend. In the following, we will attempt to identify the origin of the (small) separation of the observed MSs at magnitudes fainter than $M_{\rm F160W}\sim 20.5$. First of all, we note that the model atmospheres adopted for computing the color-${\rm T_{eff}}$ transformations do not account for the peculiar chemical patterns of the various sub-populations present in NGC~2808. In particular, they do not take into account the effect of light-elements anti-correlations, which have been shown to be relevant for the MS color in the UV and Str{\"o}mgren bands (S11, M12). In order to explore the impact of light-element variations on the NIR WFC3 bands, we have computed synthetic spectra trying to account for the chemical patterns of the stars belonging to the distinct MSs in NGC~2808. For this calculation, we used the ATLAS9 and SYNTHE Kurucz programs in the range from {8000\AA}\, to {18000\AA}\, (Kurucz 2005, Sbordone et al. 2007)\footnote{\sf{http://wwwuser.oat.ts.astro.it/castelli/}}. For the $MS_{\rm I}$ and $MS_{\rm II}$, we adopted a Helium content of Y=0.25 and Y=0.38 respectively, as suggested by isochrone-fitting on the upper MS (M12). For the $MS_{\rm I}$, we assumed average chemical abundance of O-rich stars ([O/Fe]=0.4, as measured by Carretta et al.\ 2006), and adopted the carbon and nitrogen abundance ([C/Fe]=$-$0.3, [N/Fe]=0.5) measured by Bragaglia et al.\ (2010). For the $MS_{\rm II}$, we used [O/Fe]=$-$0.6 (the O abundance measured by Carretta et al.\ 2006 for the O-poor group), and [C/Fe]=$-$0.7, and [N/Fe]=2.0 (as measured by Bragaglia et al.\ 2010 for a bMS star). Table~1 summarizes the adopted chemical abundances for the two sequences. For both MSs we used ${\rm T_{\rm eff}=4000K}$, log(g)=5.0, and a microturbolence 1.0 $\rm {km~s^{-1}}$. Our synthesis includes the following molecules in the Kurucz compilation: $\rm {CO}$, $\rm {C_{2}}$, $\rm {CN}$, $\rm {OH}$, $\rm {MgH}$, $\rm {SiH}$, $\rm {H_{2}O}$, $\rm {TiO}$ ($\rm {H_{2}O}$, from Partridge \& Schwenke 1997; $\rm {TiO}$ from Schwenke 1998) $\rm {VO}$ and $\rm {ZrO}$ (B.\ Plez priv. communication) The resulting synthetic spectra (Fig.~4, upper-right panel) have been integrated over the transmission of the WFC3/IR F110W and the F160W filters (lower-right panel) to produce synthetic magnitudes and colors. We found a $\Delta(M_{\rm F110W}-M_{\rm F160W})=0.10$ color difference between the simulated $MS_{\rm I}$ and $MS_{\rm II}$ stars, consistent with the observed color difference (Fig.~2) at $m_{\rm F160W}$=21.5: $\Delta(m_{\rm F110W}-m_{\rm F160W})$=0.06$\pm$0.01 mag. The middle-right panel of Fig.~4 shows the flux difference as a function of the wavelength between the two MSs spectra. The $\rm {H_{2}O}$ molecules have the strongest effect on the synthetic spectra, and cause the significant lower flux of the rMS in the filter F160W. We consider the agreement between the simulated and observed color differences satisfactory, accounting for the high sensitivity to light-elements abundances of the stellar spectra at these wavelengths, and that the adopted C and N abundances are based on the measurement on just one bMS and one rMS star (Bragaglia et al.\ 2010). \begin{table} \center \begin{tabular}{ccccc} \hline \hline MS & Y & [C/Fe] & [N/Fe] & [O/Fe] \\ \hline rMS & 0.25 & $-$0.3 & 0.5 & 0.4 \\ mMS & 0.32 & NA & NA & 0.0 \\ bMS & 0.38 & $-$0.7 & 2.0 & $-$0.6 \\ \hline MSI & 0.25 & $-$0.3 & 0.5 & 0.4 \\ % MSII& 0.38 & $-$0.7 & 2.0 & $-$0.6 \\ % \hline \hline \end{tabular} \label{tab1} \caption{Average chemical abundances of bMS, mMS, and rMS stars and abundanced adopted for the $MS_{\rm I}$ and the $MS_{\rm II}$.} \end{table}
| 12 | 6 |
1206.5529
|
1206
|
1206.2895_arXiv.txt
|
Reprocessing of the Parkes Multibeam Pulsar Survey has resulted in the discovery of five previously unknown pulsars and several as-yet-unconfirmed candidates. PSR J0922$-$52 has a period of 9.68~ms and a DM of 122.4~pc cm$^{-3}$. PSR J1147$-$66 has a period of 3.72~ms and a DM of 133.8~pc cm$^{-3}$. PSR J1227$-$6208 has a period of 34.53~ms, a DM of 362.6~pc cm$^{-3}$, is in a 6.7 day binary orbit, and was independently detected in an ongoing high-resolution Parkes survey by Thornton et al.\ and also in independent processing by Einstein@Home volunteers. PSR J1546$-$59 has a period of 7.80~ms and a DM of 168.3~pc cm$^{-3}$. PSR J1725$-$3853 is an isolated 4.79-ms pulsar with a DM of 158.2~pc cm$^{-3}$. These pulsars were likely missed in earlier processing efforts due to the fact that they have both high DMs and short periods, and also the large number of candidates that needed to be looked through. These discoveries suggest that further pulsars are awaiting discovery in the multibeam survey data.
|
While targeted searches have been useful in finding unique pulsars, most pulsars known today have been found in large-scale, blind pulsar surveys. One such survey, the Parkes Multibeam Pulsar Survey \citep[PMPS;][]{Manchester:2001}, surveyed a strip along the Galactic plane using the 13-beam receiver on the Parkes 64-m telescope. Initial processing of the data resulted in the discovery of 742 pulsars \citep{Manchester:2001, Morris:2002, Kramer:2003, Hobbs:2004, Faulkner:2004, Lorimer:2006}. Another 44 pulsars and 30 RRATs (rotating radio transients) were found in further reprocessings \citep{Eatough:2009, Eatough:2010, Eatough:2011, Keith:2009, McLaughlin:2006, Keane:2010, Keane:2011}, and an additional 21 pulsars have been found so far by Einstein@Home\footnote{\url{http://einstein.phys.uwm.edu/radiopulsar/html/PMPS\_discoveries/}} (Knispel et al., in prep). The 44 additional pulsars were found due to the implementation of new techniques for removing terrestrial interference and new techniques for sorting pulsar candidates. In this paper, we present the discovery of a further five pulsars in the PMPS data. The motivation for our re-analysis of the PMPS data was a single-pulse study, which will be presented elsewhere. Single-pulse studies involve the search for and characterization of transient, non-periodic bursts. We performed periodicity searches as well as single-pulse searches since the additional processing time was negligible. In Section \ref{data}, we describe the data reduction and analysis. Section \ref{psrs} details the five pulsars that we discovered, and conclusions are given in Section \ref{conc}.
|
\label{conc} Reprocessing of the Parkes Multibeam Pulsar Survey resulted in the discovery and confirmation of five new pulsars, PSR J0922$-$52, PSR J1147$-$66, PSR J1227$-$6208, PSR J1546$-$59, and PSR J1725$-$3853. PSR J1227$-$6208 was independently confirmed by Einstein@Home as well as the HTRU team in their medium-latitude survey and will be presented by Thornton et al.\ (in prep). Our discovery of PSRs J0922$-$52, J1147$-$66, J1227$-$6208, J1546$-$59, and J1725$-$3853 brings the total number of millisecond pulsars found in the PMPS to 25. We present a timing solution for PSR J1725$-$3853, and continued timing observations will allow us to further improve this solution. Our discovery of these five pulsars emphasizes the value of archiving pulsar search data and indicates that there are a number of as-yet-undiscovered pulsars present in the PMPS data. Given the number of pulsar candidates present, automated searches are the most efficient way to reduce the number of candidates to an amount that can be viewed in a reasonable amount of time. Due to the fact that they have both high DMs and short periods, many of our candidates are weak and close to the detection threshold, so there is a good chance they were not ranked highly by previous automated searches. \citet{Keith:2009} found that weak pulsars and pulsars with high DMs were ranked highly by automated searches. However, most of these pulsars have long periods, i.e.\ periods on the order of hundreds of milliseconds. As the ratio of DM to period increases, the detected pulse profile is significantly broadened and begins to look more sinusoidal. These candidates are harder to select via ranking systems. We note that \citet{Eatough:2010} found that artificial neural networks have difficulty detecting short period pulsars, with their own detecting only 50\% of pulsars with periods less than 10~ms. In our search strategy, every single candidate is being inspected by eye. In many of the earlier analyses of the PMPS data (e.g.~Manchester et al.~2001), the candidates were also viewed by eye and it is not clear why these were not found earlier. Perhaps they were simply missed due to human fatigue. In the following year, we hope to follow up and confirm many of our candidates. Along with the re-analysis of the PMPS survey data presented here, and the ongoing search by Einstein@Home, we expect the sample of millisecond pulsars found in the PMPS to increase further.
| 12 | 6 |
1206.2895
|
1206
|
1206.0774_arXiv.txt
|
We observe two secondary eclipses of the strongly irradiated transiting planet WASP-33b, in the $K_s$ band at 2.15\,$\mu$m, and one secondary eclipse each at 3.6\,$\mu$m and 4.5\,$\mu$m using Warm Spitzer. This planet orbits an A5V $\delta$-Scuti star that is known to exhibit low amplitude non-radial p-mode oscillations at about 0.1\% semi-amplitude. We detect stellar oscillations in all of our infrared eclipse data, and also in one night of observations at J-band (1.25\,$\mu$m) out of eclipse. The oscillation amplitude, in all infrared bands except $K_s$, is about the same as in the optical. However, the stellar oscillations in $K_s$ band (2.15\,$\mu$m) have about twice the amplitude (0.2\%) as seen in the optical, possibly because the Brackett-$\gamma$ line falls in this bandpass. As regards the exoplanetary eclipse, we use our best-fit values for the eclipse depth, as well as the 0.9\,$\mu$m eclipse observed by \citet{smith}, to explore possible states of the exoplanetary atmosphere, based on the method of \citet{madhu09}. On this basis we find two possible states for the atmospheric structure of WASP-33b. One possibility is a non-inverted temperature structure in spite of the strong irradiance, but this model requires an enhanced carbon abundance ($C/O>1$). The alternative model has solar composition, but an inverted temperature structure. Spectroscopy of the planet at secondary eclipse, using a spectral resolution that can resolve the water vapor band structure, should be able to break the degeneracy between these very different possible states of the exoplanetary atmosphere. However, both of those model atmospheres absorb nearly all of the stellar irradiance with minimal longitudinal re-distribution of energy, strengthening the hypothesis of \citet{cowan} that the most strongly irradiated planets circulate energy poorly. Our measurement of the central phase of the eclipse yields $e\,cos\,\omega=0.0003\pm0.00013$, which we regard as being consistent with a circular orbit.
|
Extrasolar planets that orbit close to their stars are subject to an intense flux of stellar irradiation. The rotation of a very close-in planet is expected to become tidally locked to its orbital period on an astrophysically short time scale \citep{guillot}. Consequently, the most close-in exoplanets will receive stellar irradiation exclusively on their star-facing hemispheres. The resulting heating is believed to be distributed by strong zonal winds \citep{showman}, but the dynamics of the zonal re-distribution, and therefore the overall energy budget of the planet, are affected by the vertical temperature structure of the planetary atmosphere. Many close-in planets exhibit inverted temperature structures \citep{knutson08, seager-deming}, probably driven by radiative absorption in a high altitude layer of the atmosphere \citep{burrows07}. The nature of the absorber has been actively discussed \citep{fortney, spiegel}, but remains unknown. One promising avenue of investigation is to look for correlations between the planetary temperature inversion and the stellar flux at ultraviolet (UV) wavelengths \citep{knutson10}. Stellar UV radiation has the potential to dissociate absorbing molecular species, and to create (or destroy) absorbers via photochemistry \citep{zahnle}. The spectral distribution of UV flux may be critical to the inversion phenomenon. Therefore it is desirable to investigate planets orbiting strong sources of far-UV radiation (i.e., magnetically active stars), as well as planets receiving irradiation by thermal UV radiation (i.e., hot stars). An important planet in the latter category is WASP-33b, that orbits an A-type $\delta$-Scuti star with an orbital period of 1.22 days \citep{collier-cameron, herrero}. The large radius and high temperature of an A-type star produce stronger irradiance than would be the case for a solar-type star. Although only an upper limit is available for the mass of WASP-33b \citep{collier-cameron}, the planet is important because it is among the most strongly irradiated planets. In contrast to other strongly irradiated planets such as WASP-12, \citep{cowan12, crossfield, zhao, campo, croll, madhu11a}, little is currently known about the response of WASP-33b to the strong stellar irradiation. \citet{smith} measured the thermal emission of WASP-33b from secondary eclipse observations at $0.9$\,$\mu$m, but there are currently no reported detections of the planet at wavelengths longward of 1\,$\mu$m. Stellar intensity oscillations of WASP-33 are seen with 0.1\% semi-amplitude at optical wavelengths \citep{herrero}. The stellar oscillations may exhibit a greater or lesser amplitude at infrared (IR) wavelengths. The dependence of the oscillation amplitude on wavelength potentially carries information on the physics of the oscillations in the stellar atmosphere. In this paper, we report measurement of the thermal emission from WASP-33b, based on ground-based observations of two secondary eclipses in the $K_s$ band ($2.15$\,$\mu$m), space-borne observations of eclipses at 3.6- and 4.5\,$\mu$m by Warm Spitzer, and measurement of the intensity oscillations of the star in all these IR bands, as well as in J-band ($1.25$\,$\mu$m). We describe the observations and extraction of photometry from the data in Sec.~2~\&~3. In Sec.~4, we analyze the data to determine the parameters of the planet's eclipse and the oscillatory properties of the star. We explore and discuss the implications of our results in Sec.~5, and Sec.~6 summarizes our results.
|
\subsection{Stellar Oscillations} The first and most obvious result from our observations is the existence and prominence of the stellar oscillations. WASP-33 was already known to exhibit oscillations, but the amplitude observed by \citet{herrero} in the optical (Johnson R-band) was about 0.001. Our results (Figures 3-5, \& Figures 7-8) show oscillation amplitudes in agreement with the optical, except for $K_s$ band where the ampitude is about twice the optical value (2.15\,$\mu$m, Table~2), as noted in Sec.~4.3. Because the largest difference with the optical amplitude is seen in our ground-based ($K_s$-band) data, we contemplated whether the difference could be attributed to errors in our ground-based result. An argument against that possibility is the prominence of the stellar oscillation in the raw photometry (e.g., upper panel of Figure~2). We therefore explore whether properties of the stellar atmosphere that may be unique to $K_s$ band could cause the oscillations to have greater amplitude at that wavelength. \subsection{Stellar Atmospheric Effects} We here consider the possibility that the larger $K_s$ band oscillation amplitude as compared to the optical is due to the different height of formation for continuum radiation in the stellar atmosphere, in concert with height-dependent variations in the mode amplitudes. Due to the increase in atomic hydrogen bound-free continuous opacity in the infrared, our $K_s$ band observations of WASP-33 sample a greater height in the stellar atmosphere than observed by \citet{herrero}. The upward propagation of a pressure-mode oscillation in a stellar atmosphere can in principle cause the mode amplitude to increase. As a propagating mode encounters lower mass density, the wave velocity - and hence the temperature perturbation in the compression - increase. However, propagation is strongly affected by the stratification of the stellar atmosphere \citep{marmolino}. Frequencies less than the acoustic cutoff frequency will not propagate, and their velocity amplitude decreases with height. To the extent that the temperature amplitude scales with velocity, it too will decrease with height for non-propagating modes. The acoustic cutoff frequency is $c/2H$, where $c$ is sound speed and $H$ is the pressure scale height. We calculated the acoustic cutoff frequency and other parameters for WASP-33, using a Teff/log(g)/[M/H] = 7500/4.5/0.0 model atmosphere from \citet{kurucz}. We find that the acoustic cutoff corresponds to an oscillatory period of about 1 minute. The much longer period oscillations we observe for WASP-33 are therefore not propagating, and their amplitudes should decay with height. The dominant opacity due to atomic hydrogen \citep{menzel} is higher at $2.15\,\mu$m versus the optical by a factor of about 1.6, translating to a height difference of about 60 km. That is not sufficient to account for significant changes in the mode properties, even for propagating modes and, as noted above, these modes do not propagate. Moreover, if height dependence of the stellar continuous spectrum were significant to our observed amplitudes, then we would expect even larger amplitudes in the Spitzer bands than at 2.15\,$\mu$m, which are not observed. However, there is one unique feature of the $K_s$ band that may well be responsible for a higher oscillation mode amplitude. The Brackett-$\gamma$ line at 2.165\,$\mu$m is centered in the $K_s$ bandpass. The strong opacity in that line for an A5V star could have a large potential effect on oscillation amplitudes. The impact of strong oscillations in the line, when diluted over the broad $K_s$ band, could potentially be calculated using techniques beyond the scope of this paper (i.e., radiation hydrodynamics). A more direct method would be to obtain infared spectroscopy of the star and directly measure the oscillations in the infrared hydrogen lines. \subsection{Orbit of WASP-33b} Our measured times of central eclipse can in principle determine $e\,cos\,\omega$ for the planet's orbit (e.g., \citealp{knutson09}). Considering the 25 seconds of light travel time across the planet's orbit, we expect to find the eclipse at phase $0.50024$ if the orbit is circular. Weighting both our ground-based and Spitzer eclipses (Table~2) by the inverse of their formal variances, we find an average eclipse phase of $0.50044\pm0.00008$, totally dominated by the 3.6\,$\mu$m eclipse. Thus we find that $e\,cos\,\omega$ - approximated as $\pi/2$ times the phase offset from 0.5 - is $0.0003\pm0.00013$. The central phase measurement for these eclipses is complicated by the stellar oscillations, so more-than-usual caution is needed in the interpretation of the measured central phase. Moreover, our value for $e\,cos\,\omega$ differs from zero by less than $3\sigma$, so our results provide little evidence for a non-circular orbit. \subsection{Atmosphere of WASP-33b} Figure~9 shows our result for the eclipse of WASP-33b in comparison to two models of its atmosphere, both of which agree with the available measurements to date. One of these models has a temperature inversion with solar composition, and one has a non-inverted atmospheric structure with a carbon-rich composition \citep{madhu11b}. Their temperature profiles are shown in the bottom panel of Figure~9, with the approximate formation depths of the four bandpasses overplotted as points. The $K_s$ bandpass is relatively devoid of strong molecular absorption features, and probes the relatively deep planetary atmosphere (pressure, $P$ $\sim$ 0.6 bars), relatively independent of the composition of the atmosphere (asterisks on Figure~9). (The 3.6\,$\mu$m bandpass also peaks relatively deep in the atmosphere, but has significant contribution from higher altitudes, having more molecular absorption than does the $K_s$ band.) The large eclipse depth we observe in $K_s$ band (brightness temperature $\approx 3400$K) thus indicates a hot atmosphere at depth, and a high effective temperature for the planet. Both models illustrated on Figure~9 have hot lower atmospheres (both above 2500 Kelvins) and both have inefficient longitudinal energy re-distribution. These models are consistent with the observed tendency for the most strongly irradiated planets to exhibit the least longitudinal re-distribution of heat \citep{cowan}. We find that these very hot models are necessary to reproduce our results as well as the result of \citet{smith}, and we conclude that WASP-33 strengthens the \citet{cowan} result. The two models we show are representative of a larger set of solutions that explain the data with and without thermal inversions. Given that there are 10 model parameters \citep{madhu09, madhu10} and only four data points, it is not possible to derive a unique model fit to the data. We ran large MCMC chains (of $\sim 10^6$ models) with and without thermal inversions, and identified regions of composition space in each case that are favored by the data \citep{madhu10}. Both models on Figure~9 are unusual as compared for example to the well-observed archetype HD\,189733b \citep{charb08}. One model on Figure~9 adopts solar composition but with an inverted temperature structure (temperature rising with height), while the other model has temperature declining with height, but requires a carbon-rich composition. We integrate the fluxes of each planetary model, and the Kurucz model stellar atmosphere, over the observational bandpasses, and ratio those integrals. These band-integrated points are shown as squares on Figure~9. The $\chi^2$ values for the models as compared to all four observed points (our three measurements, plus \citealp{smith}) are 7.9 for the inverted solar-composition model and 2.8 for the non-inverted carbon-rich model. The $K_s$-band point at 2.15\,$\mu$m favors the non-inverted model. Although the difference is not sufficiently significant to rule out the inverted model at this time, additional eclipse observations in the $K_s$ band would be helpful to rule out an inverted atmospheric structure. In our population of models with thermal inversions, several models with slightly different inverted temperature structure fit the data almost equally well. However, none of them fit the K-band point to within the 1$\sigma$ errors while also fitting the remaining points. The Figure~9 model is the best among this set of inverted models. In our models without thermal inversions, the best-fit model requires a carbon-rich composition (i.e., $C/O \geq 1$). However, at the 2$\sigma$ level of significance per wavelength point, several solar composition models (not illustrated) provide an acceptable fit to the data. So although the carbon-rich composition is favored, a solar abundance composition cannot be absolutely ruled out. Our results illustrate the limitations of eclipse photometry in broad bands, especially for challenging cases like planets orbiting oscillating stars. Once we admit the possibility of non-solar compositions (because we are largely ignorant of true exoplanetary compositions), the range of models that can fit broad-band photometry can be large, in this case extending to inverted and non-inverted models with drastically different temperature structure. The degeneracy is exacerbated by the relatively small range of atmospheric pressures probed by the four bandpasses we analyze (points on the bottom panel of Figure~9). Fortunately, future observations can break this degeneracy using HST/WFC3 spectroscopy near 1.4\,$\mu$m \citep{berta12}. The water band near 1.4\,$\mu$m is sufficiently strong that eclipse observations with the Hubble WFC3 grism should be feasible. Although water absorption in the carbon-rich model is supressed by $C/O > 1$, the water emission in the solar-composition inverted model is predicted to be significant, readily detectable near 1.4\,$\mu$m (see Figure~9). Moreover, spectroscopic techniques can potentially probe a larger depth range in exoplanetary atmospheres than does photometry, because the cores of resolved spectral features have strong opacities. Our results therefore illustrate the complementary value of acquiring both broad-band and spectroscopic observations of transiting exoplanets at secondary eclipse.
| 12 | 6 |
1206.0774
|
1206
|
1206.4157_arXiv.txt
|
Numerical simulations of hot accretion flow, both hydrodynamical and magnetohydrodynamical, have shown that the mass accretion rate decreases with decreasing radius; consequently the density profile of accretion flow becomes flatter compared to the case of a constant accretion rate. This result has important theoretical and observational implications. However, because of technical difficulties, the radial dynamic range in almost all previous simulations usually spans at most two orders of magnitude. This small dynamical range, combined with the effects of boundary conditions, makes the simulation results suspectable. Especially, the radial profiles of density and inflow rate may not be precise enough to be used to compare with observations. In this paper we present a ``two-zone'' approach to expand the radial dynamical range from two to four orders of magnitude. We confirm previous results and find that from $r_s$ to $ 10^4r_s$ the radial profiles of accretion rate and density can be well described by $\dot{M}(r)\propto r^s$ and $\rho\propto r^{-p}$. The values of (s, p) are (0.48, 0.65) and (0.4, 0.85), for viscous parameter $\alpha=0.001$ and $0.01$, respectively. Or more precisely, the accretion rate is constant (i.e., $s=0$) within $\sim 10r_s$; but beyond $10r_s$, we have $s=0.65$ and $0.54$ for $\alpha=0.001$ and $0.01$, respectively. We find that the values of both $s$ and $p$ are similar in all numerical simulation works, including previous and the present ones, no matter a magnetic field is included or not and what kind of initial conditions are adopted. Such an apparently surprising ``common'' result can be explained by the most updated version of the adiabatic inflow-outflow model (ADIOS). The density profile we obtain is in good quantitative agreement with that obtained from the detailed observations and modeling to Sgr A* and NGC~3115. The origin and implication of such a profile will be investigated in a subsequent paper.
|
Hot accretion flow, such as advection-dominated accretion flows (ADAFs; Ichimura 1977; Rees et al. 1982; Narayan \& Yi 1994; 1995; Abramowicz et al. 1995; see Narayan, Mahadevan \& Quataert 1998; Kato, Fukue \& Mineshige 1998; and Yuan \& Narayan 2013 for reviews), is of great interest because of its widespread applications in low-luminosity AGNs, including the spuermassive black hole in our Galactic center, and the quiescent and hard states of black hole X-ray binaries (see reviews by Narayan 2005; Yuan 2007; Narayan \& McClintock 2008; Ho 2008; and Yuan 2011). In the early analytical works, the mass accretion rate is assumed to be independent of radius, $\dot{M}(r) = {\rm constant}$. In this case, the radial profile of density satisfies $\rho (r)\propto r^{-3/2}$ (e.g., Narayan \& Yi 1994). Numerous hydrodynamical (HD) and magnehydrodynamical (MHD) numerical simulations have been done, with most of them focusing on the dynamics of the accretion flow (e.g., Igumenshchev \& Abramowicz 1999, 2000; Stone, Pringle \& Begelman 1999, hereafter SPB99; Stone \& Pringle 2001; Hawley, Balbus \& Stone 2001; Machida, Matsumoto \& Mineshige 2001; McKinney \& Gammie 2002; Hawley \& Balbus 2002; Igumenshchev, Narayan \& Abramowicz 2003; Pen, Matzener \& Wong 2003; De Villiers, Hawley \& Krolik 2003; Proga \& Begelman 2003a, 2003b; Pang et al. 2011; McKinney, Tchekhovskoy \& Blandford 2012; Narayan et al. 2012). The effect of strong radiation was studied by Yuan \& Bu (2010), and most recently by Li, Ostriker \& Sunyaev (2012). One of the most surprising -- which is perhaps also the most important -- findings of these simulations is that the mass accretion rate (or precisely the inflow rate; refer to eq. [7] in the present paper for its definition), is found to be not a constant; but rather, it decreases with decreasing radius. Denoting the mass accretion rate as $\dot{M}(r)\propto r^{s}$, numerical simulations have found that $s\sim 0.5-1$ (see \S 4.1 for a review). Consequently, the density profile flattens compared to the previous $\rho(r)\propto r^{-1.5}$: we now have $\rho(r)\propto r^{-p}$ with $p\la 1$. Such results have obtained strong observational supports in the case of the supermassive black hole in our Galactic center, Sgr A* (Yuan, Quataert \& Narayan 2003; refer to \S4.2.1 for details.), the low-luminosity AGN NGC~3115 (Wong et al. 2011; refer to \S4.2.2 for details), and black holes in elliptical galaxies (Di Matteo et al. 2000; Mushotzky et al. 2000). In addition to the obvious theoretical interest, the radial profiles of accretion rate and density have also important observational applications. This is because they will determine the emitted spectrum and other radiative features of an accretion flow (e.g., Quataert \& Narayan 1999; Yuan, Quataert \& Narayan 2003). For example, in the case of Sgr A*, the mass accretion rate at the Bondi radius can be determined directly by observations. Then depending on the radial profile of the accretion rate (or more exactly the density), the radiation of the accretion flow is completely different. The radial profile of accretion rate also determines the evolution of black hole mass and spin. In many current numerical simulations, due to resolution difficulty, we can at most resolve the Bondi radius and determine the Bondi accretion rate there. Then the evolution of mass and spin of black holes will be determined by the fraction of the Bondi accretion rate that finally falls onto the black hole, which is determined by the radial profile of accretion rate. It is thus important to carefully investigate the radial profiles of accretion rate and density. One problem of almost all previous simulations is that the radial dynamical range is rather small, usually at most two orders of magnitude. This is technically because it would be so time-consuming that it is almost impossible to simulate an accretion flow, if the dynamical range is too large. In addition, as is well known the simulation results are usually not reliable close to the boundary due to the boundary condition effects. These cast some shade on the previous simulation results, especially the exact quantitative radial profiles of the physical quantities. The situation is even worse for MHD simulations compared to HD ones. Because the Alfv\'en speed is very large in the region of low density and strong magnetic field, MHD simulation is much more expensive than HD simulations. The radial dynamical range is thus more limited, and it is harder to evolve the simulation for long time which further constraints the range over which a steady state is reached. A large dynamical range is also useful to investigate the following problem. Previous works (SPB99; Igumenshchev \& Abramowicz 1999; Yuan \& Bu 2010) have found that the Bernoulli parameter of most outflow in their simulations is indeed negative\footnote{In our subsequent paper (Yuan, Bu \& Wu 2012, hereafter Paper II) we found that depending on the initial condition of the simulation, the Bernoulli parameter can be negative or positive.}. One may expect that outflow may not be able to escape to infinity, but may rejoin the accretion flow at a certain distance. The fact that all previous simulations never found the accumulation of matter in the accretion flow could be because of two possible reasons. One is that the simulation time is not long enough for accumulation to occur. However, the radial velocity of outflow is roughly in the order of the local Keplerian velocity (Paper II). We can therefore expect that if the outflow would finally rejoin the accretion flow, the timescale required for accumulation would be shorter than the accretion timescale by a factor of $\alpha$. { Thus this possibility is unlikely.} Another possible reason is that the radial dynamical range is too small. The accumulation may occur at a radius larger than the outer boundary of all current simulations. To examine this possibility, a larger dynamical range is required. In the present paper we simulate two-dimensional HD accretion flows. Especially, a ``two-zone'' approach { will be} adopted which helps us to overcome the technical problem and achieve a large dynamic range spanning four orders of magnitude. It is widely believed that in reality the magnetic stress associated with the MHD turbulence driven by the magnetorotational instability (MRI) transfers angular momentum (Balbus \& Hawley 1991; 1998). Therefore, we should in principle use MHD simulation. In the present paper we don't include magnetic field but instead include an anomalous shear stress to mimic the magnetic stress. However, as we will describe in Paper II, in HD and MHD accretion flows, the mechanisms of producing the accretion rate profile are different. One may ask whether the radial profile of accretion rate obtained in the present HD simulation is the same with that obtained in more realistic MHD simulations. In this regard, the recent work by Begelman (2012) gives a positive answer. The comparison between our HD simulation with MHD simulations also confirms this point (refer to \S4.1 for details). The structure of the present paper is as follows. In \S2, we introduce the details of our ``two-zone'' simulation approach. The results of simulations are presented in \S3. We find that the profiles of the mass accretion rate and density still follows a perfect power-law form and the power-law index almost remains unchanged compared to previous results. In \S4 we compare our results with previous HD and MHD simulation works (\S4.1) and observations (\S4.2). We find broadly good agreement among them. The last section (\S5) devotes to a summary.
|
One of the most important finding of both HD and MHD numerical simulations of hot accretion flow in the recent years is that the mass accretion rate decreases with decreasing radius. Correspondingly, the density profile becomes flatter compared to the previous prediction when the accretion rate is constant of radius. One main problem with previous simulation is that because of technical difficulty the radial dynamical range in simulations is usually very limited, typically spanning less than two orders of magnitude. The boundary condition effect makes the radial range over which we can reliably measure the profile of physical quantities even smaller. The previous simulation results are therefore somewhat suspectable. In this paper we adopt a ``two-zone'' approach to simulate an axisymmetric accretion flow, extending the dynamical range to over four orders of magnitude, i.e, from $\sim r_s$ to $40000r_s$. We confirm previous results that the profiles of inflow rate and density can be well described by power-law forms. Within $10r_s$, $\dot{M}_{\rm in}(r)\sim const.$. Beyond $10r_s$, the power-law slopes are a function of the viscous parameter $\alpha$. For $\alpha=0.001$, they are described by $\rho(r)\propto r^{-0.65}$ and $\dot{M}_{\rm in}(r)\propto r^{0.65}$. For $\alpha=0.01$, the results are $\rho(r)\propto r^{-0.85}$ and $\dot{M}_{\rm in}(r)\propto r^{0.54}$. We also combine from literature all available numerical simulations which have presented the radial profile of density, both two-dimensional and three-dimensional, HD and MHD. We find that all these simulations give somewhat similar results, $\rho \propto r^{-(0.5-1)}$, and this is also consistent with our results. The diversity of the power-law index seems to come from the differences of the value of $\alpha$, the gravitational potential of the black hole, the initial condition of the simulation, { and the strength of the magnetic field. The rough consistency among} various simulations can be explained by the most recent ADIOS (adiabatic inflow-outflow solution) model (Begelman 2012). In this work it was found that after considering both the inflow and outflow zones at the equal footing and a conserved outward energy flux, the value of $s$ is well constrained to be in a narrow range. The radial profiles of accretion rate and density obtained by numerical simulations are in good agreement with observations. In the case of Sgr A*, detailed modeling to the multi-waveband spectrum find that $\dot{M}(r)\propto r^{0.3}$ and $\rho\propto r^{-1}$. In the case of NGC~3115, for the first time, {\em Chandra} observations resolve the accretion flow within Bondi radius, and find $\rho\propto r^{-1.03^{+0.23}_{-0.21}}$.
| 12 | 6 |
1206.4157
|
1206
|
1206.6152_arXiv.txt
|
We present a scheme for numerical simulations of collisionless self-gravitating systems which directly integrates the Vlasov--Poisson equations in six-dimensional phase space. By the results from a suite of large-scale numerical simulations, we demonstrate that the present scheme can simulate collisionless self-gravitating systems properly. The integration scheme is based on the positive flux conservation method recently developed in plasma physics. We test the accuracy of our code by performing several test calculations including the stability of King spheres, the gravitational instability and the Landau damping. We show that the mass and the energy are accurately conserved for all the test cases we study. The results are in good agreement with linear theory predictions and/or analytic solutions. The distribution function keeps the property of positivity and remains non-oscillatory. The largest simulations are run on $64^{6}$ grids. The computation speed scales well with the number of processors, and thus our code performs efficiently on massively parallel supercomputers.
|
Gravitational interaction is one of the most important physical processes in the dynamics and the formation of astrophysical objects such as star clusters, galaxies, and the large scale structure of the universe. Stars and dark matter in these self-gravitating systems are essentially collisionless, except for a few cases such as globular clusters and stars around supermassive blackholes. The dynamics of the collisionless systems is described by the collisionless Boltzmann equation or the Vlasov equation. Conventionally, gravitational $N$-body simulations are used to follow the evolution of collisionless systems. In such simulations, particles represent sampled points of the distribution function in the phase space. The particles -- point masses -- interact gravitationally with other particles, through which their orbits are determined. They are actually super-particles of stars or dark matter particles. The gravitational potential field reproduced in a $N$-body simulation is therefore intrinsically grainy rather than what it should be in the real physical system. It is well known that two-body encounters can alter the distribution function in the way which violate the collisionless feature of the systems, and undesired artificial two-body relaxation is often seen in $N$-body simulations. There is another inherent problem in $N$-body simulations. Gravitational softening needs to be introduced to avoid artificial large-angle scattering of particles caused by close encounters. Physical quantities such as mass density and velocity field are subject to intrinsic random noise owing to the finite number of particles, especially in low-density regions. To overcome these shortcomings of the $N$-body simulations, several alternative approaches have been explored. For example, the self-consistent field (SCF) method \citep{Hernquist1992, Hozumi1997} integrates orbits of particles under the gravitational field calculated by expanding the density and the gravitational potential into a set of basis functions. In the SCF method, the particles do not directly interact with one another but move on the smooth gravitational potential calculated from the overall distribution of the particles. Despite of these attractive features, the major disadvantage of the SCF method is its inflexibility that the basis set must be chosen so that the lowest order terms reproduce the global structure of the systems under investigation \citep{MWeinberg1999}. In other words, the SCF method can be applied only to the secular evolution of the collisionless systems. The ultimate approach for numerical simulations of the collisionless self-gravitating systems would be direct integration of the collisionless Boltzmann equation, or Vlasov equation, combined with the Poisson equation. The advantage of the Vlasov--Poisson simulations was already shown by \citet{Janin1971} and \citet{Cuperman1971}, who studied one-dimensional violent relaxation problems using the water-bag method \citep{Hohl1967, Roberts1967}. \citet{Fujiwara1981,Fujiwara1983}, for the first time, successfully solved the Vlasov--Poisson equations for one-dimensional and spherically symmetric systems using the finite volume method. Other grid-based approaches include the seminal splitting method of \citet{Cheng1976}, more generally the semi-Lagrangean methods \citep{Sonnendrucker1998}, a finite element method \citep{Zaki1988}, a finite volume method \citep{Filbet2001}, the spectral method \citep{Klimas1987, Klimas1994}, and a more recent multi-moment method \citep{Minoshima2011}. A comparison study of some of these methods is presented in \citet{Filbet2003}. So far, such direct integration of the Vlasov equation has been applied only to problems in one or two spatial dimensions. Solving the Vlasov equation in six-dimensional phase space requires an extremely large memory and computational time. However, the rapid development of massively parallel supercomputers has made it possible to simulate collisionless self-gravitating systems in the full six-dimensional phase space by numerically integrating the Vlasov--Poisson equations with a scientifically meaningful resolution. In this paper, we present the results from a suite of large simulations of collisionless self-gravitating systems. To this end, we develop a fully parallelized Vlasov--Poisson solver. We perform an array of test calculations to examine the accuracy of our simulation code. We compare the obtained results with analytic solutions as well as linear theory predictions. We discuss the advantage and disadvantage of the Vlasov--Poisson approach over the conventional $N$-body method. The rest of the paper is organized as follows. Section 2 is devoted to describe the detailed implementation of our numerical code to directly integrate the Vlasov--Poisson equations. In section 3, we present the results of several test runs and their comparison with those obtained with the $N$-body method. The CPU timing and the parallelization efficiency are presented in section 4. Finally, in section 5, we summarize our results.
|
In this paper, we have developed a fully parallelized Vlasov--Poisson solver in six-dimensional phase space for collisionless self-gravitating systems. The Vlasov solver is based on the recently proposed positive flux conservation scheme, whereas the Poisson solver utilizes the conventional convolution method based on the discrete Fourier transform. We have conducted large simulations of collisionless self-gravitating systems on the phase space discretized onto $64^{6}$ grids. We have performed a suite of test calculations to examine the accuracy and performance of our simulation code. The results of the test suite are summarized as follows. In Test 1, we examine the overall accuracy of the PFC scheme to solve a 1-dimensional advection equation which is adopted in all the simulations presented in this paper. The mass and the energy conservations are confirmed to an accuracy of $10^{-5}$ for the one-dimensional advection problem. The initial distribution function is well-preserved, without significant smearing due to numerical diffusion. In 1D and 3D tests for the time evolution of the density perturbation through gravatational interactions (Test 2 and 4, respectively), the growth and damping rates of the density perturbations are consistent with the linear theory prediction at early phases. The Galilean invariance is also explicitly shown (Test 3). In Test 5, a stable spherical solution of the Vlasov--Poisson equations, the King sphere, is also reproduced in full six-dimensional phase space. The results manifest that our time-integration scheme is accurate. Finally, our code works efficiently on massively parallel computers. It runs well on up to 1024 CPU cores and scales well with the problem size and with the number of processors. We summarize the advantages of the simulations of collisionless self-gravitating systems based on the Vlasov--Poisson equations over the conventional $N$-body simultaions as follows. Since the matter distribution in the velocity space is explicitly represented in the form of a continuum distribution function, physical processes that are sensitive to the velocity perturbations such as Landau damping can be treated accurately as seen in Test-2 and 4. The collisionless feature is assured in the Vlasov--Poisson simulations, while artificial two-body relaxation could compromise the results of $N$-body simulations. The resolution in the velocity space in the Vlasov--Poisson simulations is shown to be significantly better than that of $N$-body simulations in which the particle distribution in the velocity space is intrinsically rather noisy. Currently the spatial resolution of the Vlasov--Poisson simulations is not as impressive as those of the state-of-the-art $N$-body simulations. However, the performance of our grid-based Vlasov solver scales well with the number of processors. Thus we expect the simulation size can be steadily increased as the available computing power increases in the near future. We foresee direct integration of the collisionless Boltzmann equation will be a promising method in the era of exa-flops computing. Further improvements of the Vlasov--Poisson solver we have developed includes an adaptive mesh approach to improve the spatial and velocity resolutions without significantly increasing the required amount of the memory, and an adoption of more sophisticated schemes to solve one-dimensional advection equations to reduce numerical errors caused by the coarse-grained discretization of the phase space.
| 12 | 6 |
1206.6152
|
1206
|
1206.0012_arXiv.txt
|
An issue currently under debate in the literature is how far from the black hole is the {\sl Fermi}-observed GeV emission of powerful blazars emitted. Here we present a diagnostic tool for testing whether the GeV emission site is located within the sub-pc broad emission line (BLR) region or further out in the pc scale molecular torus (MT) environment. Within the BLR the scattering takes place at the onset of the Klein-Nishina regime, causing the electron cooling time to become almost energy independent and as a result, the variation of high-energy emission is expected to be achromatic. Contrarily, if the emission site is located outside the BLR, the expected GeV variability is energy-dependent and with amplitude increasing with energy. We demonstrate this using time-dependent numerical simulations of blazar variability and discuss the applicability of our method.
|
\label{sec:intro} Blazars are by far the most common objects detected in the gamma-ray sky \citep{abdo112fgl}. \textit{Fermi} has detected blazar variability as short as a few hours \citep[e.g.][]{abdo10b}. During these flares, the GeV luminosity has been known to increase by a factor of up to several compared to its pre-flare luminosity. Because blazars cannot be resolved at these energies (or at any other energy, with the possible exception of VLBA observations), it is impossible to determine the location of these flares by direct detection. To address this issue, we propose a diagnostic test that utilizes \textit{Fermi} variability data of short flares to determine the location of the GeV emission in high-power blazars, namely flat spectrum radio quasars (FSRQ).
|
We have presented a diagnostic test that utilizes blazar variability to determine the location of the GeV emitting site in blazars. The energy difference in seed photons originating from the BLR versus seed photons originating from the MT causes electrons within the emitting site to cool in different energy regimes. For the case where the GeV emitting site is located within the BLR, cooling takes place at the onset of the KN regime, and the resultant electron cooling time is energy-independent. We have demonstrated that the associated light curves exhibits decay times that are approximately energy independent. Conversely, for the case where the GeV emitting site is located outside the BLR, cooling takes place in the Thomson regime and the electron cooling times are heavily energy dependent. In this case, the associated light curves exhibit energy dependence of their decay times. The energy dependence of the decay time of the light curves is visible within the \textit{Fermi} energies; these differences can be used as a diagnostic test to determine whether the GeV emitting region is located inside or outside the BLR. These effects are observable within the time resolution of $\sim$ few hours that \textit{Fermi} has achieved for bright flares and are not erased due to light-travel time effects. Light curves from a sufficiently bright and rapid flare \cite[such as that in 3C 454.3;][]{abdo3c454} should be compared at different energies. If the GeV emitting site is located within the BLR, the decay times will exhibit no energy dependence, whereas if the emitting site is located within the MT, the decay times will exhibit energy dependence. \bigskip
| 12 | 6 |
1206.0012
|
1206
|
1206.2367_arXiv.txt
|
We consider the evaporation of close in planets by the star's intrinsic EUV and X-ray radiation. We calculate evaporation rates by solving the hydrodynamical problem for planetary evaporation including heating from both X-ray and EUV radiation. We show that most close-in planets ($a<0.1$ AU) are evaporating hydrodynamically, with the evaporation occurring in two distinct regimes: X-ray driven, in which the X-ray heated flow contains a sonic point, and EUV driven, in which the X-ray region is entirely sub-sonic. The mass-loss rates scale as $L_X/a^2$ for X-ray driven evaporation, and as $\Phi_*^{1/2}/a$ for EUV driven evaporation at early times, with mass-loss rates of order $10^{10}-10^{14}$~g~s$^{-1}$. No exact scaling exists for the mass-loss rate with planet mass and planet radius, however, in general evaporation proceeds more rapidly for planets with lower densities and higher masses. Furthermore, we find that in general the transition from X-ray driven to EUV driven evaporation occurs at lower X-ray luminosities for planets closer to their parent stars and for planets with lower densities. Coupling our evaporation models to the evolution of the high energy radiation - which falls with time - we are able to follow the evolution of evaporating planets. We find that most planets start off evaporating in the X-ray driven regime, but switch to EUV driven once the X-ray luminosity falls below a critical value. The evolution models suggest that while `hot Jupiters' are evaporating, they are not evaporating at a rate sufficient to remove the entire gaseous envelope on Gyr time-scales. However, we do find that close in Neptune mass planets are more susceptible to complete evaporation of their envelopes. Thus we conclude that planetary evaporation is more important for lower mass planets, particularly those in the `hot Neptune'/`super Earth' regime.
|
\label{introduction} The majority of planets detected to date are found to be close ($<0.5$AU) to their parent star. At these small separations, and particularly at early times, they will be strongly irradiated. The bolometric flux of the host star may inflate the planet's radius, above that which would be expected at larger separations, due to heating (e.g \citealt{baraffe2008}). However it is the high energy radiation (UV and X-rays) that will be important for the evolution of the planet's upper atmosphere, where the gas temperatures may become close to the escape temperature. It is important to understand the process of planetary evaporation as it may have important evolutionary consequences for close-in planets, and it has been suggested that gas giants might entirely loose their gaseous envelopes through such a process, leaving behind a rocky core (e.g. \citealt{bjackson2010}). Observational evidence for planetary evaporation exists through the detection of extended atmospheres in several stellar lines that give planetary radii considerably larger than in the optical and infrared. In particular the atmosphere extends beyond the Roche-radius, indicating the gas is no longer gravitationally bound to the planet. The two best studied examples thus far are HD~209458b (\citealt{vidalmadjar2003, vidalmadjar2004}) and HD~188733b (\citealt{lecavelier2010}), which both have estimated mass-loss rates in the range $\sim10^{10-13}$ g s$^{-1}$. Currently, theoretical models of planetary evaporation are limited and are derived under simplistic assumptions, additionally there is little consensus whether it is driven by Extreme-UV (EUV) or X-ray heating. There is even debate as to whether evaporation is in the hydrodynamic limit, or proceeds through ballistic loss of particles (e.g. Jean's escape) where the upper atmosphere is no longer pressure dominated. {Perhaps the simplest approach is to assume that every photon received at the planet's surface is turned into mass-loss at some efficiency (\citealt{watson1981, lecavelier2007}). Such an approach can only provide an order of magnitude estimate of the mass-loss rate, though it is likely to be fairly accurate in the case of `energy-limited' evaporation, by which we mean that the dominant energy loss process is $P{\rm d} V$ work as discussed by \citet{watson1981}. This may indeed represent an observable region of parameter space at late times in the case of EUV driven evaporation (\citealt{murrayclay2009}). Nonetheless such an approach masks many of the complexities associated with thermally driven evaporative winds. Thermally driven winds are free to absorb energy up to their sonic surface, which may in principle, be located far from the launch point (\citealt{parker1960}). This results in the interception of a much higher fraction of the stellar high-energy flux than the simple planetary disk, an effect \citet{lammer2003} discussed by introducing a further efficiency factor into the `energy-limited' formalism in the form of an expansion radius ($\beta$) based on the work of \citealt{watson1981}. The inclusion of the expansion radius has been dropped in recent years as detailed models of EUV heating in hot Jupiters suggested very little energy is absorbed high in the flow, with most energy deposited near or at the base of the flow (e.g. Yelle et al. 2004; Garcia Munoz 2007; \citealt{leitzinger2011}). Although it is unclear whether EUV heated flows may absorb significant amount of energy high in the flow for planets with different properties compared to hot Jupiters, and whether the X-rays can provide significant heating to the gas at large atmospheric heights, as suggested by \citet{cecchi2006}.} {In addition, one must account for the reduction in the gravitational binding of the planetary atmosphere induced by the stellar gravitational field, as discussed by \citet{erkaev2007}. In the energy-limited formalism this is accomplished by the introduction of another efficiency factor based on the assumption one only need overcome the Roche potential rather than the gravitational field of the planet in isolation\footnote{Note: later we discuss how the effect of the star's gravity appears through the derivative of the potential rather than its absolute value}. Thus the energy limited formalism presented by \citet{erkaev2007} gives rise to a mass-loss rate of the form \begin{equation} \dot{m}=\eta\frac{L_{\rm HE}R_p^3}{4GM_p a^2K(R_{\rm Roche}/R_p)}, \label{eqn:elimited} \end{equation} where $\eta$ is the `efficiency' of the flow, $L_{\rm HE}$ is the high energy luminosity of the central star, $M_P$, $R_p$ \& $a$ are the planet mass, radius and orbital distance and $K(R_{\rm{Roche}}/R_P)$ accounts for the reduction in the planetary binding energy due to the Roche lobe. Eq. \ref{eqn:elimited} has been used for several parameter studies of both EUV evaporation (e.g. Lammer et al. 2009) and X-ray evaporation (e.g. \citealt{davis2009,jackson2012}); however, the `energy limited' approach possesses tunable parameters, for which there is little reason to expect to be independent of the physical properties of the system. As such Eq~\ref{eqn:elimited} is of limited use in understanding the true details of planetary evaporation over a range of parameter space. } Further, there is no reason that evaporation must occur in the energy-limited regime and it may instead be that radiative losses dominate the energy budget rather than $P{\rm d} V$ work. In the case of EUV evaporation at high luminosities \citet{murrayclay2009} showed that this results in a qualitatively different scaling with both the high-energy luminosity and orbital distance. It is also necessary to determine whether the planetary evaporation is indeed occurring in the hydrodynamic limit, for which one needs full solutions to verify that the flow is pressure dominated all the way to the sonic surface. {Several hydrodynamic studies of planetary evaporation have been undertaken that go beyond the `energy-limited' formalism. \citet{yelle2004}, \citet{tian2005} and \citet{murrayclay2009} calculate the hydrodynamic escape for a pure EUV heated model, while \citet{yelle2004} additionally solves for the hydrogen and helium structure of the flow. Of these only \citet{murrayclay2009} solve for the EUV radiation transfer and heating rate directly. However, both \citet{yelle2004} and \citet{tian2005} use fixed heating efficiencies (for photo-electric heating in the case of \citealt{yelle2004} and the total heating efficiency in the case of \citealt{tian2005}). \citet{penz2008} include both X-ray and EUV, but they set the X-ray heating rate to a fixed efficiency, which is then varied between 10 and 60 per cent to obtain various flow solutions. \citet{cecchi2006} consider pure X-ray heating of a static plane-parallel atmosphere and determine the X-ray driven heating with consideration of the hydrogen and helium photochemistry. They conclude that at high X-ray luminosities similar to those found around young stars (e.g. $L_X\sim10^{30}$ erg s$^{-1}$), it may be X-rays that dominate the heating. Conversely several hydrodynamical studies of EUV evaporation have been successfully applied to the observations of HD 209458b, correctly reproducing the observed mass-loss rates of $\sim 10^{10}-10^{11}$ g s$^{-1}$, suggesting X-rays may be unimportant in this particular case (e.g. \citealt{garcia2007,murrayclay2009,koskinen2010a}). What is not clear, however, is the structure of X-ray driven flows, the interactions that take place between a hydrodynamic flow that has X-ray and EUV heated regions and how a flow may transitions from X-ray dominated to EUV dominated. } As a prelude to performing multi-dimensional hydrodynamic calculations, in this work we build 1D, on-axis, hydrodynamical solutions to the problem of planetary evaporation including both EUV and X-ray radiation fields under the approximation of radiative equilibrium. This allows us to understand whether planetary evaporation will be `energy-limited' or not, whether it will occur in the hydrodynamic limit, and what the interactions between the EUV and X-ray fields yield in terms of evaporation. Our paper is organised as follows: in Section~\ref{sec:heat} we discuss the various heating mechanisms; in Section~\ref{sec:basichydro} we derive our hydrodynamic solutions for EUV and X-ray heating; in Section~\ref{sec:evol} we consider simple evolution of planets undergoing evaporation; in Section~\ref{sec:discuss} we discuss the implications of our results and our assumptions, and finally we present our conclusions in Section~\ref{sec:conc}.
|
\label{sec:conc} In this work we have investigated the role of both X-ray and EUV heating in evaporating a close-in planet's atmosphere, using 1D hydrodynamic models. We have considered how the mass-loss rates, and the driving mechanism, vary within the observable parameter space including: planet mass, planet density, separation, stellar mass, metallicity of the planet atmosphere and X-ray/EUV luminosity. Then under the assumption that the EUV and X-ray luminosities follow an identical evolution in time, with the same initial luminosities, we have calculated the mass evolution of evaporating planets that evolve at constant density. Our main conclusions are as follows: \begin{enumerate} \item We identify two separate cases of planetary evaporation: X-ray driven, where the X-ray flow undergoes a sonic transition, and EUV driven, where the X-ray heated portion of the flow remains sub-sonic. In general X-ray evaporation occurs at high X-ray luminosities, low planetary densities, high planetary masses and small separations. Whereas EUV evaporation dominates at low X-ray luminosities, high planetary densities, low planetary masses and large separations. \item We find that at separations of $<$0.1~AU, most planets will be evaporating hydrodynamically rather than through a ballistic mass-loss process. However, at separations greater than $\sim 0.1-0.5$~AU dense, Jupiter mass planets, may not be able to evaporate hydrodynamically. \item In the case of X-ray driven evaporation, the flow is close to radiative equilibrium and energy loss from the flow is dominated by line cooling. The mass-loss rates scale linearly with X-ray luminosity and inversely with the separation squared ($\dot{m} \propto L_X/a^2$), but no exact scalings with planetary mass and planetary radii exist. \item We find that as the high-energy luminosity falls over time, the evaporative flow may undergo a transition from X-ray driven at early times to EUV driven at late times. This transition occurs at lower X-ray luminosities (and hence later times) for planets with at smaller separations. \item Considering the evolution of Jupiter and Neptune mass planets, we find it is unlikely that an initially Jupiter mass planet can be completely evaporated within Gyr timescales, only losing a few percent of its original mass. However, we find that Neptune mass planets are much more susceptible to complete evaporation. Within 3~Gyr Neptune mass planets at densities of $\la$0.3~g~cm$^{-3}$ are completely evaporated at a separation of 0.025~AU, while Neptune mass planets at densities of $\la$1 g cm$^{-3}$ are completely evaporated at a separation of 0.0125~AU. \item Using our evolutionary models we infer that at late times ($\sim$Gyrs), planets at separations $\la$0.025AU will still be undergoing X-ray driven evaporation, whereas at larger separations the evaporation will generally be in the EUV driven regime. \end{enumerate}
| 12 | 6 |
1206.2367
|
1206
|
1206.1364_arXiv.txt
|
We present simulations of Keck Interferometer ASTRA and VLTI GRAVITY observations of mock star fields in orbit within $\sim50$ milliarcseconds of Sgr A*. Dual-field phase referencing techniques, as implemented on ASTRA and planned for GRAVITY, will provide the sensitivity to observe Sgr A* with long-baseline infrared interferometers. Our results show an improvement in the confusion noise limit over current astrometric surveys, opening a window to study stellar sources in the region. Since the Keck Interferometer has only a single baseline, the improvement in the confusion limit depends on source position angles. The GRAVITY instrument will yield a more compact and symmetric PSF, providing an improvement in confusion noise which will not depend as strongly on position angle. Our Keck results show the ability to characterize the star field as containing zero, few, or many bright stellar sources. We are also able to detect and track a source down to $m_K\sim18$ through the least confused regions of our field of view at a precision of $\sim200~\mu$as along the baseline direction. This level of precision improves with source brightness. Our GRAVITY results show the potential to detect and track multiple sources in the field. GRAVITY will perform $\sim10~\mu$as astrometry on a $m_K=16.3$ source and $\sim200~\mu$as astrometry on a $m_K=18.8$ source in six hours of monitoring a crowded field. Monitoring the orbits of several stars will provide the ability to distinguish between multiple post-Newtonian orbital effects, including those due to an extended mass distribution around Sgr A* and to low-order General Relativistic effects. ASTRA and GRAVITY both have the potential to detect and monitor sources very close to Sgr A*. Early characterizations of the field by ASTRA including the possibility of a precise source detection, could provide valuable information for future GRAVITY implementation and observation.
|
Over the last 20 years, high resolution infrared imaging techniques have provided precise astrometric measurements of stellar sources at the Galactic Center. Focused astrometric monitoring campaigns have revealed a population of mostly young early-type stars (the S-cluster) in orbit about the location of the radio and infrared source dubbed Sagittarius A* (Sgr A*). In fact, \citet{Ghez08} and \citet{Gill09a} both analyze their own distinct data sets to deduce a mass of $4.5\pm0.4\times10^{6} \mathrm{M}_{\odot}$ located coincident with Sgr A*. This mass must all be within the periapsis of the star S16/S0-16\footnote{The UCLA and the MPE groups have adopted different naming conventions for the S-cluster}, which is only ~40 AU. The implied mass density provides compelling proof that Sgr A* is the luminous manifestation of an accreting black hole. In addition to providing a measurement of the mass of Sgr A*, the orbits of the stars also provide a direct measurement of the distance to the black hole, $8.36\pm0.44$ kpc \citep{Ghez08}. If Sgr A* actually resides at the dynamic center of the Milky Way, then measuring its distance also represents a measurement of the solar distance from the Galactic Center ($R_0$). Monitoring stellar orbits about Sgr A* also provide a measurement of the sun's peculiar motion in the direction of the Galactic Center ($\Theta_0$). As discussed by \citet{Olling00}, $R_0$ and $\Theta_0$ are ubiquitous parameters in the description of the structure and dynamics of the Milky Way \citep[see also][]{Reid2009}. Uncertainty in the values of $R_0$ and $\Theta_0$ are the largest sources of error in the determination of the ratio of the galactic halo's long and short axes \citep[$q$,][]{Olling00}. The parameter $q$ is sensitive to different galaxy formation scenarios and dark matter candidates, and if $R_0$ and $\Theta_0$ were known at the $1\%$ level, the constraints on $q$ would help to differentiate theories of galaxy formation and dark matter \citep{Olling00}. In addition, a very precise knowledge of $R_0$ could affect our calibration of the lowest rungs of the cosmic distance ladder by improving our distance measurements to galactic sources such as Cepheids and RR Lyrae variables\citep{Ghez08}. The existence of the S-cluster is intriguing because it is rich with young stars and because forming these stars in situ represents a theoretical problem given the strong tidal forces in the region. The alternative of formation at larger radii and subsequent migration is strongly constrained by the deduced young age of the stars. However, because the S-stars are known to be younger than the relaxation time in the environment \citep[a B star's main-sequence lifetime is $\sim10^{7}$ years compared to the relaxation time of $\sim 2\times10^8$ years;][]{Weinberg05} their orbits should encode some information about the kinematics of the cluster at the time it formed. Thus, perhaps as a bonus, astrometric monitoring of the stars in our Galaxy's nuclear cluster has the potential to inform the community not only on matters of General Relativity and galaxy formation, but also on star formation in extreme environments. The deduced mass and distance of Sgr A* make it the largest black hole on the sky, in terms of angular diameter, and an excellent candidate for study. Improving astrometric measurements and discovering stars on even shorter period orbits will improve our understanding of the gravitational potential which binds the stars, possibly exposing a dark matter cusp at the center of our galaxy, and should inform our understanding of gravity on scales not yet explored by precise experiments. For example, \citet{Weinberg05} modeled a distribution of stars on very short period orbits about Sgr A* and showed that post-Newtonian effects on the orbital paths could be detected with the astrometric precision and sensitivity of a future thirty-meter telescope. Existing and upcoming near-IR interferometers can provide even better resolution, and enable some of the same science. In their treatment \citet{Weinberg05} assumed Gaussian point spread functions, which tend to zero in the wings faster than the more realistic Airy pattern which distributes light in rings away from the central core. These rings present a contrast barrier in conventional imaging. Likewise, the even more complicated point spread functions (PSFs) provided by interferometers result in contrast and detection limits and can bias astrometric measurements. \citet{Fritz10} showed that halo noise and source confusion are the factors limiting astrometric accuracy. These effects, which are both related to the angular resolution of the telescope and the luminosity function of the sources in the region (i.e. the dynamic range), present a fundamental astrometric hurdle which cannot be overcome with even the largest single aperture telescopes of today \citep{Ghez08,Gill09a}. In fact, simulations by \citet{Ghez08} and \citet{Gill09a} showed that astrometric errors could be as large as 3 milliarcseconds due to confusion with undetected sources. This level of astrometric uncertainty, present close to Sgr A* where stars experience the deepest part of the potential, has precluded the detection of any post-Newtonian effects on stellar orbits to this point and has limited the precision with which the distance to the Galactic Center can be measured. The limiting magnitude and astrometric precision of Galactic Center observations has improved as early speckle observations \citep[e.g.][]{Eckart92} were supplemented by adaptive optics (AO) and laser guide star AO \citep[e.g.][]{Ghez05}. The current state of the art is a limiting magnitude of $\sim$19 at K and an astrometric precision of $\sim100\mu$as. However, these limits are only achieved far from the crowded central region immediately surrounding Sgr A*. In this paper we investigate whether, with the increased resolution of infrared interferometers and the concomitant reduction in confusion, we can detect heretofore undetected or unnoticed stars on orbits with very short periods within 50 mas of Sgr A*. We also explore the astrometric precision with which such sources could be monitored with an IR interferometer. According to \citet{GhezTalk} a factor of $\sim3$ more stars with periods less than 20 yrs are expected to be orbiting Sgr A*. These stars, if they can be detected and monitored, will provide a detailed description of the central potential \citep[a minimum of three short-period orbits are required for a complete characterization;][]{Rubilar2001}. Additionally, such stars will provide the best targets for observing General Relativistic effects since they are deepest in the potential well of Sgr A*. Although the higher resolution provided by interferometry is beneficial for increasing the detectability of sources in the crowded region and for increasing the astrometric precision attainable, there are many potential complicating factors which do not apply to conventional full aperture imaging. For example, in full aperture imaging, collecting area increases as the square of the resolution. In interferometers, however, the collecting area is independent of the effective spatial resolution. This means that although the confusion limit is somewhat alleviated by the higher angular resolution available, photon noise quickly becomes a problem in the detection of faint sources. This fact is further exacerbated by the low typical throughput of interferometers (e.g., $\sim2\%$ for the Keck Interferometer). Additionally, the sparse nature of an interferometer's collecting area results in an incomplete sampling of the Fourier components of the source distribution on the sky. This causes an incomplete knowledge of the sky-plane light distribution resulting in PSFs with large sidelobes. Finally, Michelson interferometers like the Keck Interferometer and the VLT Interferometer (VLTI) have small fields of view, $\sim50$ mas, which typically only include a single object; clearly this presents difficulty for astrometry. We attempt to understand the scale of these effects by simulating data and inferring results. The outline of the paper is as follows. In Section 2 we discuss the construction of mock star fields within 50 mas of the Galactic Center. In Section 3 we discuss our observation simulator and all included sources of noise and uncertainty. Section 4 covers our algorithm for making relative astrometric measurements by fitting to the visibility curves. Section 5 includes a presentation of our results. Section 6 provides a discussion of the potential advances and difficulties. Although we try to keep the discussion general, we focus on ASTRA at the Keck Interferometer as we are most familiar with that instrument and it is currently capable of making these observations. We also provide a discussion of VLTI GRAVITY \citep{GRAVITY3} simulations.
|
In Section \ref{ResultsSec}, our Keck Interferometer ASTRA simulations show the ability to detect and track a stellar source on an orbit within $\sim50$ mas of Sgr A* with a single baseline interferometer. This performance depends on the source contrast and position angle with respect to Sgr A*. However, we demonstrate the potential to detect and track an $m_K\sim18$ star when Sgr A* is at $m_K=17.3$ and the star and Sgr A* are well separated along the baseline direction (left panel of Figure \ref{Field2Select}). We show that $\sim150~\mu$as astrometry is possible along the baseline direction and $\sim3$ mas precision is possible in the transverse direction during unconfused epochs. Our precision improves if the sources are brighter. Since a single baseline interferometer produces an extended PSF, confusion still affects our ability to accurately detect and track sources when their sidelobes overlap. While at first glance ASTRA seems quite limited compared to GRAVITY in its ability to detect and track stars within $\sim50$ mas of Sgr A*, we show that the single baseline instrument could significantly contribute to the Galactic Center science case. Specifically, we show that multi-epoch observations have the ability to distinguish whether the region contains no bright sources, one or two bright sources, or several bright sources (see Figures \ref{Field1Select}, \ref{Field2Select}, and \ref{confusionFig}). Since the source content in the region is truly unknown, any additional information about the stellar density near the Galactic Center would be quite valuable. New information could inform, for example, dynamical theories of the nuclear cluster which must explain the positions of the stars. Further, the higher throughput, larger apertures, and fewer beam splits provide a larger signal in the ASTRA fringes (compare for example Tables \ref{SNField2} and \ref{VLTSNField2}). While confusion noise will constrain ASTRA observations, if no star brighter than $m_K\sim19$ exists in the field ASTRA may have an advantage in making a detection. Because ASTRA is currently capable of making these observations the potential exists to provide the community with some constraints before GRAVITY comes online at the VLTI and before ASTRA operations cease at Keck. While long-term operations of ASTRA are not currently planned, we note that if ASTRA and GRAVITY observations could be obtained contemportaneously, some importvement in the recovery of faint sources may be possible. In simulations where we combined ASTRA and GRAVITY data (using the assumptions in Table \ref{VisParams} for each instrument), we found that we can recover the $m_K=19.8$ source in some epochs where it is not recovered using either ASTRA or GRAVITY data alone. Our GRAVITY simulations show that that instrument will attain a lower confusion limit than ASTRA. This lower confusion in GRAVITY observations is due to the increased uv-coverage provided by the VLTI array. This makes it possible to detect and monitor multiple sources in the field. We demonstrate the potential for $\sim10~\mu$as precision astrometry on Sgr A* at $m_K=16.3$ and $\sim100~\mu$as precision astrometry on sources as faint as $m_K=18.8$ in six hours of observing our simulated star fields. However, we show that the decreased throughput at GRAVITY and the larger number of beam splits required to create six baselines will impose a detection limit at GRAVITY which will make it difficult to detect sources at $m_K\gtrsim19$. In fact, we show that for one simulated three-night run using GRAVITY, we are unable to recover the position of the $m_K=18.8$ source. While this reflects contrast and fiber function issues to some extent, it shows that in real observations GRAVITY may struggle to detect sources at this brightness level. GRAVITY's ability to recover precise astrometry for multiple sources within $\sim50$ mas from Sgr A* suggests it should be able to constrain the shape of an extended mass distribution at the Galactic Center\citep{Rubilar2001, Weinberg05}. Any model of the central structure must include the mass of the black hole and the mass and radial profile of an extended distribution of matter. To constrain these parameters and to break the first-order degeneracy between the retrograde precession due to the extended matter and the prograde precession attributable to General Relativity, multiple stars with distinct angular momenta will be needed \citep{Rubilar2001, Weinberg05}. Since the astrometric signal of orbital precession increases linearly with the number of revolutions, monitoring stars on short-period orbits within $\sim50$ mas is preferred, since a larger signal can be detected in shorter time. Our GRAVITY simulations also demonstrate the astrometric precision needed to detect relativistic effects on stellar orbits. Our simulated performance of $\sim100~\mu$as suggests that low order effects of relativity, such as the prograde precession, will be detectable \citep{Weinberg05}. However, higher order relativistic effects, such as detecting the influence of the black hole spin on stellar orbits, will be more difficult, requiring measurements more precise than those demonstrated here\citep{Weinberg05, Merritt2011}. A recent paper by \citet{Vincent11} modeled the imaging mode astrometric performance of GRAVITY, applying the CLEAN algorithm to images formed using the interferometric visibilities. In that paper, the authors mainly investigate the astrometric precision attainable on Sgr A* when it is very bright. They compare their performance after a whole night of observing to individual 100 second exposures. They show that $\sim40~\mu$as precision is attainable on Sgr A* in 100 seconds when it is very bright and the field is simple. Our simulations show that astrometric precision on the order of the angular extent of the inner-most stable circular orbit of the black hole ($\sim30~\mu$as) is attainable on Sgr A* even in the midst of our more complicated star field. However, $\sim10~\mu$as precision is attained after 6 hours of observing; time resolved astrometry in our fields will necessarily be less precise. Not only are shorter observations less sensitive to sources in the field, but with less time spent on-source the uv-coverage is reduced. Both of these effects combine to degrade the astrometric precision by decreasing the signal-to-noise ratio and increasing the confusion. We demonstrate that as astrometry on Sgr A* becomes more difficult due to confusion with bright stars in the small field, astrometry on those bright stars becomes easier. Thus GRAVITY should provide some traction on investigating General Relativistic effects, either through observations of Sgr A* itself given a faint star field or by tracking stars in the vicinity of Sgr A* given a brighter star field. Although our simulations did not include Sgr A* variability explicitly, variability could provide an interesting paradigm for making these observations. During high states, we will be able to conduct precise astrometry of Sgr A*, anchoring our field. During low states, the decreased contrast will provide an opportunity to probe for fainter stellar sources in the region. This back-and-forth approach could be harnessed to precisely monitor faint sources. To demonstrate these effects, we ran our simulator with Sgr A* set to very low brightness but with the star field magnitudes kept constant. During these runs, we were able to recover stellar positions more easily, since confusion with Sgr A* was reduced. On the other hand, a very bright Sgr A* is easily detected with a high level of precision. The timescales of Sgr A* variability are conducive to seeing both high and low states while observing. Flares are observed on timescales of $\sim10-100$ minutes and Sgr A* often changes flux by more than one magnitude.
| 12 | 6 |
1206.1364
|
1206
|
1206.6291_arXiv.txt
|
The Gaia-ESO Survey is a wide field spectroscopic survey recently started with the FLAMES@VLT in Cerro Paranal, Chile. It will produce radial velocities more accurate than Gaia's for faint stars (down to V$\simeq$18), and astrophysical parameters and abundances for approximately 100\,000 stars, belonging to all Galactic populations. 300 nights were assigned in 5 years (with the last year subject to approval after a detailed report). In particular, to connect with other ongoing and planned spectroscopic surveys, a detailed calibration program --- for the astrophysical parameters derivation --- is planned, including well known clusters, Gaia benchmark stars, and special equatorial calibration fields designed for wide field/multifiber spectrographs.
|
Gaia-ESO is a public spectroscopic survey, targeting $\geq$10$^5$~stars, systematically covering all major components of the Milky Way, from halo to star forming regions, providing the first homogeneous overview of the distributions of kinematics and elemental abundances. This alone will revolutionise knowledge of Galactic and stellar evolution: when combined with Gaia astrometry the survey will quantify the formation history and evolution of young, mature and ancient Galactic populations. With well-defined samples, it will survey the bulge, thick and thin discs and halo components, and open star clusters of all ages and masses. The FLAMES spectra will: quantify individual elemental abundances in each star; yield precise radial velocities for a 4-D kinematic phase-space; map kinematic gradients and abundance - phase-space structure throughout the Galaxy; follow the formation, evolution and dissolution of open clusters as they populate the disc, and provide a legacy dataset that will add enormous value to the Gaia mission and ongoing ESO imaging surveys. \subsection{Scientific aims} How disc galaxies form and evolve, and how their component stars and stellar populations form and evolve, are among the most fundamental questions in contemporary astrophysics \citep{kormendy10,peebles11,komatsu11}. The Gaia-ESO survey will contribute to those key questions, by revolutionising our knowledge of the formation and evolution of the Milky Way Galaxy and the stars that populate it. Because stars form in associations and clusters rather than singly, understanding star formation in the Milky Way also implies studying cluster formation. The key to decoding the history of galaxy evolution involves chemical element mapping, which quantifies timescales, mixing and accretion length scales, and star formation histories; spatial distributions, which relate to structures and gradients; and kinematics, which relates to both the felt but unseen dark matter, and dynamical histories of clusters and merger events \citep{freeman02}. With Gaia, and calibrated stellar models, one will also add ages. Manifestly, very large samples are required to define all these distribution functions and their spatial and temporal gradients. With more than 10$^5$ stars and 100 clusters, each with complete 6D space mapping when combined with Gaia, and with the addition of astrophysical parameters (T$_{\rm{eff}}$, log$g$, [M/H]), abundance ratios (iron-peak and $\alpha$-elements, plus other species for 10\,000 stars), and of ages for clusters, the Gaia-ESO Survey is the dataset needed to answer those questions. The expected scientific output is enormous, and a brief summary of the main survey goals is reported in the following. \medskip {\bf Clusters and stellar evolution.} Theories of cluster formation range from the highly dynamic through to quasi-equilibrium and slow contraction scenarios. These different routes lead to different initial cluster structures and kinematics \citep{jackson10}. Whilst hydrodynamic and N-body simulations are developing, a fundamental requirement is an extensive body of detailed observations. A complete comparison requires precise position and velocity phase-space information resolving the internal cluster kinematics ($\leq$0.5~km/s). Moreover, each star cluster provides a (near-)coeval snapshot of the stellar mass function, suitable for testing stellar evolution models from pre-main sequence phases right through to advanced evolutionary stages. Much of the input physics in stellar models can be tested by its effects on stellar luminosities, radii and the lifetimes of different evolutionary phases. Homogeneous spectroscopy will provide estimates of stellar parameters and reddening for large samples of stars over a wide range of masses, in clusters with a wide range of ages and mean chemical compositions. \medskip {\bf The halo and the Bulge.} Recent surveys have revealed that the halos of both our own and other Local Group galaxies are rich in substructures \citep{belokurov06}. These not only trace the Galaxy's past, but have enormous potential as probes of its gravitational field and hence as tracers of the still very uncertain distribution of dark matter \citep{helmi04}. High precision radial velocities for many stars at latitudes $|b|>30\deg$ will lead to the discovery of more substructures. Their abundance patterns will indicate clearly whether a given structure represents a disrupted object and of which type, or has formed dynamically by resonant orbit-trapping. The kinematics of streams will place tight constraints on the distribution of dark matter. In simulations of galaxy formation, mergers tend to produce substantial bulges made of stars that either formed in a disc that was destroyed in a merger, or formed during a burst of star formation that accompanied the merger \citep{abadi03}. Such ``classical" bulges are kinematically distinguishable from ``pseudo-bulges" that form when a disc becomes bar unstable, and the bar buckles into a peanut-shaped bulge \citep{peebles11,kormendy10}. In common with the great majority of late-type galaxies, the Galaxy's inner bulge appears to be a pseudo-bulge, but $\rm{\Lambda}$CDM simulations suggest that it should also host a classical bulge, perhaps that observed at larger radii. By studying the kinematics and chemistry of K giants at $|b|>5\deg$ we will either confirm the classical bulge or place limits on it which will pose a challenge to $\rm{\Lambda}$CDM theory. \medskip {\bf The discs.} Thick discs seem common in large spiral galaxies \citep{gilmore83,yoachim06}. Are they evidence that the last major merger event occurred very much longer ago than is expected in standard cosmologies? Are they artifacts of thin disc dynamical evolution? Are they both or neither of these? How did the metallicity of the ISM evolve at very early times? How does this vary with Galactocentric distance? Do major infall events occasionally depress the metallicity of the ISM17? The Gaia-ESO Survey will determine quantitative kinematics and abundance patterns for large samples of thick disc F ang G stars over one outer radial and three vertical scale lengths to help elucidate these key questions in Galaxy formation and evolution. The selected sample of $\simeq$5000 F and G stars (see below) within 1~kpc from the Sun covers both thin and thick discs, and all ages and metallicities. Using field stars and clusters, where ages are also known, the Gaia-ESO Survey will explore the region from about 6 to more than 20 kpc in Galactocentric distance, and will trace chemical evolution as a function of age and Galactocentric radius across a disc radial scale length. These are key inputs to models for the formation and evolution of the Galaxy disc. Current estimates suffer from poor statistics, inhomogeneous abundance determinations and absence of data at key ages and orbits \citep{nordstrom04}. The Gaia-ESO Survey will also address current disc structure, that which hosts the star formation. Spiral structure is fundamental to the dynamics of the disc: it dominates the secular rise in the random velocities of stars, and may even cause radial migration of stars and gas \citep{antoja10}. Currently, we are not even clear about the global morphology of our spiral structure, and the information we have on its dynamics largely relates to gas, not stars. We will initiate a study of the kinematic distortion in the disc potential due to the bar/spirals by measuring some 1000s of radial velocities down key arm, inter-arm and near-bar lines of sight. \subsection{Survey organization} \begin{figure} \plotone{Pancino_E_1_1.eps} \caption{An overwiev of the Gaia-ESO Survey data flow system. \label{pancino1_fig_smp}} \end{figure} The survey has approximately 300 co-investigators, and the work is structured in a series of documents agreed with ESO, principally the Survey Management Plan and the Survey Implementation Plan. Fig.~\ref{pancino1_fig_smp} shows the work organization flow, where each WG (Working group) is indicated. The obtained raw data will become publicly available through the ESO archive as soon as they are obtained. There will be different advanced data products releases: \begin{itemize} \item{semestral data releases: will begin 12 months after observations started (31 December 2011) and they will refer to all targets that were completed six months before the release date; they will contain reduced 1D spectra with variance, radial velocity with uncertainty, basic target information (including variability);} \item{annual data releases: they will start 18 months after observations started and will refer to all targets that were completed six months before the release data; they will contain astrophysical parameters determination for the single stars and for the clusters as a whole;} \item{final data release: containing the full determinable set of astrophysical parameters for each individual target, and for the open clusters as systems, with updated and consistent calibration.} \end{itemize} \subsection{Observing strategy} The Gaia-ESO Survey was awarded 300 observing nights (60 nights per year, with the last year subject to approval after a progress review) with FLAMES at the ESO VLT (Very Large Telescope). FLAMES \citep{FLAMES} feeds fibers to two spectrographs: UVES \citep{UVES}, with a resolution of R$\simeq$47\,000, receives 8 fibers and GIRAFFE, with a resolution ranging from R$\simeq$15\,000 to 20\,000, receives 132 fibers. Part of the fibers are dedicated to the sky, and a few special fibers are illuminated by wavelength calibration lamps, allowing for a radial velocity determination to better than 100~m/s. Observations started in December 2011. A selection of the order of 10$^5$ stars belonging to all Galactic components will be obtained from exisiting photometric surveys such as 2MASS \citep{2MASS}, VISTA \citep{VISTA}, SDSS \citep{SDSS} and from dedicated photometries either found in the literature \citep[][to name a few]{dias02,kharchenko05} or specifically derived from public archival data. Observations are restricted to +10$\deg$$\geq$Dec$\geq$--10$\deg$ whenever possible, to minimize airmass limits, and to 9$\geq$V$\geq$19~mag (where for V$>$17~mag only radial velocities will be measured). The primary targets in the various Galactic components will be: \begin{itemize} \item{bulge: $\simeq$10\,000 K giants belonging to the red clump (I$\simeq$156~mag), for an abundance analysis of iron-peak and $\alpha$-elements with both UVES and GIRAFFE;} \item{halo and thick disk: F and G stars, with 17$\geq$r$\geq$18~mag, for iron-peak and $\alpha$-elements down to [Fe/H]$\simeq$--1.0~dex; stars belonging to known streams (e.g., Sgr) will be targeted; the halo targets are expected to be many thousands, as are the thin+thick disk stars;} \item{outer thick disk (2--4~kpc fonr the Sun): F and G stars, with 25\% of the fibers allocated to candidate K giants (r$\leq$18~mag) for studying the warp and the Monoceros stream;} \item{thin disk dynamics: six fields at I$\leq$19~mag will target red clump stars for disk spiral arm/bar dynamics, and only radial velocities will be obtained;} \item{Solar neighborhood: UVES parallel observations of approximately 5000 G stars within 1~kpc from the Sun, for a detailed abundance analysis of all available elements in the 4800--6800~\AA\ range.} \item{Open clusters: a total of $\sim$100 clusters of all ages (excluding the embedded phase) will be observed, choosing high-probability members of all spectral types --- as appropriated --- from O to K dwarfs and giants, and including unveiled PMS (Pre-Main Sequence) stars; the faintest targets will provide accurate radial velocities, the brightest ones a detailed chemical abundance analysis;} \item{calibration fields: these are discussed in Sect.~\ref{pancino1_sec_cal};} \item{archival data: the Gaia-ESO Survey will analyse all ESO archival data consistent with the observing set-ups and the scientific goals of the survey.} \end{itemize}
| 12 | 6 |
1206.6291
|
|
1206
|
1206.1478_arXiv.txt
|
We revisit the gauge issue in cosmological perturbation theory, and highlight its relation to the notion of covariance in general relativity. We also discuss the similarities and differences of the covariant approach in perturbation theory to the Bardeen or metric approach in a non-technical fashion.
|
\label{intro} Perturbation theory is these days a standard tool in theoretical cosmology. Since the introduction of the theory more than sixty years ago, the ``gauge issue'' has been troubling cosmologists. Although the problem has been resolved by now, at all orders in perturbation theory, there still seems to be some confusion as to its origins. We aim at clarifying these issues in this short note, by highlighting previous results that might be well known to the specialist, but not necessarily to the wider community. \\ After the pioneering work by Lifshitz in 1946 \cite{Lifshitz1946}, Bardeen in 1980 \cite{Bardeen80} demonstrated how the gauge issue can be rigorously solved in the metric based approach. The reviews by Kodama and Sasaki \cite{KS} and Mukhanov, Feldman and Brandenberger \cite{MFB} further contributed to the success of this approach. More recently the gauge issue has also been studied beyond linear order in cosmological perturbation theory, leading to a rich body of work using the Bardeen and related gauge-invariant formalisms \cite{Bruni96,Mukhanov96,MW2003,Noh2004,Bartolo_review,Nakamura2007,MM2008,MW2008,CMMN2011}. A different approach has been developed, which is usually referred to as the ``covariant'' approach, following Ellis and Bruni \cite{Ellis:1989jt} (and earlier work by \cite{sachs,hawking66}). However, as we show below, also the covariant approach has to face the gauge issue if a ``background'' spacetime is introduced.\\ But what do we mean by gauge dependence in cosmological perturbation theory, where does it actually come from, and what makes it so difficult? In cosmological perturbation theory we split quantities into a background and small perturbations, both for the matter variables and the metric. Gauge dependence then stems from requiring a unique background spacetime on which the background quantities are defined, that does not follow the coordinate or gauge transformation, whereas the perturbations do obey the transformation. This allows us to talk about e.g.~\emph{the} Friedmann-Robertson-Walker (FRW) background around which we perturb our quantities. Before we define once more what we mean by gauge-invariance in the setting of cosmological perturbation theory below, let us briefly state what it is not. It should not be mistaken for or mixed up with {covariance}, the requirement that the governing equations do not depend on the coordinate system chosen. Indeed, it is well known that covariance can be broken in cosmology without conceptual or other problems arising, e.g.~in order to choose a particular coordinate system that makes the calculation simpler \cite{EM1995}. Gauge-invariance in cosmological perturbation theory should also not be confused with the gauge choice in standard General Relativity (GR). We can choose four arbitrary coordinate functions in the metric tensor (thanks to the four constraint equations in Einstein's field equations, see e.g.~Ref.~\cite{MTW}). In cosmological perturbation theory the symmetries of the physical spacetime, namely homogeneity and isotropy, lead us to choose a background that is FRW (with zero background curvature for convenience), and we can then use covariance to choose our coordinates in the background such that the line element has a particularly simple form, i.e. \be ds^2=dt^2+a^2(t)\delta_{ij}dx^idx^j\,, \ee where $a$ is the scale factor and $\delta_{ij}$ the flat background metric. This is related to the ``geodesic slicing'' in numerical relativity, which is selected by choosing a lapse function normalised to unity, and choosing a vanishing shift vector selects Gaussian normal coordinates (see e.g.~Ref.~\cite{Baumgarte2009}). Hence the ``standard GR coordinate freedom'' is used, actually used up, in choosing and specifying the background. \\ This note is aimed at the non-specialist and we try to keep our discussions as non-technical as possible, working rather by way of example than by introducing theorems. Nevertheless, in the following two sections we have to define gauge-dependence and gauge-invariance in a more rigorous way than above. In Section \ref{relating} we show how quantities in the covariant formalism are related to the ones in standard metric perturbation theory, and comment briefly on the issue of non-locality in perturbation theory in Section \ref{nonlocal}, and conclude with a short discussion in Section \ref{discussion}. Finally we highlight in Appendix \ref{example} the difference between covariance and gauge-invariance. We use predominantly coordinate time $t$, and denote derivatives with respect to $t$ with a dot. Conformal time $\eta$ is related to $t$ by $dt=a\ d\eta$, where $a$ is the scale factor. Greek indices $\mu, \nu$, and $\lambda$ range from $0$ to $3$, lower case Latin indices, $i$, $j$, and $k$, have the range $1,2,3$.
| 12 | 6 |
1206.1478
|
|
1206
|
1206.6634_arXiv.txt
|
Collisionless relativistic shocks have been the focus of intense theoretical and numerical investigations in recent years. The acceleration of particles, the generation of electromagnetic microturbulence and the building up of a shock front are three interrelated essential ingredients of a relativistic collisionless shock wave. In this paper we investigate two issues of importance in this context: (1) the transport of suprathermal particles in the excited microturbulence upstream of the shock and its consequences regarding particle acceleration; (2) the preheating of incoming background electrons as they cross the shock precursor and experience relativistic oscillations in the microturbulent electric fields. We place emphasis on the importance of the motion of the electromagnetic disturbances relatively to the background plasma and to the shock front. This investigation is carried out for the two major instabilities involved in the precursor of relativistic shocks, the filamentation instability and the oblique two stream instability. Finally, we use our results to discuss the maximal acceleration at the external shock of a gamma-ray burst; we find in particular a maximal synchrotron photon energy of the order of a few GeV.
|
The microphysics of collisionless relativistic shocks has been intensively investigated in recent years, through both numerical simulations and theoretical investigations. As demonstrated in particular by \cite{S08a,S08b}, the physics of these shock waves in the unmagnetized limit involves the interplay of three phenomena: the formation of the shock through the deceleration and reflection of particles against a microturbulent magnetic barrier, the self-generation of this microturbulence upstream of the shock by back scattered particles and the development of Fermi type acceleration. So far, particle acceleration has been observed in PIC simulations of unmagnetized relativistic shocks (\citealp{S08b,Kea09,Mea09,SS09,SS11a}), and indeed one must expect the development of the Fermi process when the magnetization is very weak, because microturbulence can then grow and provide the necessary scattering (\citealp{LPR06,LP10}). At larger levels of magnetization of the upstream flow, the shorter precusor scale may prevent the development of microinstabilities, and in the absence of cross-field scattering, Fermi powerlaws cannot develop (\citealp{Nea06,LPR06}); this picture has been validated in particular by the simulations of \cite{SS11a}. Nevertheless, the long timescales and high energies that are inferred in powerful astrophysical sources remain well out of reach of these state of the art numerical simulations. It is therefore important to build on the basis of these numerical experiments a theoretical understanding of the various processes at play in these shock waves. In the present work, we are interested in the physics of the microturbulence upstream of a relativistic weakly magnetized shock. Two fast growing microinstabilities have received significant attention regarding the development of microturbulence upstream of a relativistic shock front: the filamentation (often termed Weibel) mode (e.g. \citealp{ML99,WA04,LE06,AW07a,AW07b,B09,LP10,Rea11,LP11a,Sea11}) and the two stream instability (hereafter OTSI, e.g. \citealp{BFP05,B09,LP10,LP11a,Sea11}). Both instabilities follow from the interpenetration of the beam of back scattered particles and the incoming background plasma in the shock precursor (as viewed from the shock frame). One should nevertheless mention the possibility of a Buneman instability, if the returning particles carry a net current, which turns out to grow faster than the previous two, see e.g. \cite{B09} and \cite{LP11a} for a discussion. However, the Buneman instability saturates through the heating of the background electrons, so that it presumably serves as an efficient source of preheating. In the present work, we are mostly interested in the properties of particle transport (and energization) in the microturbulence upstream of a relativistic shock front and we will focus our discussion on the respective roles of the filamentation and two stream modes. In the downstream, the microturbulence appears isotropic, mostly magnetic and static, see e.g. \cite{Cea08}. The physics of transport of suprathermal particles in such a microturbulence, possibly superimposed on a weak background magnetic field, has been discussed in a previous paper (\citealp{PL11}). Upstream of the shock, this microturbulence is strongly elongated in the direction of the shock normal and in the background plasma rest frame, it carries both electric and magnetic fields. That must affect the transport properties of suprathermal particles in a non-trivial way and likely contribute to the heating of background electrons. Furthermore, we demonstrate in the present work that the filamentation modes have a finite phase velocity in the background plasma rest frame, an issue which to our knowledge has not been addressed before in the present context. We find that this motion has important consequences regarding both the transport of suprathermal particles, in particular the acceleration timescale, and the preheating of the background electrons, which turns out to be fast and efficient. This paper is organized as follows. In Section~2, we discuss the motion of the frame in which the Weibel filaments are static, and we summarize previous findings on a similar issue for the OTSI mode. We investigate the influence of the motion of the electromagnetic modes on the reflection process at the shock front. In Section~3 we study the transport of suprathermal particles in both Weibel and OTSI turbulence, on the basis of numerical simulations of test particle propagation. We place emphasis on the issue of scattering in three dimensions. Section~4 discusses electron heating. We show that the relativistic oscillation of the incoming background electrons in the electric field of the microturbulence modes lead to efficient preheating on a short timescale. In Section~5 we apply our results to the concrete case of the external relativistic shock of a gamma-ray burst. We summarize our results in Section~6.
|
The development of a collisionless shock involves three essential interrelated ingredients: the generation of suprathermal particles, the generation of magnetic turbulence, the building up of a reflecting barrier for a part of the incoming particles. This paradigm applies successfully to non-relativistic as well as to relativistic weakly magnetized shock waves. Numerical and theoretical works have made significant progress in understanding the physics and in providing quantitative results that become useful for astrophysical investigations. This includes not only the spectrum index and cut off of the distribution of accelerated particles, but also the conversion factors into cosmic rays, magnetic turbulence and radiation. In this paper we have presented new theoretical investigations regarding the transport of suprathermal particles in the microturbulence upstream of the relativistic shock, and the preheating of the background electrons. We have placed emphasis on the fact that the microturbulent modes actually move relatively the background plasma, with a possibly large Lorentz factor depending on the background electron temperature. This motion of the microturbulence generates a motional electric field in the frame in which the filaments are static, which leads to fast heating of the background electrons through relativistic oscillations. Despite that the Weibel instability generates magnetic filaments -- in the background plasma frame -- whereas the oblique two stream instability generates almost electrostatic waves, they behave similarly in their proper frame, in which they are composed of an electrostatic field and a magnetostatic field of almost the same amplitude. This heating mechanism is particularly efficient: within a transverse coherence length of the perturbations, it heats the electrons to $\sim \xi_{\rm B} m_pc^2$, in which $\xi_{\rm B}$ should be understood as the local (position dependent) fraction of energy density stored in the electromagnetic component. Because the coherence length is much shorter than the size of the precursor, this brings forward the picture in which the electrons are instantaneously heated to the above temperature, so that their temperature rises gradually towards near equipartition as they approach the shock front, a picture which appears in satisfactory agreement with the results of \cite{SS09}, \cite{SS11a}. As we have discussed, one should expect $\xi_B\sim\xi_{\rm cr}$ at the shock front, from the condition that the Weibel turbulence has become sufficiently strong to reflect the incoming particles. The Weibel turbulence thus apparently draws the maximum amount from the suprathermal particle energy reservoir, in qualitative agreement with PIC simulations. Electron preheating modifies the generation of microturbulence: it saturates the oblique two stream instability and slows down the propagation of Weibel modes. So we envisage that the nose of the precursor contains fast propagating Weibel modes and then, closer to the shock front, relativistic thermal electrons that enlarge the characteristic scale. The oblique two stream remain however likely active in the cold phase at the tip of the shock precursor, like Buneman instabilities which also preheat the electrons. We have also discussed in some detail the properties of transport of the suprathermal particles in the microturbulence. The filamentary nature of the magnetic filaments strongly limits the scattering of these particles in the longitudinal direction. The acceleration process is accordingly slowed down by the time it takes for the particle to probe effectively the inhomogeneities in the longitudinal direction, as quantified here by the factor $\chi$. This strongly suggests that PIC simulations of the Fermi process in 2D probably involves mirror effects on the shock front rather than actual upstream/downstream scattering, especially at the ``low'' energies corresponding to the first Fermi cycles probed by these simulations. To probe the 3D scattering regime discussed here, one would need 3D PIC simulations with very long integration timescales, in order to accelerate particles to energies such that their Larmor radius in the turbulent field becomes larger than the coherence length. Shocks in AGN, blazar jets, or in the internal flow of GRBs are mildly relativistic and therefore not subject to the severe restriction imposed to the Fermi process by the mean field as it happens in the ultra-relativistic regime. Thus, as argued here and in, e.g. \cite{L9b}, \cite{PL11b}, those objects are better candidates as sources of ultra-high energy cosmic rays. In pulsar wind nebulae, reconnections likely contribute to injecting high energy particles in the shock and a suprathermal tail with a hard component may be generated (\citealp{L03,PL07,SS11b}). At the weakly magnetized external shock of a gamma-ray burst, Fermi acceleration should be operative and then lead to extended synchrotron spectrum up to GeV energies; although, if the shock propagates in a sufficiently magnetized circumburst environment, the Fermi process may be, in a first step, quenched by the mean field, which would lead to distinct signatures (\citealp{LP11b}).
| 12 | 6 |
1206.6634
|
1206
|
1206.1086_arXiv.txt
|
We have conducted a series of numerical experiments using spherically symmetric, general relativistic, neutrino radiation hydrodynamics with the code \aboltz\ to examine the effects of modern neutrino opacities on the development of supernova simulations. We test the effects of opacities by removing opacities or by undoing opacity improvements for individual opacities and groups of opacities. We find that improvements to electron capture (EC) on nuclei, namely EC on an ensemble of nuclei using modern nuclear structure models rather than the simpler independent-particle approximation (IPA) for EC on a mean nucleus, plays the most important role during core collapse of all tested neutrino opacities. Low-energy neutrinos emitted by modern nuclear EC preferentially escape during collapse without the energy downscattering on electrons required to enhance neutrino escape and deleptonization for the models with IPA nuclear EC. During shock breakout the primary influence on the emergent neutrinos arises from NIS on electrons. For the accretion phase, non-isoenergetic scattering on free nucleons and pair emission by $e^+e^-$ annihilation have the largest impact on the neutrino emission and shock evolution. Other opacities evaluated, including nucleon--nucleon bremsstrahlung and especially neutrino--positron scattering, have little measurable impact on neutrino emission or shock dynamics. Modern treatments of nuclear electron capture, $e^+e^-$-annihilation pair emission, and non-isoenergetic scattering on electrons and free nucleons are critical elements of core-collapse simulations of all dimensionality.
|
As the core of a massive star collapses, electron capture (EC) on protons (free or within nuclei) reduces the electron fraction, $Y_e$, and releases neutrinos that stream from the core. At densities near \den{6}{11}, the mean-free path for neutrinos of mean energy becomes comparable to the size of the core and the neutrinos become ``trapped.'' The trapping of neutrinos effectively halts the deleptonization (reduction of $Y_e$) of the core as the emission of neutrinos through EC is balanced by reabsorption of the neutrinos on neutrons (either free or within nuclei). Neutrino opacity regulates the deleptonization and sets the minimum core $Y_L$ ($Y_e$ plus the neutrino fraction, $Y_\nu$), which controls the size of the homologous inner core, $\Mshock \propto {Y_L}^2$ \citep{Yahi83}. When the density in the core exceeds nuclear density, the nuclear equation of state (EoS) stiffens, and a bounce shock forms at the sonic point that defines the edge of the homologous core. The expanding shock loses energy to neutrino emission and nuclear dissociation and stalls. The neutrino weak interactions (emission, absorption, and scattering) regulate energy loss by the prompt shock to neutrino radiation and thus affect the stalling of the shock. The revival of the stalled shock by neutrino heating is likewise regulated by the neutrino opacities. As for photons in stellar atmospheres, we can define ``neutrinospheres,'' where the neutrinos of each species and energy effectively decouple from the matter in the stellar core. The neutrinosphere radii, \Rnu{\nu}, are dependent on both flavor and energy with \Rnu{\nue} larger than \Rnu{\numt} because of the increased number of weak interaction channels for \nue\ (neutral and charged current). The neutrinosphere radii increase with increasing neutrino energy due to the larger opacities for higher energy neutrinos. The emission temperatures at the various neutrinospheres effectively set the flux of neutrinos in each energy--species group and therefore the spectrum of neutrinos available for absorption in the semi-transparent heating, or ``gain,'' region between the proto-neutron star and the shock. Non-isoenergetic scattering (NIS) changes the energy and direction of the neutrinos, each of which plays an important role in all phases of the supernova evolution. Scattering to a lower energy can change the neutrino's environment from opaque to semi-transparent and allow a neutrino that would otherwise be trapped to escape, both increasing the luminosity of neutrinos available for absorption in the gain region above the core and enhancing lepton escape from the core. The earliest models of neutrino heating in core-collapse supernovae by \citet{CoWh66} included only emission by electron capture and redeposited half of the energy lost to core neutrino emission in the layers above the proto-neutron star, driving a powerful explosion of the outer layers of the star. Subsequent spherically symmetric models included more detailed treatment of neutrino transport to revive the shock: gray diffusion \citep{Arne66}, two-fluid schemes \citep{HiNoWo84,CovaBa86}, multi-group flux-limited diffusion \citep{Brue75,Arne77,BoWi82,Brue85,MyBlHo87}, and Boltzmann transport \citep{MeBr93b,YaJaSu99}. \begin{deluxetable*}{cccc} \tabletypesize{\scriptsize} \tablecaption{Neutrino Opacity Summary Table\label{tab:opac}} \tablecolumns{4} \tablewidth{0pt} \tablehead{ \colhead{Interaction} & \colhead{Base} & \colhead{Alternate} & \colhead{Model} } \startdata $\nu e^- \leftrightarrow \nu' e^-$ & \citet{SchSh82} & None & \basenes \\ $\nu e^+ \leftrightarrow \nu' e^+$ & & & \basenps \\ $\nu n \leftrightarrow \nu' n$ & \citet{RePrLa98} & \citet{Brue85} & \basereds \\ $\nu p \leftrightarrow \nu' p$ && &\\ $e^- p \leftrightarrow \nu_e n $ &\citet{RePrLa98} & \citet{Brue85} & \baserea \\ $e^+ n \leftrightarrow \bar{\nu}_e p $ && & \\ $\nu A \leftrightarrow \nu A$ & \citet{Brue85} & \emph{No Change} & \nodata \\ $\nu \alpha \leftrightarrow \nu \alpha$ & \citet{Brue85} & \emph{No Change} & \nodata \\ $e^- (A,Z) \leftrightarrow \nu_e (A,Z-1) $ &\citet{LaMa00}, & \citet{Brue85}, & \ipa \\ &\citet{LaMaSa03} & \cite{Full82} & \\ $ e^+e^- \leftrightarrow \nu \bar{\nu} $ & \citet{SchSh82} &None & \basepair \\ $ NN \leftrightarrow NN\nu\bar{\nu}$& \citet{HaRa98} & None & \basebrem \enddata \end{deluxetable*} The neutrino opacities used evolved in complexity and completeness \citep{TuSch75,LaPe76,YuBu76,BlvR78} using the new weak interaction theory \citep{Glas61,Wein67,Sala68} concurrently with relevant experimental results including: the detection of neutral-current interactions in neutrino--nucleon scattering \citep{Haetal73} and the discovery of $\tau^-$ \citep{Perl75}, whose neutrino partner, \nutau, was widely assumed to exist, but was not detected until the turn-of-the-millenium \citep{DONUT01}. \citet{SchSh82} and \citet{Brue85} assembled comprehensive neutrino opacity sets that included energy coupling in the scattering (NIS) and were oriented toward numerical implementation. The \citet{Brue85} opacity set (``B85'' hereafter) has been widely adapted both in content and form and has widely served as the ``canonical'' opacity set. The B85 opacity set includes emission, absorption, and isoenergetic scattering (IS) on heavy nuclei, $\alpha$-particles, and free nucleons; NIS on electrons; and $\nu\bar{\nu}$-pair emission from $e^+e^-$ annihilation. (Though derived in \cite{Brue85}, NIS on positrons is often omitted from simulations using B85 opacities.) In the more than 25 years since the compilation of the B85 opacity set, the search for opacity improvements (driven in part, previously, by the possibility that spherically symmetric models might explode if sufficiently detailed) has continued. Some of the newer neutrino channels identified, developed for simulations, and widely adopted include: nucleon--nucleon bremsstrahlung \citep[][and a related inelastic $\nu$-nucleon scattering channel]{HaRa98}; more kinematically complete $\nu$-nucleon emission, absorption, and scattering opacities \citep{BuSa98,RePrLa98}; the pair--flavor conversion process \citep{BuJaKe03}; and tabulated EC rates using ensembles of nuclei with detailed level structures \citep{LaMaSa03,JuLaHi10}. Other refinements and corrections to opacities that have been added to many simulations include: weak magnetism for interactions with free nucleons \citep{Horo02}; ion-ion correlations between nuclei \citep{BoWi82,Horo97,ItAsTo04}; and changes from the effective mass of the nucleons in dense matter \citep[cf.,][]{RePrLa99}. For dense matter, from where nuclei become correlated through nuclear matter, the next frontier in the computation of $\nu$--nucleon/nucleus interactions is the development of EoS tables with consistent neutrino opacities for emission, absorption, scattering, and neutrino-pair processes \citep{RePrLa98,MaFiLo12,RoRe12}. Updated neutrino opacity sets have been assembled by several authors \citep{Burr01,BuRaJa06,BrDiMe06,LeMeMe12}. Prior studies in spherical symmetry have examined the impact of the addition, or modification, of a single opacity \citep{MeBr93c,BuJaKe03,MeLiHi03,HiMeMe03,MaJaBu05,LaMaMu08} and of multiple, simultaneous, opacity changes in spherical symmetry \citep{BuRaJa06,LeMeMe12} and in axisymmetry (2D) \citep{BuRaJa06,MuJaMa12}. This is the first study detailing the effects of each of the opacity changes made to create a modernized opacity set. In this paper, we start from the full set of opacities used in \citet{LeMeMe12} and test not only each component of the opacity change in that paper and each opacity upgrade relative to the B85 opacities, but also reexamine the omission of neutrino--electron scattering (NES) and all NIS opacities and omission of each pair-source opacity. In each of our simulations we retain at minimum the B85-formulation of scattering on nucleons and nuclei and emission and absorption on nucleons and nuclei to ensure that the total opacity is not radically changed. While the differences found among the tests of opacity removal are generally consistent with prior single-opacity studies, we find that opacity changes in the context of a detailed opacity set can have different impacts than changing the same opacity in a less complete opacity set. This contextual effect is most prominent for NES during collapse, where the previously identified role of NES in enhancing neutrino escape and core deleptonization during collapse by downscattering neutrinos to lower energies is muted by detailed EC on nuclei. We identify, within our modern opacity set, critical opacities needed for reliable computation of the shock dynamics and neutrino emission during the collapse, shock breakout, and accretion phases, as well as opacities of little impact on the simulation or the observational neutrino properties.
|
In this paper we have systematically examined the effects of each of the updated opacities in our modernized opacity set over the initial 150~ms post-bounce, spherically symmetric phase of core-collapse supernovae. To summarize our primary findings: (1) During collapse, electron capture on heavy nuclei dominates the emission of neutrinos and the deleptonization of the core. If modern EC rates are used with a detailed NSE composition, as in LMSH or \citet{JuLaHi10}, the direct emission of low-energy neutrinos obviates the need for NES to fill the low-energy portion of the neutrino spectrum. (2) Omitting NES results in an $\approx 15$\% increase in the breakout-burst \nue-luminosity. (3) Changes in shock formation due to deleptonization are the primary opacity-driven source of variation in early shock evolution. (4) During the accretion phase, nucleon NIS enhances the \nue\nuebar-luminosities, net heating, and drives the shock further out, enhancing the potential of shock revival by multidimensional effects. (5) Cooling by \numt\numtbar-pair emission from $e^+e^-$-annihilation removes energy from the system that could otherwise be used to revive the shock. (6) All of the NIS opacities (except scattering on positrons) and $e^+e^-$-annihilation affect the neutrino luminosities and/or \meanE{\nu}\ during accretion. (7) Positron scattering shows no impact on the outcome or observables during our simulations. We have identified non-linear behaviors in the interplay among opacities, which illustrate that the context provided by the included opacities is important in evaluating individual opacities. Some examples of neutrino opacity interplay include: \begin{itemize} \item Emission from nuclear EC and energy downscattering by NES compete to fill the lowest energy bins during collapse. The escape of low-energy \nue\ increases core deleptonization. The low-energy spectrum of neutrinos emitted by the LMSH EC table fills the low-energy phase space adequately without NES; thus, we do not see an impact on deleptonization when NES is omitted as we do in the case of models using the IPA EC, which does not fill this part of the spectrum directly. \item Thermalization of \numt\numtbar\ by individual NIS opacities is not simply additive. Removing either NES or nucleon NIS results in a modest increase in \meanE{\numt}, while removing both results in a much larger increase, as thermalization by scattering above the emission region is absent. \item Neutrino emission by pair sources also exhibits saturation effects. In models including $e^+e^-$ annihilation, bremsstrahlung has only a minor impact on the emitted neutrino properties, but when bremsstrahlung is the only pair source, its removal has a much larger impact. \end{itemize} We can identify from our tested set necessary neutrino--matter interactions required for modern supernova modeling in any dimension. \begin{itemize} \item Modern nuclear EC \citep[LMSH, ][ or equivalent]{JuLaHi10} should be considered an essential ingredient in any realistic supernova simulation as was previously noted by \citet{HiMeMe03}. Relying on the IPA EC artificially alters the electron capture, deleptonization, and the impact of other opacities. \item Nucleon NIS extends the shock radius via an increase in \nue\nuebar-luminosity. The related enhancements to capture on free nucleons, though relatively modest in effect, should be included for physical consistency of the nucleon opacities. \item NES significantly reduces \nue\ emission during breakout and contributes to thermalizing the \numt\numtbar\ spectra. \item \numt\numtbar-pair emission by $e^+e^-$-annihilation is an important source of cooling during the accretion phase, while bremsstrahlung plays only a small role \citep[as also seen in][]{ThBuPi03} unless $e^+e^-$-annihilation is omitted. Bremsstrahlung may become more important at later epochs as trapped \numt\numtbar\ diffuse out. \end{itemize} Omitting any of these opacities would alter the observable neutrino properties, and thus would introduce unnecessary systematic errors in the analysis of observed supernova neutrino signals. The modern opacities discussed in this paper are physically well-motivated improvements to the reference \citet{Brue85} opacity set. Including these improved opacities increases the physical fidelity of the neutrino--matter interactions in supernova simulations, while omitting them risks potential systematic errors in the dynamical and observational properties of simulated supernovae.
| 12 | 6 |
1206.1086
|
1206
|
1206.1938_arXiv.txt
|
Many population synthesis and stellar evolution studies have addressed the evolution of close binary systems in which the primary is a compact remnant and the secondary is filling its Roche lobe, thus triggering mass transfer. Although tidal locking is expected in such systems, most studies have neglected the rotationally-induced mixing that may occur. Here we study the possible effects of mixing in the mass-losing stars for a range in secondary star masses and metallicities. We find that tidal locking can induce rotational mixing prior to contact and thus affect the evolution of the secondary star if the effects of the Spruit-Tayler dynamo are included both for angular momentum and chemical transport. Once contact is made, the effect of mass transfer tends to be more rapid than the evolutionary time scale, so the effects of mixing are no longer directly important, but the mass transfer strips matter to inner layers that may have been affected by the mixing. These effects are enhanced for secondaries of 1-1.2~$M_{\odot}$ and for lower metallicities. We discuss the possible implications for the paucity of carbon in the secondaries of the cataclysmic variable SS Cyg and the black hole candidate XTE~J1118+480 and for the progenitor evolution of Type Ia supernovae. We also address the issue of the origin of blue straggler stars in globular and open clusters. We find that for models that include rotation consistent with that observed for some blue straggler stars, evolution is chemically homogeneous. This leads to tracks in the HR diagram that are brighter and bluer than the non-rotating main-sequence turn-off point. Rotational mixing could thus be one of the factors that contribute to the formation of blue stragglers.
|
Cataclysmic variables (CVs) have been recognized as binary systems with white dwarf primaries and studied for decades (Warner 2003). A closely related field, the study of high and low-mass X-ray binaries (HMXBs and LMXBs respectively) containing neutron stars and black holes in close binary systems is somewhat younger, but also mature (Tanaka \& Lewin 1995). The general scenario invoked for the low-mass systems includes evolution through a common envelope phase then subsequent shrinking of the orbit through magnetic braking or emission of gravitational radiation. When the orbit period becomes short enough, hours to days, even unevolved main sequence companions can fill their Roche lobes and transfer mass to the compact primaries. This scenario has been studied quantitatively with stellar evolution and population synthesis codes. The close binary orbits imply that tidal forces should lock the secondary stars into rotational synchronism with the orbital period and the implied rotation can be quite rapid. This synchronization mechanism is efficient for secondaries with convective envelopes. This rapid rotation may, in turn, induce rotational mixing. Rotational mixing in this context has recently been studied by De Mink et al. (2009) and Brott et al. (2011a) in high-mass systems, but most studies of compact binaries with low-mass secondaries have neglected this effect (e.g. Willems \& Kolb 2004; Han \& Podsiadlowski 2004; Belczynski et al. 2008; Lipunov et al. 2009). Ergma \& Antipova (1999) invoke ``deep mixing" to account for the apparent hydrogen-deficiency of SAX~J1808.4-3658, but give no physical model. They note that MXB~1916-05 ($P_{orb}$ = 50 min) and MX~1820-30 ($P_{orb}$ = 11.4 min) seem to require a Roche-lobe filling helium-rich secondary in order to explain its short orbital period (Paczynski \& Sienkewicz, 1981). Carbon deficiency may be another symptom of rotationally-induced mixing. Examples of carbon deficient secondaries include the black hole candidate XTE~J1118+480, which shows a distinct paucity of carbon since there is no C~IV emission detected (Haswell et al. 2002; Gelino et al. 2006) and the black hole X-ray binary A0620-00 in which the C~IV doublet is found to be anomalously weak compared to the other lines, consistent with the low carbon abundance deduced from NIR spectra of the secondary star in the system (Froning et al. 2007, 2011). Low-mass carbon deficient secondaries have also been detected in many CV systems. Harrison et al. (2004) concluded that the K dwarf secondary in the CV SS Cyg was deficient in carbon. Bitner, Robinson \& Behr (2007) provided estimates for the masses of the secondary star and the white dwarf (WD) in SS Cygni ($M_{WD} =$~0.81~$M_{\odot}$, $M_{s} =$~0.55~$M_{\odot}$) and presented a discussion on the unusual evolutionary characteristics of the secondary and Sion et al. (2010) presented an extended analysis of its carbon poor UV spectrum. Similar behavior has been observed for the CV AE Aqr (Jameson, King \& Sherrington 1980; Eracleous et al. 1994). Harisson, Osborne \& Howell (2005) presented more cases of CVs with weak CO absorption lines in their spectra, implying low C abundance, and suggested that material that has been processed through the CNO cycle is finding its way into the photospheres of secondary stars. More systems with close to zero C~IV emission were discussed in G{\"a}nsicke et al. (2003). In a potentially related context, Ibano et al. (2012) discuss the carbon deficiency in the mass-accreting primaries of Algol systems and attribute it to a carbon deficiency due to CNO burning on the lower-mass, mass-losing secondary. They do not suggest any specific mechanism for the carbon deficiency of the secondary. Extensive discussions of the reasons for carbon depletion in the secondaries of CVs are presented in Harrison, Osborne, \& Howell (2005) and Schenker et al. (2002). As argued in those works, it is possible to greatly deplete carbon by processing it in the massive stars before Roche lobe contact and then stripping off just enough of the outer layers during thermal timescale mass transfer (TTMT) to reveal layers depleted in carbon. The depletion is estimated to be up to a factor of 100 in these models. This may actually happen in some CVs like AE~Aqr since there are other reasons for suspecting the secondary in that system is evolved. Nonetheless, there are two problems invoking the mass-stripping mechanism as the only cause of carbon depletion in some CVs. First, it could be that a high fraction of CVs show the carbon anomaly. If so, current population synthesis models cannot account for such a high fraction of higher-mass progenitors (Harrison, Osborne \& Howell 2005). Second, the Schenker et al. (2002) mechanism requires fine tuning. The initial stellar masses, orbital periods, and evolutionary stages need to be exactly right at first Roche lobe contact to obtain results that agree with observations. These issues motivated us to explore the possibility that carbon is depleted by rotationally-induced mixing that processes surface material through the core, where it is subjected to partial CN burning. Rotational mixing allows the secondaries to start with lower mass and does not seem to require fine tuning. Sufficient mixing can lead to quasi-homogeneous evolution and perhaps to low-mass helium star secondary stars. This possibility is of general interest, but may be especially interesting in the context of the progenitors of Type Ia supernovae. Rotationally induced mixing may also be relevant in cases of single stars such as the ``blue straggler" stars (BSSs) in open and globular clusters. Many BSSs are observed to rotate rapidly and to have depleted C/O abundances. Some BSSs may be slow rotators, but as we describe in \S3.3, some are observed to be rapid rotators. That seems sufficient to mention the possibility of rotationally-induced mixing without knowing the origin of the rotation, nor specifically invoking binary tidal locking as the origin of the rotation. We thus also explore the possibility of rotationally-induced mixing in BSSs. As remarked above, rotationally-induced mixing in tidally-locked massive stars has been investigated in some contexts (de Mink et al. 2009; Brott et al. 2011a). Rotationally-induced mixing in massive stars has been investigated in general (Maeder 1987; Maeder \& Meynet 2011; Eskstrom et al. 2008, 2011; Brott et al. 2011b; Yoon, Dierks \& Langer 2012), in the context of the progenitors of gamma-ray bursts (Heger, Woosley \& Spruit 2005; Yoon \& Langer 2005), and in the context of very massive stars susceptible to the electron/positron pair instability by Chatzopoulos \& Wheeler (2012) and by Yoon, Dierks \& Langer (2012). Because massive stars tend to be more radiation pressure dominated, they are closer to neutral dynamical stability, and hence, all else being equal, easier to mix. Very low mass stars are thought to be fully convective, and hence to mix spontaneously, but are also so long lived that they do not evolve in the brief history of the Universe. The case that interests us here are stars of modest mass, of order the solar mass. These stars have outer convective, mixing, envelopes, but inner radiative cores that may resist rotationally-induced mixing. The issue requires quantitative investigation and that is the subject of this paper. In \S2 we describe the stellar evolution models. We present our results in \S3 and discuss the implications and conclusions in \S4. An appendix presents a calibration of rotating, magnetic MESA models with work in the literature.
|
\label{disc} G{\"a}nsicke et al.(2003) presented a variety of CVs with very large N$_{V}/$C$_{IV}$ flux ratios in far ultraviolet (FUV) spectra. In the same study it is estimated that 10-15\% of close CVs that have gone through a phase of TTMT show this kind of surface abundance anomalies. Similar cases of large N$_{V}/$C$_{IV}$ flux ratios have been observed in some black hole binary systems like XTE~J1118+480 (Haswell et al. 2002; Gelino et al. 2006). Most low-mass close binaries are also synchronized and their secondaries are rapidly rotating and therefore evolve quasi-homogeneously due to rotationally-induced mixing. Motivated by these observations, we ran a grid of evolutionary models of low mass secondaries for different degrees of metallicity and rotational velocity in order to study the effects of rotationally-induced mixing in these systems. Vigorous rotationally-induced mixing led to a more chemically homogeneous evolution than in non-rotating standard evolution and enabled CNO processing of material in a larger portion of the stellar interior. As a consequence, the hydrogen and carbon surface abundances are reduced and the helium and nitrogen abundances enhanced. This effect is found to be stronger for intermediate mass (1-1.2~$M_{\odot}$), increased rotation, and decreased metallicity for the secondary star. The magnitude of this effect is also bigger for longer time-scales after tidal locking and before encountering RLOF mass loss. Once RLOF mass loss starts, the surface abundances do not change significantly and by the time RLOF ends the secondary may be left with low enough mass that the core temperature is not high enough to burn the material that is mixed inwards, therefore preventing further homogenization and significant surface abundance changes. Since carbon depletion is more pronounced for higher masses, it is possible that the secondaries of carbon depleted systems were once more massive, even up to 1.2-1.5~$M_{\odot}$, and then lost a significant amount of mass. This can be achieved via a phase of unstable thermal time-scale mass transfer (TTMST; Schenker et al. 2002; Podsiadlowski, Han \& Rappaport 2003; G{\"a}nsicke et al. 2003). In this case, systems with secondaries with mass up to 2~$M_{\odot}$ may subsequently evolve into CVs with low mass secondaries and slow transfer rates. If the secondary were a fast rotator, the mass transferred will have a high ratio of $X_{N,s}/X_{C,s}$, in agreement with what is spectroscopically observed. Therefore we conclude that rotationally-induced mixing could be one way to explain the carbon-depletion features of some of the systems discussed above. Altering the abundance of the material accreted onto the white dwarf may affect the subsequent evolution of the white dwarf. Systems containing a white dwarf and a low mass helium-rich companion are observed (Maxted et al. 2000; Mereghetti et al. 2011). Helium overabundance is spectroscopically observed in some recurrent novae, U Sco (Williams et al. 1981; Hanes 1985; Starrfield et al. 1988) and V394 (Sekiguchi et al. 1989) and some classical novae, Nova LMC 1990 no. 2 (Sekiguchi et al. 1990; Shore et al. 1991) and V445 Puppis (Nova Puppis 2000; Ashok \& Banerjee 2003; Kato \& Hachisu 2003; Kato et al. 2008; Woudt et al. 2009; Goranski et al. 2010). In most considerations in the literature, the helium-rich secondaries are the cores of stars stripped of their red-giant envelopes by mass transfer (Iben \& Tutukov 1994; Yoon \& Langer (2003); Solheim \& Yungelson 2005; Ruiter et al. 2009, 2011; Wang et al. 2009a,b; Wang \& Han 2009; Meng \& Yang 2010). Here, we suggest that helium-rich secondaries can arise through rotationally-induced mixing of main sequence stars. Some of our models exhibit enhanced $X_{He,s}/X_{H,s}$ therefore providing accreting material of a different mixture than has been extensively modeled to date (solar H/He or pure He). As discussed in \S 2 and in Appendix A, we find interesting levels of rotationally-induced mixing only if we include the effects of the Spruit-Tayler dynamo on the transport of both angular momentum and chemical abundances. We suspect that rotation, especially differential rotation, will induce magnetic effects and that the omission of magnetic effects is inappropriate. Whether the Spruit-Tayler mechanism as employed in shellular models is the ``correct" or only magnetic effect is not so clear. Inclusion of the Spruit-Tayler mechanism in rotating stellar evolution calculations is ``state-of-the-art," and we include it in order to capture some magnetic effects and to compare to other work in the literature that makes comparable assumptions (Appendix A). We emphasize that the inclusion of chemical mixing due to magnetic fields as parametrized by Spruit (2002) is observationally motivated in the present work since it is necessary in order to explain the observed surface abundance changes in some low-mass secondary stars, members of close binaries that are rapid rotators, in the context of stellar evolution with the inclusion of the effects of rotation. The inclusion of magneto-rotational effects in stellar evolution is a topic that surely warrants more attention (Brown et al. 2011). The inclusion of the effects of rotation in the evolution of some low mass secondaries may thus have implications for the progenitors of Type Ia SNe. Accretion of hydrogen onto a white dwarf will tend to generate double shell sources that are susceptible to thermonuclear instabilities, including nova explosions. Even with high accretion rates that allow steady hydrogen shell burning, the subsequent helium shell burning is often found to be unstable (Iben \& Tutukov 1989; Cassisi et al. 1998; Kato \& Hachisu 1999) making it very difficult to construct satisfactory models that grow the white dwarf to near the Chandrasekhar mass, carbon ignition and thermonuclear explosion. At low accretion rates, the helium shell source in accreting white dwarf models may be thermally unstable even for non-degenerate cases (Cassisi et al. 1998; Langer et al. 2002). Accretion from a hydrogen-poor secondary may modify some of these constraints (Webbink et al. 1987; Truran et al. 1988; Livio \& Truran 1992). A higher helium abundance will tend to lead to more stable shell burning. This might alter the conditions of shell burning and hence the constraints necessary for sucessful Type Ia explosions. Based on our models, the $X_{He,s}/X_{H,s}$ ratio would increase during the accretion process since deeper regions of the rotationally mixed stars become accessible. Further exploration of this issue requires thermonuclear hydrodynamic simulations. We note that although our rotating models linger longer on the main sequence, the luminosity does increase monotonically. Models that are more helium enriched will thus also tend to be somewhat brighter than ZAMS models of the same mass. All of our models with noticeable helium enrichment are brighter than the upper limit set on a particular SN Ia progenitor system by Schaefer \& Pagnotta (2012). Helium detonations on white dwarfs have also been proposed to be related to the progenitors of the predicted class of subluminous .Ia SNe (Shen et al. 2010). Events such as SN~2002bj (Poznanski et al. 2010) and SN~2010X (Kasliwal et al. 2010) show strong He lines in their spectra, but no sign of H. A potential channel to .Ia progenitors could be one of a close synchronized binary system with a rapidly rotating secondary star that undergoes chemically homogeneous evolution leading to surface He enrichment. Once RLOF mass loss sets in, this He rich material from the secondary will accrete on the WD and, provided that the accretion rate is appropriate for stable shell burning, it may set the initial conditions appropriate for a .Ia progenitor. Rotationally-induced mixing seems to play a role in the evolution of solar mass rotating single stars as well. As an example we examined the case of BSSs found in many galactic clusters. We found that the inclusion of the effects of rotation in the evolution of solar-type stars might lead some of those with equatorial rotational velocity greater than 10~km~s$^{-1}$ to evolve past the MS turn-off point in the HR diagram. In general, rotation seems to be relevant even in the case of post-MS, yellow supergiant stars (YSGs). Neugent et al. (2012) show that models with rotation agree better with the observed properties of YSGs in the LMC than do models with no rotation. These results illustrate the importance of rotationally-induced mixing leading to chemically quasi-homogeneous evolution of low mass secondaries in binary systems that are synchronized. Rotationally-induced mixing may be fundamental in understanding observational features of some CVs, black hole binaries or Type Ia SNe and to even some single solar-type stars. This possibility deserves further consideration and modeling. We thank the MESA team for making this valuable tool readily available and especially thank Bill Paxton for his ready advice and council in running the code. EC would like to thank JJ Hermes for useful discussions. This research is supported in part by NSF AST-1109801.
| 12 | 6 |
1206.1938
|
1206
|
1206.1109_arXiv.txt
|
We present the first numerical approximation of the scalar Schwarzschild Green function in the time domain, which reveals several universal features of wave propagation in black hole spacetimes. We demonstrate the trapping of energy near the photon sphere and confirm its exponential decay. The trapped wavefront passes through caustics resulting in echoes that propagate to infinity. The arrival times and the decay rate of these \emph{caustic echoes} are consistent with propagation along null geodesics and the large $\ell$ limit of quasinormal modes. We show that the fourfold singularity structure of the retarded Green function is due to the well-known action of a Hilbert transform on the trapped wavefront at caustics. A twofold cycle is obtained for degenerate source-observer configurations along the caustic line, where the energy amplification increases with an inverse power of the scale of the source. Finally, we discuss the tail piece of the solution due to propagation within the light cone, up to and including null infinity, and argue that, even with ideal instruments, only a finite number of echoes can be observed. Putting these pieces together, we provide a heuristic expression that approximates the Green function with a few free parameters. Accurate calculations and approximations of the Green function are the most general way of solving for wave propagation in curved spacetimes and should be useful in a variety of studies such as the computation of the self-force on a particle.
|
A general technique to study the full response of a black hole to generic perturbations is to explore the Green function. While the Green function (aptly called the propagator) is simple in flat spacetime, it has a rich structure in curved spacetimes. Recently, Ori discovered that the Green function in Schwarzschild spacetime displays a fourfold periodic structure \cite{Ori}. This fourfold structure can be understood in terms of trapped null geodesics, similar to the classical interpretation of quasinormal mode ringing as energy leakage from the photon sphere \cite{AmesThorne:1968, Goebel:1972}. At each half revolution along the trapped orbit, the trapped wavefront passes a caustic undergoing a transformation with a fourfold cycle. Ori investigated this cycle using a quasinormal mode expansion method. He also performed an acoustic experiment providing evidence for the structure of trapped signals through caustics. The fourfold cycle has been formally analyzed in General Relativity for the first time by Casals, Dolan, Ottewill, and Wardell in \cite{Casals:2009xa,Casals:2010zc} in the example of Nariai spacetimes. Recently, Casals and Nolan developed a Kirchhoff's integral representation of the Green function on Pleba\'nski--Hacyan spacetimes, confirming the appearance of the fourfold singularity structure in these black-hole models \cite{Casals:2012px}. Going beyond toy models, Dolan and Ottewill discussed the Green function in Schwarzschild spacetime using large $\ell$ quasinormal mode sums \cite{Dolan:2011fh} based on their expansion method \cite{Dolan:2009nk}. The essential singularity structure of the retarded Green function in arbitrary spacetimes has been discussed by Harte and Drivas \cite{Harte:2012uw}. They approximate the region of any spacetime near a null geodesic by a pp-wave spacetime in the Penrose limit. Their analysis implies, in particular, that the fourfold structure should be valid also in Kerr spacetimes. Motivated by these theoretical studies and by Ori's acoustic experiment, we perform a numerical experiment and analyze in detail the response of a black hole to compactly supported scalar perturbations. We describe the problem and our numerical setup in Sec.~\ref{sec:setup}. The main part of this paper (Sec.~\ref{sec:results}) contains our results organized by scales, from the geometrical optics limit (short wavelength) to the curvature scale (long wavelength). After a qualitative description of the evolution of compactly supported wave packets in Sec.~\ref{sec:overview}, we discuss the propagation of the signal along null geodesics and the subsequent caustic echoes as measured by an observer at infinity (Sec.~\ref{sec:echoes}). Wave propagation through caustics and the fourfold structure of the Green function is studied in Sec.~\ref{sec:hilbert}. We show that the fourfold structure is due to the action of a Hilbert transform at each passage through a caustic. In Sec.~\ref{sec:twofold} we present a twofold cycle for degenerate source-observer configurations and find an inverse power relation between energy magnification at caustics and the source scale. We argue that the trapping of energy near the black hole is the universal cyclic feature manifested in the Green function, not the number of the cycle (e.g., four or two). In Sec.~\ref{sec:tail} we analyze the tail of the signal due to scattering off the background curvature, which dominates at late times implying that only a finite number of echoes can be observed even with ideal instruments. Putting these pieces together in Sec.~\ref{sec:full}, we provide a heuristic expression for the Green function with a few free parameters. We present our findings, discuss the limitations of our method, and pose problems for future research in Sec.~\ref{sec:conclusions}. The Appendixes complement the main text. The topics include hyperboloidal compactification for numerical simulations (Appendix \ref{app:layer}), the Schwarzschild Green function in the geometrical optics limit (Appendix \ref{app:optics}), and the Hilbert transform at caustics (Appendix \ref{app:hilbert}).
|
\label{sec:conclusions} We numerically solved the scalar wave equation on a Schwarzschild background \eqref{eq:sc} with a narrow Gaussian source \eqref{eq:source} thus yielding an approximation to the Schwarzschild Green function \eqref{eq:green}. For the numerical computations we used the Spectral Einstein Code {\texttt SpEC} \cite{SpECWebsite}. The main result of our study is the numerical approximation of the full retarded Schwarzschild Green function in the time domain. This computation allowed us to demonstrate a cyclic singularity structure due to the trapping of energy near the photon sphere. The numerical evolution, visualized in Figs.~\ref{fig:3D_1}-\ref{fig:3D_4} and in \cite{video}, proceeds as follows. The narrow Gaussian source triggers a high-frequency wavefront that propagates along null geodesics in accordance with geometrical optics. Part of the energy of the initial wavefront gets trapped at the black hole horizon and leaks out to infinity decaying exponentially in time. At each half revolution around the photon sphere the trapped wavefront forms a caustic resulting in echoes that propagate out to infinity. The wavefront undergoes a Hilbert transform at the caustics causing a $- \pi/2$ phase shift in its profile, which results in a fourfold cycle of caustic echoes seen by generic observers. This cycle is known as the fourfold singularity structure of the retarded Green function \cite{Ori, Casals:2009xa,Casals:2010zc, Dolan:2011fh,Casals:2012px,Harte:2012uw}. The fourfold structure is a recent discovery in the context of curved spacetimes but, in hindsight, it is a simple consequence of well-known facts. The $\pi/2$ phase shift of wavefronts at caustics has already been discovered in the late 19th century and is widely known as the Gouy phase shift in optics \cite{Gouy, Hartmann:2009}. Combined with the notion of trapping (e.g., due to the presence of a photon sphere), this knowledge immediately implies a fourfold cycle in a spherically symmetric, asymptotically flat spacetime \footnote{Trapping may also occur globally in cosmological spacetimes (e.g., the Einstein static universe), which may result in a different phase shift and therefore a different $n$-fold structure.}. The viewpoint of a phase shift of the Green function at caustics seems more fundamental than the fourfold structure. For example, a phase shift may be observed in regions of moderate curvature due to gravitational lensing where no trapping occurs, whereas trapping is required for the observation of $n$-fold cycles. In addition, a nongeneric set of observers, those on the caustic line, see a twofold cycle. Hence, the number of echoes in a cycle is observer-dependent. With the full numerical approximation to the Green function at hand, we also obtained an interesting result regarding gravitational lensing. If backscatter off background curvature is included, only a finite number of images are visible, even with ideal instruments, for any source of finite wavelength because caustic echoes decay exponentially in amplitude while backscatter (typically neglected in lensing studies) decays only polynomially. Further results can be summarized as follows. The arrival and decay of successive caustic echoes are consistent with the orbital period and Lyapunov exponent of null geodesics trapped at the photon sphere. The arrival times of successive half-period echoes depend on the source-observer configuration, with degeneracy resulting in a twofold cycle when the source and the observer are aligned with the black hole. This is the caustic line along which the amplified signal propagates. The energy magnification at the caustic follows an inverse power law with the scale of the wavefront in accordance with predictions going beyond the geometrical optics limit \cite{KayKeller}. The backscatter follows well-known polynomial decay rates at null infinity and at finite distances, which limits the number of echoes measurable by observers. We formulated an analytic approximation to the Schwarzschild Green function in the geometrical optics limit including wavefront propagation through caustics. Combined with our quantitative understanding of the dynamics, this formula allowed us to capture the essential features of the observed signal in a heuristic expression. Given the simplicity of our approximations, it is remarkable that the expression agrees so well with the numerical calculation. The only sources of error in the numerical computation of the Schwarzschild Green function are the finite width of the Gaussian source \eqref{eq:source} and the truncation error due to discretization of the scalar wave equation. The boundary error typically present in such simulations is eliminated by hyperboloidal scri-fixing in a layer \cite{Zenginoglu:2007jw,Zenginoglu:2010cq}. We emphasize that hyperboloidal compactification is not necessary for the numerical study of the Green function near the black hole. Many of our results are reproducible using standard foliations. However, hyperboloidal compactification helps focusing the resolution to the strong field domain without contamination from artificial boundaries and without wasting computational resources on the asymptotic domain. It allows us to compute the long-time evolution accurately at low cost, and provides us direct numerical access to measurements of an idealized observer at future null infinity. The error scales in our computation are related. To evolve a narrow Gaussian source, we need a large number of collocation points for the spectral expansion of the variables. Failure to do so results in Gibbs phenomena and contaminates the evolution. (Some high frequency noise in the late-time evolution can be seen in the lower curve of Fig.~\ref{fig:tail}). Numerical convergence tests and the agreement between theory and experiment indicate that our errors are small but we did not present a detailed error analysis in this paper. Such an analysis will be required when comparing the numerical simulations to accurate approximations of the Green function or when computing the self-force acting on a particle using the numerically computed Green function. For these calculations, horizon-source ratios larger than 10:1 might be necessary. The numerical method must be further improved for very high ratios, possibly using a second order in space formulation \cite{Taylor:2010ki}, implicit-explicit time stepping \cite{Lau:2008fb}, and adaptive mesh refinement. There are also adapted methods to solve for high-frequency wave propagation, such as the frozen Gaussian beam method \cite{LuYang} or the butterfly algorithm \cite{Butterfly}, that may improve the efficiency of the numerical simulation considerably. An immediate extension of our study would be the numerical computation of retarded Green functions in Kerr spacetime. In rotating black hole spacetimes, frame dragging plays a role in the wavefront propagation. There is no photon sphere in Kerr spacetime; instead, there are spherical photon orbits bounded by the location of pro- and retrograde circular photon orbits \cite{Teo:2003} which may participate in the Cauchy evolution in a similar way as does the photon sphere in Schwarzschild spacetime. The large $\ell$ limit of the quasinormal mode spectrum and its relation to spherical photon orbits in Kerr spacetime have recently been analyzed in \cite{Yang:2012}. Such analytic knowledge can be combined with numerical experiments to reveal the structure of the Green function in Kerr spacetimes and to provide good approximations to it. The visualization of a numerical Kerr Green function simulation using {\tt SpEC} can be found in \cite{videoKerr}. An interesting application of numerical approximations of Green functions would be the computation of the self-force on a small compact object moving in a supermassive black hole spacetime. Note that the Green function provides a very general way of solving for wave propagation in a background spacetime. If good approximations to it can be found, possibly augmented by data from numerical computations, the method can be applied to essentially any problem on the given background via suitable convolutions. To this end, it may be useful to have sparse representations of the numerical Green function. The improvement of Green function approximations may benefit from developments in various fields. Formation of caustics in black hole spacetimes is an example of the emergence of discrete structures from continuous ones, a hallmark of catastrophe theory \cite{Arnold}. A development of geometric diffraction theory and wave optics for black holes may allow us to compute the Green function through caustics without matching arguments while also providing more accurate analytical approximations. Exciting developments in these directions can be expected in the near future.
| 12 | 6 |
1206.1109
|
1206
|
1206.5799_arXiv.txt
|
We provide new, high-resolution $A(K_s)$ extinction maps of the heavily reddened Galactic midplane based on the Rayleigh-Jeans Color Excess (``RJCE'') method. RJCE determines star-by-star reddening based on a combination of near- and mid-infrared photometry. The new RJCE-generated maps have $2^\prime \times 2^\prime$ pixels and span some of the most severely extinguished regions of the Galaxy --- those covered with {\it Spitzer}+IRAC imaging by the GLIMPSE-I, -II, -3D, and Vela-Carina surveys, from $256^{\circ}<l<65^{\circ}$ and, in general, for $|b| \le 1^{\circ}$--$1.5^{\circ}$ (extending up to $|b|\leq4^{\circ}$ in the bulge). Using RJCE extinction measurements, we generate dereddened color-magnitude diagrams and, in turn, create maps based on main sequence, red clump, and red giant star tracers, each probing different distances and thereby providing coarse three-dimensional information on the relative placement of dust cloud structures. The maps generated from red giant stars, which reach to $\sim$18--20 kpc, probe beyond most of the Milky Way extinction in most directions and provide close to a ``total Galactic extinction'' map --- at minimum they provide high angular resolution maps of lower limits on $A(K_s)$. Because these maps are generated directly from measurements of reddening by the very dust being mapped, rather than inferred on the basis of some less direct means, they are likely the most accurate to date for charting in detail the highly patchy differential extinction in the Galactic midplane. We provide downloadable FITS files and an IDL tool for retrieving extinction values for any line of sight within our mapped regions.
|
\label{sec:intro} The existence of interstellar dust and its light-obscuring effects, though postulated more than a century and a half ago by Struve (1847) as one (incorrect) solution to Olber's Paradox, was not definitively proven until Trumpler's (1930) insightful experiment to compare distances of open clusters derived in separate extinction-dependent and extinction-independent methods. Though the amount of extinction resulting from this dust was historically often approximated with a standard accumulation by distance under an assumed plane-parallel distribution (i.e., the cosecant law; e.g., Shane \& Wirtanen 1967, Peterson 1970, Noonan 1971, Sandage 1973, de Vaucouleurs, de Vaucouleurs \& Corwin 1976, de Vaucouleurs \& Buta 1983, Fabbri et al. 1986; but see Kron \& Guetter 1973, Holmberg 1974, Knude 1996 for examples of discussions of simple variations about the basic cosecant law), it was always well-understood that the distribution of Galactic dust is in fact quite irregular.\footnote{Even relatively recently, Knude (1996) went through great pains to determine whether the cosecant law can at least provide a reasonable approximation in the North Galactic polar cap and concluded that only a piecewise application of the cosecant law with varying coefficients can work, and only in certain ranges of Galactic latitude and longitude.} Once it is appreciated that an irregular selective obscuration of a more regular distribution of stars, and not an irregular distribution of the stars themselves, is shaping the net configuration of observed starlight, then any observation of the density of --- or light from --- stars in the Galactic plane of the Milky Way clearly illustrates this patchiness (e.g., Herschel's [1785] drawings of the distribution of stars in the Milky Way, or the early photographs of the Galactic plane by Barnard et al.\ 1927). For extragalactic studies, a long-standing default strategy has been simply to steer clear of the ``Zone of Avoidance" at low Galactic latitudes altogether, rather than contend with assessing the amount of foreground extinction. Unfortunately, Nature is not always so accommodating with the placement of important and interesting sources, and corrections for foreground dust --- generally attributable to dust in our own Milky Way --- are almost always needed; even at the highest Galactic latitudes, one can encounter appreciable amounts of dust (e.g., the North Galactic Pole has $A(B)$ as high as $0.05$ to $0.1$ mags, depending on the reddening calibration and extinction law used; e.g., Hilditch et al.\ 1983, Knude 1996, Peek \& Graves 2010). Early attempts to map the variation of total line-of-sight Galactic extinction explored a number of techniques. For example, under an assumed constancy of dust-to-gas ratio, the net column density of HI, easily measured via 21-cm observations, could be converted into a dust column density (e.g., Lilley 1955, Sturch 1969, Savage \& Jenkins 1972, Knapp \& Kerr 1974, Burstein \& Heiles 1982). Under the assumption of a homogeneous spatial distribution of galaxies, the counts of galaxies to a given magnitude limit were also used to infer the degree of extinction along a line of sight (Burstein \& Heiles 1978, 1982). Similarly, the assumption of spatial constancy of the {\it stellar} distribution (at least on relatively small angular scales) has been employed to derive extinction using star counts --- comparing stellar densities across a clearly extinguished region (often on the edges of a dark cloud) to those in nearby ``control'' regions (e.g., Wolf 1923, Bok 1956, Froebrich et al.\ 2005). Directly {\em measuring} the effects of dust via such affected tracers is the most reliable method to map the Galactic extinction. Extracting the reddening and extinction effects of foreground dust from the intrinsic spectral energy distributions (SEDs) of observed sources has traditionally required direct, detailed spectroscopic information of each source to classify it explicitly and thereby infer its intrinsic properties independent of observed colors --- quite a demanding prospect in most situations. In recent decades, a large body of work has amassed that attempts to determine the total amount of extinction foreground to heavily-reddened sources by {\it photometric} means; under the assumption of a homogeneous color distribution of either stars or galaxies (or particular classes of either), deviations from the mean observed colors are attributed to interstellar reddening. The decreased temperature dependencies of infrared (IR) colors, combined with the decreased extinction effects at IR wavelengths, has led to the wide adoption of IR and optical-IR color excesses as high-quality gauges of interstellar reddening, especially in highly extinguished regions (since e.g., Jones et al. 1980, 1984, Smith 1987). Lada et al.\ (1994) introduced a powerful and efficient method of extinction mapping with the NICE (Near Infrared Color Excess) technique, which applies elements of both IR excess measurements and star-counting techniques to large sets of IR photometry; this method has undergone significant evolution (NICER, Lombardi \& Alves 2001; V-NICE, Gosling et al.\ 2009; NICEST, Lombardi 2009) and has been applied to a series of dense clouds and dark nebulae (e.g., Alves et al.\ 1998, Lada et al.\ 2009, Lombardi et al.\ 2010). The color excess method has also been applied to galaxy colors (e.g., Peek \& Graves 2010), though galaxy ensembles are obviously best-suited to gauging {\it total} line-of-sight Galactic reddening. Greater accuracy may be attained through use of objects with well-defined (and limited ranges of) colors like RR Lyrae stars, globular clusters, or red clump stars. Another method advocated by Burstein and collaborators (Burstein et al.\ 1988, Faber et al.\ 1989) is based on the observation that the integrated spectra of the stellar populations of giant elliptical galaxies are strikingly uniform, so that the intrinsic $(B-V)_0$ colors of these systems can be inferred on the basis of the spectroscopic measurement of their Mg$_2$ line index. Early investigations into the consistency of extinction derived with these various methods generally led to disappointing results, with no simple relationships found amongst the different dust proxies (Heiles 1976). Partly this is because of the failure of the very assumptions on which each method is based --- e.g., the high ``noise" in galaxy counts due to large scale structure, or variations in the dust-to-gas ratio (Seki 1973, Jenkins \& Savage 1974, Bohlin 1975, Savage et al. 1977, Burstein \& Heiles 1978, Fong et al. 1987, Burstein 2003). Currently the most commonly used large-scale reddening maps are those by Schlegel, Finkbeiner \& Davis (1998, ``SFD" hereafter), which have been derived from 100$\mu$m emission maps using the COBE/DIRBE and IRAS/ISSA data. These maps have proven reliable for differential line-of-sight reddening in low extinction regions, albeit with some uncertainties in zero-points (see discussion by Burstein 2003). Unfortunately, these maps have a resolution of only $\sim$6$^\prime$, which is particularly problematical where the reddening varies dramatically on much smaller angular scales. In addition, a number of studies have shown that the SFD maps overestimate the extinction at low latitudes by as much as 50\% in $A(V)$ (Stanek 1998a,b, Arce \& Goodman 1999a, Chen et al.\ 1999, Ivans et al.\ 1999, von Braun \& Mateo 2001, Choloniewski \& Valentijn 2003, Rocha-Pinto et al.\ 2004, Dutra et al.\ 2003a,b, Cambr\'esy et al.\ 2005, Am\^ores \& L\'epine 2005, 2007, Yasuda et al.\ 2007, Peek \& Graves 2010). A physical reason for the complications of the SFD maps at low latitudes is explored in the analysis in Paper I --- namely that far-infrared-{\it emitting} dust, which provides the basis of the SFD extinction maps, is simply not a good proxy for the dust causing {\it extinction} at shorter wavelengths. Comparison to other extinction tracers reveals that many of the SFD ``high extinction'' knots actually trace supernova remnant or star-forming environments, and a number of cold, dense clouds can be identified in extinction that lack the far-IR emission actually traced by the SFD maps. Thus, the midplane extinction in the Milky Way is far from being unambiguously mapped, and for studies of the Milky Way itself, the patchy intermingling of dust and stars remains a particularly troublesome obstacle. Both photometric and spectroscopic parallax determinations must include an accurate assessment of the extinction {\it foreground} to a star to gauge its distance. While studies of specific dark clouds using stellar IR color excess methods (particularly the extensive NICE family of techniques) have achieved remarkable success at mapping extinction, reliable assessments of extinction foreground to stars and astronomical sources {\it not} associated with these dark clouds have proven more elusive. Now, more accurate measurements of individual stellar extinction levels, including full three-dimensional spatial distribution information, is becoming possible through combined near- and mid-IR observations of the Rayleigh-Jeans flux distributions of stars (Majewski et al. 2011, Paper I hereafter); because the long wavelength SEDs of normal stars have approximately the same shape (i.e., colors) on their Rayleigh-Jeans tails, the {\it observed} Rayleigh-Jeans colors contain information on the foreground reddening to a star explicitly. We show in Paper I that this Rayleigh-Jeans Color Excess (RJCE) method is superior to the SFD method for mapping the extinction by midplane dust and is an improvement over the other IR color-excess methods due to the improved homogeneity of RJCE's adopted color indices. An additional advantage of the RJCE method over its predecessors is that the former cleanly separates reddening from intrinsic stellar colors and preserves the latter for use in the identification of stellar types (e.g., main sequence versus red clump versus red giant); thus, we can use the RJCE method to fairly reliably isolate the most distant stellar proxies (i.e., red giants) to create the best assessment of the total reddening along a given line of sight. Alternatively, one can isolate a rather reliable standard candle (in the form of red clump stars) to bring greater accuracy to distance estimates. In combination, stellar types of different intrinsic luminosity can yield the distance distribution of the dust along the line of sight. In this contribution to the present series of papers on the RJCE method, we make new, two-dimensional extinction maps of the Galactic midplane across the entire Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE-I; Benjamin et al.\ 2003; GLIMPSE-II/-3D Churchwell et al.\ 2009), and Vela-Carina ({\it Spitzer} PID 40791) IRAC survey areas. Section~\ref{sec:overview} summarizes how the maps were created; the reader is directed to Paper I for a fuller description and analysis of the RJCE method and its application to different color index combinations and different stellar types. In Section~\ref{sec:atlas} we present a full atlas of these maps based on use of main sequence, red clump, and red giant tracers, and in Section~\ref{sec:caveats} we alert the reader to various caveats for using the maps. Electronic versions of these maps have been made publicly available, and we describe how to access them in Section~\ref{sec:publicmaps}.
|
\label{sec:conc} We have developed a method for measuring line-of-sight extinction that combines near- and mid-infrared photometry (from 2MASS + {\it Spitzer}-IRAC) to calculate stellar reddening in a process that is (i) robust to variations in intrinsic stellar type {\it and} (ii) recovers the intrinsic stellar type. This Rayleigh-Jeans Color Excess (RJCE) technique represents a major improvement on previous color-excess measurements because it includes reddening corrections of temperature-sensitive near-infrared colors which allows us to create dereddened CMDs (extremely useful for stellar population studies) and select reasonably pure samples of stars of specific stellar type or luminosity class. In Paper I of this series, we described the RJCE method in great detail. This installment presents a large, publicly-available atlas of two-dimensional, high angular resolution extinction maps created from RJCE-derived extinction values. We take advantage of RJCE's ability to discriminate stellar spectral type to produce extinction maps generated independently from three groups of stars dominated by distinct stellar populations (main sequence [MS] dwarfs, red clump [RC] giants, and red giant branch [RGB] stars), each of which probes different heliocentric distance ranges and thus traces the net dust column to different distances. Comparison of these maps for any given section of the Galactic midplane provides rough {\it three}-dimensional information on the intrinsic dust distribution and allows clouds and cloud complexes to be isolated to specific distance ranges. We present a total of ten different types of extinction maps (in units of $A[K_s]$), each encompassing $\sim$515 deg$^2$ of the dustiest regions of the Galactic midplane, using data from the 2MASS-PSC merged with {\it Spitzer}-IRAC photometry from the GLIMPSE-I/-II/-3D and Vela-Carina surveys. For each of the three stellar tracer subsamples (MS, RC, and RGB) and ``all stars'', we provide maps giving two different statistical estimates of the $(H-[4.5\mu])$-derived extinction: the median and 90th percentile $A(K_s)$ in each spatial pixel. The three 90th percentile maps probably provide the most reliable estimate of the total integrated extinction affecting each subsample population to the maximum distance probed. Additionally, we provide median and 90th percentile $([3.6\mu]-[4.5\mu])$-derived extinction maps of ``all stars'', which provide reasonable extinction estimates for very dusty regions where the other maps fail due to lack of stars. Section \ref{sec:caveats} provides caveats to the applicability of our maps as well as distance limits for the different tracer populations. We find that our RGB 90th percentile maps very likely represent the total Galactic extinction in near all directions. Our 90th percentile RC maps probe to an average distance of $\sim$8 kpc, while the MS maps are limited to 2--4 kpc. The possibility of using MIR-only colors to estimate extinction where NIR-MIR colors are unavailable (due to the increased extinction in the NIR bands or the lower resolution of 2MASS) is also explored. Though MIR-only colors do not carry enough information to allow stellar type selection (and thus reliable distance estimates), we find that they can provide extinction estimates in the most highly extinguished portions of our maps (such as cloud cores and regions near the Galactic center). Thus, we include in our public atlas extinction maps derived from MIR-only reddening to serve as strong lower limits to the total extinction; this is most useful in the inner Galaxy, where even the RGB maps from typical RJCE colors are insufficient to probe to the far edge of the Galactic disk. An extensive program for application and improvement of the RJCE methodology is anticipated. We are working to improve the RJCE extinction estimates using a more refined treatment of stellar properties, and the ongoing APOGEE survey (Majewski et al.\ 2010) will allow us to compare RJCE-derived stellar types to spectroscopically-determined ones. We are evaluating the benefit of using optimized ``hybrid''-color schemes (i.e., merging extinction estimated using long-baseline NIR-MIR colors and MIR-only colors) where high extinction or confusion limits the depth of the NIR photometry. Our ultimate goal is to apply this dereddening methodology to ascertain the three-dimensional distribution of both dust and stars within the Galactic midplane. We have already taken advantage of our extensive data set to characterize the wavelength dependence of IR extinction throughout the midplane (Zasowski et al.\ 2009), and work is under way to use the new, reliably-cleaned CMDs to explore heavily-reddened or otherwise elusive Galactic structures, such as the central bar(s) and the outer spiral arms and the edges of the disk.
| 12 | 6 |
1206.5799
|
1206
|
1206.3389_arXiv.txt
|
Double radio relics in galaxy clusters are rare phenomena that trace shocks in the outskirts of merging galaxy clusters. We have carried out a spectral and polarization study of the spectacular double relics in the galaxy cluster A3376 using the Giant Metrewave Radio Telescope at 150 and 325 MHz and the Very Large Array at 1400 MHz. The polarization study at 1400 MHz reveals a high degree of polarization ($\sim30\%$) and aligned magnetic field vectors (not corrected for Faraday rotation) in the eastern relic. A highly polarized ($>60\%$) filamentary radio source of size $\sim300$ kpc near the eastern relic and north of the bent-jet radio galaxy is detected for the first time. The western relic is less polarized and does not show aligned magnetic field vectors. The distribution of spectral indices between 325 and 1400 MHz over the radio relics show steepening from the outer to the inner edges of the relics. The spectral indices of the eastern and the western relics imply Mach numbers in the range 2.2 to 3.3. Remarkable features such as the inward filament extending from the E-relic, the highly polarized filament, the complex polarization properties of the W-relic and the separation of the BCG from the ICM by a distance $>900$ kpc are noticed in the cluster. A comparison with simulated cluster mergers is required to understand the complex properties of the double relics in the context of the merger in A3376. An upper limit (log(P$_{1.4GHz}$ W Hz$^{-1}$)$<23.0$) on the strength of a Mpc size radio halo in A3376 is estimated.
|
Clusters of galaxies, being the largest gravitationally bound structures in the Universe are interesting sites to study extreme phenomena. Evolution of galaxy clusters occurs through mergers of galaxy groups and galaxy sub-clusters involving dissipation of gravitational binding energies $\sim10^{64}$ erg in the intra-cluster medium (ICM) via shocks and turbulence \citep{ryu03}. There is growing evidence that cluster-cluster mergers are connected to the presence of diffuse large scale radio sources called radio halos and radio relics \citep{fer08}. The channeling of the gravitational energy into the acceleration of particles and possibly amplification of the cluster magnetic field are not well understood and are currently the topics of active research. Radio halos are $\sim$Mpc size radio sources, located co-spatially with the X-ray emission from the ICM. Acceleration of particles in the ICM through turbulence and production of relativistic electrons as secondary products of hadronic collisions in the ICM are the two mechanisms proposed for the generation of radio halos \citep[see][and references therein]{bru11}. Radio relics are elongated, polarized, filamentary and sometimes arc-like radio sources. One class of radio relics has been proposed to be remnants of radio galaxies evolving passively in the surrounding medium or revived by adiabatic compression by environmental shock waves \citep{ens01}. The solitary filamentary relics of sizes $\sim50-500$ kpc, sometimes located close to radio galaxies in clusters are likely to have these origins \citep{kal11}. The radio relics of the other class have arc-like morphologies, $\sim$Mpc extents and are located at the peripheries of galaxy clusters. These are believed to be tracers of the cluster merger shocks or accretion shocks \citep{ens98}. The shocks are stronger toward the outskirts of clusters where the density of electrons is very low (n$_e<10^{-4}$ cm$^{-3}$). Therefore, detecting them in X-rays is a challenge \citep{aka11}. The radio relics thus offer a unique window to trace the shocks and the ICM at cluster peripheries. Shocks are known to accelerate electrons by the diffusive shock acceleration (DSA) mechanism and compress magnetic fields along the direction of propagation \citep{dru83}. The DSA produces a power law distribution of relativistic electrons and thus provides a link between the spectral index of the radio emission and the strength of the shock. The alignment of magnetic fields results in polarized radio emission from radio relics. Thus, the integrated spectra, spectral index distribution and polarization of radio relics are crucial to find the properties of shocks in the ICM. However, radio relics are rare and only a handful of them are known. Therefore studying the properties of the known sources in as much detail as possible is important. Even rarer are the cases when the arc-like relics occur in pairs around galaxy clusters. Such relics occur in cluster-cluster mergers with the merger axes nearly in the plane of the sky. The effects of projection in studying the shocks and the merger in such a configuration are expected to be minimal. There are only nine clusters where such ``double relics'' have been discovered, namely, ZwCl $2341.1+0000$ \citep{bag02,wee09}, A3376, PLCK $G287.0+32.9$ \citep{bag02,bag06,bag11}, A3667 \citep{rot97}, ZwCl $0008.8+5215$, CIZA J$2242.8+5301$ \citep{wee11c,wee10}, RXCJ $1314.4-2515$ \citep{fer05}, A2345 \citep{gio99,bon09} and A1240 \citep{kem01,bon09}. There are three more candidate double radio relics, namely $0217+70$ \citep{bro11}, A3365 \citep{wee11b} and A1758N \citep{gio09}. In this paper we present a polarization and spectral study of the double relics in A3376 using the Giant Metrewave Radio Telescope (GMRT) and the Very Large Array (VLA). Abell 3376 is a nearby ($z=$0.046) X-ray luminous ($L_X\sim 2\times10^{44} h^{-2}_{70}$ erg s$^{-1}$) cluster with spectacular double relics \citep{bag06}. It has an average temperature of $\sim 4$ keV and the X-ray surface brightness has a comet-like appearance which indicates the ongoing dynamical activity in the cluster. The virial mass of this cluster is estimated to be $\sim3.64\times10^{14}h_{70}^{-1}$ M$_\odot$ \citep{gir98}. The two radio relics in A3376 are separated by a distance of $\sim$ 2 Mpc and are located almost symmetrically around the X-ray emission from the ICM. The previous study of these relics at 1.4 GHz revealed the basic morphology of these relics and stated the possibilities that either outgoing cluster merger shocks or accretion shocks are responsible for the relics \citep{bag06}. In this paper we provide a more detailed description. The paper is organised as follows. The observations and data reduction are described in section 2. The properties of the relics revealed from the radio images and the spectral index images are presented in section 3. In section 4 the implications of these properties are discussed. The work is summarized in section 5. We adopt a $\Lambda$CDM cosmology with $H_0$ = 71 km s$^{-1}$ Mpc$^{-1}$, $\Omega_M$ = 0.27, and $\Omega _\Lambda = 0.73$, resulting in a scale of 0.89 kpc arcsec$^{-1}$ for the redshift, 0.046 of A3376. The spectral index, $\alpha$ is defined as $S\propto\nu^\alpha$, where $S$ is the flux density and $\nu$, the frequency.
|
The cluster A3376 is a spectacular massive, merging cluster of galaxies. The galaxy distribution shows atleast two sub-clusters located along the axis of elongation of the X-ray surface brightness \citep{fli06}. The giant ring-like radio relics at the outskirts of the cluster are located along the same axis. The alignment of magnetic field vectors in the E-relic and the spectral index steepening toward inner edges of the relics support the scenario of shock acceleration at the radio relics. The acceleration of electrons at the shock by DSA results in a power law spectrum of the electrons. In a fully ionized plasma the slope of the power law spectrum, $\delta_{inj}$, is related to the Mach number, $M$, of the shock as given by \citep[e.g.][]{bla87}, \begin{equation} \delta_{inj} = -2 \frac{M^2 + 1}{M^2 - 1} \end{equation} The spectral index of the accelerated electrons is $\alpha_{inj} = (\delta_{inj} + 1) / 2$. If we assume that the shock is located at the radio relics and that the synchrotron and inverse Compton losses have not affected the spectrum of the accelerated electrons, then the flattest spectrum will represent the spectral index at injection. The flattest spectral index in the southern arc in the E-relic as read from the spectral index map is $-0.70\pm0.15$ (Fig.~\ref{spix}, top left). The implied Mach number is $3.31\pm0.29$. The spectral index at the outer edge of the W-relic is $-1.0\pm0.2$ and the implied Mach number is $2.23\pm0.40$ (Fig.~\ref{spix}, bottom left). These Mach numbers imply that the shocks at the relics are cluster merger shocks and not accretion shocks (M$>$10). Deep X-ray observations with sensitive instruments can provide an independent measure of the properties of shocks through the measurements of temperature and pressure jumps at the location of radio relics. The $SUZAKU$ X-ray observations of A3376 by \citet{aka11b} reveal temperature and pressure jumps across the W-relic. A temperature jump from $1.35\pm0.35$ keV in the pre-shock region to $4.81\pm0.29$ keV in the post-shock region is reported at the W-relic. They find Mach numbers of $2.94\pm0.60$ and $4.78\pm0.49$ from the temperature and pressure jumps, respectively. The radio Mach number of the W-relic is consistent with the one calculated using the temperature jump. The Mach number estimated from the pressure jump is less reliable due to the assumptions, such as of spherical symmetry, that are used in the determination of the electron density profile \citep{aka11b}. In the process of structure formation, large scale shocks are driven into the diffuse medium. High Mach number shocks ($M>10$) are formed in filaments surrounding the virializing cores of clusters. On the other hand, low Mach number ($M<10$) shocks are formed in the clusters. Most of the kinetic energy of the accreted matter is dissipated by the relatively low Mach number shocks ($M<4$) \citep{min00,ryu03}. These Mach numbers are consistent with those found from the spectral indices of the A3376 radio relics and also other relics \citep{wee10,fin10}. These findings imply shock velocities $\sim1000$ km s$^{-1}$ at the radio relics. This shock velocity is comparable to that in supernova remnants, however the Mach numbers are much lower \citep{jon12}. The low Mach number shocks are believed to be inefficient in accelerating electrons from the thermal ICM to relativistic energies as required to produce the radio relics \citep{kan02}. Thus the understanding of the generation of relativistic electrons through DSA at such low Mach number shocks is still incomplete. Nevertheless the coincidence of such shocks with the radio relics does imply their role in the reacceleration of a pre-existing population of relativistic electrons or in strengthening the magnetic fields. \subsection{Remarkable features of A3376} The spectral and polarization study of double radio relics in A3376 has revealed several new features. The properties of the A3376 relics such as -- aligned polarization vectors and spectral steepening from outer to inner edges, are similar to the radio relics in other galaxy clusters. Majority of the single and double relics at cluster outskirts have been found to be located along the direction of elongation of the X-ray surface brightness \citep{wee11b}. The A3376 relics are in line with this property of other relics as well. However there are some remarkable properties of the relics in A3376 and of the cluster itself that we have noticed. The $\sim$500 kpc long inward filament of the E-relic is a peculiar feature. It has a width of $\sim 300$ kpc and has steep spectral index. Backflows from shock fronts, under standard assumptions can have maximum widths of up to $\sim200-250$ kpc \citep{bru08}. The widths of radio relics have been explained as due to such back flows \citep{bru08,wee10}. However the inward filament in A3376 is different from such a backflow in that it extends from only a section of the E-relic, creating a `notch' at that location. A possibility that the `notch' may be due to the breakup of the shock front in an encounter with a filament has been expressed recently \citep{pau11}. A highly polarized filament of extent $\sim300\times50$ kpc$^{2}$ north of the bent-jet radio galaxy with magnetic fields aligned in the same direction as in the southern arc of the E-relic is reavealed for the first time. This polarized filament is located $\sim200$ kpc behind the northern part of the E-relic as projected in the sky plane. The W-relic, though has an arc-like morphology at the edge, lacks an aligned magnetic field. It is possible that the turbulence in the backflow of the shock has resulted in the complex geometry of the field. Faraday rotation by the ICM can rotate the polarization vectors. The relics are located outside the dense part of the ICM (Fig.~\ref{pband}) and thus this effect is expected to be small \citep{cla04}. Deeper observations mapping the polarized emission and a model for the ICM density in A3376 are required. There are two prominent galaxies in A3376. One is the brightest cluster galaxy (BCG), ESO 307-13, and the other is the bent-jet radio galaxy near the peak of the X-ray emission, MRC $0600-399$ (Fig.~\ref{pband}). Most cD galaxies and BCGs are located at the cores of galaxy clusters with dense ICM surrounding them \citep{bau70}. Many of those are powerful radio galaxies and play a major role in heating of the ICM. The BCG in A3376 is unique due to its separation of $>900$ kpc from the peak of X-ray surface brightness. The powerful cluster-cluster merger in A3376 may have led to a setting in which the BCG is `orphaned'. Simulation studies may be able to point out the details of a merger which can result in BCG-ICM peak separation as large as $>900$ kpc. Mapping of dark-matter distribution in A3376 with the gravitational lensing method is likely to shed additional light on the complex merger dynamics. A3376 is well suited for a detailed comparison with simulated cluster mergers, given that it is a well studied cluster at X-rays, optical and radio wavelengths \citep[][and present work]{aka11b,fli06,bag06}. Details of the merger geometry and the properties of individual sub-clusters can be obtained by matching simulations with observations as has been carried out in the case of the cluster CIZA J2242.8+5301 \citep{wee11a}. The double relics in CIZA J2242.8+5301 fit the picture of outgoing merger shocks and have been modelled by a toy model of cluster merger shocks. However, in the case of A3376, due to the morphological details of the E and W-relics which indicate an interaction with the large scale structure filaments, a cluster merger in a cosmological simulation will be more appropriate. This will provide further insights into the formation of the double relics in A3376 and cluster mergers in general. \subsection{A Radio halo in A3376?} Radio halos are diffuse radio sources that trace relativistic electrons and magnetic fields in galaxy cluster centers. Like the relics, they are also rare and have been found to occur preferentially in clusters undergoing mergers \citep{cas10}. It is still not understood why certain merging clusters have radio relics whereas others have radio halos. Also there are cases where single radio relics and radio halos are in the same cluster. It is important to understand whether the formation of a radio halo and of radio relics in a galaxy cluster is simultaneous or it is separated in time. This will provide an insight into the details of the underlying mechanisms of their generation in cluster mergers. In this context, we examined whether A3376 has a radio halo. No emission from a radio halo is detected in the 150, 325 and 1400 MHz images. To obtain upperlimits on the radio power of radio halos a method of injection of fake radio halos has been used \citep[for e.g.][]{ven08,bru07}. We used AIPS task `UVSUB' to inject uniform spherical halos of total flux densities in the range 50 to 500 mJy in the 325 MHz data. The radius of the injected halo was 500 kpc and the location RA 06h01m20.52s DEC -39d59m50.8 (J2000), which is approximately midway between the two relics. We found that a radio halo of 100 mJy at the level of suspecting diffuse emission (positive residuals) was detected. Using this as a limiting flux density of detection at 325 MHz, if we assume a spectral index of -1.0 over the frequency range 325 - 1400 MHz, a limit on the radio power of 1.02$\times10^{23}$ W Hz$^{-1}$ is obtained at 1400 MHz. A radio power of 1.91 $\times10^{23}$ W Hz$^{-1}$ at 1.4 GHz is expected if A3376 were to follow the X-ray luminosity and 1.4 GHz power correlation for giant radio halos \citep{cas06}. The upperlimit is a factor of $\sim2$ below the expected radio halo power. Therefore in the picture of radio halo evolution, this may be either an early stage of halo formation or a fading stage after attaining the peak radio power.
| 12 | 6 |
1206.3389
|
1206
|
1206.1345_arXiv.txt
|
We present imaging observations at 1.3 mm wavelength of Class I protostars in the Taurus star forming region, obtained with the CARMA interferometer. Of an initial sample of 10 objects, we detected and imaged millimeter wavelength emission from 9. One of the 9 is resolved into two sources, and detailed analysis of this binary protostellar system is deferred to a future paper. For the remaining 8 objects, we use the CARMA data to determine the basic morphology of the millimeter emission. Combining the millimeter data with 0.9 $\mu$m images of scattered light, Spitzer IRS spectra, and broadband SEDs (all from the literature), we attempt to determine the structure of the circumstellar material. We consider models including both circumstellar disks and envelopes, and constrain the masses (and other structural parameters) of each of these components. We show that the disk masses in our sample span a range from $\la 0.01$ to $\ga 0.1$ M$_{\odot}$. The disk masses for our sample are significantly higher than for samples of more evolved Class II objects. Thus, Class I disk masses probably provide a more accurate estimate of the initial mass budget for star and planet formation. However, the disk masses determined here are lower than required by theories of giant planet formation. The masses also appear too low for gravitational instability, which could lead to high mass accretion rates. Even in these Class I disks, substantial particle growth may have hidden much of the disk mass in hard-to-see larger bodies.
|
Stars form from clouds of dust and gas. As these clouds collapse and conserve angular momentum, matter that is not initially located near the polar axis falls onto a rotationally-supported disk, Most of the material that eventually makes up the star falls initially onto the disk, with some matter subsequently losing angular momentum and accreting onto the protostar. The basic picture of star formation thus involves the free-fall collapse of material from an extended envelope (or cloud) onto a disk, and then viscous accretion through the disk and onto a protostar. At the earliest stages of collapse, one would see a roughly spherical cloud with no embedded protostar. These so-called starless cores have now been identified in a number of star forming regions \citep[e.g.,][]{SCHNEE+07,STUTZ+09}. As collapse proceeds, a protostar and compact disk form, still surrounded by a substantial, roughly spherical envelope. Matter continues to fall onto the disk, while viscosity sources in the disk allow net outward angular momentum transport and inward mass accretion. In time the envelope completes its collapse, leaving a pre-main-sequence star surrounded by a massive disk. The disk continues to accrete onto the star, losing mass over time, eventually leaving the central pre-main sequence object surrounded by only tenuous circumstellar matter. Each of these stages of protostellar evolution produces observational diagnostics, and an empirical picture has been developed that links evolutionary phases with properties of the emergent spectral energy distributions \citep{LADA87,AWB93}. Class 0 objects show highly obscured SEDs that peak at sub-mm wavelengths. These are thought to be protostars still deeply embedded in massive envelopes. Class I sources show SEDs that peak in the mid-IR. Class I objects are thought to be surrounded by massive disks embedded in non-spherically-symmetric envelopes \citep[e.g.,][]{EISNER+05b}. In Class II objects light from the central object is visible, although some short-wavelength emission is reprocessed and emitted at longer wavelengths. These are the T Tauri and Herbig Ae/Be stars, known to be pre-main-sequence stars surrounded by optically thick disks \citep[e.g.,][]{BURROWS+96,MO96,CES05}. Finally, Class III sources are pre-main-sequence stars either devoid of circumstellar material or surrounded by only tenuous, optically thin circumstellar matter \citep[e.g.,][]{PADGETT+06}. The relative lengths of the Class 0, I, and II evolutionary stages can be estimated by counting the number of sources belonging to different classes in individual star-forming regions. Absolute timescales are determined by fitting the relatively unobscured Class II pre-main-sequence stellar photospheric properties to theoretical evolutionary tracks \citep[e.g.,][]{WG01}. The lifetime of the Class 0 phase has been estimated as $\sim 0.1$--0.2 Myr \citep{EVANS+08,ENOCH+09}, the Class I phase as $\sim 0.2$--0.5 Myr \citep{WLY89,GREENE+94,KH95,EVANS+08}, and the Class II phase as $\sim 2$ Myr \citep[e.g.,][]{KENYON+90,CIEZA+07}. The mass of circumstellar disks in each of the evolutionary stages outlined above has crucial implications for star and planet formation. Sufficiently massive disks may become gravitationally unstable, providing high effective viscosities and allowing rapid growth of protostellar mass. The disk mass at later stages is important to planet formation, since a certain mass is required to build giant planets \citep[e.g.,][]{WEID+77}. During the Class 0 phase, disks are embedded in much more massive envelopes. High presumed infall rates \citep[$\ga 10^{-5}$ M$_{\odot}$ yr$^{-1}$; e.g.,][]{SHU77,HCK97} from envelopes to disks likely mean that these disks are gravitationally unstable. At the Class I stage, envelopes are less massive and the disks may dominate the total system mass \citep[e.g.,][]{JORGENSEN+09}. Disks in Class II objects generally appear gravitationally stable, accreting material slowly onto their central objects \citep[$\dot{M} \la 10^{-7}$ M$_{\odot}$ yr$^{-1}$; e.g.,][]{BB89,HEG95}. Class I sources thus offer the prospect of observing disks at an intermediate state when they may transitioning from roiling, gravitationally unstable disks, to more stable disks that could provide a hospitable environment for the early stages of planet formation. The masses of disks surrounding Class I sources have been constrained previously using millimeter wavelength observations \citep[e.g.,][]{HOGERHEIJDE01,OSORIO+03,WPS03,EISNER+05b,JORGENSEN+07,JORGENSEN+09}. Because much of the circumstellar dust around Class I objects is expected to be optically thin, the observed millimeter flux is correlated with mass. However knowledge of the dust opacity and temperature (as a function of radius) is needed in order to convert flux to mass. Moreover, dense regions (e.g., close to the central protostars) may be optically thick. Radiative transfer modeling of multi-wavelength data is required to disentangle these effects and provide unambiguous circumstellar mass estimates. Historically, constraints on the circumstellar matter in Class I sources came from modeling of SEDs \citep[e.g.,][]{ALS87,KCH93,ROBITAILLE+07}. These models include flattened, disk-like distributions of matter that are a consequence of angular momentum conservation \citep[e.g.,][]{ULRICH76,TSC84}. However, the SED data can often be explained with different models as well, including edge-on flared disk models \citep[e.g.,][]{CG99}. Imaging data, including scattered light images \citep[e.g.,][]{WHITNEY+03a} or millimeter images of continuum and line emission \citep[e.g.,][]{JORGENSEN+07,JORGENSEN+09}, have also been used to constrain the circumstellar structure of Class I sources. Modeling a single dataset---e.g., an SED or scattered light image---is subject to ambiguities. Modeling multi-wavelength images and fluxes simultaneously provides tighter constraints on geometry, since emission at different wavelengths arises in different layers of circumstellar material. Scattered light at short wavelength traces low-density surface layers, while longer-wavelength (e.g., millimeter) emission arises in deeper, denser regions. Such modeling has been applied to a number of Class I sources, yielding constraints on circumstellar morphology better than afforded by modeling any single dataset \citep{OSORIO+03,WPS03,EISNER+05b}. Previous estimates of disk masses in Class I objects cover a broad range. Modeling millimeter images together with SEDs and scattered light images, disk masses of 0.01--1 M$_{\odot}$ (with most masses $\ga 0.1$ M$_{\odot}$) were determined for a handful of Class I objects \citep{OSORIO+03,WPS03,EISNER+05b}. Somewhat lower masses, spanning $\la 0.01$ up to $\sim 0.05$ M$_{\odot}$, were inferred from radiative transfer modeling of sub-millimeter continuum images of 10 Class I sources \citep{JORGENSEN+09} . Some disk mass estimates are consistent with simulations of protostellar evolution, which find disk masses of $\sim 0.2$ M$_{\odot}$ for Class I objects \citep{VOROBYOV11}. For many objects, however, estimated disk masses are substantially lower. For some objects, mass estimates place Class I disks near the limit of gravitational stability. This finding would fit naturally into the scenario of burst-mode accretion onto Class I protostars \citep{VB05}, and explain the discrepant infall rates from the envelope to the disk and from the disk onto the star \citep[e.g.,][]{KH87,WH04}. In a broader sense, the implied gravitational instability provides an easily-explained viscosity source to enable angular momentum transport in protostellar disks. Estimated disk masses in Class Is appear higher than the disk masses determined for Class II objects. The median mass of disks in nearby star-forming regions is estimated as $\sim 0.005$ M$_{\odot}$ \citep[e.g.,][]{AW05,AW07,EISNER+08}. These disks are about an order of magnitude less massive than the minimum mass solar nebula \citep[MMSN;][]{WEID+77}, suggesting that many stars in the Galaxy lack the circumstellar mass needed to form solar systems like ours. Higher inferred masses in Class I disks suggest that substantial particle growth (which depletes the observable population of small dust grains) has occurred between the Class I and II stages. Planet formation may already have advanced significantly during the first million years of disk evolution. Given the short lifetimes of particles with sizes of a few centimeters to a few meters \citep{WEIDENSCHILLING77}, this would imply growth of large planetesimals in less than $\sim 1$ Myr. Substantial uncertainties remain in the estimated Class I disk masses, placing the conjectures above on somewhat shaky footing. Our aim in this paper is to better constrain the disk masses around a relatively large sample of Class I sources. We will improve upon previous constraints using high angular resolution millimeter imaging from CARMA. We model these data together with existing data at other wavelengths, including broadband SEDs, Spitzer IRS spectra, and I-band images of scattered light.
|
The disk mass is a crucial parameter in understanding both star and planet formation. High disk masses, on the order of a tenth of the stellar mass, would imply that gravitational instability may be important. Such instability can lead to rapid accretion onto the central protostar, and may explain why accretion rates onto the star appear low compared to estimated time-averaged accretion from the envelope onto the disk. Episodes of gravitationally-enhanced accretion can lead to larger time-averaged rates but low typical instantaneous accretion rates \citep[e.g.,][]{WH04,EISNER+05b}. Disk mass is also a critical initial condition for planet formation. To form gas giants like Jupiter and Saturn requires $>0.01$ M$_{\odot}$ of matter \citep{WEID+77}. While measured disk masses around T Tauri stars are smaller \citep[e.g.,][]{AW05,EISNER+08}, this may reflect the agglomeration of small particles into larger bodies rather than a mass deficit. Data for the less evolved protostars in our sample can provide masses in systems where dust grain agglomeration is presumably less advanced. We begin by examining the distribution of disk masses for our sample, drawing values from Table \ref{tab:modfits}. Disk masses range from 0.005 to 0.5 M$_{\odot}$ across the sample, and the median disk mass is 0.008 M$_{\odot}$. The majority ($\sim 60\%$) of objects have disk masses $\ge 0.01$ M$_{\odot}$, and $\sim 10\%$ have $M_{\rm disk} \ge 0.1$ M$_{\odot}$. For comparison, across $>150$ (more evolved) Class II disks in Taurus, \citet{AW05} find a median mass of 0.005 M$_{\odot}$. In this sample of Class II objects, $\sim 20\%$ of disks are more massive than 0.01 M$_{\odot}$ and only $\sim 2\%$ are more massive than 0.1 M$_{\odot}$ \citep{AW05}. Our sample of Taurus Class I objects has significantly more massive disks than the Class II population. Indeed, many of them may still possess sufficient mass in small ($\sim $mm-sized) dust grains for the eventual formation of planetary systems like our own (depending on how the mass is distributed on scales smaller than 100 AU). The lower masses in Class II disks likely reflect that some of the mass of small particles available at the Class I stage has grown into large ($>$ meter-sized) bodies within $\sim 1$ Myr. This argument can easily be extended to Class I sources themselves. While Class I disks appear more massive than Class II disks---at least as traced by small ($\la$ mm-sized) dust grains---particles in Class I disks may already have undergone substantial processing. That is, planet formation may already be underway even at these ages. Extending the analysis in this paper to younger, less evolved Class 0 objects provides a clear path to improving the estimates of the initial mass content of protoplanetary disks. The range of disk masses observed for our sample indicates that few Class I disks are at the limit of gravitational instability. Even IRAS 04287+1801, which has a disk mass $\ge 0.1$ M$_{\odot}$, may remain stable against gravitational collapse because of the higher stellar mass contained in the multiple central system. If, however, substantial mass is hidden in larger bodies, gravitational instability may still be possible in these systems. Measured envelope masses can be used to estimate the mass infall rate from the envelope onto the disk, $\dot{M}$. Estimates of $\dot{M}$ can then be compared to the accretion rate measured from the inner disk onto the star \citep[e.g.,][]{WH04}. Such comparisons typically conclude that the infall rate from the envelope is higher than the accretion rate onto the star, suggesting that matter piles up in the disk and periodically accretes quickly in bursts \citep[e.g.,][]{KH87,WH04,EISNER+05b,VB05}. The results presented here are generally compatible with this view. However the envelope masses estimated here are highly uncertain. For example, the range of $M_{\rm env}$ allowed for IRAS 04016+2610 (Table \ref{tab:modfits}) correspond to $\dot{M}$ between $\sim 10^{-6}$ and $10^{-5}$ M$_{\odot}$ yr$^{-1}$. Much of this uncertainty is due to degeneracies with other parameters (primarily $R_{\rm out}$; see \S \ref{sec:parstudy}). Additional uncertainties arise because of the limited $uv$ coverage (i.e., range of telescope baseline separations) in our millimeter observations. The shortest baselines correspond to linear resolutions of $\sim 1000$ AU at the distance to our targets. More extended emission is largely resolved out. Thus, we are not sensitive to extended emission and, as a result, our total envelope masses are likely underestimated. Despite uncertainties in inferred values of $M_{\rm env}$, clear differences in the ratio of $M_{\rm disk}/M_{\rm env}$ are observed across our sample. The disk-to-envelope mass ratio ranges from $<0.1$ for some objects (IRAS 04016+2610) to $>1$ for others (IRAS 04287+1801). In most cases, the disk-to-envelope mass ratio is around 0.1. This suggests our sample is at an earlier evolutionary stage than Class II objects, which are essentially 100\% disk. Furthermore, one might be tempted to assign relative ages to sample objects based on $M_{\rm disk}/M_{\rm env}$ values. Another method to constrain relative ages in our sample is to examine the disk/centrifugal radii. For collapsing, rotating envelopes, the centrifugal radius grows with time because of the inside-out nature of the collapse. For the envelope models used here, one expects the centrifugal, and hence disk, radius to grow with time as $R(t) \propto t^3$. If our sample objects had similar initial specific angular momenta (which is by no means guaranteed), then the inferred centrifugal radii can be used to estimate relative ages. The disk radii inferred in our modeling have substantial uncertainties, but do reveal trends between objects (Table \ref{tab:modfits}). For example, IRAS 04016+2610 seems to have a larger disk/centrifugal radius than IRAS 04295+2251. However, IRAS 04016+2610 has a lower disk-to-envelope mass ratio than IRAS 04295+2251. While a smaller disk/centrifugal radius suggests a younger source, a larger ratio of disk-to-envelope mass suggests an older object. We therefore do not place much confidence in our ability to distinguish ages amongst our sample. To compare our inferred disk masses with expected minimum masses for planet formation theory, we turn now to the masses listed in Table \ref{tab:massdist}. The Table lists circumstellar masses enclosed within 100 AU, including both disk and inner envelope components. Since the inner regions of the envelope have a flattened density distribution (Equation \ref{eq:rhoenv}), they may appear disk-like, and may contribute to the mass budget for planet formation. We choose 100 AU because this is approximately the smallest scale we can resolve with our millimeter imaging data. However we would ideally like to probe smaller scales, since planet formation theories usually require a minimum mass within radii or 30--50 AU \citep[e.g.,][]{WEID+77,HAYASHI81}. Thus, even our 100-AU-masses (Table \ref{tab:massdist}) may over-estimate the mass available for planet formation. Even so, the masses listed in Table \ref{tab:massdist} are typically lower than the 0.01--0.1 M$_{\odot}$ usually required to form planetary systems like ours. As discussed above, this may reflect growth of small, observable dust grains into larger bodies. Probing younger sources may provide a clearer picture of how much mass is truly available to planet formation.
| 12 | 6 |
1206.1345
|
1206
|
1206.1729_arXiv.txt
|
We present the results of a year-long photometric monitoring campaign of a sample of 23 nearby ($d<60$ pc), bright ($J<12$) dM stars carried out at the Astronomical Observatory of the Autonomous Region of the Aosta Valley, in the western Italian Alps. This program represents the `pilot study' for a long-term photometric transit search for planets around a large sample of nearby M dwarfs, due to start with an array of identical 40-cm class telescopes by the Spring of 2012. In this study, we set out to $a)$ demonstrate the sensitivity to $<4$ R$_\oplus$ transiting planets with periods of a few days around our program stars, through a two-fold approach that combines a characterization of the statistical noise properties of our photometry with the determination of transit detection probabilities via simulations, and $b)$ where possible, improve our knowledge of some astrophysical properties (e.g., activity, rotation) of our targets by combining spectroscopic information and our differential photometric measurements. We achieve a typical nightly RMS photometric precision of $\sim5$ mmag, with little or no dependence on the instrumentation used or on the details of the adopted methods for differential photometry. The presence of correlated (red) noise in our data degrades the precision by a factor $\sim1.3$ with respect to a pure white noise regime. Based on a detailed stellar variability analysis, $a)$ we detected no transit-like events (an expected result given the sample size); $b)$ we determined photometric rotation periods of $\sim$0.47 days and $\sim$0.22 days for LHS 3445 and GJ 1167A, respectively; $c)$ these values agree with the large projected rotational velocities ($\sim25$ km/s and $\sim33$ km/s, respectively) inferred for both stars based on the analysis of archival spectra; $d)$ the estimated inclinations of the stellar rotation axes for LHS 3445 and GJ 1167A are consistent with those derived using a simple spot model; $e)$ short-term, low-amplitude flaring events were recorded for LHS 3445 and LHS 2686. Finally, based on simulations of transit signals of given period and amplitude injected in the actual (nightly reduced) photometric data for our sample, we derive a relationship between transit detection probability and phase coverage. We find that, using the BLS search algorithm, even when phase coverage approaches 100\%, there is a limit to the detection probability of $\approx 90\%$. Around program stars with phase coverage $>50\%$ we would have had $>80\%$ chances of detecting planets with $P<1$ day inducing fractional transit depths $>0.5\%$, corresponding to minimum detectable radii in the range $\sim1.0-2.2$ $R_\oplus$. These findings are illustrative of our high readiness level ahead of the main survey start.
|
M dwarf stars, with masses $M_\star\leq0.6$ M$_\odot$, make up the vast majority of the reservoir of nearby stars within $\sim 25-30$ pc. These stars have not traditionally been included in large numbers in the target lists of radial-velocity (RV) searches for planets for two main reasons: 1) their intrinsic faintness, which prevented Doppler surveys in the optical from achieving very high radial-velocity precision ($<5-10$ m/s) for large samples of M dwarfs (e.g., Eggenberger \& Udry 2010, and references therein), and 2) their being considered as providers of very inhospitable environments for potentially habitable planets (e.g., Tarter et al. 2007; Scalo et al. 2007, and references therein). These two paradigms are now shifting. First, the application of the transit technique to M dwarfs presents several exciting opportunities, and the advantages are especially compelling for the detection of transiting habitable, rocky planets. These include, for example, improved observing windows due to the short periods of potential planets in the stellar habitable zone (the range of distances from a given star for which water could be found in liquid form on a planetary surface. E.g., Kasting et al. 1993), or the possibility to reach detection of rocky planets due to the small radii of M dwarfs, leading to deep transits ($\Delta mag\sim0.005$ mag) easily detectable from the ground with modest-size telescopes ($30-50$ cm class), and readily confirmable with present-day precision RV measurements (owing to their moderately large RV amplitudes, on the order of 5-10 m/s). Second, while not all concerns about their habitability have been resolved yet, there has been a recent change in view for planets orbiting low-mass M stars, now often considered as potentially hospitable worlds for life and its remote detection (e.g., Seager \& Deming 2010; Barnes et al. 2011, and references therein). Advancements in our knowledge of the complex processes of planet formation and evolution cannot be achieved without a detailed understanding of the role of the central star (through its properties such as mass and metal abundance) and its environment (the circumstellar disk within which the planetary population must form). For example, the theoretical expectations (within the framework of the standard core accretion model) that giant planet frequency and upper mass limits ought to be direct functions of stellar mass $M_\star$ and metallicity [Fe/H] (e.g., Laughlin et al. 2004; Ida \& Lin 2004, 2005; Kennedy \& Kenyon 2008; Mordasini et al. 2009) have so far been confirmed on relatively firm statistical grounds only for stars (mid-F through mid-K type) with masses close to that of the Sun (Santos et al. 2004; Fischer \& Valenti 2005; Johnson et al. 2007; Sozzetti et al. 2009), while results for stars with masses wignificantly different from that of the Sun still rely on small-number statistics (e.g., Endl et al. 2006; Bonfils et al. 2007; Johnson et al. 2010, 2011, 2012). Similarly, the statistical significance of the early evidence for a relatively high frequency of low-mass planets (Neptunes and super-Earths) around low-mass stars (e.g., Forveille et al. 2011, and references therein) is still hampered by the observational bias intrinsic to long-term RV surveys (only a few hundred objects monitored), and the recent, compelling evidence from Kepler photometry (e.g., Howard et al. 2011) of increasing occurrence rates for small-radius, short-period planets around increasingly cooler stars still suffers from small-numbers statistics at the latest spectral types (only a few hundred of relatively bright M0-M1 dwarfs being included in the Kepler catalogue). Finally, the anticipated wild diversity of the structural and atmospheric properties of super-Earths (Seager \& Deming 2010, and references therein) can be most easily investigated using a sample of such planets observed as transiting companions to nearby M dwarf primaries, given that for low-mass stars the planet-to-star flux ratio is much larger than that for the Earth-Sun system \footnote{For example, in the Rayleigh-Jeans limit, this flux ratio depends on the relative surface areas and brightness temperatures of the planet and star. For a 2-$M_\oplus$ super-Earth, this ratio is in the range 0.01\%-011\% for a mid- to late-M dwarf primary (M4V-M8V), compared to 0.00044\% for the Earth-Sun system.}, thus spectral characterization of the planet via, e.g., occultation spectroscopy is much more readily attainable. These considerations have brought about renewed efforts to monitor photometrically as well as spectroscopically large samples of nearby cool dwarfs. The first spectacular success of the dedicated MEarth transit search for rocky planets around 2000 late M dwarfs was announced by Charbonneau et al. (2009), with the detection of the low-density transiting super-Earth GJ 1214b ($M_p=6.5$ M$_\oplus$, $R_p=2.7$ $R_\oplus$) around a nearby M4.5 dwarf. The primary in this system is bright enough to enable the detailed spectroscopic characterization of the planet's thick atmosphere over a broad wavelength range (Bean et al. 2010, 2011; Croll et al. 2011; Crossfield et al. 2011). The recent constraints on GJ 1214b's atmospheric composition are not only essential for breaking the degeneracy between the mass, radius and composition of both the interior and a possible atmosphere in theoretical models of super-Earths (Adams et al. 2008; Rogers \& Seager 2010; Miller-Ricci \& Fortney 2010; Miller-Ricci et al. 2011; D\'esert et al. 2011; Nettelmann et al. 2011; Menou 2011), but they also constitute a remarkable test of planetary evolution models in a mass range (for both the primary and the planet!) not seen in our Solar System. Very recently, the M2K Doppler search for close-in planets around 1600 nearby M and K dwarfs has also started producing its first results (e.g., Apps et al. 2010). Decade-long Doppler monitoring has also allowed to detect the first Saturn-mass planet in the habitable zone of a nearby mid-M dwarf (Haghighipour et al. 2010). The early-M dwarf GJ 581, already hosting a system of four low-mass (Neptunes and super-Earths) planets, is currently the focus of a hot debate on the actual existence of a fifth planet with the mass of a super-Earth orbiting right in the middle of the habitable zone (Vogt et al. 2010; Tuomi 2011; Pepe et al. 2011; Gregory 2011). There is a growing consensus among the astronomers' community that the first habitable rocky planet will be discovered (and might have been discovered already!) around a red M dwarf in the backyard of our Solar System. However, not all physical properties of low-mass stars are known precisely enough for the purpose of the detection and characterization of small-radius planets. Worse still, some of the characteristics intrinsic to late-type dwarfs can constitute a significant source of confusion in the interpretation in planet detection and characterization measurements across a range of techniques. First of all, there exist discrepancies between theory and observations in the determination of the sizes of M dwarfs, typically on the order of 10\%-15\% (Ribas 2006; Beatty et al. 2007; Charbonneau et al. 2009, and references therein). It has been suggested that this problems might be stemming from the lack of a detailed treatment of the effects of non-zero magnetic fields on the properties of low-mass, fully convective stars (Ribas 2006; L\'opez-Morales 2007; Torres et al. 2010, and references therein). As a result, the inferred composition of a transiting planet detected around an M dwarf might be subject to rather large uncertainties, particularly when it comes to super-Earths, for which, as mentioned above, degeneracies in the models of their physical structure indicate a wide range of possible compositions for similar masses and radii (Seager \& Deming 2010, and references therein). Indeed, for the two known transiting planets around M dwarfs, GJ 436b and GJ 1214b, uncertainties in the planetary parameters are dominated by the limits in the knowledge of the stellar parameters. Second, there are at present difficulties in spectroscopically determining with a high degree of precision M dwarf metallicities\footnote{M-dwarf spectra are dominated by chemically complex molecular features. As a result, the identification of the continuum in an M dwarf spectrum is challenging, rendering line-based metallicity indicators unreliable. The poorly constrained molecular opacity data currently available make the determination of metallicity through spectral synthesis also difficult (e.g., Gustafsson 1989; West et al. 2011, and references therein).} (Bean et al. 2006; Woolf \& Wallerstein 2006; Woolf et al. 2009; Rojas-Ayala et al. 2010), which are only partially mitigated by recent attempts at deriving photometric calibrations (Bonfils et al. 2005; Casagrande et al. 2008; Johnson \& Apps 2009; Schlaufman \& Laughlin 2010). In addition, studies of the rotation-activity relation\footnote{The connection between stellar rotation and activity is usually investigated by means of 1) spectroscopic measurements of the rotational velocity $v\sin i$, usually coupled to measurements of the H$\alpha$ luminosity (e.g., Reiners \& Basri 2010, and references therein), 2) spectroscopic monitoring of temporal evolution of the $R^\prime_{HK}$ activity index as determined from the Ca II H \& K emission line cores (e.g., Wright et al. 2004), and 3) photometric determination of rotation periods for stars with significant spot coverage (e.g., Strassmeier et al. 2000).} for M dwarfs using large stellar samples are limited to young and active stellar samples (e.g., Shkolnik et al. 2009; L\'opez-Santiago et al. 2010, and references therein), often in young open clusters (e.g., Meibom et al. 2009; Hartman et al. 2009, and references therein), while our understanding of the rotation-activity connection for M dwarfs with age greater than $t\sim 0.5$ Gyr (e.g., Pizzolato et al. 2003; Reiners 2007; Jenkins et al. 2009; West \& Basri 2009) is still subject to rather large uncertainties due to the sparseness of the data. All these issues hamper at present the possibility of determining precisely the ages of (particularly mid- and late-) M dwarfs in the field, and this in turn has a significant impact on the calibration of the fundamental evolutionary properties of the planets they might be hosting. Third, as measurements of chromospheric activity indicators (H$\alpha$ line) have shown how the fraction of active M dwarfs increases as a function of spectral sub-type (e.g., Bochanski et al. 2005; West et al. 2011), activity-related phenomena such as stellar spots, plages, and flares become increasingly a matter of concern for planet detection and characterization programs targeting late-type stars. Stellar surface inhomogeneities can hamper the detection, and sometimes even mimic the signal, of exoplanets (e.g., Queloz et al. 2001), and seriously complicate the characterization of their properties. This problem has already become acute in the case of active solar analogs hosting transiting planets. An illustrative example is provided by the ongoing debate on the actual mass of CoRoT-7b, varying (including 1-$\sigma$ uncertainties as large as 20\%) between 1 $M_\oplus$ and 9 $M_\oplus$ (!), depending on how one decides to deal with the modelling of the planetary signal superposed to the much larger activity-induced stellar `jitter' in both the photometric and the radial-velocity measurements (Queloz et al. 2009; Hatzes et al. 2010; Pont et al. 2011; Ferraz-Mello et al. 2011). Recently, the first serious studies attempting to gauge the limits to planet detection induced by stellar activity-related phenomena, and strategies aiming at minimizing such effects, have been undertaken. These have focused primarily on the impact of, and possibility of calibrating out, activity-induced jitter in high-precision radial-velocity and astrometric measurements (Makarov et al. 2009; Lagrange et al. 2010; Boisse et al. 2011, and references therein; Dumusque et al. 2011; Sozzetti 2011, and references therein). Very recently, the first analyses of the impact of starspots on radial-velocity searches for earth-mass planets in orbit about M dwarf stars have been carried out by Reiners et al. (2010) and Barnes et al. (2011), who also addressed the merit of moving from the optical to infrared wavelengths (where the starpots-induced RV noise might be significantly reduced). All the above considerations clearly underline how achieving the goal of the detection {\it and} characterization of low-mass, potentially habitable, rocky planets around low-mass stars requires the construction of a large (all-sky) sample of nearby, relatively bright M dwarfs with well-characterized properties. This will necessitate the combined use of time-series of spectroscopic, astrometric, and photometric data of high quality. In particular, the jitter levels will have to be quantified in detail for each target individually, as the jitter properties may vary from star to star within the same spectral class, as suggested by recent findings based on high-precision Kepler photometry (e.g., Ciardi et al. 2011) and high-resolution, high-S/N spectroscopy (e.g., Zechmeister et al. 2009). With kick-off in December 2009, we have carried out a year-long pilot study for an upcoming photometric transiting search for small-size planets around thousands of nearby M dwarfs which will utilize an array of five 40-cm telescopes at the Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA), in the western Italian Alps. The OAVdA site was selected on the basis of a detailed site characterization study (Damasso et al. 2010). The pilot study was focused on the medium-term (typically for 2 months) photometric monitoring, using small-size instrumentation (25-80 cm class telescope systems), of a sample of $23$ cool M0-M6 dwarfs with good parallaxes from the TOrino Parallax Program (TOPP; Smart et al. 2010). The primary objectives we set out to achieve in this study were $a)$ to demonstrate sensitivity to $<4$ R$_\oplus$ (i.e., smaller than radius of Neptune) transiting planets with periods of a few days around our sample, through a two-fold approach that combines a characterization of the statistical noise properties of our photometry with the determination of transit detection probabilities via simulations, and $b)$ where possible, to better our knowledge of some astrophysical properties (e.g., activity, rotation, age) of our targets through a combination of spectroscopic and astrometric information and our differential photometric measurements. In \S~2 we describe the OAVdA instrumentation utilized during the pilot study, and outline the dedicated pipeline for the data processing and analysis of the photometric data we have developed. We discuss in \S~3 the main characteristics of the M dwarf sample targeted by the pilot study, and present in \S~4 the main results of the study in terms of 1) achieved short-term and medium-term photometric sensitivity for our sample, 2) improved characterization of the properties of the cool M dwarfs observed, by combining the knowledge of their photometric micro-variability time-scales with other available spectroscopic, photometric, and astrometric observations, and 3) a careful assessment of the limits to transiting planetary companions for each star in our sample. We conclude in \S~5 by summarizing our findings and by discussing the preparatory steps for the upcoming long-term photometric monitoring program to characterize the micro-variability features of and search for transiting small-size planetary companions to a well-defined sample of low-mass stars, to be carried at the OAVdA site in the near future.
|
We report results of a one-year long photometric monitoring campaign of a sample of 23 nearby ($d < 60$ pc), bright ($J < 12$) M dwarfs carried out in Italy at the Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA), using small-size ($<1$-m class) telescopes. This survey was conceived as a necessary preparatory step towards a long-term search for transiting, small-radius planets around thousands of dM stars, which will be conducted at OAVdA with an array of automated 40-cm telescopes, beginning early 2012. This `pilot study' was designed to achieve two goals: $1)$ demonstrate the sensitivity to $<4$ $R_\oplus$ transiting planets with periods of a few days around our program stars, through a two-fold approach that combines a characterization of the statistical noise properties of our photometry with the determination of transit detection probabilities via simulations, and b) where possible, improve our knowledge of some astrophysical properties (e.g., activity, rotation) of our targets through a combination of spectroscopic information and our differential photometric measurements. At a technical level, the results we obtained during the pilot study are instrumental to the accurate design and fine tuning of several aspects of our upcoming photometric survey, such as the definition of the best observational strategy, the optmization of the target list, and the identification of improvements to be carried out on the pipeline for the photometric data reduction and time-series periodicity analysis. Our main findings can be summarized as follows: $\bullet$ $\textit{Photometric precision}$. We achieve a typical nightly RMS photometric precision of $\sim5$ mmag, with little or no dependence on the instrumentation adopted or on the details of the methodology (different comparison stars selection criteria, use of different detrending algorithms) utilized to perform differential photometry on the targets. We also carried out an analysis of the impact of correlated (red) noise on time-scales of $\backsim$ 30 min, which showed that it is typically a factor $\backsim$ 1.3 greater than pure white noise, with a weak dependence on the method used to perform differential photometry. This result reveals that our data are only mildly affected by short-term correlated systematics. The estimated photometric precision degrades to $\sim9$ mmag when the ensemble light curves are determined over the typical $\sim2$ months duration of the observations for each target. Such degradation is understood in terms of a combination of unmodeled medium-term systematics in our data and intrinsic variability of our target stars. $\bullet$ $\textit{Stellar variability analysis}$. We searched for periodic transit-like events in the photometric dataset for each target using the BLS algorithm. No such signal was recovered for any target. This is an expected result given the sample size, thus meaningful constraints/upper limits on the planet fraction as a function of radius and orbital separation cannot be provided. The light curves of our program stars were inspected for evidence of periodic signals of approximately sinusoidal shape, which could be interpreted as due to the presence of rotating spots on the stellar photosphere. For two stars in our sample, LHS 3445 and GJ 1167A, we found clear evidence of a periodicity in the light curve ascribable to such effect. We determined photometric rotation periods of $\sim0.47$ days and $\sim0.22$ days for LHS 3445 and GJ 1167A, respectively; these estimates were confirmed by the large projected rotational velocities ($v\sin i \sim 25$ km/s and $v\sin i\sim 33$ km/s, respectively) inferred for both stars based on the analysis of archival high-resolution Keck/HIRES spectra. The estimated inclinations of the stellar rotation axes for LHS 3445 and GJ 1167A agree with those derived using a simple spot model, which successfully reproduces the observed sinusoidal photometric variations in both cases (the dispersion of the post-fit residuals is on the order of the sample photometric precision). Finally, we detected short-term, low-amplitude flaring events in the differential photometric measurements of LHS 3445 and LHS 2686 (the latter not known to be a flare star). LHS 3445 was observed flaring three times, and two flares were recorded almost consecutively during the same night, with an approximately equal decay time of $\backsim$ 4.5 min, possibly a case of homologous flares. $\bullet$ $\textit{Sensitivity to small-radius transiting planets}$. We carried out large-scale simulations of transit signals (of periods in the range $0.5-5$ days and depths in the range 0.5\%-2\% in flux units) injected in the actual (nightly reduced) photometric data for our sample. A total of 400,000 light curves were analysed for each target using a real-life transit events search algorithm (BLS). The study of the BLS transit recovery rates and overall performance for a sub-sample of stars with good, fair, and poor phase coverage highlighted the capability of BLS to identify the correct period (when multiple transits were observed) even for signals with depth close to the typical photometric precision of the data ($\sim5$ mmag), albeit with low statistical confidence, as well as some of its performance limitations which are driven by the specific choice of its most relevant setup parameters. We expressed our main findings in terms of two easy-to-use comparison metrics, i.e. transit detection probabilities and phase coverage. We found a quasi-linear relationship between the two quantities. Based on the BLS algorithm, there appears to be a limit of $\approx 90\%$ in the probability of detecting a transit even when the phase coverage approaches $100\%$. Around stars in our sample with good phase coverage ($> 50\%$), we would have had $> 80\%$ chances of detecting companions with $P < 1$ day and transit depths $>0.5\%$ in flux units. Correspondingly, around these stars we would have been sensitive to companions with radii as small as $\sim1.0-2.2$ $R_\oplus$. The main findings reported here provide useful information for the purpose of the design and implementation of the operations of a ground-based M dwarf transit survey, with the aim of maximizing the chances for small-radius planet detection and improving our understanding of several astrophysically interesting properties of M dwarfs, particularly when investigated by means of statistical analyses of large stellar samples. Together with other similar efforts carried out by other groups, such as the pioneering MEarth program, the photometric database populated by our survey data will be of great help, for example, a) to improve the characterization of nearby M dwarf stars, when combined with Gaia's exquisitely accurate astrometry (e.g., Sozzetti 2011), and b) to optimize the target selection criteria for red dwarfs which might be included in next-generation space-based transit survey programs, such as TESS (Ricker et al. 2010) and PLATO (Rauer \& Catala 2011) or which might be selected for spectroscopic characterization of planetary atmospheres of transiting planets found orbiting cool, nearby stars with future space-borne infrared observatories such as EChO (Tinetti et al. 2011) and FINESSE (Swain 2010). A forthcoming paper will present in detail all relevant aspects of the upcoming survey, including overall systems description, operations control software, target selection criteria, robust reduction pipeline and archiving.
| 12 | 6 |
1206.1729
|
1206
|
1206.3024_arXiv.txt
|
Formalisms for both non-relativistic as well as relativistic versions of field emission of electrons in presence of strong quantizing magnetic field, relevant for strongly magnetized neutron stars or magnetars are developed. In the non-relativistic scenario, where electrons obey Schr{$\ddot{\rm{o}}$}dinger equation, we have noticed that when Landau levels are populated for electrons in presence of strong quantizing magnetic field the transmission probability exactly vanishes unless the electrons are spin polarized in the opposite direction to the external magnetic field. On the other hand, the cold electron emission under the influence of strong electrostatic field at the poles is totally forbidden from the surface of those compact objects for which the surface magnetic field strength is $\gg 10^{15}$G (in the eventuality that they may exist). Whereas in the relativistic case, where the electrons obey Dirac equation, the presence of strong quantizing magnetic field completely forbids the emission of electrons from the surface of compact objects if $B >10^{13}$G.
|
There are mainly three kinds of electron emission processes from metal surface, they are: (i) thermionic emission, (ii) photoelectric emission and (iii) cold emission or field emission. The field emission or cold emission, which we have investigated in the present article in the context of strongly magnetized neutron stars or magnetars, is an electron emission process induced by strong external electrostatic field at zero or extremely low temperature. Field emission can happen from solid and liquid surfaces, or from individual atoms. It has been noticed that the field emission from metals occurs in presence of high electric field: the gradients are typically higher than 1000 volts per micron and the emission is strongly dependent upon the work function of the material. Unlike the thermionic emission and photo-emission of electrons, the field emission process can only be explained by quantum tunneling of electrons, which has no counter classical explanation. However, for general type surface barrier, this purely quantum mechanical problem can not be solved exactly, a semi-classical approximation, known as WKB (the name is an acronym for Wentzel-Kramers-Brilloun) is needed to get tunneling coefficients. Now to explain cold electron emission from metals, one may assume that because of quantum fluctuation, electrons from the sea of conduction electrons (degenerate electron gas) always try to tunnel out through the metallic surface (surface barrier). However, as soon as an electron comes out, it induces an image charge on the metal surface, which pulls it back and does not allow this emitted electron to move far away from metal surface in the atomic scale. But if some strong attractive electrostatic field is applied near the metallic surface, then depending on the Fermi energy of electrons, the height of the surface barrier and the local work function, the electrons may overcome the effect of image charge and get liberated. Since the external strong electric field is causing such emission and does not depend on the thermal properties of the metal, even the metal can be at zero temperature, it is called field emission or cold emission. The theory of field emission from bulk metals was first proposed by Fowler and Nordheim in an epoch making paper in the proceedings of Royal Society of London in the year 1928 \cite{FN1} (see also \cite{FN2,FN3,FN4,nano} for further discussion). Fowler-Nordheim tunneling is the wave-mechanical tunneling of electrons through a triangular type barrier produced at the surface of an electron conductor by applying a very high electric field. Now the cold emission or field emission processes not only have significance in the terrestrial laboratories, but is found to be equally important in the electron emission processes from cold and compact stellar objects, such as neutron stars. In the case of a rotating neutron star, the existing large magnetic field, $\geq 10^{12}$G \cite{ST} for the conventional radio pulsars or $\geq 10^{15}$G for the magnetars inner field \cite{mag}, produces a strong electric field at the poles, approximately given by $F\sim 2\times 10^8P^{-1}B_{12}$ Volt cm$^{-1}$ and is parallel to $\vec B$ at the poles \cite{ST}, here $P$ is the time period of the neutron star in second and $B_{12}$ is the measure of magnetic field strength in the units of $10^{12}$. At the proximity of polar region of a strongly magnetized neutron star, the potential difference changes almost linearly with distance from the polar cap, which is a region very close to the magnetic pole. The repulsive surface barrier in combination with this attractive potential, forms a triangular type barrier at the poles. Therefore if electron emission from the poles of neutron stars is field emission type, then Fowler-Nordheim equation with proper modification may be used to investigate such emission process. Now, the study of plasma formation in a pulsar magneto-sphere is a quite old but still an unresolved astrophysical issue, in particular the magneto-spheres of strongly magnetized neutron stars/magnetars \cite{VM1,VM2,YD}. In the formation of magneto-spheric plasma, it is generally assumed that there must be an initial high energy electron flux from the magnetized neutron stars. Since the magnetic field at the poles of neutron stars/magnetars are strong enough, the emitted electrons flow only along the magnetic field lines. The flow of high energy electrons along the direction of magnetic lines of forces and their penetration through the light cylinder is conventionally pictured with the current carrying conductors. Naturally, if the conductor is broken near the pulsar surface the entire potential difference will be developed across a thin gap, called polar gap. This is of course based on the assumption that above a critical height from the polar gap, because of high electrical conductivity of the plasma, the electric field $F$, parallel to the magnetic field near the poles is quenched. Further, a steady acceleration of electrons originating at the polar region of neutron stars, travelling along the field lines, will produce magnetically convertible curvature $\gamma$-rays. If these curvature $\gamma$-ray photons have energies $>2m_ec^2$ (with $m_e$ is the electron rest mass and $c$ is the velocity of light), then pairs of $e^--e^+$ will be produced in enormous amount with very high efficiency near the polar gap. These produced $e^--e^+$ pairs form what is known as the magneto-spheric plasma \cite{ST,R2,R3,R4,R6,R66,R7,R8}. The cold emission, therefore plays a significant role in magneto-spheric plasma formation. In turn, the motion of charged particles in the magnetosphere in presence of strong magnetic field causes pulsar emission in the form of synchrotron radiation. Therefore the cold emission process indirectly also affects the intensity of synchrotron radiation. Further the exactly solvable models with simple type tunneling barrier lead to equations \cite{FN1,FN2} that underestimates the emission current density by a factor of 1000 or more. If a more realistic type barrier model is used by inserting an exact surface potential in the simplest form of the Schr${\ddot{\rm{o}}}$dinger equation, then a complicated mathematical problem arises over the resulting differential equation. It is in principle therefore mathematically impossible to solve the equation exactly in terms of the usual functions of mathematical physics, or in any simple way. Moreover, to the best of our knowledge, neither the non-relativistic nor the relativistic version of cold emission processes in presence of strong quantizing magnetic field, relevant for electron emission from the poles of strongly magnetized neutron stars/magnetars, even with simple type potential barriers have been properly investigated. In the conventional pulsar model it is generally assumed that the emission of electrons and thereby formation of magnetosphere is mainly caused by strong electric field at the polar region which is produced by the strong magnetic field of rotating neutron stars. Taking this physical picture into consideration, in this article, we have developed formalisms for both non-relativistic and relativistic scenarios of field emissions for electrons from the poles of neutron stars with $10^{10}{\rm{G}}\leq B \leq 10^{17}$G. In the next section we have studied the effect of strong quantizing magnetic field on the field emission of electrons for the non-relativistic case. In section-3, we have repeated the same calculation for the relativistic scenario. In the last section we have given the conclusions and future prospects of this work.
|
The non-relativistic scenario of cold electron emission in presence of strong magnetic field is believed to be the first attempt in this direction. While obtaining the electron transmission probability in the non-relativistic scenario under the influence of strong electric field at the poles, we have noticed that in our theoretical formalism, the emission is allowed if we take electron spin into account and also the electrons have conventional spin polarization, i.e., opposite to the direction of external magnetic field. Even if all these criteria are satisfied, at extremely high magnetic field strength since the electron work function becomes large enough, the transmission coefficient drops to zero. Since there are no such stellar objects with surface magnetic field strength $\gg 10^{15}$G, the vanishingly small transmission coefficients will therefore not be possible in reality. The low charge density magneto-sphere will therefore only be possible if such super exotic compact stellar objects with ultra-strong surface magnetic field exist in nature. In the conventional magnetar or strongly magnetized neutron star case, the electron field current is quite high, very close to the peak value, which is also obvious from the figure. As a result there will be enough curvature gamma photons produced by the energetic electrons, which in turn produce enormous amount of $e^--e^+$ pairs to form normal magneto-spheric plasma. In our model the only difference from non-magnetic or low magnetic emission case is that the primary electrons are spin polarized in the direction opposite to the direction of external magnetic field. As a consequence, for the conventional magnetar case, the results obtain in \cite{APJ} on the formation of corona of magnetars will not be seriously affected. Therefore, in the magnetar magnetosphere of a neutron star with $B \leq 10^{15}$G, the primary electrons are all spin polarized along $-\vec B$. Since the electron emission current is almost zero for the objects with ultra-high magnetic field strength ($\gg 10^{15}$G), then if the electron emission process in such exotic objects is dominated by cold emission, the charge density of $e^--e^+$-plasma in the magnetosphere will be extremely low. As a consequence there will be very weak synchrotron emission in the radio wave band. The other possible mechanism by which $e^--e^+$-plasma can be produced in the magnetosphere of magnetars are (i) thermoelectric emission of electrons from the polar region and (ii) photo emission from the same region. However the work function at the polar region of a typical magnetar is several GeV, whereas the temperature can be at most a few hundred MeV for an young magnetar. The thermionic emission will therefore be suppressed by the Boltzmann factor $\exp(-w_f/kT)$. Whereas in the case of photo emission, the energy of the induced photon must be of GeV order ($\gamma$-photons). At the polar region, if any such photons exist to liberate electrons, they must have produced as curvature photons by high energy electrons moving along the magnetic lines of forces. Since the possibility of such electrons is very rare, the number of high frequency photon is also vanishingly small, as a result there will be almost no creation of secondary $e^--e^+$-pairs in the photo emission process. In conclusions, from our relativistic formalism of cold emission of electrons we can state that relativistic electrons populating the neutron star interior can not be extracted from cold emission from the poles of a neutron star, independently from the magnetic field strength. Non-relativistic electrons with anti-parallel spin can be extracted for standard (observed) values of magnetic field strengths, but can not be extracted from the surface of objects with $B\gg 10^{15}$G (in the eventuality that such exotic objects can exist).
| 12 | 6 |
1206.3024
|
1206
|
1206.1021_arXiv.txt
|
{ Within the next few years, several instruments aiming at imaging extrasolar planets will see first light. In parallel, low mass planets are being searched around red dwarfs which offer more favorable conditions, both for radial velocity detection and transit studies, than solar-type stars. We review recent advancements in modeling the stellar to substellar transition. The revised solar oxygen abundances and cloud models allow to reproduce the photometric and spectroscopic properties of this transition to a degree never achieved before, but problems remain in the important M-L transition characteristic of the \teff\ range of characterisable exoplanets.
|
Since spectroscopic observations of very low mass stars (late 80s), brown dwarfs (mid 90s), and extrasolar planets (mid 2000s) are available, one of the most important challenges in modeling their atmospheres and spectroscopic properties lies in high temperature molecular opacities and cloud formation. K dwarfs show the onset of formation metal hydrides (starting around \teff\ $\sim 4500$\,K), TiO and CO (below \teff\ $\sim 4000$\,K), while water vapor forms in early M dwarfs (\teff\ $\sim 3900-2000$\,K), and methane, ammonia and carbon dioxide are detected in late-type brown dwarfs (\teff\ $\sim 300-1600$\,K) and in extrasolar giant planets. Cloud formation is also an important factor in the detectability of biosignatures, and for the habitability of exoplanets \citep[Kasting 2001]{Paillet2005}\nocite{Kasting2001}. Extrasolar planets for which we can currently characterize their atmospheres are either those observed by transit (\teff\ $\sim 1000-2000$\,K depending on their radius relative to that of the central star) or by imaging (young planets of \teff\ $\sim 500-2000$\,K depending on their mass and age). Several infrared integral field spectrographs combined with coronagraph and adaptive optic instruments are coming online before 2013 (SPHERE at the VLT, the Gemini Planet Imager at Gemini south, Project1640 at Mount Palomar, etc.). The E-ELT 41\,m telescope in Spain due around 2020 will also be ideally suited for planet imaging. M dwarfs are the most numerous stars, constituting 80\% of the stellar budget of the Galaxy, and around 600 brown dwarfs and planets are currently known despite their faintness in the solar neighborhood vicinity. Single very low mass (VLM) stars and brown dwarfs are therefore more directly observable and characterizable then exoplanets. They represent, beyond their own importance, a wonderful testbed for the understanding of exo-planetary atmospheric properties together with solar system studies. Planets can even share the atmospheric composition of brown dwarfs of same \teff\ (see section \ref{s:Comp} below). The models developed for VLMs and brown dwarfs are therefore a unique tool, if they can explain the stellar-substellar transition, for the characterization of imaged exoplanets. In this paper, we review the ability of recently published models in reproducing constraints along the M-L-T spectral transition. \vspace{-2.6cm}
|
We have compared the behavior of the recently published model atmospheres from various authors across the M-L-T spectral transition from M dwarfs through L type and T type brown dwarfs and confronted them to constraints. If the onset of dust formation is occurring below \teff\ = 2900\,K, the greenhouse or line blanketing effects of dust cloud formation impact strongly ($J-K_s < 2.0$) the near-infrared SED of late-M and L-type atmospheres with $1300 <$ \teff\ $< 2600$\,K. The BT-Settl models by Allard et al. (2012)\nocite{Allard2012} are the only models to span the entire regime. In the M dwarf range, the results appear to favor the BT-Settl based on the \cite{Asplund09} solar abundances versus MARCS and ATLAS 9 models based on other values. In the brown dwarf (and planetary) regime, on the other hand, the unified cloud model by \cite{tsuji02} succeeds extremely well in reproducing the constraints, while the BT-Settl models also show a plausible transition. However, no models succeed in reproducing the M-L transition between 2900 and 2000\,K. This \teff\ range is similar to that of young (directly observable by imaging) and strongly irradiated planets (Hot Jupiters).
| 12 | 6 |
1206.1021
|
1206
|
1206.5091_arXiv.txt
|
{Through an optical campaign performed at 4 telescopes located in the northern and the southern hemispheres, plus archival data from two on-line sky surveys, we have obtained optical spectroscopy for 29 counterparts of unclassified or poorly studied hard X-ray emitting objects detected with {\it Swift}/BAT and listed in the 39 months Palermo catalogue. All these objects have also observations taken with {\it Swift}/XRT or {\it XMM}-EPIC which not only allow us to pinpoint their optical counterpart, but also to study their X-ray spectral properties (column density, power law photon index and F$_{2-10}$ keV flux). We find that 28 sources in our sample are AGN; 7 are classified as type 1 while 21 are of type 2; the remaining object is a galactic cataclysmic variable. Among our type 1 AGN, we find 5 objects of intermediate Seyfert type (1.2-1.9) and one Narrow Line Seyfert 1 galaxy; for 4 out of 7 sources, we have been able to estimate the central black hole mass. Three of the type 2 AGN of our sample display optical features typical of the LINER class and one is a likely Compton thick AGN. All galaxies classified in this work are relatively nearby objects since their redshifts lie in the range 0.008-0.075; the only galactic object found lies at an estimated distance of 90 pc. We have also investigated the optical versus X-ray emission ratio of the galaxies of our sample to test the AGN unified model. For them, we have also compared the X-ray absorption (due to gas) with the optical reddening (due to dust): we find that for most of our sources, specifically those of type 1.9-2.0 the former is higher than the latter confirming early results by Maiolino et al. (2001); this is possibly due to the properties of dust in the circumnuclear obscuring torus of the AGN. }%
|
A critically important region of the astrophysical spectrum is the hard X-ray band, from 15 to 200 keV, which is being recently explored in detail by two satellites, {\it INTEGRAL} (Winkler et al. 2003) and {\it Swift} (Gehrels et al. 2004) which carry instruments like IBIS (Ubertini et al. 2003) and BAT (Barthelmy 2004) operating in the 20-200 keV band. These spacecrafts permit a study of the processes taking place in this observational window providing a deep look into the physics of hard X-ray sources. These telescopes operate in a complementary way, as the first concentrates on mapping the galactic plane, while the second mainly covers the high galactic latitude sky, so that together they provide the best sample of objects yet selected in the hard X-ray domain. So far, both instruments have detected a large number of known and new objects, discovered new classes of sources and allowed finding and studying highly absorbed objects. In particular, the nature of many of the objects detected above 20 keV by both satellites is often unknown, the sources are optically unclassified and their types can only be speculated on the basis of few available X-ray or radio observations. Optical follow up of these sources is therefore mandatory. Specifically, the optical spectra can provide not only an accurate source classification, but also fundamental parameters which together with multiwaveband studies, for example in the soft X-ray band, can provide information on these newly detected objects. In this paper we focus on the X-ray and optical follow up work on a number of objects with unknown classification and/or redshift, reported in the 39 months Swift/BAT survey catalogue (Cusumano et al. 2010a). We note that the identifications of the present paper are also reported in the Palermo 54 months catalogue (Cusumano et al. 2010b) with preliminary classifications given by us via private communications. Our aim is indeed to perform a systematic study of unidentified {\it Swift}/BAT objects starting with the 39 months surveys and continuing with the identifications of those of the 54 months catalogue (Parisi et al. in preparation). This survey covers 90\% of the sky down to a flux limit of 2.5 $\times$ 10$^{-11}$ erg cm$^{-2}$ s$^{-1}$ and 50\% of the sky down to a flux limit of 1.8 $\times$ 10$^{-11}$ erg cm$^{-2}$ s$^{-1}$ in the 14-150 keV band. It lists 754 sources, of which 69\% are extragalactic, 27\% are galactic, and 4\% are of unknown type. Within this BAT survey, we have selected a sample of 29 objects either without optical identification, or not well studied, or without published optical spectra. For all these sources we first performed the X-ray data analysis to reduce the source positional uncertainty from arcmin to arcsec-sized radii and derive information on the main spectral parameters (photon index, column density and 2-10 keV flux). Then, within the reduced X-ray error boxes, we identified the putative optical counterpart to the BAT object and performed optical spectroscopic follow up work. Following the method applied by Masetti et al. (2004, 2006a,b, 2008, 2009, 2010, 2012) and Parisi et al. (2009) we determined the nature of all selected objects and discussed their properties. A preliminary classification of these sources is given in the Palermo 54 months BAT catalogue (Cusumano et al. 2010b), while here we publish for the first time the optical spectra and detailed optical information (see Tab. \ref{cvo}, \ref{agn1} and \ref{agn2}). We also checked for the presence of peculiar sources, such as Compton thick AGN, absorbed Seyfert 1 and unabsorbed Seyfert 2, using the diagnostic method of Malizia et al. (2007), and finally we used the plot of Maiolino et al. (2001) to verify a possible mismatch between the X-ray gas absorption and the optical dust reddening. The paper is structured as follow: in Sect. 2 we report information on the soft X-ray data analysis; in Sect. 3 we give a description of the optical observations, the telescope employed, and provide information on the data reduction method used. Sect. 4 reports and discusses the main optical results (line fluxes, distances, galactic and local extinction, central black hole masses etc.). In Sect. 5 the X-ray and the optical results are compared in view of the object classification and gas versus dust absorption. In Sect. 6, we summarize the main conclusions of our work.
|
In this work, we have either given for the first time, or confirmed, or corrected, the optical spectroscopic identification of 29 sources belonging to the Palermo 39 months {\it Swift}/BAT catalogue (Cusumano et al. 2010a). This was achieved through a multisite observational campaign in Europe, South Africa and Central America. We found that our sample is composed of 28 AGN (7 of type 1 and 21 of type 2), with redshifts between 0.008 and 0.075, and 1 CV. Among the extragalactic sources we found some peculiar objects, such as 3 AGN showing LINER features and 1 with the properties of NLS1. For four type 1 AGN we have estimated the BLR size, velocity and the central black hole mass. We have also performed an X-ray spectral analysis of the entire sample and found that overall our sources display X-ray spectra typical of their optical class. More specifically, we have compared the optical versus X-ray classification of our galaxies, in order to test the AGN unified theory. We find a generally good match between optical class and X-ray absorption, thus providing evidence for the validity of the unified scheme. However, in a few sources there is a clear discrepancy between optical and X-ray classification: PBC J0543.6-2738 is a Seyfert 1.2 displaying mild X-ray absorption, possibly due to outflowing gas; PBC J1345.4+4141 is instead a Seyfert 1.9 showing no absorption although its optical class may be related to reddening occurring on large scale structures or due to a low optical ionization state. More convincingly outside the unified scheme is PBC J2333.9-2343 which is a Seyfert 2 without intrinsic X-ray column density; this source has many features which make it very similar to broad line blazars and yet has only narrow lines in its optical spectrum. Another Seyfert 2 displaying no absorption is PBC J2148.2$-$3455, but through the use of our diagnostic diagram and information gathered in the literature we conclude that this source is a Compton thick or heavily absorbed AGN, which is therefore compatible with its optical class. We also compared the X-ray gas absorption with the optical dust reddening for the AGN sample: we find that for most of our sources, specifically those of type 1.9-2, the former is higher than the latter, confirming early results by Maiolino et al. (2001); possibly this is due to the properties of dust in the circumnuclear obscuring torus of the AGN. As a final remark, we would like to stress the importance of combining optical with X-ray spectroscopy for hard X-ray selected objects: using information in both wavebands is not only possible to increase the number of source identification and classification, but also to perform statistically significant population studies, to understand the physical processes that occurring in these objects and to study the AGN unified model.
| 12 | 6 |
1206.5091
|
1206
|
1206.5058_arXiv.txt
|
{Presently only 30\% of short gamma ray bursts (SGRBs) have accurate redshifts, and this sample is highly biased by the limited sensitivity of {\it Swift} to detect SGRBs. We account for the dominant biases to calculate a realistic SGRB rate density out to $z = 0.5$ using the {\it Swift} sample of peak fluxes, redshifts, and those SGRBs with a beaming angle constraint from X-ray/optical observations. Assuming a significant fraction of binary neutron star mergers produce SGRBs, we calculate lower and upper detection rate limits of (1-180) per Yr by an advanced LIGO and Virgo coincidence search. Our detection rate is compatible with extrapolations using Galactic pulsar observations and population synthesis. } \FullConference{Gamma-Ray Bursts 2012 Conference -GRB2012,\\ May 07-11, 2012\\ Munich, Germany} \begin{document}
|
Binary neutron star mergers (NS-NS) are favoured as the progenitors for short gamma ray bursts (SGRBs), based on the association of some SGRBs with an older stellar population, and host galaxy types \cite{2005ApJ...630L.165L,2007ApJ...665.1220Z}. Kicks imparted to NSs at birth will produce velocities of several hundred km s$^{-1}$, implying that binary inspiraling systems may occur far from their site of origin. Fong, Berger \& Fox \cite{2010ApJ...708....9F} using Hubble Space Telescope observations to measure SGRB-galaxy offsets, find the offset distribution compares favourably with the predicted distribution for NS-NS binaries. Within 5 years, co-ordinated gamma-ray, X-ray, optical and gravitational-wave observations may allow the strong gravity regime of the central engine of compact object mergers to be probed. Such `multi-messenger' observations provide the opportunity to probe these events across a vast energy spectrum, and to constrain the progenitor populations of SGRBs. Furthermore, co-ordinated optical and gravitational-wave searches may play an important role in confirming the first direct gravitational-wave observations of compact object mergers \cite{2011MNRAS.415L..26C}. It is becoming increasingly important to constrain the rate of compact object mergers and their proposed optical counterparts in the context of up-coming gravitational-wave searches. We calculate a beaming-corrected SGRB rate density using the {\it Swift} sample of SGRB peak fluxes, redshifts and inferred beaming angles from X-ray observations. For our GRB selection criteria we use the Jochen Greiner catalogue of localized GRBs (see Table 1) and select bursts indicated as short that have reliable redshifts up to 2012 April. We avoid using a SGRB luminosity function, models for progenitor rate evolution, and a beaming angle distribution, all of which have large uncertainties. Instead, we focus on observed and measured parameters that take into account selection effects that modify {\it Swift}'{\it s} detection sensitivity to SGRBs. Finally, we use our SGRB rate density estimates to infer a detection rate of binary NS mergers by advanced LIGO (aLIGO) and Virgo (AdV) interferometers. Despite the poor statistics, this approach gives meaningful results and can be followed up when a larger sample of SGRB observations becomes available.
| 12 | 6 |
1206.5058
|
|
1206
|
1206.2164_arXiv.txt
|
We investigate the possibility that a heavy scalar field, whose mass exceeds the Hubble scale during inflation, could leave non-negligible signatures in the Cosmic Microwave Background (CMB) temperature anisotropy power spectrum through the parametric resonance between its background oscillations and the inflaton fluctuations. By assuming the heavy scalar field couples with the inflaton derivatively, we show that the resonance can be efficient without spoiling the slow-roll inflation. The primordial power spectrum modulated by the resonance has a sharp peak at a specific scale and could be an origin of the anomalies observed in the angular power spectrum of the CMB. In some values of parameters, the modulated spectrum can fit the observed data better than the simple power-law power spectrum, though the resultant improvement of the fit is not large enough and hence other observations such as non-Gaussianity are necessary to confirm that the CMB anomalies are originated from the resonant effect of the heavy scalar field. The resonant signatures can provide an opportunity to observe heavy degrees of freedom during inflation and improve our understanding of physics behind inflation.
|
\label{s:intro} Cosmic inflation is the standard paradigm that provides the initial conditions for structure formation and the anisotropies in cosmic microwave background (CMB) as well as the global properties of the spacetime \cite{Starobinsky:1980te, Sato:1980yn, Guth:1980zm}. In the inflationary scenario, the accelerated expansion stretches quantum fluctuations on microscopic scales to cosmological scales, providing the seed for macroscopic observables as the anisotropies in the CMB. The wavelengths of the fluctuations are extremely short in the earliest epoch. Thus the cosmological observations provide a window into short-distance physics which is beyond the reach of terrestrial experiments. The cosmological fluctuations, which have been generated quantum mechanically, are statistical in nature. In the simplest single-field slow-roll inflation models, they are approximately Gaussian-distributed and their power spectrum is nearly scale-invariant. Then we usually characterize them over the observable range of scales in terms of a power-law-type power spectrum, which is parametrized simply by two or three parameters: the amplitude, the spectral index, and the running. Though the two- (or three-) parameter spectrum consistently explains the observed CMB anisotropies \cite{Komatsu:2010fb}, it could miss valuable information on physics behind inflation. Recent high-resolution CMB data already implies the presence of fine features in the primordial power spectrum. Indeed, several groups, including one of the present authors (JY), reported statistically significant discrepancy between the prediction from a power-law primordial power spectrum and the CMB data \cite{TocchiniValentini:2005ja, Nagata:2008tk}. Using non-parametric reconstruction methods, they have found large anomalies in the reconstructed power spectrum, which are localized around wavenumbers $k \simeq 0.003~\mr{Mpc}^{-1}$ and $k \simeq 0.009~\mr{Mpc}^{-1}$. On the other hand, a number of effects that cause deviations from a power-law power spectrum have been investigated in literatures, including trans-Planckian effects \cite{Martin:2000xs, Danielsson:2002kx,Schalm:2004qk}, a burst of particle production \cite{Romano:2008rr, Barnaby:2009dd}, temporal violation of slow-roll approximation \cite{Leach:2000yw, Saito:2008em, Starobinsky:1992ts, Adams:2001vc, Kaloper:2003nv, Battefeld:2010rf}, turns in the inflationary trajectory \cite{Burgess:2002ub, Achucarro:2010da, Shiu:2011qw}, a sharp water field transition \cite{Abolhasani:2012px}, and a sudden change of sound velocity \cite{Nakashima:2010sa}. They modify evolution of the inflaton fluctuations in their own way and leave their characteristic signatures on the primordial power spectrum. Thus fine features in the power spectrum could contain rich information such as detailed structures of inflaton Lagrangian or existence of other degrees of freedom. In this paper, we consider an effect of coherent oscillations of a heavy scalar field whose mass exceeds the Hubble scale, $m \gg H$. Heavy scalar fields are ubiquitous in models of inflation embedded in supergravity and string theory. They appear as moduli fields, Kaluza-Klein modes, the scalar supersymmetric partner of inflaton, or others. In usual treatment, the dynamics of a heavy scalar field is neglected assuming that it is stuck to their potential minima during inflation because its excitation decays quickly \cite{Yamaguchi:2005qm}. The instantaneously-excited oscillations, however, can be important when we measure the primordial power spectrum with high resolution. An impact of the excitation has already been discussed in Ref. \cite{Burgess:2002ub} for a hybrid-inflation model. More recently, Refs. \cite{Shiu:2011qw, Cespedes:2012hu, Gao:2012} have discussed that oscillations excited by a sharp turn in multi-dimensional potential leave a ringing signature in the primordial power spectrum. In both cases, the signatures arise because the evolution of the fluctuations becomes non-adiabatic \cite{Martin:2000xs} by a sudden energy transfer between the inflaton and a heavy scalar field through their couplings in the potential. In addition, it has been discussed in Ref. \cite{Chen:2011zf} that a ringing feature in the power spectrum is induced through the gravitational couplings without considering direct couplings between inflaton and a heavy scalar field. In this paper, instead, we point out that a resonant enhancement of the fluctuations efficiently occurs deep in the horizon, $k/a \sim m \gg H$, through derivative couplings with a heavy scalar field. The derivative couplings are allowed even if a shift symmetry is imposed to ensure the flatness of the inflaton potential. Then there is no reason why they are absent in the action from the effective-field-theory point of view \cite{Weinberg:2008hq, Khosravi:2012qg}. Though the derivative couplings are usually irrelevant at low energy scale, they can play an important role on the evolution of the inflaton fluctuations in the resonance epoch. This is because the inflaton fluctuations and the heavy scalar field rapidly oscillate in the resonance epoch. Hence, effects of the derivative couplings on the evolution of the inflaton fluctuations are large there while their effects on the background evolution is relatively small because the derivative of the background inflaton field is slow-roll suppressed. In the following sections, we estimate the enhancement of the primordial power spectrum by the resonance assuming non-derivative couplings are sufficiently suppressed. In contrast to other effects as the slow-roll violation \cite{Kumazaki:2011eb}, the feature induced by the resonance can be sharp and large even in the case that adiabaticity is mildly violated because the resonance coherently accumulates small effects. The instantaneously excited oscillations do not affect the slow-roll background evolution much in this case unless the heavy scalar field dominates the energy density because the flatness of the inflaton potential is ensured even during the oscillations. The organization of this paper is as follows. In \S \ref{s:model}, we present our model to realize an efficient enhancement of the fluctuations and discuss conditions on the model required for the slow-roll inflation. In \S \ref{s:amp}, we estimate the enhancement of the fluctuations by the parametric resonance and discuss consistency of our model with the anomalies observed in the CMB spectrum. Finally, we provide our summary of this paper in \S \ref{s:summary}.
|
\label{s:summary} In this paper, we have discussed the possibility that a heavy scalar field, whose mass exceeds the Hubble scale, $m \gg H$, could leave non-negligible signatures in the CMB spectrum through parametric resonance between its background oscillations and the inflaton fluctuations. The resonance could be efficient without spoiling the slow-roll inflation if the heavy scalar field couples with the inflaton derivatively; the feature induced by the resonance can be sharp and large even in the case that adiabaticity is only mildly violated because the resonance coherently accumulates small effects. In the analysis, we have assumed that the oscillations of the heavy scalar field are instantaneously excited at e-folds $N_p \simeq \ln(m/H)+N_{\ast}$, where $N_{\ast}$ is the number of e-folds from the end of inflation when the peak modes crossed the horizon. This assumption will be appropriate if inflation begins at the e-folds $N_p$ and the heavy scalar field is initially displaced from its minimum, which is natural in the cases that the minima differ before and during inflation, or inflation occurs after a tunneling from a neighboring minimum \cite{Bucher:1994gb,Sasaki:1994yt,Freivogel:2005vv,Yamauchi:2011qq,Sugimura:2011tk}, for example. As another possibility, the oscillations could be dynamically excited when the heavy scalar field becomes momentarily light/tachyonic or the slow-roll condition is temporary violated. In the latter case, effects of the slow-roll violation on the resonance should be taken into account to consider large excitations of the heavy scalar field \cite{Avgoustidis:2012yc}. We will address this issue using a specific model in another paper. We have also estimated the goodness-of-fit of our model with the anomalies observed in the CMB spectrum. The resultant improvement of the fit has not been large enough to confirm that the CMB anomalies are originated from the resonance, though a systematic analysis has not been performed for technical difficulties. To test our model further from observations, non-Gaussianity in the CMB anisotropies will be helpful. Since oscillatory components are induced in the interactions, the higher-point correlation functions are also enhanced at specific scales by the resonance \cite{Chen:2008wn, Flauger:2010ja, Chen:2010bka, Behbahani:2011it}. We will estimate the amplitude and the shape of this non-Gaussianity in an upcoming paper.
| 12 | 6 |
1206.2164
|
1206
|
1206.5744_arXiv.txt
|
We present a model for the non-thermal emission from the historical supernova remnant SN 1006. We constrain the synchrotron parameters of the model with archival radio and hard X-ray data. Our stationary emission model includes two populations of electrons, which is justified by multi-frequency images of the object. From the set of parameters that predict the correct synchrotron flux we select those which are able to account, either partly or entirely, for the gamma-ray emission of the source as seen by HESS. We use the results from this model as well as the latest constraints imposed by the \emph{Fermi} observatory and conclude that the TeV emission cannot be accounted for by $\pi^0$ decay from high-energy ions with a single power-law distribution, of the form $dN_{\mbox{\tiny proton}}/dE_p \propto E_p^{-s}$, and $s\gtrsim2$.
|
Supernova remnants (SNRs) are thought to be the main source of galactic cosmic rays, high-energy ($E_p\lesssim 10^{15}$ eV) particles (mostly protons) that populate the galaxy, and whose distribution is a power-law. SNRs are energetically favorable and the Fermi mechanism is the natural process by which these objects are able to inject part of their energy into charged particles \citep{bel78,bla87}. Such diffusive shock acceleration (DSA) could account for the observed shape of the cosmic ray distribution. A direct detection of high-energy protons and nuclei at the sources is hard to obtain, however, and the preferable mechanism to accomplish this task is the detection of MeV--TeV $\gamma$-ray emission from the decay of neutral pions resulting from inelastic collisions between high-energy ions and ambient ions (the so-called hadronic $\gamma$-ray emission). This hadronic signal then has to be separated from (mostly MeV) radiation from the galactic background as well as from (MeV--TeV) radiation from high-energy electrons in SNRs (the so-called leptonic $\gamma$-ray emission). High-energy electrons were first detected in SNRs through their non-thermal radio spectrum. This radiation is produced when accelerated electrons move in the presence of magnetic fields, which result either from shock compression of the interstellar field or from amplification by cosmic ray instabilities \citep[see][for a recent review]{schure2012}. These electrons typically have energies in the GeV range. The presence of TeV electrons in young SNRs has been confirmed by X-ray observations. High-resolution observations of young SNRs (e.g., taken by the \emph{Chandra} X-Ray Observatory) show synchrotron emission associated with the forward shock \citep[e.g.,][]{got01,ber02,hwa02,rho02,lon03,vink03,ber04,araya2010}. The $\gamma$-ray leptonic emission results from inverse-Compton (IC) up-scattering of background photon fields by the synchrotron-emitting electrons and from bremsstrahlung emission from collisions between these electrons and ambient plasma. Leptonic and hadronic high-energy emission could in principle be distinguished based on their relative flux normalization as well as the intrinsic differences in their spectra. However, due to the limited knowledge on the physical parameters of some SNRs, the model degeneracy and limited observations, the identification of hadronic signatures in their non-thermal spectra can be quite challenging. Spectral energy distributions (SEDs) of SNRs interacting with molecular clouds (which are typically old, with an age $> 10^3$ years), such as W28, W41, W49B, W51C, IC 443, G8.7-0.1 and G359.1-0.5, seem to favor a hadronic origin for the emission \citep{abdo2010b,mehault2011,abdo2010c,abdo2009,abdo2010a,ajello2012,hui2011}, while other recent studies show that the SEDs of some young SNRs with a hard GeV spectrum are probably leptonic-dominated, such as RX J1713.7-3946 \citep{abdo2011a} and RX J0852.0-4622 \citep{tanaka2011}, and have spectral slopes at GeV energies that are consistent with the corresponding IC spectra expected from synchrotron-emitting electrons. Other young objects, such as the famous historical SNRs Cassiopeia A \citep{arayacui2010,abdo2010d} and Tycho's SNR \citep{mythesis2011} show a soft GeV spectrum which, it might be argued, favors the hadronic scenario \citep[see][however, for an alternative explanation for the emission from Tycho's SNR]{atoyan2011}. Recently, an attempt to unify the properties of $\gamma$-ray emitting SNRs showed that as the density of the environment of the SNR increases, so does the brightness of the hadronic component \citep{yuan2012}. Regardless of the nature of the high-energy photon emission, it seems clear that the spectral shape below and around hundreds of MeVs is fundamental for its identification. The recently-launched \emph{Fermi} satellite \citep{atw09} has allowed probing this region of the spectrum, although the increasing PSF of its Large Area Telescope (LAT) at these energies and the high galactic background levels may complicate the analysis for some sources. Here we present a model for the non-thermal emission from SN 1006, the remnant of a type Ia supernova reported by Chinese and Arab astronomers in 1006 \citep{stephenson2002}. The SNR is located far from the galactic center (galactic latitude $\sim 14.5\,^{\circ}$), in a ``clean'' environment with low density \citep[$\sim 0.085$ cm$^{-3}$, see][]{katsuda2009}, at an estimated distance of 2.2 kpc from Earth \citep{winkler2003}. We adopt these values here and develop a two-zone leptonic model to find the sets of reasonable parameters that account for the synchrotron emission observed and are also consistent with the $\gamma$-ray flux as seen by the H.E.S.S. atmospheric Cherenkov telescopes \citep{acero2010}. As fundamental part of the data used, we included the latest constraints on GeV observations of the source, obtained through analysis of 3.5 years of \emph{Fermi} LAT data. Although the analysis shows that the source is not yet significantly detected at GeV energies, the established upper limit for the emission is used to constrain the SED models. The results of our simplified model indicate that the TeV flux can only be accounted for by leptonic emission from high-energy electrons in a relatively low ($\sim 30\,\mu$G) magnetic field, hadronic emission from a hard power-law particle distribution, or by a mixed leptonic-hadronic scenario. In the later cases, hadronic emission from ions with a soft power-law distribution with index higher than 2 can be ruled out as the main cause of TeV photons.
|
From the simple model presented here, we can conclude that if a value for the magnetic field in Zone 2 is used which would reproduces the widths of X-ray filaments near the forward shock of SN 1006 ($\sim 80\,\mu$G), then a leptonic scenario for the $\gamma$-ray emission implies that high-energy photons should originate mainly from radio-emitting electrons in Zone 1. In this scenario, the required electron spectrum is described by a broken power-law with indices 2.14 (as required by the radio data) and 2.8, and a break around a particle energy of 360 GeV, as required by the H.E.S.S. observations. For a lower magnetic field in Zone 2 ($20 - 30\,\mu$G), the level of the observed $\gamma$-ray flux can be attributed mainly to this Zone. We cannot rule out either scenario with our current knowledge of the magnetic field. The shape of the TeV spectrum in our model could be improved with a combination of such relatively low magnetic field values in both Zones. The more interesting result obtained from our analysis of the observations is related to the constraints imposed by cumulative observations from the \emph{Fermi} LAT, which allow us to conclude that the TeV emission from SN 1006 cannot be produced by $\pi^0$ decay from a hadronic population with a ``soft'' power-law distribution (i.e., with an index $\sim 2.0$ or higher), such as the ones typically used in similar phenomenological models of broad-band SEDs of SNRs \citep[e.g.,][]{arayacui2010,abdo2010a,abdo2010c,abdo2010e,mythesis2011,giordano2012}, but they are consistent with a mixed leptonic-hadronic (or leptonic-dominated) model for the case where the index of the high-energy ion component is around 2, or with a pure leptonic model for softer cosmic ray distributions, as is seen in Figs. \ref{fig2} and \ref{fig3}. Of course, the steeper the hadronic distribution, the lower its contribution to the TeV $\gamma$-ray flux should be. We cannot rule out a hard hadronic radiation spectrum (i.e., with a particle index below $2$). It is important to stress the fact that our model only rules out hadronic distributions that are single steep power-laws at all energies as the main cause of the TeV emission from the source, and which differ from the ones predicted by some nonlinear models with efficient acceleration \citep[e.g.,][]{chevalier1983,malkov1999,blondin2001} which show spectral hardening at high energies. However, such proton distributions are not seen in other high-efficiency acceleration models \citep[e.g.,][]{ellison2010}. We also point out that our model is an extremely simple approximation which neglects all aspects of the temporal dynamics as well as nonlinear effects from the backreaction of accelerated particles in the fluid dynamics \citep[see, e.g.,][for a description of spectral curvature seen in the radio spectrum of SN 1006 and possibly resulting from nonlinear dynamics]{allen2008}, MHD turbulence and source photons other than the CMB that could be up-scattered and contribute to the IC flux. In fact, as can be seen in Fig. \ref{fig1}, the shape of the H.E.S.S. spectrum of SN 1006 is hard to reproduce with our model, which is true for any other phenomenological IC--CMB emission model unless a rather odd spectral shape is used for electrons in Zone 1 (e.g., a distribution with a spectral break at low energies and a very steep spectrum, with a power-law index of $\sim 3.7$, above the break energy). A full broadband nonlinear model of the non-thermal emission could perhaps account for the spectral shape at TeV energies, but our main conclusion would still be valid. Based on our model it can be pointed out, as explained before, that a lower magnetic field in the X-ray emitting region is supported by the H.E.S.S. observations if the nature of the TeV emission is leptonic. The bipolar morphology of the $\gamma$-ray emission seen by H.E.S.S. indicates that it originates in the polar caps of the remnant, and in their proposed leptonic scenario, the flux level is consistent with a field value of $30\, \mu$G as pointed out by the authors \citep{acero2010}. For their hadronic scenario, they find that a field of $120\, \mu$G is consistent with the data, and necessary to ``suppress'' the leptonic emission. Our results from Section \ref{magneticfield} are consistent with their leptonic emission scenario. We have already pointed out that a field value of $30\, \mu$G in Zone 2 of our model can also account for the H.E.S.S. observations. On the other hand, other authors have derived a higher value for the magnetic field. Using a detailed nonlinear kinetic model for its non-thermal X-ray emission, some estimates of the magnetic field in SN 1006 favor a value of $150\, \mu$G \citep{volk2005}, which then translates into a predicted IC flux that is lower than the $\gamma-$ray flux observed by H.E.S.S., as can also be concluded with our model. This has lead other authors to argue that the TeV emission might be predominantly hadronic \citep{berezhko2009}. We can only point out that if such were the case, then our GeV limit on the emission implies that the hadronic $\gamma$-ray spectrum should be hard at GeV energies, which is our main conclusion, and this is in accordance with the model shown by these authors \citep{berezhko2009}. The main leptonic scenario for the TeV emission in our two-Zone model presents other difficulties. The break in the particle spectra in Zone 1 which is necessary to reproduce the observations cannot be accounted for by synchrotron cooling alone. The particle break was introduced in the basis of observations. A break in the predicted IC emission would be in general required by the LAT constraints and the break energy itself would be needed to reproduce the observed TeV spectral shape. With respect to the predicted bremsstrahlung flux, the fact that this emission (which reproduces the particle spectrum directly) from SN 1006 is found to be negligible for all the leptonic parameters shown here means that the spectrum of the source at GeV energies would either be hard and leptonic in nature, hard and hadronic in nature or a relatively flat spectrum of mixed origin. The results of the \emph{Fermi} LAT data analysis shown in Table \ref{table1} seem to indicate that the data favor a hard spectrum for the emission (as shown by the increasing values of the TS for lower photon indices), which would also be consistent with the hadronic model mentioned above \citep{berezhko2009}. This will only be confirmed with a significant GeV detection of the source in the future. With respect to hadronic emission from a particle population with an index of 2 (Fig. \ref{fig3}), it is seen that the data are more consistent with mixed leptonic and hadronic contributions (e.g., of comparable fluxes at TeV energies) rather than a predominantly hadronic scenario, for which the resulting fluxes are slightly above the GeV upper limit. Finally, we point out that despite its problems, a leptonic origin of the non-thermal emission from SN 1006 at all energies would be consistent with the fact that other ``SN 1006-like'' SNRs such as RX J1713.7-3946 \citep{koyama1997}, show $\gamma$-ray spectra and shock structure consistent with leptonic emission \citep{ellison2010,abdo2011a}. Also, it has been proposed recently that non-thermal emission from SNRs in low density environments (such as SN 1006) is caused primarily by high-energy leptons \citep{yuan2012}. We cannot of course conclude that the TeV emission from the source is mainly hadronic or leptonic, but we stress the fact that the data rule out certain hadronic emission models such as the ones that have been used to account for the observations of other young SNRs, such as Cas A \citep{abdo2010b,arayacui2010} and Tycho's SNR \citep{giordano2012}.
| 12 | 6 |
1206.5744
|
1206
|
1206.6167_arXiv.txt
|
Massive black holes have been discovered in all closely examined galaxies with high velocity dispersion. The case is not as clear for lower-dispersion systems such as low-mass galaxies and globular clusters. Here we suggest that above a critical velocity dispersion $\sim 40$~km~s$^{-1}$, massive central black holes will form in relaxed stellar systems at any cosmic epoch. This is because above this dispersion primordial binaries cannot support the system against deep core collapse. If, as previous simulations show, the black holes formed in the cluster settle to produce a dense subcluster, then given the extremely high densities reached during core collapse the holes will merge with each other. For low velocity dispersions and hence low cluster escape speeds, mergers will typically kick out all or all but one of the holes due to three-body kicks or the asymmetric emission of gravitational radiation. If one hole remains, it will tidally disrupt stars at a high rate. If none remain, one is formed after runaway collisions between stars, then it tidally disrupts stars at a high rate. The accretion rate after disruption is many orders of magnitude above Eddington. If, as several studies suggest, the hole can accept matter at that rate because the generated radiation is trapped and advected, then it will grow quickly and form a massive central black hole.
|
Observations over the last two decades have revealed central massive black holes in all sufficiently well-observed massive galaxies (e.g., \citealt{2011ApJ...738...17G}). However, the case is not as clear for lower-mass galaxies or globular clusters, and indeed although there is evidence for black holes in some low-mass galaxies \citep{2010ApJ...721...26G,2011ApJ...727...20K} there are examples of galaxies that clearly do not have black holes that follow the standard mass -- velocity dispersion ($M-\sigma$) relation \citep{2001Sci...293.1116M,2001AJ....122.2469G} and the case for globular clusters is far from clear (e.g., \citealt{2002AJ....124.3270G, 2003ApJ...595..187M, 2003ApJ...582L..21B,2012ApJ...750L..27S}). Here we approach this question by focusing on the velocity dispersion rather than the mass of a stellar system. In Section 2 we show that above a critical velocity dispersion $\sigma_{\rm crit}\sim 40~{\rm km~s}^{-1}$, the total binding energy in primordial binaries that can be tapped in three- and four-body interactions is significantly less than the total binding energy of the system as a whole, and hence if such systems are dynamically relaxed they will undergo deep core collapse essentially unhindered by dynamical heating from binaries (thus leading to one of the scenarios discussed by \citealt{1978MNRAS.185..847B} in the context of more massive clusters). We note that the galaxies seen thus far without massive black holes have velocity dispersions below this limit (e.g., NGC 205 has $\sigma=39$~km~s$^{-1}$ and M33 has $\sigma=24$~km~s$^{-1}$; see \citealt{2009ApJ...698..198G} and references therein). In Section 3 we discuss the evolution of binary-free systems. Previous studies have demonstrated that the black holes in such systems sink rapidly to the center and interact mostly with each other in a dense subcluster. This leads to three paths, all of which culminate in the formation of a massive black hole: (1)~For sufficiently high escape speed systems dynamical interactions result in runaway merging of the black holes into a massive hole. For lower escape speed systems either one or zero black holes remain after ejection of merged pairs due to asymmetric emission of gravitational radiation during coalescence or Newtonian recoil from interactions of black holes with dynamically formed binaries. (2)~If one black hole remains then it tidally disrupts ordinary stars and consumes the remnant disks quickly, hence grows rapidly into a massive black hole; other growth mechanisms, such as the accretion of nascent gas or winds, are insignificant. (3)~If no black holes remain then runaway collisions form a massive star that evolves into a black hole, and this first black hole grows via accumulation of tidally disrupted stars. Thus once binary support is removed, massive black hole formation is assured as long as holes consume tidal remnants quickly. In Section 4 we determine the minimum mass of a black hole formed via these paths and discuss the implications of this scenario.
|
We have discussed the evolution of a relaxed cluster that has a velocity dispersion $\sigma\gtorder 40$~km~s$^{-1}$, which is large enough to render binaries insignificant, but that does not initially contain a massive central black hole. We argue that a massive hole will inevitably form if it can swallow tidal debris rapidly: interactions in the black hole subcluster will leave either zero or one hole. In the case of zero, a black hole will form from the product of runaway stellar merging. In either case, the hole will feed quickly from the remnants of the stars it tidally disrupts, and hence will grow until it has significant dynamical effects on the cluster and thus slows its own growth. It is not guaranteed that the holes will then follow the same $M-\sigma$ relation that exists for higher velocity dispersion systems. It is also not guaranteed that clusters with lower velocity dispersions will {\it not} have black holes, but it is possible that massive black-hole formation is prevented as long as binaries have a significant heating effect (see \citealt{2008ApJ...686..303G} for a numerical exploration of the heating due to binaries or a massive central object).
| 12 | 6 |
1206.6167
|
1206
|
1206.6350.txt
|
Eclipsing binaries (EBs) provide critical laboratories for empirically testing predictions of theoretical models of stellar structure and evolution. Pre-main sequence (PMS) EBs are particularly valuable, both due to their rarity and the highly dynamic nature of PMS evolution, such that a dense grid of PMS EBs is required to properly calibrate theoretical PMS models. Analyzing multi-epoch, multi-color light curves for $\sim$2400 candidate Orion Nebula Cluster (ONC) members from our Warm Spitzer Exploration Science Program YSOVAR, we have identified twelve stars whose light curves show eclipse features. Four of these 12 EBs are previously known. Supplementing our light curves with follow-up optical and near-infrared spectroscopy, we establish two of the candidates as likely field EBs lying behind the ONC. We confirm the remaining six candidate systems, however, as newly identified ONC PMS EBs. These systems increase the number of known PMS EBs by over 50\%, and include the highest mass ($\theta^1$ Ori E, for which we provide a complete set of well determined parameters including component masses of 2.807 and 2.797 M$_{\odot}$) and longest period (ISOY J053505.71-052354.1, P$\sim$20 days) PMS EBs currently known. In two cases ($\theta^1$ Ori E and ISOY J053526.88-044730.7), enough photometric and spectroscopic data exists to attempt an orbit solution and derive the system parameters. For the remaining systems, we combine our data with literature information to provide a preliminary characterization sufficient to guide follow-up investigations of these rare, benchmark systems.
|
The Orion Nebula Cluster (ONC) contains several thousand members, and since it is nearby, it provides an excellent empirical laboratory to study the physical properties of pre-main sequence (PMS) stars and brown dwarfs. The ONC is particularly useful for comparison of the observed luminosities and effective temperatures of PMS stars to theoretical model predictions \citep{H97,DaRio10}. Such comparisons can, in theory, allow an estimate of the masses of individual stars as well as both the mean age and the age spread for the stars in a cluster. For such estimates to be meaningful, however, the theoretical tracks and isochrones must be vetted against observations to insure that they are well calibrated. Empirical measurements of the masses, radii, and temperatures of stars, over a range of masses, are necessary for understanding stellar evolution and for deriving well-calibrated theoretical models. The most rigorous means to measure precise stellar properties is via identification and characterization of PMS eclipsing binary (EB) stars because, through a complete analysis of spectroscopy and photometry of these systems, the individual masses, radii, temperatures, and absolute luminosities of the two stars can be accurately derived. However, the identification of such systems is difficult due to the need for monitoring observations and the fact that the system must have an inclination close to 90$^\circ$ to be detected. The paucity of known PMS EBs has meant that the theoretical models lack rigorous empirical confirmation, and thus that masses derived from those tracks have significant systematic uncertainties associated with them \citep{H04}. The situation has begun to change recently with the advent of sensitive wide-field cameras, robotic telescopes and automated photometry pipelines, allowing deep, wide, long duration time series monitoring programs to be conducted. These programs have now led to the identification of seven low-mass PMS EBs with individual masses lower than 1.5 M$_\sun$: RXJ 0529.4+0041A \citep{Covino00}, V1174 Ori \citep{Stassun04}, 2MJ0535-05 \citep{Stassun06, Stassun07}, JW 380 \citep{Irwin07}, Par 1802 \citep{Cargile08, Stassun08}, ASAS J0528+03 \citep{Stempels08}, and MML 53 \citep{Hebb10, Hebb11}. These systems have components ranging in mass from 0.036 M$_\sun$ (2MJ0535-05B) to 1.38 M$_\sun$ (ASAS J0528+03A). All but ASAS J0528+03, MML 53, and RXJ 0529.4+0041 are associated with the ONC. There are just another four EB systems where either only the secondary is on the PMS or both components are more massive PMS stars: EK Cep \citep{Popper87}, TY CrA \citep{Casey98}, RS Cha \citep{Alecian05,Alecian07} and perhaps also V578 Mon \citep{Garcia11} although its components are B type stars that may already be on the main sequence. The masses of a handful PMS low-mass stars have been measured using other methods (see \citet{H04, Boden05,Simon00,Tognelli11} for a summary on dynamical mass determination and calibration of PMS tracks). %EKCep: 2.02 Msun ZAMS + 1.12 Msun PMS %TYCrA 3.16 Msun ZAMS + 1.64 Msun PMS %RSCha 1.89 Msun PMS + 1.87 Msun PMS %V578 > 10 Msun Despite the recent discoveries, it is still important to search for additional PMS EBs. Main sequence solar-type stars are well described by state-of-the-art stellar evolution models (i.e., observations agree well with theoretical isochrones); however, recent measurements of the stellar properties of low-mass dwarfs and young PMS stars remain problematic for the existing models. Recent work has suggested that in addition to mass and age, other parameters, such as magnetic field strength or rotation, may be necessary to fully characterize young, low mass stars. Magnetic fields in young, rapidly rotating low mass stars are thought to inhibit convection and thereby cause those stars to have larger radii and cooler temperatures than would otherwise be the case \citep{MoralesJC10, Macdonald10}. This effect has been invoked to explain the properties of the 1 Myr old brown dwarf EB in Orion (2M0535-05) where the more massive component is unexpectedly cooler than its companion \citep{Reiners07,Chabrier07,Stassun07,Mohanty10}. The effects of magnetic fields on stellar structure are not included in the models and are not completely understood \citep{Chabrier07}. Most PMS eclipsing binaries discovered to date have short enough orbital periods that their components are expected to have their rotation periods tidally locked to the orbital period. Therefore, they are likely to be rapidly rotating and have strong magnetic fields, and hence have inflated radii (see \citet{Kraus11}). Identification of PMS EBs with longer periods, where tidal locking is not expected, could offer a direct test of the proposed link between magnetic fields, rotation and radii. Moreover, 2M0535-05 remains the only known brown dwarf EB. In this paper, we report the identification and initial characterization of six new PMS EB candidates in the ONC, discovered as part of the YSOVAR (Young Stellar Object VARiability) Spitzer Exploration Science program \citep{Morales11}. These systems have been overlooked in the past probably because the area surrounding the Trapezium stars is filled with bright nebulosity, making the optical photometry very unreliable, but also because cadence and duration of observations in some previous studies were not ideal. Details of the discovery observations are reported in Section 2. Follow-up observations are presented in Section 3 and 4. In section 5 we provide a description of the available data and preliminary analysis for the 6 PMS EBs, based in most cases upon the light curves, in order to provide a basic initial characterization. Two additional systems are likely field star EBs lying behind the ONC and are described in the Appendix.
|
We have identified six new EB star systems that are believed to be members of the Orion Nebula Cluster and thus are PMS EBs. For one of them, $\theta^1$ Ori E, we provide an orbital solution with a complete set of well determined parameters. The masses derived for its components are 2.807 and 2.797 M$_\sun$ and thus $\theta^1$ Ori E is the most massive EB known to date with clear PMS nature. For a second system, ISOY J0535-0447, we provide a preliminary orbital solution based on our light curves and available radial velocity data. For the other four, we provide periods and relatively well-defined light curves, often based on multi-year data. One of these systems, ISOY J0535-0523, is the longest period (P$\sim$20 days) PMS EB currently known. Such a long period suggests that the components will be less affected by tidal effects providing a direct test between magnetic fields, rotation and radii. Another two systems seem to have secondary components in the brown dwarf domain providing, if confirmed, additional examples to the only one known PMS brown dwarf EB. These systems increase the number of known PMS EBs by over 50\%, and the unique properties of several of these systems ensure that they will offer the potential for considerably improving the empirical calibration of the PMS models for low mass stars and brown dwarfs. However, additional observations are needed to fully characterize the systems, in particular high resolution spectroscopy at several epochs is needed to derive the orbital parameters of these systems. %% The displaymath environment will produce the same sort of equation as %% the equation environment, except that the equation will not be numbered %% by LaTeX. %% If you wish to include an acknowledgments section in your paper, %% separate it off from the body of the text using the
| 12 | 6 |
1206.6350
|
1206
|
1206.5813_arXiv.txt
|
Collisional ring galaxies are the outcome of nearly axisymmetric high-speed encounters between a disc and an intruder galaxy. We investigate the properties of collisional ring galaxies as a function of the impact parameter, the initial relative velocity and the inclination angle. We employ new adaptive mesh refinement simulations to trace the evolution with time of both stars and gas, taking into account star formation and supernova feedback. Axisymmetric encounters produce circular primary rings followed by smaller secondary rings, while off-centre interactions produce asymmetric rings with displaced nuclei. We propose an analytical treatment of the disc warping induced by an inclination angle greater then zero. The star formation history of our models is mainly influenced by the impact parameter: axisymmetric collisions induce impulsive short-lived starburst episodes, whereas off-centre encounters produce long-lived star formation. We compute synthetic colour maps of our models and we find that rings have a $B-V$ colour typically $\sim 0.2 \; {\rm mag}$ bluer than the inner and outer disc, in agreement with observations.
|
Collisional ring galaxies (CRGs) consist of one or more sharply defined star-forming rings, generally (but not always) with a nucleus inside \citep*{madore+09}. Theoretical models, both analytical (e.g. \citealt{struck-marcell+90}; \citealt{lotan+90}; \citealt{gerberlamb94}; \citealt{appleton+96}) and numerical (e.g. \citealt{lynds+76}; \citealt{theys+77}; \citealt{appleton+87}; \citealt{appleton+90}; \citealt{hernquist+93}; \citealt{struck-marcell+93}; \citeauthor*{gerber+94} \citeyear{gerber+94}, \citeyear{gerber+96}; \citealt{horellou+01}; \citealt*{donghia+08}; \citealt{ghosh+08}; \citeauthor{mapelli+08} \citeyear{mapelli+08}, \citeyear{mapelli+08b}; \citealt{mapelli+12}; \citealt{smith+12}), suggest that CRGs are the result of nearly axisymmetric high-speed encounters between a disk galaxy (the `target' or `primary' galaxy) and an intruder galaxy. After the interaction, radially expanding density waves form because of the crowding of star orbits in the target disk. This causes gas compression and the triggering of a starburst episode along the expanding ring (e.g. \citealt{higdon+95}; \citealt{higdon+97}; \citealt{mayya+05}; \citealt*{bizyaev+07}; \citealt{rappaport+10}; \citealt{fogarty+11}). CRGs are unique laboratories for the study of galaxy collisions because of their simple interaction geometry. For example, the kinematics of the ring provides information about the dynamics of the interaction (e.g. \citealt{fosbury+77}; \citealt*{few+82}; \citealt{charmandaris+94}; \citealt{bizyaev+07}; \citealt{fogarty+11}). This information is used to constrain $N$-body/hydrodynamical models reproducing the formation process of well studied CRGs such as the Cartwheel galaxy (e.g. \citealt{hernquist+93}; \citealt{struck-marcell+93}; \citealt{horellou+01}; \citealt{mapelli+08}) and Arp 147 (e.g. \citealt*{gerber+92}; \citealt{mapelli+12}). Numerical simulations are helpful tools to explore the parameter space of the collision and to disentangle the effect of each parameter on the evolution of CRGs. \citet{gerber+96} study the properties of CRGs formed in axisymmetric encounters with different intruder-to-target mass ratios. They show that, as the intruder mass increases, the ring becomes sharper, expands more rapidly and the secondary ring is less developed. \citet{mapelli+12} explore the connection between gas fraction and star formation (SF) in simulations of empty CRGs (i.e. CRGs without a central nucleus, such as Arp 147), and find that the gas fraction strongly influences the peak of SF rate (SFR) after the starburst. \citet{smith+12} perform a large parameter study with the aim of reproducing the dynamical properties of the Auriga's Wheel \citep{conn+11}, but they do not take into account the effects of the interaction parameters on the SF. In this paper, we investigate how the geometry of the impact affects the morphology and SF history of CRGs. We employ a suite of adaptive mesh refinement (AMR) numerical simulations to study systematically the properties of CRGs as a function of the interaction parameters that define the geometry of the encounter. This is the first time that the AMR technique is applied to a wide grid of simulations studying the formation of CRGs. Our choice is particularly important, as the AMR technique ensures a better treatment of hydrodynamical instabilities and shocks with respect to particle-based schemes (e.g. \citealt{agertz+07}; \citealt{price+08}). The paper is organized as follows: in Section \ref{section2} we describe the main characteristics of our suite of simulations and briefly discuss the parameters of interest. In Section \ref{section3} we present the results, and focus on the morphology and SF history of our models. We also extract synthetic photometric information about the colour of the ring and we compare it with observations. In Section \ref{section4} we summarize our main findings.
|
\label{section4} In this paper, we investigate the properties of CRGs as a function of the interaction parameters by means of AMR hydrodynamical simulations. We focus on three parameters: the impact parameter, the initial relative velocity and the inclination angle. All the simulations show a few common features, such as the radius of the ring ($R_{\rm ring} \simeq 6-10 \; {\rm kpc}$) at time $\tau_{\rm ring} \simeq 50 \; {\rm Myr}$ after the interaction, which is weakly influenced by the three interaction parameters described above. On the other hand, axisymmetric encounters produce CRGs noticeably different with respect to those formed by off-centre interactions. Axisymmetric interactions result in a circular primary ring followed by a smaller secondary ring, whereas CRGs born from off-centre collisions show asymmetric rings and a displaced nucleus. In the most asymmetric cases ($b = 10 \; {\rm kpc}$ and $\vartheta = 30^{\circ}$) the ring is not connected. The maximum impact parameter to form a connected ring is $b \lesssim 3 R_{\rm d}$, where $R_{\rm d}$ is the scale length of the target disc. Interactions with $\vartheta > 0^{\circ}$ induce a torque on the target disc producing a vertical warp. In the special case of encounters with $b=0 \; {\rm kpc}$ and $\vartheta > 0^{\circ}$, the ring develops on a plane tilted with respect to the original target disc plane and we propose a simple analytical treatment to predict the overall warping of the target disc after the interaction. After the interaction, the ring expansion enhances the SF in the target disc, reaching a typical SFR $\sim 10 \; {\rm M_{\odot} \, yr^{-1}}$, in agreement with observations (\citealt{higdon+97}, \citealt{fogarty+11}). We show that the initial velocity and the inclination angle have weak effects on the peak of the starburst and on the evolution with time of the global SFR. Instead, the impact parameter has a crucial effect on SF: symmetric encounters cause a short-lived starburst episode, whereas off-centre interactions produce long-lasting ($\gtrsim 100 \; {\rm Myr}$) SF events. The expanding ring is the region mainly affected by SF, as suggested by observations (e.g. \citealt{higdon+97}, \citealt{romano+08}). This is confirmed by the synthetic colour maps (based on the models by \citealt{marigo+08} and \citealt{girardi+10}) that we compute from the simulations. We find an average $B-V$ colour $\sim 0.5 \; {\rm mag}$ for the ring, with clumps of massive SF with $B-V \lesssim 0.4 \; {\rm mag}$. The ring is typically $\sim 0.1-0.2 \; {\rm mag}$ bluer than the rest of the galaxy, in agreement with the $B-V$ colour profiles measured by \citet{romano+08} for a sample of 15 CRGs. A number of issues cannot be explained by our simulations. For example, it is still unclear which mechanism regulates SF in the inner regions of the ring, since HI/H$\alpha$ observations suggest that secondary rings are gas-poor (e.g., the Cartwheel, \citealt{higdon+95}; \citealt{higdon+96}; but see also \citealt{bizyaev+07} about Arp 10), while our simulations predict the opposite. This may be due to several reasons, such as the initial distribution of gas inside the disc, or the idealized sub-grid SF process that does not take into account the chemical abundances and the role of $\rm H_2$. Thus, future works will require more realistic initial gas distributions and/or more detailed recipes of SF (e.g. $\rm H_2$ regulated SF, \citealt*{krumholz+09}; \citealt{kuhlen+12}) to better constrain the SF in CRGs. Another interesting issue we did not explore (but plan to investigate in the future) is the effect of a gas-rich intruder. In this respect, we remind that the SPH simulations of \citet{struck+97} suggest that the main differences between encounters with (disc-like) gas-rich and gas-poor intruders are related to the SF history, whereas the effects on the ring morphology are quite limited, even if some features (such as plumes) appear to be more developed in the gas-rich case.
| 12 | 6 |
1206.5813
|
1206
|
1206.7027_arXiv.txt
|
A survey toward 674 Planck cold clumps of the Early Cold Core Catalogue (ECC) in the J=1-0 transitions of $^{12}$CO, $^{13}$CO and C$^{18}$O has been carried out using the PMO 13.7 m telescope. 673 clumps were detected with the $^{12}$CO and $^{13}$CO, and $68\%$ of the samples have C$^{18}$O emission. Additional velocity components were also identified. A close consistency of the three line peak velocities was revealed for the first time. Kinematic distances are given out for all the velocity components and half of the clumps are located within 0.5 and 1.5 kpc. Excitation temperatures range from 4 to 27 K, slightly larger than those of $T_d$. Line width analysis shows that the majority of ECC clumps are low mass clumps. Column densities N$_{H_{2}}$ span from 10$^{20}$ to 4.5$\times10^{22}$ cm$^{-2}$ with an average value of (4.4$\pm$3.6)$\times10^{21}$ cm$^{-2}$. N$_{H_{2}}$ cumulative fraction distribution deviates from the lognormal distribution, which is attributed to optical depth. The average abundance ratio of the $^{13}$CO to C$^{18}$O in these clumps is 7.0$\pm$3.8, higher than the terrestrial value. Dust and gas are well coupled in 95\% of the clumps. Blue profile, red profile and line asymmetry in total was found in less than 10\% of the clumps, generally indicating star formation is not developed yet. Ten clumps were mapped. Twelve velocity components and 22 cores were obtained. Their morphologies include extended diffuse, dense isolated, cometary and filament, of which the last is the majority. 20 cores are starless. Only 7 cores seem to be in gravitationally bound state. Planck cold clumps are the most quiescent among the samples of weak-red IRAS, infrared dark clouds, UC~H{\sc ii} region candidates, EGOs and methanol maser sources, suggesting that Planck cold clumps have expanded the horizon of cold Astronomy.
|
Large samples significantly improve our understanding of star formation. At the beginning of star formation studies in the early 70s, the Palomar Sky Survey (PSS) plates provided astronomers optical selected nebulae as targets of star forming regions. The catalogued Shapeless HII regions \citep{shar59} from PSS served as sources for investigating gas and dust properties of molecular cloud complex \citep{evans77,Har77}. Nearby dark cores as well as cloud fragments were from Lynds dark nebula \citep{str75,sne80,clar81}. After visual inspection, 70 small opaque spots were chosen for the surveys of low-mass cores with the $^{13}$CO, C$^{18}$O and NH$_{3}$ respectively \citep{my83a,my83b}. A number of sources resulted in these earliest observations are still primary examples in low mass star formation so far. However, "optical dark" selection method is limited for probing star forming in the deep of molecular clouds. \cite{bal83} chose infrared sources for detecting high velocity outflows in high-mass star formation regions. Particularly IRAS point sources afforded plenty samples for high mass star formation regions. Based on the similar shapes of the far infrared flux distribution of all embedded O type stars, the IRAS color-color criteria were used to choose UC HII region candidates \citep{wood89} and further refined by molecular line studies \citep{ce92,wat97}. Precursors of UC HII regions were also obtained from luminous IRAS sources and used for a number of surveys to examine the early characteristics of high mass star formation \citep{mol96,sr02,beu02,wu06}. In recent years, earlier samples for high mass star formation come from infrared dark clouds surveyed by MSX. These are extinction features against the bright mid-infrared background of the Galaxy \citep{egan98}. A number of starless massive cores were detected, which are with narrower line widths and lower rotation temperatures than both UC HII region precursors and UCHII regions but with similar masses \citep{ra06,sr05}. However, MSX is limited to $\vert$b$\vert$$\leq6^{\arcdeg}$ of our Galaxy. Now Planck Surveys provide a wealth of early sources which are cold and with unprecedented complete space distribution. The cold core Catalogue of Planck Objects (C3PO) includes 10783 sources which are mainly cold clumps, intermediate structures of the fragmentation scenario. Their temperatures and densities range from 7 to 17 K and 30 to 10$^{5}$ cm$^{-3}$ respectively, derived from the fluxes in the three highest frequency Planck bands (353, 545, 857 GHz) and the 3000 GHz of IRAS band \citep{ade11a}. This enables us to probe the characteristics of the prestellar phase or starless clumps. The all sky nature of the Planck cold clump sample is particularly useful for studying the global properties of Galactic star formation. Follow up study with high resolution observations by Herschel Satellite revealed extended regions of cold dust with colour temperatures down to 11 K. The results show different evolutionary stages ranging from a quiescent, cold filament to clumps with star formation activities \citep{ju10}. These known properties of Planck cold clumps currently were revealed with various bands of continuum emissions and only a set of 8 C3PO sources selected from different environment \citep{ade11b} were investigated with molecular lines. Examination with molecular lines is another essential aspect for understanding the properties of the Planck cold clumps. Molecular line studies of the Planck clumps, which are an unbiased sample of cold dust clumps in the Milky Way, will provide clues to probe a number of critical questions about clumps and star formation: What are the morphologies, physical parameters and their variations in the Galaxy? What are the initial conditions of star formation, which we do not yet know in our current state of knowledge? What are the dynamic factors in a variety of the clumps and is there any premonition of collapse? Is there any depletion and what are cold chemistry phenomena? In which environment can the cold clump exist? What is the highest Galactic latitude where stars can form? CO is the most common tool to probe molecular regions. Although there is "dark gas" which is undetected in the available CO and HI surveys \citep{ade11c}, CO is still a basic probe to address the above questions. In this paper we report a survey of Planck cold clumps with J=1-0 lines of the $^{12}$CO and its major isotopes $^{13}$CO and C$^{18}$O using the telescope of Purple Mountain Observatory at Qinghai province in western China. Our target sources are chosen from the Early Cold Core Catalogue (ECC), which are the most reliable detections of C3PO clumps. So far we have surveyed 674 sources with single point observations and mapped a subset of ten clumps in different locations. In the next section the observations are described. In section 3 we present the results. The discussions are in section 4 and a summary is given in section 5.
|
\subsection{The line center velocities} The well coincidence of three transitions observed towards the Planck clumps is not usual in star formation regions. Line center velocities of different molecular species could be significant offset from the systematic velocity in active star forming regions. In the six NH$_{3}$ clumps of G084.81-01.09, the deviations between the $^{12}$CO and $^{13}$CO are all larger than 1 km~s$^{-1}$ \citep{zhang11}. V$_{lsr}$ of the $^{12}$CO deviated from that of $^{13}$CO or C$^{18}$O are also seen in infared dark clouds. In 61 infrared dark clouds, there are 10\% sources with V$_{lsr}$ deviation of $\gtrsim$ 1 km~s$^{-1}$ from the $^{12}$CO and the C$^{18}$O lines \citep{du08}. The rather large discrepancy between the V$_{lsr}$ of $^{12}$CO and $^{13}$CO can be also seen in the sub-millimeter clumps \citep{qin08}. Line center velocity difference of various molecular species may origin from molecular layers with different temperature or trace different kinematical gas layers \citep{Ber97,mu11}. The deviation between V$_{13}$ and V$_{18}$ of the Planck clumps also tends to be smaller than those of \cite{my83a}. All these suggest that the cold clumps are the quietest molecular regions found so far as a whole. \subsection{Distances of the clumps:} Distance is essential to investigate the spatial distribution and physical conditions of the clumps. \cite{ade11d} have estimated distance for 2619 C3PO clumps using various extinction signatures. They also found that there are 127 Planck cold clumps associated with IRDCs which have a kinematic distance from \cite{si06}. In our sample there are only 2 clumps closed to the sources of \cite{si06} at the 0 latitude Galactic layer. There are certainly a part of the ECC clumps have distance estimated with extinction methods. We estimated the kinematic distances of the clumps using the Vlsr of the clumps which could be a comparison for those with known distance. We adopt the rotation curve of \cite{cle85} R$_{\sun}$=8.5 kpc and $\Theta_{\sun}$=220 km~s$^{-1}$ in our calculation. To see the possible physical relation of the components in clumps with double and three peaks, the distance of each component was calculated. For the clumps within the inside of the solar circle there are two solutions. The clumps are perhaps located at the front of Galactic bulk of the diffuse background, since extinction is rising along a line of sight that crosses a dust clump \citep{ade11a}. So the near value of the distances was adopted. Among our sample there is a number of clumps located in molecular complex with known distance. Since these complexes are with rather large areas and clumps resident inside are with different V$_{lsr}$, the kinematic distances of the clumps within one complex are quite different. Therefore for every clump within the same complex their distances are also given out as the kinematic distances. However, in a case that a clump has ambiguity on the distance, the one close to the known distance of the complex was adopted. The histogram of the kinematic distances is plotted in Figure 8. Distances were obtained for 741 $^{13}$CO components. 51\% of the components are with distances within 0.5 and 1.5 kpc. The mean value is 1.57 kpc, smaller than those associated with infrared dark clouds by \cite{si06}. The reason may be due to cloud properties, of which most of our clumps or components belong to low mass group and the infrared dark clouds of \cite{si06} are at the first quadrant of the mid-plane and with distances between 0.7 to 7.8 kpc \citep{si06}. \subsection{Physical Parameter distributions in the Galaxy} \subsubsection{Excitation temperature and the ratio of line strength of $^{12}$CO and $^{13}$CO} Figure 9 presents the distribution of the T$_{ex}$ and the ratio of T$_{12}$/T$_{13}$. Fig. 9 a$)$, c$)$ are for radial changes and b$)$, d$)$ for the altitude from the Galactic plane. The excitation temperature is higher than 10 K from 4 to 8 kpc. The early observations also showed the high excitation of the gas emission at the 3-7 kpc molecular ring (Goldsmith 1987 and the references there in). Around 8 kpc, T$_{ex}$ is also larger than 10 K, which may be related to the emission of the giant molecular clouds near the Sagittarius arm. The ratio of T$_{12}$ to T$_{13}$ is high at R$\sim$5 kpc, then deceases with R and has a valley between 5 - 8 kpc, then have a lowest value at $\sim$6 kpc, suggesting the brightness temperature of $^{13}$CO (1-0) is relatively high in this region. Fig. 9 b$)$ shows that excitation temperature changes with the altitude. There are two peaks, 11 and 13 K at Z$\sim$350 pc and $\sim$470 pc respectively. The changes of the ratio of T$_{12}$/T$_{13}$ shown in Fig. 9 d$)$ are rather monotone and reach the low value at Z$\sim$470 pc, suggesting the brightness temperature of $^{13}$CO is relatively high at this altitude. \subsubsection{Velocity dispersion} Variations of the velocity dispersion with the distance from the Galactic center, and the altitude from the Galactic plane are investigated. The radial variations of $\sigma_{3D}$, $\sigma_{NT}$ and the ratio of $\sigma_{NT}/\sigma_{Therm}$ are plotted in Figure 10 a$)$, c$)$ and e$)$ respectively. The variation of the $\sigma_{3D}$ and $\sigma_{NT}$ as well as the ratio of $\sigma_{NT}/\sigma_{Therm}$ with R are about the same and they reached the maximum at R$\sim$5 kpc, which suggest that the dynamic process is most violent at the 5 kpc Galactic ring. From 6 kpc, the $\sigma_{3D}$, $\sigma_{NT}$ and the ratio of $\sigma_{NT}/\sigma_{Therm}$ seem linearly increase with R, indicating turbulence becomes more violent in the outer part of the Galaxy. Figure 10 b$)$, d$)$, f$)$ present changes of the velocity dispersions $\sigma_{3D}$, $\sigma_{NT}$ and the ratio of $\sigma_{NT}/\sigma_{Therm}$ with the altitude. One can see that they all decrease with the increasing of the altitude from the Galactic disk to highness 475-525 pc, showing the closer to the galactic plane, the stronger of the turbulent process. At Z$\sim$680 pc all of them reached a minor peak. We found the clumps at this minor peak are distributed around (l$\sim$174$\arcdeg$, b$\sim$17$\arcdeg$) or (l$\sim$4$\arcdeg$, b$\sim$17$\arcdeg$), this minor peak may be concerned with the emission regions of Taurus and $\rho$ Oph. From panel e$)$ and f$)$, one can see non-thermal motion dominates the line broadening. This is the first time to obtain an evidence for non-thermal line broadening from survey of the $^{13}$CO (1-0) lines. One can see that there are some differences among the radial variations of the velocity dispersion and excitation temperature. The maximum of T$_{ex}$ -R variation is at rather high values around 4- 8 kpc and reaches maximum at 6 kpc. The T$_{ex}$ variation is milder than that of $\sigma_{NT}$ suggesting that the gas heating and cooling occur in a wider spatial region than the turbulence. \subsubsection{$^{13}$CO opacity, X$_{13}$/X$_{18}$ and H$_{2}$ column density} Figure 11 a$)$ shows the radial variation of the optical depth of the $^{13}$CO (1-0) lines. The smallest value is at the 5 kpc ring. Between 5.5 and 8 kpc there is a high feature, then decreases till 14 kpc. One reason for its low valley is T$_{ex}$ is rather high around 5 kpc (see Fig. 9 a$)$). Besides, its emission is relatively low comparing with that of the $^{12}$CO. For example, G017.22-01.47 at R= 4.90 kpc is $\tau_{13}$ =0.3, T$_{ex}$ =10.1 K and T$_{13}$=0.42 K; G033.70-00.01, R=5.05 kpc, $\tau_{13}$ =0.5, T$_{ex}$ =9.2 K and T$_{13}$=1.12 K; G028.56-00.24, R= 5.28 kpc, $\tau_{13}$= 0.4, T$_{ex}$ =10.9 K, T$_{13}$=1.13 K. The ratio of X$_{13}$ to X$_{18}$ presented in Figure 11 c$)$ is rather low between 5-7 kpc and its corresponding values range from $\sim$6 to 7, still higher than the terrestrial value. At 8 kpc and $>$10 kpc the value is near 8. Figure 11 e$)$ shows the radial variation of the column density of hydrogen molecules. Clearly it presents an enhancement at 5 kpc where the most dense and massive star formation regions within our Galaxy are located. Then it is almost at the similar level till outer region except at 9 kpc where there is a minor low valley. Owing to the small $\tau_{13}$ around 5 kpc (see Fig. 11 a$)$ the column density is mainly affected by the velocity dispersion $\sigma_{3D}$ or $\sigma_{NT}$ shown in Figure 10. To confirm the Galactic distribution of the column density, the radial distribution of the flux density at 857 GHz dust emission detected by the Planck was plotted at Figure 11 g$)$. The variations agree with that of the column density very well. At 9 kpc the 857 GHz flux is a little higher showing another dense structure (Goldsmith 1987 and the reference therein). The variation of $\tau_{13}$ with altitude is shown in Figure 11 b$)$. It exhibits a high feature between 350-550 pc and reaches its maximum at 450 pc. The change of the ratio of X$_{13}$/X$_{18}$ seen in Fig. 11 d$)$ seems to be opposite to that of $\tau_{13}$ with its lowest point at Z=450 pc. Fig. 11 f$)$ presents the variation of the molecular hydrogen column density with Z. At Z= 300 and 500 pc, the values are higher than in the other regions. There is a low valley at Z=450. Combining the altitude variation of $\tau_{13}$ and the velocity dispersion of Fig. 10 b$)$, d$)$, f$)$ where $\sigma_{NT}$ is at low values, again showing that non-thermal line width is the major factor to determine the gas column density. Between 350-550 pc the flux at 857 GHz is higher too, which are consistent with the variation of N$_{H_{2}}$ as a whole. These results revealed that the column density reaches the maximum at R=5 kpc, a low valley at Z=450 pc and mainly caused by non-thermal velocity dispersion, which are also not reported before. \subsubsection{Parameters of the clumps in different molecular complexes} For the 12 complexes included in our sample, a statistical analysis of the physical parameters was made. The corresponding average values are presented in Table 2. They display different trends: The famous star formation regions including Ophiuchs, Orion, Oph-Sgr and Taurus harbor 253 observed clumps. They have the highest excitation temperatures and column densities. The average $^{13}$CO FWHM of these clumps are less than 1.5 km~s$^{-1}$, even in Orion it is only 1.29 km~s$^{-1}$, suggesting that low mass clumps are the dominant sources in the Planck cold clumps. Their non-thermal velocity dispersion is almost two times of the thermal one except in Ophiuchs where $\sigma_{thermal}\sim\sigma_{NT}$. Cephens harbors 87 observed clumps. The FWHM of $^{13}$CO J=1-0 line is between Orion and the above mentioned star formation regions. $\sigma_{NT}$ is also the dominant factor for the line broadening. A common character can be seen that all the 4 Quadrants and the anti-center regions have FWHM of $^{13}$CO J=1-0 line $\gtrsim$ 1.5 km~s$^{-1}$. All of them belong to the high mass group. The $\sigma_{NT}$ is about 4 times of the $\sigma_{thermal}$, indicating that these regions have stronger dynamic processes than other star formation regions. \subsection{Line profiles} There are 15 clumps having absorption dip at the line center, which is rather symmetric relative to the V$_{lsr}$. Eight of them show the dip in all the three transitions. They may be the candidates for the $^{12}$CO depletion. In the other 7 clumps, only $^{12}$CO line has the center dips which may originate from self-absorption. Mapping is needed to further examine the properties of the line center dips. 18 and 15 cores were identified have blue and red profiles (see Table 5). Blue profiles are a kind of typical feature of molecular clump collapse \citep{zhou93}. While the red profile could originate from expansion of the clump or outflow motion. The ratios of the clump with the blue and red profiles to the total clump numbers of clumps are small, which are 2.7\% and 2.2\% respectively. The blue excess $E=(N_{b}-N_{r})/N_{t}$ is 0.004, here $N_{b}$, $N_{r}$ and $N_{t}$ are the clump numbers with the detected blue and red profiles and the surveyed sample \citep{mar97}. E of the Class -I, 0 and I clumps is 0.31, 0.30 and 0.30 shown in HCN (3-2) line respectively \citep{ev03} while it is 0.15-0.17 for UC HII region precursors and 0.58 for UCHII regions detected with HCO$^{+}$(1-0) lines \citep{wu07,fu05}. Nevertheless a sample of 27 Orion starless clumps, 9 have blue profile and 10 have red one, implying that the blue excess E is -0.04 \citep{ve08}. The ratios of blue and red profiles to these cores are 33\% and 37\%, greatly exceeding those of our sample, suggesting that star formation activities occur more frequently in the Orion cores than in the Planck cold clumps. The small ratio of the blue and red profiles means that most of the Planck cold clumps do not have systematic star forming motion yet. We also identified 19 and 13 cores with blue and red line asymmetry respectively. Different from blue and red profile, line asymmetry reflects whole gas motion of the core, which may results in interaction of the core and its environment. The high velocity wings are rare in Planck cold clumps. Among the surveyed clumps, only 3 clumps were detected with blue wing and 6 with red one, 8 with both blue and red wings and 5 with pedestal feature, showing rather rare star formation feed back activities. \subsection{Conditions of the clumps at high latitude clumps} There are 41 clumps located at latitude higher than 25$\arcdeg$. Six clumps have two velocity components and one has three. Five of the clumps belong to the high mass group. T$_{ex}$ is intermediate among the 12 complexes (see Table 2). The column density is 3$\times$10$^{21}$ cm$^{-2}$ on the average. $\sigma_{NT}$ tends to be smaller among the 12 complexes but still larger than those in the Ophiechs and Oph-Sgr. Core G089.03-41.28 is with blue profile while cores G182.54-25.34 and G210.67-36.77 are with red profile. Their altitudes are 2.4, 0.64 and 0.15 kpc respectively, showing that star formation signatures also exist in clumps at high latitude. Here the kinematic distance was adopted. Since the diffuse emission was found over all the Galactic sky \citep{hau84}, many high latitude clouds such as infrared cirrus were also detected \citep{low84}. \cite{hei93} made a survey for 16$\arcdeg\leq$b$\leq44\arcdeg$, 117$\arcdeg\leq$l$\leq160\arcdeg$ in the 2nd quadrant. They found that the clouds with the CO emission are 13\% of the survey sample. \cite{ya03} also carried out a CO survey within the latitude -30$\arcdeg$-(43$\arcdeg$). They identified 110 $^{12}$CO clouds with a total of mass of 1200 M$_{\sun}$, in which all of the clouds are not dense enough to form stars. The conditions of our 41 Planck samples are more closer to star forming statues. Additionally the latitudes of the Planck clumps exceed the above samples. These results suggest that the ECC clumps are a good guide to investigate initial conditions or search for star formation. \subsection{States of the ten mapped clumps:} The different morphologies of the contour maps of the ten mapped clumps show that the Planck clumps contain a rather long evolutionary sequence, which includes diffuse and elongating regions, filament structure or cometary shape, multiple cores as well as isolated core. Assuming a core is a gravitationally bound isothermal sphere with uniform density and is supported solely by random motions, the virial mass M$_{vir}$ can be calculated following \cite{ung00}: \begin{equation} \frac{M_{vir}}{M_{\sun}}=2.10\times10^{2}(\frac{R}{pc})(\frac{\Delta V}{km~s^{-1}}) \end{equation} where R is the radius of the clump and $\Delta V$ is the line width of the $^{13}$CO (1-0). The virial masses are listed in the column 14th of Table 8. In molecular clouds, many factors including thermal pressure, turbulence, and magnetic field support the gas against gravity collapse. The Jeans mass, which takes into account of thermal and turbulent support, can be expressed as \citep{hen08}: \begin{equation} M_{J}\approx1.0a_{J}(\frac{T_{eff}}{10~K})^{3/2}(\frac{\mu}{2.33})^{-1/2}(\frac{n}{10^4~cm^{-3}})^{-1/2}M_{\sun} \end{equation} where $a_{J}$ is a dimensionless parameter of order unity which takes into account the geometrical factor, $\mu=2.72$ is the mean molecular weight, $n=\frac{N_{H_{2}}}{2R}$ is the volume density of H$_{2}$ and $T_{eff}=\frac{C_{s,eff}^{2} \mu m_{H}}{k}$ is the effective kinematic temperature. The effective sound speed $C_{s,eff}$ including turbulent support can be calculated as: \begin{equation} C_{s,eff}=[(\sigma_{NT})^{2}+(\sigma_{Therm})^{2}]^{1/2} \end{equation} The calculated Jeans masses are listed in the 15th column of Table 8. There are 7 cores with M$_{LTE}$ larger than M$_{vir}$ and M$_{J}$, which maybe under collapse. There are also 7 cores having M$_{LTE}$ agree M$_{vir}$ and M$_{J}$ within a factor of three. Considering the uncertainties in mass estimation, these cores may be in magical states. The remaining cores seem to be gravitationally unstable. One should keep in mind, these ten clumps are not a representative sample for the whole ECC, but include the morphologies of the majority of the Planck clumps. Most of the ECC clumps show diffuse molecular emission or harbor gravitationally stable dense cores (Liu, Wu \& Zhang, in preparation). The mapped clumps are noted individually as the following: G001.38+20.94: It is located in $\rho$ Oph. The gas emission is diffuse and with size $>$1 pc. The density is lower than 10$^{3}$ cm$^{-3}$ and mass $>$750 M$_{\sun}$. The excitation temperature is rather high (14 K). The average $\sigma_{3D}$ is only 0.67 km~s$^{-1}$. Actually it is located at (0.5,-1.0) with respect to L43B, the mixture of isolated globules and complex \citep{ben89}. Maybe it is in the transition between diffuse ISM and dense molecular cloud. G006.96+00.89: It is located in the 4th quadrant. Two velocity components with V$_{lsr}$ 9.33 and 41.67 km~s$^{-1}$ were detected in the clump and both have FWHM larger than 1.3 km~s$^{-1}$. The two velocity components have 4 and 1 cores respectively. No astronomical object was found associated with this clump so far. G006.96+00.89a with 4.33 km~s$^{-1}$ velocity component appears elongated from SE to NW and has a chain of at least four cores. The other component has an isolated core near the mapping center, and the cores are not very dense with n lower than 10$^{3}$ cm$^{-3}$. G049.06-04.18: It is an isolated clump and located in the first quadrant. The mass calculated with LTE is close to the Jeans and virial mass. It is CB 198 and contains IRAS 19342+1213 (J2000=19 36 37.8 +12 19 59) located at (8$\arcsec$, 43$\arcsec$) of the clump \citep{Go06}. G089.64-06.59: It is a clump of the first quadrant. Its gas clump tends to be cometary. The starless clump CB 232 AMM 1 is located at (20$\arcsec$, -36$\arcsec$) of the clump. It harbors an infrared source IRAS 21352+4307 \citep{hua99}. At about 15$\arcsec$ eastern there is a near infrared source YC1-I. The LTE mass and the Jean mass, virial mass all are close to each other. G108.85-00.80: It belongs to the 2nd quadrant. There are no associated objects or known cloud was found for this clump. It shows a filamentary structure and is compact. The $^{13}$CO (1-0) line width is 2.7 km~s$^{-1}$ and is a typical high mass clump. The LTE mass is larger than both the Jeans and virial mass. It seems very likely to be in gravitational collapse. G157.60-12.17: It locates in the Taurus complex and has two components belonging to L group. Contours of their integrated intensity show the first component is rather diffuse and the second one contains two cores. TGU 1064 is located at 65$\arcsec$ east and south \citep{do05}. G161.43-35.59: It is a high latitude clump and belongs to L group. It contains at least 4 cores. No associated object was found. G180.92+04.53: It is at the side of Anticenter of the Galaxy and belongs to the H group. G194.80-03.41. The dumbbell gas emission region elongates in north-west direction. Two large clumps are connected and each contains at least two cores. There was no associated object found. All the cores should be starless. The clump masses are all larger than the corresponding Jean and virial mass, suggesting they are at the gravitational bound states. TGU H1364 P8 is about 2$\arcmin$ away \citep{do05}. G196.2-15.5: This clump is with blue asymmetry line (see Table 6). It is associated with L1595 and a reflection nebular VDB 40 \citep{ma86}. Three cores were found in this filamentary structure. All belong to Group L. Except the M$_{J} <$ M$_{LTE}$, for the core 1, M$_{LTE}$ is less than M$_{J}$ and M$_{vir}$, but all these masses are close to each other. The morphology, structure and physical parameters of the small set of the ten mapped clumps show that Planck cold clumps cover different phases which may be 1: in a transition phase from diffuse ISM to cloud; 2: in a state close to gravitational bound. Among the 10 clumps, 4 are in filamentary or elongated shape which show that filamentary clumps may be the majority in C3PO clumps. 3: an isolated core or multiple cores; 4: starless cores, 5: in a state that harbor infrared sources. In total 22 cores were found and 20 are starless. \subsection{Gas and dust coupling} The range of the clump kinetic temperature is from 4-27 K, wider than those of dust temperatures (7-17 K) \citep{ade11a}. However there are only 12 clumps with T$_{k}>$17 K. The $\sim$98\% clumps have T$_{k}\leq$ 17 K, showing both the dust and gas are cold and couple well. Figure 12 a) shows a comparison of the T$_{k}$ and T$_{d}$ in both "Total" and "Cold" (see Fig. 12 a) ). Most of the clumps are with T$_{d}>$T$_{k}$, indicating that gas could be heated by dust in these regions \citep{gol74}. For the clumps with T$_{d}<$T$_{k}$, the gas may be due to ongoing protostellar process. For example, for the 27 clumps with T$_{k}>$16 k$ >$T$_{d}$, 6 are in or close to Ophiuchs, 8 in Taurus and 10 in Orion. The column densities deduced from dust emission and CO lines were plotted in Figure 12 b). One can see that the range of the values from dust is about 3 orders in total and that from CO lines is about 2.5 orders, sightly narrower. However both the column densities concentrate on 10$^{21}$-10$^{22}$ cm$^{-2}$. According to \cite{har98} such column density is just about the critical value of the cloud collapse. \subsection{Evolutional phases - A comparison to different star formation samples} To investigate the physical conditions and examine the possibility of stars forming in the cold clumps, we compare the line widths of $^{13}$CO (1-0) and column densities with the following CO molecular line surveys towards different kind of targets: a$)$ Methanol maser sources \citep{liu10}; b$)$ Candidates of UC HII region chosen with the IRAS colour index and flux limit \citep{wu01,wood89}; c$)$ Candidates of extremely young stellar objects chosen with redder color IRAS index and smaller flux density than those of UC HII regions \citep{wang09}; d$)$ Infrared dark clouds (IRDCs) \citep{si06}. e$)$ Extended green objects (EGOs) identified from the Spitzer GLIMPSE survey \citep{chen10} Figure 13 a) plots a cumulative fraction of the FWHM of $^{13}$CO (1-0). It shows that the methanol maser sources have the largest FWHM and the smallest slope. And the IRDCs and EGOs have similar shape with the methanol maser sources but with a slightly larger slope. When the FWHM is less than 3 km~s$^{-1}$, the slope of IRDCs is almost the same as those of the UC HII candidates and the redder-weaker IRAS sources. When FWHM becomes larger than 3 km~s$^{-1}$, the changes of the the UC HII candidates and the redder-weaker IRAS sources are much steeper than IRDCs, EGOs and the methanol maser sources. The slope of the fraction of the redder-weaker IRAS is large and its maximum value is at 6 km~s$^{-1}$. The variation of cumulative fraction function of FWHM for the Planck cold clumps is the narrowest. The FWHM of the Planck cold clumps are the smallest comparing with the other samples. For all the samples used in the comparison with Planck cold clumps, their FWHM are almost larger than 2 km~s$^{-1}$ while the cumulative fraction at FWHM$>$2 km~s$^{-1}$ of the cold clumps is less than 10\%. The comparison of column densities with the samples of the above a), c), d) and e) is presented in Figure 13 b). The cumulative fraction distribution also produces the smallest column density range for the Planck cold clumps. IRDCs have nearly the same shape with Planck cold clumps when column density below 10$^{21}$ cm$^{-2}$, but are similar with the redder-weaker IRAS sources at high densities, indicating IRDCs may be at a transition phase between Planck cold clumps and redder-weaker IRAS sources. The methanal maser sources and EGOs have the largest column densities, indicating active star formations in them. These results show that the Planck cold clumps are quiescent and have smallest column densities among these star formation samples on the whole. Most of them seem to be in transition from clouds to dense clumps.
| 12 | 6 |
1206.7027
|
1206
|
1206.5022_arXiv.txt
|
\baselineskip=15pt We present a unified model for the structure and appearance of accretion powered sources across their entire luminosity range from galactic X-ray binaries to luminous quasars, with emphasis on AGN and their phenomenology. Central to this model is the notion of MHD winds launched from the accretion disks that power these objects. These winds provide the matter that manifests as blueshifted absorption features in the UV and X-ray spectra of a large fraction of these sources; furthermore, their density distribution in the poloidal plane determines the ``appearance" (i.e. the column and velocity structure of these absorption features) as a function of the observer inclination angle. This work focuses on just the broadest characteristics of these objects; nonetheless, it provides scaling laws that allow one to reproduce within this model the properties of objects spanning a very wide luminosity range and viewed at different inclination angles, and trace them to a common underlying dynamical structure. Its general conclusion is that the AGN phenomenology can be accounted for in terms of three parameters: The wind mass flux in units of the Eddington value, $\dot m$, the observer's inclination angle $\theta$ and the logarithmic slope between the O/UV and X-ray fluxes $\alpha_{OX}$. However, because of a significant correlation between \aoxx and UV luminosity, we conclude that the AGN structure depends on only two parameters. Interestingly, the correlations implied by this model appear to extend to and consistent with the characteristics of galactic X-ray sources, suggesting the presence of a truly unified underlying structure for accretion powered sources.
|
The notion of AGN as an astronomical object of solar system dimensions and luminosity surpassing that of a galaxy has been with us for about half a century now. Since then, the advent of novel observational techniques, the accumulation of data and theoretical modeling has refined and advanced our notions as to what constitutes an AGN, with accretion onto a black hole as the source of the observed radiation now being universally accepted. At the same time, the discovery of galactic bright X-ray binary (XRB) sources, powered also by accretion onto compact objects (neutron stars and stellar size black holes) has extended the notion of accretion powered source to the stellar domain. Indeed, the general similarity of the X-ray spectral properties of AGN and galactic black hole candidates (GBHC) and XRBs in general, including their broad Fe \Ka fluorescence features \citep{Miller07}, argues for near horizon structures which are very similar, despite the huge disparity in the objects' scales. This structure is thought to consist of a Shakura-Sunyaev \citep{SS73} disk that extends to the ISCO (innermost stable circular orbit) of the corresponding flow, supplemented by an overlying hot, X-ray emitting corona. Even though it is generally accepted that the AGN radiant energy is released by the accretion of matter onto a black hole (or in certain cases by extraction of the hole's rotational energy) in a region comparable to its horizon, there is plenty of evidence that a significant fraction of the AGN power is emitted, after reprocessing, at much larger radii. [One should note however, that accretion energy can also be transported outward not only radiatively but also mechanically by the viscous stresses that transport the accretion flow's angular momentum \citep{BB99}]. Thus, the UV and optical lines that constitute, typically, a fraction $f \sim 10\%$ of the AGN bolometric luminosity, are emitted presumably by clouds at distances $\sim 0.1 - 10$ pc that cover a fraction $f$ of the AGN solid angle. In addition to the line emission, the AGN ionizing continuum is also reprocessed into IR and far--IR radiation by matter at even larger distances, which apparently subtends an even larger fraction of the AGN solid angle ($\sim 50\%$). The geometry of this component is thought to be cylindrical (rather than spherical) with a column density that depends strongly on the angle $\theta$ of the observers' line of sight (LoS) with the symmetry axis. It was proposed that such a geometry nicely unifies the Seyfert-1 and Seyfert-2 AGN subclasses \citep{AntMil85} and also those of the broad and narrow line radio galaxies (BLRG - NLRG) \citep{Barthel89}, according to the angle $\theta$: Thus, Seyfert-1s (or BLRG) are AGN in which the observer's LoS makes a small angle with their axis of symmetry, the column of the intervening cold gas is small ($N_H < 10^{21} {\rm cm}^{-2}$) and the continuum source and its surrounding broad line emission (concentrated in the inner AGN regions) are directly visible. Seyfert-2s (or NLRG) on the other hand, represent the same objects viewed at a large inclination angle, along which the column density to the source is much larger ($N_H > 10^{23} {\rm cm}^{-2}$), obscuring the continuum source and allowing the view of only the large distance (hence narrow component) of the emission lines. This obscuring structure is referred to as the ``AGN molecular torus", considering that it must consist of gas in molecular state, given its low effective temperature ($T \sim 10 - 100$ K). Statistics of Seyfert-1 and Seyfert-2 AGN imply that the height $h$ of these torii must be comparable to their distance $R$ from the AGN center, i.e. $h/R \simeq 1$. However, the value of this ratio is in conflict with that implied by hydrostatic equilibrium and the ratio of their thermal ($v_{\rm th} \sim 1 \, (T/ {\rm 100 K})$ km/s) and Keplerian ($v_{\rm K} \sim 300 - 500$ km/s) velocities, namely $h/R \simeq v_{\rm th}/v_{\rm K} \sim 10^{-3}$, thus presenting us with a conundrum concerning the physics of these structures. These spectroscopically inferred components, along with observations of narrow radio jets along the AGN symmetry axis, led to the now well known AGN picture of \citep{UP95}, which consists simply of their arrangement at the appropriate positions in the AGN vicinity. Compelling as this picture might be observationally, it includes very little, if any, of the underlying physics. The AGN constituent components are independent of each other with physical properties assigned as needed by the observations of the specific objects. However, more recent observational developments suggest that such a picture is rather incomplete. To begin with, \citet{BG92} have shown the existence of interrelations among AGN the line properties and also relations to other bands of the spectrum (notably the X-rays). Then, the increase in UV spectral resolution afforded by {\em HST} has shown that roughly 50\% of Seyfert-1s exhibit UV absorption troughs due to plasma outflowing at $v \simeq 300-1000$ km/s, too narrow to have been discerned by the earlier {\em IUE} observations \citep{Cren99}, which did detect some, but in a much smaller fraction of the overall AGN population. To these flows one must also include those of the so-called BAL QSOs, which reach velocities along the observer's LoS in excess of $10^4$ km/s \citep{Weymann91}. These are observed in about $\simeq 10\%$ of high luminosity quasars, implying that they subtend a similar fraction of the continuum source solid angle in these objects. In addition to these UV absorption features, outflowing components were also found in the AGN X-ray spectra. The increase in spectral resolution provided by {\em ASCA} showed that approximately $50\%$ of Seyfert-1s exhibit also blue-shifted absorption features in their X-ray spectra \citep{George00}, indicative of outflowing plasma, but of different ionization state than that responsible for the UV absorption features. More recently, \citet{Tombesi} have shown that Fe-K absorption features at velocities $v \sim 0.1c$ are rather common in nearby Seyfert galaxies and coined for them the term ultra-fast outflows (UFO). The simultaneous presence of both UV and X-ray absorbers in the same objects implies they belong to the same outflowing plasma \citep[see e.g.][]{Gab03}. However, despite a large number of studies supporting this hypothesis, \citep[][]{Mathur94,Mathur95,Collinge01,Crenshaw03,Brandt09}, an understanding of the underlying gas dynamics is lacking. A common origin for the plasma of these components as features of a common, radiatively driven flow would be hard to reconcile with their different velocities and ionization properties. An account of the observed AGN outflows, in particular of the most challenging high velocity ones of BAL QSOs was put forward semi-analytically by \citet{MCGV95}. These authors, in analogy with the winds of O-stars, proposed that they are driven off the inner regions of the QSO accretion disks by UV and optical line radiation pressure to achieve velocities consistent with those observed. The same issue was taken up in more detail in 2D numerical calculations by \citet{PSK00} who included in these calculations the detailed photoionization of the line driven wind by the QSO X-ray radiation. As shown in this work, efficient wind driving by line pressure requires that the line driven wind material be shielded from the ionizing effects of the X-rays, otherwise line driving becomes ineffective. Their calculations showed that the ``failed wind" from the highly ionized innermost regions of the AGN accretion disk did provide the required shielding. The fact that BAL QSOs are weak X-ray emitters appears to advocate for such a point of view. The ubiquity of AGN outflows implies that they should be included in the AGN structure schematic of \citet{UP95}; however, the broad range of observed velocities and their different values in the UV and X-ray bands make such a construct complicated in the absences of an underlying unifying principle. However, such attempts have been made. Thus, \citet{Elvis00}, motivated by the velocity fields produced by \citet{PSK00} in modeling the BAL QSO outflows, proposed a scheme that would supplement the AGN picture of \citet{UP95} with outflow components consistent with observed phenomenology. By limiting the fast ($v \gsim 10^4$ km/s), radiatively driven flow to a narrow angular sliver ($\Delta \theta \simeq 6^{\circ}$) around $\theta_s \simeq 50^{\circ}$ \citep{PSK00}, he accounted for the observed fraction of BAL QSOs in the overall QSO population. He then attributed the lower velocities of the typical X-ray and UV absorption features to the projection effects of viewing this flow at a larger angle $(\theta > \theta_s)$ and the absence of absorption features in fraction of the objects to the low column and high ionization of the wind at $\theta < \theta_s$. He also postulated that the angular position $\theta_s$ and the opening angle $\Delta \theta$ of the high velocity radiatively driven radial stream would vary with source luminosity in a way that could account the variation of source properties with luminosity. However, his approach ignored the outflows seen in the AGN X-ray spectra, which at the time were not as well documented. The AGN picture proposed herein is in the same spirit as that of \citet{Elvis00} in that, employing a well defined wind dynamical model, it provides a framework of systematizing the multitude of observational facts, in particular the more recent high resolution X-ray spectroscopy observations. However, it does more than that; it provides, in addition, scaling arguments similar to those put forward by \citet{Boroson02}, which allow one to incorporate within this single framework the ionization properties of Seyferts, BAL QSOs and XRBs, the structure of the AGN molecular torii and the corresponding IR spectra. This is possible because the underlying dynamical models, which span many decades in radius, are to a large extent independent of the mass of the accreting object and, as such, they can be applied to objects over a very wide range of luminosity. As we will discuss in the ensuing sections, the models we present provide the possibility of a broader classification of the structure of accreting sources in terms of a small number of parameters (2) thus providing an opportunity for a unified treatment of all accretion powered sources. { The present work will concentrate on the structure of AGN, however it will be argued that the structures of XRBs are quite similar, their appearance being different only because of their very different ionization.} In \S 2 we provide a brief review of AGN outflow phenomenology with emphasis on the more recent high spectral resolution observations of X-ray absorbers by {\em Chandra} and {\em XMM-Newton}. In \S 3 we present our model and its general scalings. In \S 4 the model is applied to produce the absorber properties of galactic and extragalactic objects as specific cases of its parameters along with its general structure properties, depicted in two diagrams that relate the absorber column, velocity and observation angle. In \S 5 we focus on the emission properties of these winds and provide an account of the observed linear relation between the H$\alpha$ and bolometric AGN luminosities as well as their IR--to--far-IR spectra. Finally in \S 6 the results are reviewed and directions for future research are outlined.
|
In the previous sections we presented a broad strokes picture of the 2D AGN structure, one that encompasses many decades in radius and frequency and supplements the well known schematic of \citet{UP95} with an outflow launched across the entire disk area and velocity roughly equal to the local Keplerian velocity at each launch radius. These outflows are responsible for the absorption features first detected in the AGN UV spectra and more recently established also in their X-ray ones. As noted in the introduction, the goal and the spirit of this paper is not to reproduce the detailed phenomenology of specific AGN spectral bands, but provide an account of their most general and robust trends; however, it purports to do so on the basis of a single, well founded, semi-analytic model for outflows off accretion disks that involves a small number of free parameters. In this same spirit, Fig. \ref{fig:fig8} presents a schematic of our model; the radius is in logarithmic space and the shading is indicative of the local {\sl column} density in the spherical$-r$ direction, which is constant, but has a strong dependence on the angle $\theta$. The gray lines are illustrative of the magnetic field geometry with the corresponding scaling of the wind velocity on each one relative to the fiducial one $v_o$ shown in the figure. As shown in section \S 3, these outflows have the interesting property that their ionization and dynamical structures scale mainly with one parameter, the dimensionless accretion rate $\dot m$. As such, they are applicable, in principle, to all accretion powered sources from galactic accreting black holes to the most luminous quasars. The mass of the object, $M$, simply provides the overall scale of an object's luminosity and size (and also a characteristic temperature for the BBB), in a way similar to that proposed by \citet{Boroson02}. \begin{figure}[t]% \begin{center}$ \begin{array}{cc} \includegraphics[trim=0in 0in 0in 0in,keepaspectratio=false,width=3.1in,angle=-0] {schematic.eps} & \end{array}$ \end{center} \caption{\small A schematic of the model presented in \S 3. The radius is shown in logarithmic scale, with the solid gray lines representing the poloidal field at each radius shown and the corresponding wind velocity relative to the fiducial one $v_o$. The shading is proportional to the local column in the $r-$direction which does not depend on $r$ but has a strong $\theta-$dependence as required by AGN unification. At sufficiently large distances, $r \gsim 10^4 \, r_o$ the flow is sufficiently cool to be molecular and acts as the torus required by AGN unification.} \label{fig:fig8} \end{figure} However, despite this economy of parameters, because of the inherently 2D character of these winds, their appearance (and that of the AGN central regions) depends quite significantly on the observer's inclination angle $\theta$, a desirable feature and in agreement with our notions of AGN unification. Furthermore, and most importantly, as noted in section \S 4, the ionization structure of these flows depends also on the spectrum of the ionizing radiation. This dependence complicates the situation because it breaks the overall wind flow scale invariance on the mass $M$. As noted earlier, it is effectively the dependence of $\alpha_{OX}$ on luminosity which is responsible for the differences in the absorption feature properties between Seyferts and BAL QSOs. This dependence of $\alpha_{OX}$ on $L(2500$\AA) (and effectively on $\dot M$) suggests that eventually the wind ionization properties may constitute a two rather than three parameter family. Finally, the high ionization of the inner regions of these flows in XRB, naturally accounts for the low velocities of the Fe-K features observed in galactic sources. The crucial and fundamental aspect of the underlying MHD wind model that allows the broad consolidation of the very diverse observational phenomenology of the previous sections ``under the same roof'' is their ability to produce density profiles that decreases like $\sim 1/r$ with the radius. It is this property that allows the ionization parameter to decrease with distance while still providing sufficient column to allow the detection of both high and low ionization ions in the AGN X-ray spectra. It is also this property that controls the velocities $v$ of the Fe-K transitions in galactic sources, Seyferts and BAL QSO, due to the relation between $v$ and $\xi$ ($v^2 \propto \xi$ for the scaling proposed herein; the BP82 scaling leads to $v \propto \xi$ and therefore to much smaller velocity for a given ion, i.e. a given value of $\xi$ -- and also to a much smaller column). Furthermore, it is this specific density profile of the wind that allows us to incorporate the physics of the AGN torii within the context of the broader physics of accretion onto the compact object, while at the same time producing IR spectra in broad agreement with observation. This confluence of the AGN spectral properties with the wind spacial structure indicates that AGN and XRB are objects that span many decades in radius and frequency, despite the fact that most of their luminosity is released within a few \sw radii. The price to pay for a density distribution such as that proposed above is the need to invoke winds whose mass flux increases with distance from the source (and more specifically like $\sim r^{1/2}$). While this feature can be accommodated by the choice of a parameter in the models of \citet{CL94}, it was given a rather transparent explanation in \citet{BB99}, in terms of the dynamics of accretion. Interestingly, recent {\em Chandra} spectroscopy \citep{BS00,Behar03,NRL} appear to support such a notion. At this point, it is not obvious how theoretically compelling is this particular feature in the general scheme of accretion properties. Why is this mass loss preferred to one that would result in, for instance, the BP82 density profile? Are there AGN with winds/accretion flows consistent with $n(r) \propto r^{-3/2}$? What parameter determines which one is chosen by nature? These are pressing questions for which we currently have no answers. However, the importance of the specific mass flux dependence on $r$ in the interpretation of the AGN X-ray and UV absorber properties will likely attract the attention of future studies on this issue. Clearly a presentation as broad as that above by necessity ignores a large number of issues, both observational and theoretical each of which is in fact a separate branch in the study of AGN physics. As such, we have ignored the effects of radiation pressure, considered in much detail numerically by Proga and collaborators \citep{PSK00,Proga03,Proga04} and semi-analytically by \cite{MCGV95}. The effects of radiation pressure in combination with those of the MHD winds discussed here have been considered by \citet{Everett05} and also by \cite{KK94} in discussing the AGN IR spectra. These works have shown the effects of radiation pressure to be local, as they depend on the local flow opacity, thus breaking the similarity of the angular dependence of the solutions. It was shown in these works that radiation pressure ``pushes" to open up the field lines to produce a density dependence on $\theta$ different from that given in Fig. \ref{fig:fig2}a and hence would influence the population ratios of objects observed at a given column density. However, the effects of radiation pressure do not affect the dependence of wind mass flux on the distance ($\dot m \propto r^{1/2}$), which is set by conditions on the disk; it is this property that determines the radial dependence of the wind density, the property necessary to account for their observed phenomenology. As noted above, a radiation driven wind, while 2D in the region of launch, it will appear radial at sufficiently large distance producing density profiles $\simeq 1/r^2$ there. As appealing and compelling as the notion of radiation driven winds is, there is little evidence for them, at least in the AGN and XRB X-ray absorber spectra. Advocating radiation driven 2D winds across the entire accretion disk, in a fashion similar to those of \S 3, appears difficult because the photon field does not have enough momentum at these large distances to drive a wind with the required mass flux. Interestingly the $\phi-$component of the magnetic field, decreasing like $B_{\phi} \propto 1/r$ has precisely the momentum needed to drive a wind with $\dot m \propto r^{1/2}$. In this respect one should bear in mind that these winds produce most of the kinetic energy at small radii, most of the mass flux at large radii and equal momentum per decade of radius. Another issue that was only briefly touched upon in section 5, is that of line emission. It is generally thought that the line emission in AGN comes from clouds in pressure equilibrium with a hot intercloud medium, the result of the X-ray heating thermal instability \citep{Krolik81}. Our simple estimates, even though they have ignored this possibility, they nonetheless provide an account for the observed correlation of the H$\alpha$ (a transition with minimal radiative transfer nuances) with the AGN bolometric luminosity. However, one should bear in mind that our model winds do allow for the formation of such clouds at sufficiently small latitudes (below the Alfv\'en surface) where the flow is close to hydrostatic equilibrium, i.e. under conditions of a given pressure. We expect that past the Alfv\'en point, where the flows are under conditions of given density, the formation of these clouds will be less forthcoming. The issue of cloud or wind AGN line emission is an issue that deserves more attention and study, given the smoothness of the AGN lines profiles that implies a very large number clouds involved in this process \citep{Arav97}, but certainly beyond the scope of the present paper. Our treatment of the AGN IR emission has also glossed over much of what it constitutes an altogether distinct subfield of AGN study. It has been suggested that clouds are also involved in this component of the AGN spectra, however with different properties and at radii larger than those of the UV and optical line emitting clouds \citep{Nenkova08}. This is clearly a point that will have to be looked upon with greater care. A complicating factor in this direction is that of star formation in the AGN environment, whose IR contribution introduces additional parameters in such a study. Finally, with respect to the IR and far-IR AGN spectra, we would like to point to the synergy between X-ray spectroscopy and far-IR observations discussed in \S 5.1 that would help establish the consistency of this scheme across two very different frequency bands. Finally, we close with a few words on the ``feedback" of our winds on the surrounding medium, which likely provides the mass that eventually ``feeds" the AGN. First, the angular distribution of the flow, as determined by the poloidal field structure, due to its collimation, interacts with only part of the surrounding stellar cluster. Second, the energy flux of the winds considered here, despite their increasing mass flux with radius, is still dominated by the flux at small radii ($\dot E = \dot m v^2/2 \propto r^{-1/2}$); however, they do carry equal momentum per decade of radius ($\dot P = \dot m v \propto r^0$), a fact with potential feedback effects, perhaps the subject of a future publication. Finally, the radiation effects of the AGN are also limited in $\theta$ due precisely to the winds' column increase with this parameter. However, as shown in \citet{Tueller08}, the fraction of {\em Swift-BAT} selected AGN at galactic latitude $|b|>15^{\circ}$ with X-ray column $N_H > 10^{22} \, {\rm cm}^{-2}$ decreases from $\simeq 0.5$ to close to zero above luminosity $L \simeq 10^{44} \; {\rm erg \,s}^{-1}$. Therefore, considering that the observed column pertains not only to the AGN wind but also to the entire matter distribution along the LoS, the radiative effects of high luminosity AGN may affect significantly the evolution of their environment. Such constraints will have to be taken into account producing a global evolutionary sequence for our models, which are beyond the scope of the present paper.
| 12 | 6 |
1206.5022
|
1206
|
1206.2434_arXiv.txt
|
The presence of hot X-ray emitting gas is ubiquitous in massive early-type galaxies. However, much less is known about the content and physical status of the hot X-ray gas in low-mass ellipticals. In the present paper we study the X-ray gas content of four low-mass elliptical galaxies using archival \textit{Chandra} X-ray observations. The sample galaxies, NGC821, NGC3379, NGC4278, and NGC4697, have approximately identical K-band luminosities, and hence stellar masses, yet their X-ray appearance is strikingly different. We conclude that the unresolved emission in NGC821 and NGC3379 is built up from a multitude of faint compact objects, such as coronally active binaries and cataclysmic variables. Despite the non-detection of X-ray gas, these galaxies may host low density, and hence low luminosity, X-ray gas components, which undergo a Type Ia supernova (SN Ia) driven outflow. We detect hot X-ray gas with a temperature of $kT\sim0.35$ keV in NGC4278, the component of which has a steeper surface brightness distribution than the stellar light. Within the central $50\arcsec$ ($\sim$$3.9$ kpc) the estimated gas mass is $\sim$$3\times10^{7} \ \rm{M_{\odot}}$, implying a gas mass fraction of $\sim$$0.06\%$. We demonstrate that the X-ray gas exhibits a bipolar morphology in the northeast-southwest direction, indicating that it may be outflowing from the galaxy. The mass and energy budget of the outflow can be maintained by evolved stars and SNe Ia, respectively. The X-ray gas in NGC4697 has an average temperature of $kT\sim0.3$ keV, and a significantly broader distribution than the stellar light. The total gas mass within $90\arcsec$ ($\sim$$5.1$ kpc) is $\sim$$2.1\times10^{8} \ \rm{M_{\odot}}$, hence the gas mass fraction is $\sim$$0.4\%$. Based on the distribution and physical parameters of the X-ray gas, we conclude that it is most likely in hydrostatic equilibrium, although a subsonic outflow may be present.
|
Although the hot X-ray emitting gas content of massive ($M_{\star}>10^{11} \ \rm{M_{\odot}}$) elliptical galaxies has been studied in detail \citep[e.g.][]{forman85,mathews03,randall06,forman07,kraft11}, the X-ray gas content of low-mass ellipticals is less explored. The major issue in studying low-mass ellipticals ($M<10^{11} \ \rm{M_{\odot}}$) is their relatively X-ray faint nature. In particular, the observed X-ray emission from low-mass elliptical galaxies is dominated by the populations of resolved and unresolved compact X-ray sources. Besides the populations of compact objects, emission from hot X-ray gas may also be present, the detection of which may be compromised by the underlying emission from unresolved compact objects. Moreover, given the shallow potential well of such galaxies, the hot X-ray emitting gas may not be in a stationary state. SNe Ia might be energetically capable of driving galactic-scale outflows \citep{david06}. In agreement with this result, a galactic-scale outflow had been detected in the bulge of M31 \citep{li07,bogdan08} and in the Sombrero galaxy \citep{li11}. \begin{figure*}[t] \begin{center} \leavevmode \epsfxsize=8.5cm\epsfbox{ngc821_img1.eps} \hspace{0.4cm} \epsfxsize=8.5cm\epsfbox{ngc3379_img1.eps} \epsfxsize=8.5cm\epsfbox{ngc4278_img1.eps} \hspace{0.4cm} \epsfxsize=8.5cm\epsfbox{ngc4697_img1.eps} \caption{$0.5-2$ keV band raw \textit{Chandra} images of the four analyzed galaxies. The majority of the bright point sources are low-mass X-ray binaries associated with the galaxies, while minor fraction of them are background AGN. The overplotted elliptic regions show the $D_{\rm{25}}$ ellipses, whose extent listed in Table \ref{tab:list2}.} \vspace{0.5cm} \label{fig:img} \end{center} \end{figure*} Detailed X-ray studies of the Milky Way and nearby galaxies have led to a better understanding of the origin of the resolved and the unresolved X-ray emission. With the superior angular resolution of \textit{Chandra}, the population of bright low-mass X-ray binaries (LMXBs) could be studied in detail \citep[e.g.][]{gilfanov04}. Moreover, it has been established that (at least) a portion of unresolved X-ray emission is associated with the stellar population and is the superposition of a multitude of faint compact sources, such as active binaries (ABs) and cataclysmic variables \citep[CVs;][]{sazonov06,revnivtsev06,revnivtsev09}. Thus, if sufficiently deep \textit{Chandra} observations are available, then the various X-ray emitting components can be identified in nearby galaxies, hence the diffuse emission from hot X-ray gas can be separated from the population of resolved and faint unresolved compact objects. This extensive knowledge permits us to determine whether low-mass ellipticals host X-ray emitting gas and, additionally, to address the state of the hot gas. In the present paper, we study four elliptical galaxies, whose optical appearances are nearly identical, yet their X-ray properties are strikingly different. The four galaxies, NGC821, NGC3379, NGC4278, and NGC4697, are relatively nearby ($D=9.8-24.1$ Mpc) and have deep \textit{Chandra} observations (Figure \ref{fig:img}). Therefore, we are able to identify and remove the bulk of the X-ray emission from LMXBs, hence bright point sources do not significantly contaminate the diffuse emission. Furthermore, the low and stable instrumental background of \textit{Chandra} permits us to reliably study low surface brightness emission. The goals of this paper are twofold. First, we aim to unveil whether the sample galaxies host a significant amount of hot X-ray emitting gas. Second, if they do possess X-ray gas, we intend to measure its properties, morphology, and understand its physical state. \begin{table*} \caption{Elliptical galaxies studied in this paper.} \begin{minipage}{18.5cm} \renewcommand{\arraystretch}{1.3} \centering \begin{tabular}{c c c c c c c c c c c} \hline Name & Distance & $L_{K} $ & $M_{\star}/L_{K} $ & $M_{\star}$ & $N_{H}$ & Morph. & $ T_{\mathrm{obs}} $ & $ T_{\mathrm{filt}} $ & $L_{\mathrm{lim}}$ & $D_{\rm{25}}$ \\ & (Mpc) &($\mathrm{L_{K,\odot}}$) & ($M_{\odot}/L_{K,\odot} $) & ($M_{\odot}$) & (cm$^{-2}$) & type & (ks) & (ks) & ($ \mathrm{erg \ s^{-1}} $) & ($2a, 2b, \theta $) \\ & (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) \\ \hline NGC821 & $ 24.1^a $ & $ 8.2 \times 10^{10}$ & 0.83 & $ 6.8 \times 10^{10}$ & $ 6.4 \times 10^{20}$ & E6 & $ 229.7 $ & $ 187.6 $& $ 2 \times10^{37} $ & $ 2.45\arcmin, 2.10 \arcmin, 26.0\degr $ \\ NGC3379 & $ 9.8^b $ & $ 6.1 \times 10^{10}$& 0.83 & $ 5.1 \times 10^{10}$ &$ 2.9 \times 10^{20}$ & E1 &$ 341.4 $ & $ 310.0 $& $ 2 \times 10^{36} $ & $ 4.90\arcmin, 4.27 \arcmin, 71.0\degr $ \\ NGC4278 & $ 16.1^a $ & $ 7.1 \times 10^{10}$& 0.82 &$ 5.8 \times 10^{10}$ & $ 1.8 \times 10^{20}$ & E1-2 & $ 476.7 $ & $ 437.5 $& $ 4 \times 10^{36} $ & $ 2.88\arcmin, 2.82 \arcmin, 27.5\degr $ \\ NGC4697 & $ 11.8^a $ & $ 8.1 \times 10^{10}$& 0.82 &$ 6.6 \times 10^{10}$ & $ 2.1 \times 10^{20}$ & E6 & $ 195.7 $ & $ 159.9 $& $ 5 \times 10^{36} $ & $ 7.08\arcmin, 4.17 \arcmin, 83.1\degr $ \\ \hline \\ \end{tabular} \end{minipage} \textit{Note.} Columns are as follows. (1) References are: $^a$ \citet{tonry01} -- $^b $ \citet{m105distance}. (2) Total K-band luminosity. (3) K-band mass-to-light ratios computed from \citet{bell03} using the $B-V$ color indices of galaxies \citep{devaucouleurs91}. (4) Total stellar mass based on the K-band luminosity and the K-band mass-to-light ratios. (5) Galactic absorption \citep{dickey90}. (6) Morphological type, taken from NED (http://nedwww.ipac.caltech.edu/). (7) and (8) \textit{Chandra} exposure times before and after flare filtering. (9) Source detection sensitivity in the $ 0.5-8 $ keV energy range. (10) Major axis diameter, minor axis diameter, and position angle of the $D_{\rm{25}}$ ellipse. \\ \label{tab:list2} \end{table*} Since the X-ray emitting components of NGC821, NGC3379, NGC4278, and NGC4697 have already been analyzed to a certain extent by other authors, we briefly review previous works. The resolved and unresolved X-ray emitting components of NGC821 have been studied by \citet{pellegrini07} using \textit{Chandra} X-ray observations. In addition to their thorough analysis of bright LMXBs, they also concluded that the bulk of the unresolved emission originates from unresolved LMXBs and that hot X-ray gas may only be present in the inner $10\arcsec$ region. The unresolved X-ray emission of NGC3379 was first investigated by \citet{david05}, based on a $32$ ks \textit{Chandra} observation. They concluded that X-ray gas may be present within the central $15\arcsec$ region with a temperature of $kT=0.6$ keV. Based on a much deeper, $341$ ks, \textit{Chandra} data set, \citet{revnivtsev08} claimed that NGC3379 is virtually gas free, and the unresolved X-ray emission is built up from faint undetected compact objects, mostly by ABs and CVs. However, based on the same data set, \citet{trinchieri08} reported that NGC3379 hosts hot X-ray gas in the central $15\arcsec$ region, which is outflowing from the galaxy. Although the population of resolved sources in NGC4278 has been extensively studied \citep[e.g.][]{kim06}, the unresolved emission from NGC4278 has not been investigated in detail. The unresolved X-ray emitting components of NGC4697 were explored by \citet{sarazin01} based on a $40$ ks \textit{Chandra} observation. They demonstrated the presence of X-ray gas, which has a significantly broader distribution than the stellar light. However, more recently NGC4697 was observed by \textit{Chandra} for an additional $\sim$$150$ ks, allowing a better separation of bright LMXBs and truly diffuse emission. Additionally, accurate calibration of the population of faint compact objects only became available relatively recently. Hence, in some of the previous works, the emission from these sources could not be precisely disentangled from the hot X-ray gas. Therefore, our uniform analysis of the sample galaxies with the most up-to-date calibration of LMXBs and faint compact objects can lead to a better understanding of the X-ray gas content of low-mass ellipticals. The paper is structured as follows. In Section 2, we introduce the analyzed galaxy sample. In Section 3, we describe the reduction of the data. In Section 4, we study the X-ray gas content of the sample galaxies. The physical state of the detected X-ray gas is discussed in Section 5, and we summarize our results in Section 6.
|
We studied the unresolved X-ray emission, the hot ionized gas content, and the physical state of the hot X-ray gas in four low-mass elliptical galaxies (NGC821, NGC3379, NGC4278, NGC4697) based on archival \textit{Chandra} observations. Our results can be summarized as follows. \\ 1. We find that the bulk of the unresolved emission in NGC821 and NGC3379 originates from a large number of faint compact and stellar objects, such as CVs and ABs. Despite the non-detection of hot gas, low density, and hence low luminosity X-ray gas components may be present, which, driven by the energy input of SNe Ia, outflow from the galaxies at a steady rate. 2. We detect hot X-ray gas with a temperature of $kT\sim0.35$ keV in the central $\sim$$50\arcsec$ ($\sim$$3.9$ kpc) region of NGC4278. The total gas mass within this region is $\sim$$3\times 10^7 \ \rm{M_{\odot}}$, hence the corresponding gas mass fraction of $\sim$$0.06\%$. The X-ray gas exhibits a bipolar morphology in the northeast-southwest direction, suggesting that it is outflowing from the galaxy. We conclude that the outflowing mass can be replenished by the stellar yields of evolved stars and the outflow can be driven by the energy input of SNe Ia. Based on the existence of an outflow in NGC4278 and the energy budget of the galaxy, we place a lower limit of $\sim$$50\%$ on the supernova efficiency parameter. 3. We show that NGC4697 hosts X-ray gas at all radii, whose temperature within a region with a $\sim$$90\arcsec$ radius is $kT\sim0.3$ keV, beyond which radius the gas temperature increases to $\sim$$0.7$ keV. We identify the hotter gas with the group atmosphere surrounding NGC4697. Although the X-ray gas has a significantly broader distribution than the stellar light, it does not show any asymmetries. The gas mass within the central $\sim$$90\arcsec$ region is $\sim$$2.1\times 10^8 \ \rm{M_{\odot}}$, implying a gas mass fraction of $\sim$$0.4\%$, which is comparable with those observed in luminous massive early-type galaxies. Taken together, this evidence indicates that the X-ray gas is most likely in hydrostatic equilibrium, however a subsonic outflow cannot be excluded. \bigskip \begin{small} \noindent \'AB thanks Alexey Vikhlinin, Marat Gilfanov, and Junfeng Wang for helpful discussions. This research has made use of \textit{Chandra} data provided by the Chandra X-ray Center. The publication makes use of software provided by the Chandra X-ray Center (CXC) in the application package CIAO. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. In this work the NASA/IPAC Extragalactic Database (NED) has been used. The authors acknowledge the use of the HyperLeda database (http://leda.univ-lyon1.fr). \'AB acknowledges support provided by NASA through Einstein Postdoctoral Fellowship grant number PF1-120081 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060. WF and CJ acknowledge support from the Smithsonian Institution. \end{small}
| 12 | 6 |
1206.2434
|
1206
|
1206.2645_arXiv.txt
|
We investigate the evolution of the H$\alpha$ equivalent width, EW(H$\alpha$), with redshift and its dependence on stellar mass, using the first data from the 3D-HST survey, a large spectroscopic Treasury program with the HST-WFC3. Combining our H$\alpha$ measurements of 854 galaxies at $0.8<z<1.5$ with those of ground based surveys at lower and higher redshift, we can consistently determine the evolution of the EW(H$\alpha$) distribution from z=0 to z=2.2. We find that at all masses the characteristic EW(H$\alpha$) is decreasing towards the present epoch, and that at each redshift the EW(H$\alpha$) is lower for high-mass galaxies. We find EW(H$\alpha$) $\sim (1+z)^{1.8}$ with little mass dependence. Qualitatively, this measurement is a model-independent confirmation of the evolution of star forming galaxies with redshift. A quantitative conversion of EW(H$\alpha$) to sSFR (specific star-formation rate) is model dependent, because of differential reddening corrections between the continuum and the Balmer lines. The observed EW(H$\alpha$) can be reproduced with the characteristic evolutionary history for galaxies, whose star formation rises with cosmic time to $z \sim 2.5$ and then decreases to $z$ = 0. This implies that EW(H$\alpha$) rises to 400 $\rm\AA$ at $z = 8$. The sSFR evolves faster than EW(H$\alpha$), as the mass-to-light ratio also evolves with redshift. We find that the sSFR evolves as $(1+z)^{3.2}$, nearly independent of mass, consistent with previous reddening insensitive estimates. We confirm previous results that the observed slope of the sSFR-$z$ relation is steeper than the one predicted by models, but models and observations agree in finding little mass dependence.
|
Several studies have combined different star formation indicators in order to study the evolution of star-forming galaxies (SFGs) with redshift. At a given redshift low mass galaxies typically form more stars per unit mass (i.e., specific star-formation rate, sSFR) than more massive galaxies (Juneau et al. 2005, Zheng et al. 2007, Damen et al. 2009). In addition the sSFR of galaxies with the same mass increases at higher redshift. However, semi-analytical models and observations are at odds with regards to the rate of decline of the sSFR towards low-redshift (Damen et al. 2009, Guo et al. 2010). One of the main observational caveats is that most of the studies covering a wide redshift range use diverse SFR indicators (such as UV, IR, [OII], H$\alpha$, SED fitting). This is a consequence of the fact that it is difficult to use the same indicator over a wide range of redshifts. One therefore has to rely on various conversion factors, often intercalibrated at $z=0$ and re-applied at higher redshift. \begin{figure*}[!t!] \centering \includegraphics[width=18cm]{fig1.ps} \caption{EW(H$\alpha$) against mass, for different redshift samples. Vertical lines represent the limiting mass of the analysis. Black symbols are objects with H$\alpha$ detection with S/N $>$ 3 and red arrows represent upper limits. The green diagonal lines represent the detection limit of the 3D-HST data. Blue solid lines represent the mean EW(H$\alpha$) of detected SFGs, in 0.5 dex mass bins. Red solid lines represent the mean EW(H$\alpha$) of all galaxies, assuming EW(H$\alpha$)=0 for non-detected objects. Errors of the means are computed with a bootstrap approach. At each redshift higher mass galaxies have lower EW(H$\alpha$) than less massive objects.} \label{EWmass} \end{figure*} A well-calibrated standard indicator of the SFR is the H$\alpha$ luminosity (Kennicutt, 1998). However, H$\alpha$ is shifted into the infrared at $z > 0.5$, and it is difficult to measure due to the limitations of ground-based near-IR spectroscopy. Comparing measures of H$\alpha$ at different redshifts has therefore been a challenge. Most of the H$\alpha$ studies at high redshift are based on narrow-band photometry (e.g. the HiZELS survey, Geach et al. 2008). The 3D-HST survey (Brammer et al., 2012) provides a large sample of rest-frame optical spectra with the WFC3 grism, which includes the H$\alpha$ emission in the redshift range $0.8 < z < 1.5$. Taking advantage of the first data from the survey (45\% of the final survey products) we investigate for the first time the star formation history (SFH) of the Universe with H$\alpha$ spectroscopy, using a consistent SFR indicator over a wide redshift range. We evaluate the dependence of the H$\alpha$ Equivalent Width, EW(H$\alpha$), on stellar mass ($\rm M_{*}$) and redshift (up to $z \sim 2$), comparing the 3D-HST data with other surveys in mass selected samples with $\rm M_{*} > 10^{10} M_{\odot}$. Since EW(H$\alpha$) is defined as the ratio of the H$\alpha$ luminosity to the underlying stellar continuum, it represents a measure of the the current to past average star formation. It is therefore a model independent, directly observed proxy for sSFR. We also derive SFRs from the H$\alpha$ fluxes. We evaluate the mean sSFR in stellar mass bins and study its evolution with redshift. The slope of the sSFR-$z$ relation in different mass bins indicates how fast the star formation is quenched in galaxies of various masses. Finally, we compare our findings to other studies (both observations and models), discussing the physical implications and reasons for any disagreements. \begin{figure*} \includegraphics[width=18cm]{fig2top.ps} \\ \includegraphics[width=18cm]{fig2bottom.ps} \caption{Evolution of EW(H$\alpha$) (top) and sSFR(H$\alpha$) (bottom) with redshift, in different mass bins, for SFGs (left) and all objects (right). Errors on the average EWs have been evaluating through bootstrapping. Dotted lines are the best fit power laws ${\rm EW}(z) \sim (1+z)^{p}$. At fixed mass the average EW(H$\alpha$) and sSFR(H$\alpha$) increase with redshift, with a power law of ${\rm EW(H\alpha)} \sim (1+z)^{1.8}$ and ${\rm sSFR(H\alpha)} \sim (1+z)^{3.3}$ with little mass dependence. The effect of a luminosity dependent dust correction (Garn et al. 2010) correction is shown by the right axis. The effect of A(H$\alpha$)=1 is shown by the black arrow.} \label{evolutionEW} \end{figure*}
|
We have used the 3D-HST survey to measure the evolution of the EW(H$\alpha$) from z=0 to z=2. We show that the EW(H$\alpha$) evolves strongly with redshift, at a constant mass, like $(1+z)^{1.8}$. The evolution is independent of stellar mass. The equivalent width goes down with mass (at constant redshift). The increase with redshift demonstrates the strong evolution of star forming galaxies, using a consistent and completely model independent indicator. We explore briefly the implied sSFR evolution, ignoring dust extinction. We find that the evolution with redshift is strong (sSFR $\sim (1+z)^{3.2}$). This stronger evolution is expected as the mass-to-light ratio of galaxies evolves with time, and this enters the correction from EW to sSFR. The increase with redshift is faster that predicted by semi-analytical models (e.g., Guo \& White 2008), consistent with earlier results. We construct the characteristic SFH of a $\rm 10^{11} M_{\odot}$ galaxy. This simple history reproduces the observed evolution of the EW(H$\alpha$) to $z$=2.5, and even to $z$=4. It implies that the EW(H$\alpha$) continue to increase to higher redshifts, up to 400 $\rm\AA$ at $z$=8. This has a significant impact for the photometry and spectroscopy of these high redshift sources. The study can be expanded in the future when the entire 3D-HST survey will be available, doubling the sample and including the ACS grism. In addition to increased statistics, the ACS grism will allow evaluation of the Balmer decrement and therefore a precise dust corrected evaluation of SFR. Moreover, a statistically significant H$\alpha$ sample at $z\sim 1$ will be central to understand the composition, the scatter and the physical origin of the so called 'star-forming-main sequence'.
| 12 | 6 |
1206.2645
|
1206
|
1206.0640_arXiv.txt
|
Monojet and monophoton final states with large missing transverse energy (${\not E}_T$) are important for dark matter (DM) searches at colliders. We present analytic expressions for the differential cross sections for the parton-level processes, $q\overline{q}(qg)\rightarrow g(q) \chi \overline{\chi}$ and $q\overline{q}\rightarrow \gamma\chi \overline{\chi}$, for a neutral DM particle with a magnetic dipole moment (MDM) or an electric dipole moment (EDM). We collectively call such DM candidates dipole moment dark matter (DMDM). We also provide monojet cross sections for scalar, vector and axial-vector interactions. We then use ATLAS/CMS monojet${+\not E}_T$ data and CMS monophoton$+{\not E}_T$ data to constrain DMDM. We find that 7~TeV LHC bounds on the MDM DM-proton scattering cross section are about six orders of magnitude weaker than on the conventional spin-independent cross section.
|
Collider data have provided an important avenue for dark matter (DM) searches, especially for candidates lighter than about 10~GeV~\cite{tait,tait2,chi2}, for which direct detection experiments have diminished sensitivity due to the small recoil energy of the scattering process. In fact, current assumption-dependent bounds on spin-dependent DM-nucleon scattering from LHC data, obtained using an effective field theory framework, are comparable or even superior to those from direct detection experiments for DM lighter than a TeV~\cite{tait2,chi2}. The final states that have proven to be effective for DM studies at colliders are those with a single jet or single photon and large missing transverse energy (${\not E}_T$) or transverse momentum. Our goal is study these signatures for DM that possesses a magnetic dipole moment (MDM) or an electric dipole moment (EDM)~\cite{kamion}; earlier work can be found in Ref.~\cite{fortin}. Thus, the DM may be a Dirac fermion, but not a Majorana fermion. We refer to these DM candidates as dipole moment dark matter (DMDM). We begin with a derivation of the differential cross sections for the parton-level processes that give monojet$+{\not E}_T$ and monophoton$+{\not E}_T$ final states at the LHC. We then use 7~TeV $j+{\not E}_T$ data from ATLAS~\cite{atlas} and CMS~\cite{cms4.7fb}, and $\gamma+{\not E}_T$ data from CMS~\cite{CMS-monophoton} to constrain DMDM. Finally, we place bounds on the MDM DM-proton scattering cross section.
| 12 | 6 |
1206.0640
|
|
1206
|
1206.0476_arXiv.txt
|
We report the discovery of quasi-periodic oscillations (QPO) at $\sim$11 mHz in two RXTE observations and one Chandra observation of the black hole candidate H1743--322. The QPO is observed only at the beginning of the 2010 and 2011 outbursts at similar hard color and intensity, suggestive of an accretion state dependence for the QPO. Although its frequency appears to be correlated with X-ray intensity on timescales of a day, in successive outbursts eight months apart we measure a QPO frequency that differs by less than $\approx$2.2 mHz while the intensity had changed significantly. We show that this $\sim$11 mHz QPO is different from the so-called Type-C QPOs seen in black holes and that the mechanisms that produce the two flavors of variability are most probably independent. After comparing this QPO with other variability phenomena seen in accreting black holes and neutron stars, we conclude that it best resembles the so-called ``1 Hz'' QPOs seen in dipping neutron star systems, although having a significantly lower (1-2 orders of magnitude) frequency. If confirmed, H1743--322 is the first black hole showing this type of variability. Given the unusual characteristics and the hard-state dependence of the $\sim$11~mHz QPO, we also speculate whether these oscillations could instead be related to the radio jets observed in H1743--322. A systematic search for this type of low-frequency QPOs in similar systems is needed to test this speculation. In any case, it remains unexplained why these QPOs have only been seen in the last two outbursts of H1743--322.
|
\label{sec:intro} Quasi-periodic oscillations (QPOs) with characteristic frequencies between $\sim$1 mHz and hundreds of Hz have now been observed in the X-ray flux of many low-mass X-ray binaries (LMXBs) containing neutron stars (NSs) and black holes (BHs). The characteristics of many of these QPOs are known to generally correlate with the source spectral states and/or X-ray luminosity \citep[see, e.g.,][for a review]{Vanderklis06}. A number of QPOs and broad band variability components can be present simultaneously in the power spectra of the X-ray light curves of accreting NS systems. These can be modeled with Lorentzian components and are often denoted by their characteristic frequencies \citep[examples include the so-called break, the hump, the LF QPO, the \textit{$\ell$ow} component and the upper and lower kilohertz QPOs, e.g.,][]{Altamirano08}. Their frequencies are known to be correlated to each other \citep{Wijnands99a,Belloni02}. However, there are also components which appear to be uncorrelated. Among these uncorrelated exceptions are: (i) the hecto-Hz QPOs which have frequencies constrained within $\sim$100~Hz and $\sim$300~Hz \citep[e.g.,][]{Altamirano08}, (ii) the 1~Hz QPOs in dipping sources \citep[e.g.,][]{Jonker99, Jonker00, Homan03a}, (iii) a QPO with frequencies in the mHz range which very likely results from marginally stable nuclear burning of hydrogen/helium on the NS surface \citep[e.g.,][]{Heger07} and (iv) the 1~Hz flaring observed in two accreting millisecond X-ray pulsars when the sources were observed at low-luminosities \citep[e.g.][]{Wijnands04,Patruno10b}. BHs generally show three main types of low-frequency QPOs \citep[Types A, B and C, e.g.,][]{Casella05} and, in a few cases, high-frequency QPOs \citep[with frequencies between 70~Hz and 450~Hz, e.g.,][for a review]{Vanderklis06}. In some cases observed QPOs are not easily identified with either Type A, B or C; this may be due to having data of low statistical quality or a source being observed in an unusual spectral state. In general, some of the same variability components appear to be present in both NS and BHs \citep{Miyamoto93,Vanderklis94,Belloni02}. For example, \citealt{Casella05} argue that the Type A, B and C QPOs in black holes correspond to the so-called Flaring Branch, Normal Branch and Horizontal Branch Oscillations, respectively, that were identified in high luminosity NS systems (the ``Z'' sources). Outside of the Type A, B, and C QPO classifications there is additional low-frequency variability in BHs, including for example the ``heart-beat'' QPOs, observed so far only in the BHs GRS~1915+105 \citep[e.g, ][]{Belloni00} and IGR~J17091--3624 \citep[e.g.,][]{Altamirano11d}. Recently, \citet{Strohmayer11a} reported on a \textit{Rossi X-ray Timing Explorer} (RXTE) observation of the 2011 outburst of the black hole candidate (BHC) H1743--322. In addition to the typical Type-C QPO and strong broad-band noise generally seen at the beginning of the outbursts of BH systems, \citet{Strohmayer11a} found an unusual $\sim$91s QPO which they suggested might be due to a second active source in the $1^o$ Proportional Counter Array \citep[PCA; ][]{Jahoda06} field of view (FoV). However, subsequent observations with {\it Swift} and {\it INTEGRAL} did not show any additional nearby sources. Triggered by the possibility that this $\sim$91s QPO might instead be intrinsic to H1743--322, we searched RXTE, Swift and {\it Chandra} data for other instances of similar QPOs. In this Letter we report the discovery of a similar QPO in additional {\it RXTE} and {\it Chandra} observations of H1743--322 and discuss the implications of our findings. H1743--322 was first detected in outburst in 1977 \citep{Kaluzienski77} and then rediscovered by {\it INTEGRAL} in 2003 \citep{Revnivtsev03b}. Since 2003 several smaller outbursts of H1743--322 have been observed \cite[see][and references therein]{Motta10}. From its similarities with the dynamically confirmed BH X-ray binary XTE J1550-564, the source was classified as a BH candidate \citep[but also see \citealt{Homan05b}]{McClintock09}. H1743--22 is at a distance of $8.5\pm0.8$~kpc \citep{Steiner11} and, from the evidence of X-ray dipping behavior in one observation \citep{Homan05b}, the inclination angle of its accretion disc is believed to be relatively high ($>70^o$) to our line of sight. However, this high inclination needs to be confirmed, as no thorough analysis of the dipping behavior has yet been reported. \begin{figure*} \centering \resizebox{2\columnwidth}{!}{\rotatebox{0}{\includegraphics[clip]{./f1.eps}}} \caption{Crab-normalized light curves of all outbursts of the BHC H1743--322 as seen with RXTE pointed observations. Each point corresponds to an average per observation. The inset shows the last two outbursts. The triangles mark the times when we detected the mHz QPOs.} \label{fig:lc} \end{figure*} \begin{figure} \centering \resizebox{1\columnwidth}{!}{\rotatebox{0}{\includegraphics[clip]{./f2.eps}}} \caption{Hardness--intensity diagram of all outbursts of the BHC H1743--322 as seen with RXTE pointed observations. Each point corresponds to an average per observation. Inset: blow-up of the region in which we detected the mHz QPOs, with triangles denoting the mHz QPO observations. Arrows $\alpha$ and $\beta$ mark the comparison power spectra in Figure~\ref{fig:pds}. } \label{fig:hid} \end{figure} \begin{figure} \centering \resizebox{1\columnwidth}{!}{\rotatebox{0}{\includegraphics[clip]{./f3.eps}}} \caption{10s binned RXTE light curves (2--60 keV) of the 3 orbits in which we detect the mHz QPOs. Panels A and B correspond to two orbits in observation 95368-01-01-00. Panel C corresponds to the single orbit observation 96425-01-01-00. } \label{fig:mhzlc} \end{figure} \begin{figure*} \centering \resizebox{2.\columnwidth}{!}{\rotatebox{0}{\includegraphics[clip]{./f4.eps}}} \caption{\textit{Left}: Average power spectra of the two RXTE observations where we detect the mHz QPOs. In the upper panel (2010 observation) the Type-C QPOs are at $0.919\pm0.001$~Hz and $1.852\pm0.001$~Hz while in the lower panel (2011 observation) they are at $0.424\pm0.003$~Hz and $0.856\pm0.004$~Hz. Their quality factors (Q) are $13.0\pm0.5$, $10.0\pm0.6$, $11\pm2$ and $9\pm1$ and their fractional rms amplitudes $11.9\pm0.2$\%, $9.4\pm0.2$\% $10.7\pm0.4$\% $10.9\pm0.5$\%, respectively. The inset panels show the fractional rms amplitude vs. energy for the 11 mHz QPOs. \textit{Right}: Comparison power spectra without mHz QPOs but at similar spectral state (see Figure~\ref{fig:hid} and Section~\ref{sec:results}). The vertical dotted lines drawn at 12.5 mHz and 1 Hz are shown to guide the eye.} \label{fig:pds} \end{figure*} \begin{figure} \centering \resizebox{1\columnwidth}{!}{\rotatebox{0}{\includegraphics[clip]{./f5.ps}}} \caption{Dynamical power spectra from the dispersed (i.e., excluding the zeroth order image) HETG {\it Chandra} data showing the frequency evolution of the mHz QPO. We computed overlapping power spectra by using 5000 s intervals, with a new interval beginning every 1000 s. Contours of constant Leahy-normalized power are drawn at values of 25, 40, 50, 60, 75, 90, 100 and 110. Start time is August 8th, 2010, 23:03:48UT.} \label{fig:dyn} \end{figure}
|
We report the discovery of QPOs at $\sim$11 mHz in two RXTE and one Chandra observation of the BHC H1743--322. In successive outbursts eight months apart we measure a QPO frequency that differs by less than $\approx1.5$ mHz (including the 60ks duration of the {\it Chandra} observation, see Figure~\ref{fig:dyn}). The fractional rms amplitude of the oscillation appears to be correlated with energy in the 2011 observation, but consistent with a constant value in the 2010 observation. The QPO is observed at the beginning of two different outbursts at similar hard color and intensity, suggestive of an accretion state dependence for the QPO. Although the {\it Chandra} data reveal that the QPO frequency might be correlated with intensity on timescales of hours, this correlation probably changes in between outbursts, as we find the same frequency (within $\approx0.4$ mHz) in observations separated by about 800 days and at source intensities different by $\approx10$ mCrab \citep[this resembles the so called ``parallel tracks'' observed in the frequency vs. intensity diagrams of NS kHz QPOs, e.g, ][]{Mendez99a}. Except for the 11 mHz QPOs, the RXTE power spectra of these two observations are typical of the low-hard state of BH LMXBs, showing Type-C QPOs on top of strong broad band noise. Given that (i) the power spectra characteristics do not change with mHz QPO phase and (ii) the frequency of the mHz QPOs is rather constant ($\lesssim0.4$mHz) between the 2010 and 2011 RXTE observation, while the Type-C QPO frequency varies by a factor of about 2, we conclude that mechanisms that produce the mHz QPOs and Type C QPOs are not closely related. The fact that the frequency of these new oscillations is fairly constant raises the question of whether they represent a characteristic frequency of a process not yet identified before. Several types of QPOs with frequencies in the mHz range have been reported in two BH systems and in some NS systems. Below we compare our results with those seen in other sources and discuss whether we can identify the 11~mHz QPOs with any of them based on the characteristics of the oscillations and the source state in which they occur. Highly structured, high-amplitude variability has been seen in the BH systems GRS~1915+105 \citep[e.g.,][]{Belloni00} and IGR~J17091--3624 \citep[e.g.,][]{Altamirano11d}. Some of these variations are known as ``heartbeats'' and are thought to be due to limit cycles of accretion and ejection in an unstable disk \citep[e.g.,][]{Neilsen11}. These ``heartbeat'' QPOs are in the mHz range, occur only during the high-luminosity, soft-state of these two BH systems and, at least in the case of IGR~J17091--3624, can have rms amplitudes as low as $\sim$3\% \citep[e.g.,][]{Altamirano11d}. For H1743--322 we only find the new mHz QPOs during the rise of the outburst \citep[at $L_X < 3 \cdot 10^{37}$ egs s$^{-1}$, e.g.,][]{Motta10}, when the spectrum of the source is dominated by the hard component. GRS~1915+105 is thought to be very often at an Eddington or a super-Eddington luminosity \citep[e.g., ][]{Done04}; this could also be the case of IGR~J17091--3624 although the distance to this source is not yet known \citep[see discussion in ][]{Altamirano11d}. Given the major differences between source state and luminosity in GRS~1915+105 and IGR~J17091--3624 as compared with H1743--322, we conclude that the mHz QPOS in H1743--322 most probably represent a different phenomenon than the ``heartbeat'' QPOs and the other highly-structured low-frequency variability seen in GRS~1915+105 and IGR~J17091--3624. QPOs with intensity-independent frequencies in the mHz range have been found in at least four NS systems \citep{Revnivtsev01,Strohmayer11}. The occurrence of these QPOs depends on source state, but they are thought to be the signature of marginally stable burning of helium on the NS surface \citep{Heger07}. A similar QPO, but with an intensity-dependent frequency was also found in the 11 Hz X-ray pulsar IGR J17480--2446 in Terzan 5 \citep{Linares11}. The fact that (i) the occurrence of these NS oscillations are intimately related with thermonuclear X-ray bursts, (ii) are thought to come from the NS surface and (iii) their spectrum is generally soft \citep{Revnivtsev01,Altamirano08c}, indicates that they are most probably a different phenomena from what we detect in H1743--322. \citet{Wijnands04} reported a modulation at $\sim$1~Hz in the light curve of the accreting millisecond X-ray pulsar (AMXP) SAX~J1808.4--3658. A similar type of QPO \citep{Patruno10b} was found in the AMXP NGC~6440 X-2 \citep{Altamirano09}. These QPOs have been seen at low luminosities (less than a few $10^{36}$ erg s$^{-1}$), at frequencies between 0.8 and 1.6 Hz and with large amplitudes (up to 100\% fractional rms \citep{Patruno09d}). The high amplitude of theses oscillations, the fact that they have only been seen in AMXPs, and that their occurrence is most probably related to the onset of the propeller regime \citep{Patruno09d} suggests that these $\sim$1~Hz QPOs are not related to those we see in H1743--322. A so called ``1~Hz QPO'' has been reported for (four) dipping NS systems \citep{Jonker99, Jonker00, Homan03a,Bhattacharyya06c}. These QPOs appear to be different from the ``zoo'' of correlated low-frequency features seen in the power spectra of NS systems. The fractional rms amplitude of these QPOs is approximately constant and energy independent during the persistent emission, dips and thermonuclear X-ray bursts. Although the QPO frequency has been seen to vary between 0.6 and 2.4 Hz in two of the sources \citep{Jonker00, Homan99}, the ``1~Hz QPO'' name stands for the fact that its frequency can be rather constant for long periods of time. It has been suggested that these QPOs are related only to high inclination sources from which we might be observing modulation effects of the accretion stream material falling onto the disk, or some kind of modulation produced at the disk edge \citep[e.g.,][and references within]{Jonker00,Smale01,Vanderklis06}. The fact that H1743--322 is thought to be a high inclination source \citep{Homan05b}, that the fractional rms amplitude of the mHz QPOs we find does not vary strongly with energy and that its frequency is stable, indicate that they might be related to the process that produces the so called ``1~Hz QPO'' in dipping NS systems. If true, this would be the first BH system showing such QPOs, raising the question of why the frequency of the QPO is between one and two orders of magnitude lower in H1743--322 than in the NS. One possibility is that the frequency range in which this QPO occurs scales with mass or that it depends on the orbital period of the system, as H1743--322 is thought to have an orbital period longer than 10 hr \citep{Jonker10} while the NS systems have orbital periods shorter than 6 hr \citep[e.g.,][]{Jonker99, Jonker00, Homan03a}. It is worth noting that the high inclination dipping BH 4U~1630--47 shows QPOs with frequency as low as $\sim$0.1~Hz, however, these QPOs are due to semi-regular short ($\sim$5 sec) dips \citep{Dieters00}. Following \citet{Kuulkers98} we produced colors using 1 sec light curves in different bands of the 2010 and 2011 observation of H1743--322. We do not observe any hardening (or any other variation) of the spectra as a function of QPO phase, implying that the 11 mHz QPOs are most probably not regular dips as seen in 4U~1630--47. H1743--322 is well known for its radio jets \citep[e.g.,][]{Steiner11, Miller-Jones12}. \citet{Markoff05} have suggested that the hard state emission could be due to synchrotron self-Compton emission from the base of the jet, and \citet{Russell10} have recently suggested that the jet mechanism might have dominated the X-ray variability in a portion of the hard state of the 2000 outburst of the BHC XTE~J1550--556. The 11 mHz QPOs we find in H1743--322 appear to be different from most types of variability seen in other BH and NS systems, and so we speculate whether these oscillations could be related to the radio jets observed in H1743--322. Unfortunately no radio measurements have been reported as yet for the 2010 and 2011 outbursts of H1743--322 \citep[and the radio flux is known to change between outbursts,][]{Miller-Jones12} and to our knowledge no model yet predicts that the jet could sometimes modulate the X-ray flux at a characteristic frequency. Clearly more theoretical work is needed in this direction. If related to the jets, it remains unexplained why these low-frequency QPOs have not yet been identified in other BHs with known radio emission. Clearly, a systematic search for this type of low-frequency QPO in the RXTE BH archive is needed to test this speculation.
| 12 | 6 |
1206.0476
|
1206
|
1206.4313_arXiv.txt
|
As brown dwarfs cool, a variety of species condense in their atmospheres, forming clouds. Iron and silicate clouds shape the emergent spectra of L dwarfs, but these clouds dissipate at the L/T transition. A variety of other condensates are expected to form in cooler T dwarf atmospheres. These include Cr, MnS, \nas, ZnS, and KCl, but the opacity of these optically thinner clouds has not been included in previous atmosphere models. Here, we examine their effect on model T and Y dwarf atmospheres. The cloud structures and opacities are calculated using the \ct{AM01} cloud model, which is coupled to an atmosphere model to produce atmospheric pressure-temperature profiles in radiative-convective equilibrium. We generate a suite of models between \teff\ = 400 and 1300 K, log $g$=4.0 and 5.5, and condensate sedimentation efficiencies from \fsed=2 to 5. Model spectra are compared to two red T dwarfs, Ross 458C and UGPS 0722--05; models that include clouds are found to match observed spectra significantly better than cloudless models. The emergence of sulfide clouds in cool atmospheres, particularly \nas, may be a more natural explanation for the ``cloudy'' spectra of these objects, rather than the re-emergence of silicate clouds that wane at the L-to-T transition. We find that sulfide clouds provide a mechanism to match the near- and mid-infrared colors of observed T dwarfs. Our results indicate that including the opacity of condensates in T dwarf atmospheres is necessary to accurately determine the physical characteristics of many of the observed objects.
|
Since the first brown dwarfs were discovered two decades ago \cp{Becklin88, Nakajima95}, hundreds more brown dwarfs have been discovered using wide field infrared surveys. These substellar objects, too low in mass to fuse hydrogen in their cores, range in mass from $\sim$ 13 to 75 \mj\ and are classified by their spectra into L, T, and most recently Y dwarfs \cp{Kirkpatrick05, Cushing11}. Without hydrogen fusion as an internal energy source, brown dwarfs never reach a main-sequence state of constant luminosity; instead, they cool over time and will transition through the brown dwarf spectral sequence as different molecules and condensates form in their atmospheres. To model their atmospheres accurately requires an understanding of both the chemistry and physics of the materials that will condense into clouds. \subsection{Modeling L and T Dwarfs} \subsubsection{L dwarfs} Grain or condensate formation has been predicted to play an important role in L dwarf atmospheres since before the first brown dwarfs were discovered \cp{Lunine86, Lunine89}. Modern equilibrium thermochemical models predict that a variety of different condensates will form in L dwarf atmospheres \cp{Fegley94, Lodders99}; by comparing models to observations, it is now well-established that a variety of refractory materials condense in L dwarfs \cp[see, e.g.][]{Tsuji96, Allard01,Marley02,Burrows06,Cushing08}. The condensates that appear to dominate, based on the abundances of elements available to condense, are corundum (Al$_2$O$_3$), iron (Fe), enstatite (MgSiO$_3$), and forsterite (Mg$_2$SiO$_4$), and these species form cloud layers, removing atoms found within the clouds from the lower pressure atmosphere above \cp{Fegley96, Lodders02, Lodders03, Lodders06, Visscher10}. Within windows between major molecular absorption bands, there is little gas opacity so, in models without clouds, the emergent flux comes from hotter layers deep within the atmosphere. Cloud opacity tends to suppress the flux in the near-infrared within these windows; a thick cloud layer limits the depth from which the planet can radiate, removing some of the flux at these wavelengths, and forcing it to other wavelengths \cp{AM01}. When the opacity of these clouds is included in radiative-convective equilibrium models of brown dwarf atmospheres, the resulting model spectra match those of observed L dwarfs \cp{Cushing06, Cushing08, Saumon08, Stephens09}. Observations show that there is a range of colors for a given spectral type, which are believed to be associated with cloud variations or metallicity, but the details of this are not fully understood. Regardless, observed colors and spectra of L dwarfs cannot be well-matched without a significant cloud layer \cp{Burrows06}. \subsubsection{T Dwarfs} As a brown dwarf continues to cool, it undergoes a significant transformation in its observed spectrum when it reaches an effective temperature of approximately 1400 K. Objects cooler than this transitional effective temperature begin to show methane absorption features in their near-infrared spectra and, when these features appear, are classified as T dwarfs \cp{Burgasser02, Kirkpatrick05}. Within a small range of effective temperature, the iron and silicate clouds become dramatically less important. \ct{Marley10} show that this transition could potentially be explained by the breaking up of these cloud layers into patchy clouds, but the details of the transition are still very much unknown. However, the recent discovery of highly photometrically variable early T dwarfs suggests that cloud patchiness may indeed play a role \cp{Radigan12, Artigau09}. Regardless, as the clouds dissipate, the atmospheric windows in the near-infrared clear. Flux emerges from deeper, hotter atmospheric layers, and the brown dwarf becomes much bluer in $J-K$ color (see Figure \ref{intro-colormag}). \subsubsection{History of Modeling T Dwarfs} The first T dwarf discovered, Gl229B \cp{Nakajima95, Oppenheimer95}, was modeled by \ct{Marley96}, \ct{Allard96}, \ct{Fegley96}, and \ct{Tsuji96} using cloud-free models. These models assume that the condensate-forming materials have been removed from the gas phase, but do not contribute to the cloud opacity. Early T dwarfs are generally quite well-modeled using cloudless atmospheric models. However, recent observations of cooler T dwarfs suggest that T dwarfs of type T8 or later (\teff $\lesssim$ 800 K) appear to be systematically redder in $J-K$ and $J-H$ colors than the cloudless models predict (see Figure \ref{intro-colormag}). One of the challenges of modeling brown dwarf spectra is the uncertainties in the absorption bands of major gas species such as methane and ammonia, as well as absorption due to collisional processes. Recent work by \ct{Saumon12} has modeled a range of brown dwarfs using improved line lists for ammonia from \ct{Yurchenko11} and an improved treatment of the pressure-induced opacity of H$_2$ collisions from \ct{Richard12}. This work improves the accuracy of model near-infrared spectra and reddens the $J-K$ colors of the model spectra with effective temperatures between 500 and 1500 K. The color shift is due to decreased opacity in $K$ band from collision-induced absorption and, for \teff $\lesssim$ 500 K model only, increased ammonia opacity in $J$ band. However, these improvements do not change the colors enough to match the colors of the coolest T dwarfs. \begin{figure}[] \begin{minipage}[b]{\linewidth} \includegraphics[width=3.6in]{fig1a.eps} \vspace{-4mm} \end{minipage} \begin{minipage}[b]{\linewidth} \includegraphics[width=3.6in]{fig1b.eps} \vspace{-4mm} \end{minipage} \caption{Color-magnitude diagrams of L and T dwarfs. \emph{Top:} Observed brown dwarf $J-H$ color is plotted against the absolute $H$ magnitude for all known brown dwarfs with measured parallax. M dwarfs are plotted as black circles, L dwarfs as red circles, and T dwarfs as blue circles. Observational data are from \ct{Dupuy12}. Models are plotted as solid lines. Blue lines are cloudless models and red lines are cloudy (\fsed=2) models that include iron, silicate, and corundum clouds. Each labeled temperature marks the approximate location of the model with that effective temperature. The surface gravity of all models is log $g$ =5.0 (1000m/s$^2$). \emph{Bottom: } Same as above, but $J-K$ color is plotted against the absolute $K$ magnitude. } \label{intro-colormag} \end{figure} Clouds are a natural way to redden near-infrared spectra. Cloud opacity limits the emergent flux most prominently in $J$ band, so it reddens the $J-K$ and $J-H$ colors of the models. \ct{Burgasser10} suggest that the remnants of the iron and silicate clouds could redden these cool T dwarfs, but here we suggest instead that the formation of other condensates, which naturally arise from equilibrium chemistry calculations, may play an important role. \subsubsection{Y Dwarfs} The proposed spectral class Y encompasses brown dwarfs that have cooled below \teff$\sim$500 K; a handful of these cool objects have recently been discovered \cp{Cushing11, Kirkpatrick12}. At these temperatures, NH$_3$ begins to play a more significant role in shaping the near-infrared spectra, and sodium and potassium wane in importance in the optical because they condense into clouds. Appreciable amounts of H$_2$O and NH$_3$ will condense into clouds at \teff$\sim$350 K and $\sim$200 K, respectively, and will further alter Y dwarf spectra. As we discover and characterize more of these cold objects, the study of clouds will be crucial to understand their spectral characteristics. \subsection{Secondary Cloud Layers} Silicate, iron, and corundum, which are the condensates that dominate the cloud opacity in our L dwarf models, are not the only condensates that thermochemical models predict will form in substellar atmospheres as they cool. Other condensates will form at lower temperatures and add to the cloud opacity via the same physical processes that formed the iron and silicate cloud layers. In cool substellar atmospheres, \nas\ (sodium sulfide) has been predicted to play a potentially significant role \cp{Lodders99, Lodders06, Visscher06}. Other species expected to condense at these lower temperatures (roughly 600 to 1400 K) include Cr, MnS, ZnS, and KCl. To our knowledge, none of these five condensates have been included in a brown dwarf atmosphere model before now. \ct{Marley00} estimated column optical depths for several of these species and recognized that \nas\ could be important at low $T_{\rm eff}$ but did not include this species in subsequent modeling because of lack of adequate optical constant data. \ct{Burrows01, Burrows02} noted that \nas\ and KCl will condense in cool T dwarfs, but also noted that the indices of refraction are difficult to find. Helling and collaborators \cp{Helling06} also recognized that some of these species will form condensates in some cases but also did not compute model atmospheres that included this opacity source. \ct{Fortney05c} noted that some of these species might be detectable in extrasolar planet transit spectra which probe a longer path length through the atmosphere.
|
\subsection{Formation of Clouds} Clouds must form in brown dwarf atmospheres as they cool; there is no way to avoid the condensation of different species as the atmosphere reaches lower effective temperatures. In these models, we parameterize the opacity of clouds by creating a distribution of cloud material in the atmosphere which has a distribution of cloud particle sizes. Within the models, we can change those distributions. A cloud that sediments into a small number of large particles will settle into a thin layer and will not significantly change the emergent spectrum; the same cloud material organized into an extended cloud with small particle sizes will have a dramatic effect on the model spectrum. For these reasons, we require a model of cloud particle sizes and distribution as well as the underlying chemistry. When we consider models that include new or different clouds, we do not change any of the underlying chemistry of condensation; we change the opacity of the condensate particles and in doing so modify the effect that the cloud formation has on emergent flux. \subsection{Sulfide or Silicate Clouds?} \label{sulfsil} \ct{Burgasser10} invoked the reemergence of silicate clouds to explain the spectrum of Ross 458C. We suggest instead that the initial emergence of sulfide clouds would have a similar effect on the spectrum and provide a more natural explanation for the results. From observations, it is clear that the range in T dwarf colors just following the L/T transition is small; spectra of T dwarfs show no evidence that clouds still affect the emergent flux for objects slightly cooler than this transition. This observation suggests that the iron and silicate clouds have dissipated between 1400 and 1200 K (for typical field dwarfs) and are no longer important in T dwarf atmospheres. If iron and silicate clouds were sometimes important in T dwarf atmospheres, we would expect to see a population of relatively quite red objects at effective temperatures between that of Ross 458C and the L dwarfs; no brown dwarf with these properties has been observed. As T dwarfs cool, the range in observed infrared colors increases; a population of red T dwarfs develops, which are redder in the near-infrared than cloudless models predict. Based on these observations, we favor a mechanism that cannot strongly alter \teff$\sim$900-1200 K T dwarf atmospheres, but naturally reddens \teff$\lesssim$800 K T dwarfs. The emergence of sulfide clouds provides that natural explanation for this range in T dwarf colors at low effective temperatures. Just as the iron and silicate clouds condense in the photospheres of L dwarfs and change their observed spectra, the sulfide clouds begin to condense in the photospheres of T dwarfs with temperatures cooler than 900 K, changing their observed spectra. We have not yet investigated whether the sulfide clouds will have identifiable spectral features that would confirm their presence in T dwarf atmospheres, but given the features in the sulfide indices of refraction (see Figure \ref{na2s_n}) these features would likely be in the mid-infrared. \subsection{Outstanding Issues In T Dwarf Models} \label{outstandingissues} There are several challenges in modeling T dwarfs that have not yet been addressed in these calculations. Because of the high densities in brown dwarf atmospheres, sodium and potassium bands at optical wavelengths are extremely pressure-broadened in T dwarf spectra \cp{Tsuji99, Burrows00, Allard05, Allard07}. The wings of these broadened bands extend into the near-infrared in $Y$ and $J$ bands, creating additional opacity at those wavelengths. For these calculations, we use the line broadening treatment outlined in \ct{Burrows00}, which is somewhat \emph{ad hoc} and potentially creates some inaccuracies in the model flux in $Y$ and $J$ bands. A calculation of the molecular potentials for potassium and sodium in these high pressure environments, as is carried out in \ct{Allard05, Allard07}, would improve the accuracy of these models. Another challenge in modeling T dwarf spectra is the inadequacies of methane opacity calculations; methane is the only important gas-phase absorber with inadequate opacity measurements or calculations. Uncertainties in methane absorption bands create inaccuracies in T dwarf models, especially in $H$ band where it is a very strong absorber \cp{Saumon12}. \subsection{Breakup of \nas\ Cloud} Sulfide clouds could form partial cloud layers with patchy clouds. One way to infer patchy cloud cover is to observe variability in photometric colors; variability can indicate high-contrast cloud features rotating in and out of view. \ct{Radigan12} studied objects at the L/T transition and inferred that the iron and silicate clouds could be in the process of breaking up and forming patchy clouds in those atmospheres. A similar study of the variability of cool T dwarfs could reveal a similar physical process in sulfide clouds. \subsection{Constraining Cloud Models with More Data} A larger number of high fidelity spectra of the coldest T dwarfs would help to constrain these cloudy models. Currently there are a few objects with effective temperatures cooler than 700 K with moderate resolution spectra. A larger sample of objects would give us better statistics on the overall population of T dwarfs, with different surface gravities, metallicities, and cloud structures. \subsection{Water Clouds} At cooler effective temperatures, water clouds will condense in brown dwarf atmospheres \cp{Burrows03}. Oxygen is 300 times more abundant than sodium in a solar-composition gas and the silicate clouds only use 20\% of the total oxygen in the atmosphere, so water clouds will be much more massive and important in shaping the emergent flux. As missions like WISE find colder objects \cp{Kirkpatrick11, Cushing11} and these objects are observed spectroscopically, future models of brown dwarfs will need to include the condensation of these more volatile clouds. Before the water clouds condense, \ct{Lodders99, Lodders06} predict that RbCl and CsCl will condense; however, the abundances of Cs and Rb are very low \cp{Lodders03} so these clouds will be optically thin. If equilibrium conditions prevail, NH$_4$H$_2$PO$_4$ would also condense \cp{Fegley94, Visscher06} with a mass similar to that of the \nas\ cloud. Whether NH$_4$H$_2$PO$_4$ condenses or P remains in the gas phase as PH$_3$ (as on Jupiter and Saturn) deserves further study to examine potential effects on the spectra of the coolest brown dwarfs. \subsection{Application to Exoplanet Atmospheres} Observations and models of T dwarfs provide a testbed to study planetary atmospheres. While brown dwarfs are more massive than planets, the atmospheres of T dwarfs have similar effective temperatures to those of young giant planets \cp{Burrows97,Fortney08b}. The study of T dwarfs provides crucial tests of cloudy atmosphere models that will be applicable to directly-imaged exoplanet atmospheres. Cloud models designed originally for brown dwarfs are already being applied to exoplanets. Cloud models with iron and silicate clouds were originally developed to model L dwarf atmospheres; these models have been successfully applied to observations of the only directly imaged multiple planet system, HR 8799. Several studies of the HR 8799 planets have shown that the iron and silicate clouds play a significant role in their atmospheres \cp{Marois08, Barman11, Galicher11, Bowler10, Currie11, Madhu11c, Marley12}. As instruments like the Gemini Planet Imager and SPHERE begin to discover new planets in the next few years, we will be able to apply brown dwarf models to colder planetary atmospheres in which clouds will likely play a key role in shaping their spectra.
| 12 | 6 |
1206.4313
|
1206
|
1206.0851_arXiv.txt
|
We study some possible observational signatures of $R^n$ gravity at Galactic scales and how these signatures could be used for constraining this type of $f(R)$ gravity. For that purpose, we performed two-body simulations in $R^n$ gravity potential and analyzed the obtained trajectories of S2-like stars around Galactic center, as well as resulting parameter space of $R^n$ gravity potential. Here, we discuss the constraints on the $R^n$ gravity which can be obtained from the observations of orbits of S2-like stars with the present and next generations of large telescopes. We make comparison between the theoretical results and observations. Our results show that the most probable value for the parameter $r_c$ in $R^n$ gravity potential in the case of S2-like stars is $\sim$100 AU, while the universal parameter $\beta$ is close to 0.01. Also, the $R^n$ gravity potential induces the precession of S2-like stars orbit in opposite direction with respect to General Relativity, therefore, such a behavior of orbits qualitatively is similar to a behavior of Newtonian orbits with a bulk distribution of matter (including a stellar cluster and dark matter distributions).
|
Power-law fourth-order theories of gravity have been proposed like alternative approaches to Newtonian gravity \cite{capo06,capo07}. In this paper we study possible application of $R^n$ gravity on Galactic scales, for explaining observed precession of orbits of S-stars, as well as weather these observations could be used for constraining this type of $f(R)$ gravity \cite{soti10}. S-stars are the bright stars which move around the massive black hole in the center of our Galaxy \cite{gill09a,gill09b,ghez08}. For one of them, called S2, there are some observational indications that this orbit deviates from the Keplerian case due to relativistic procession \cite{gill09a}. Besides, an extended dark mass which probably exists in the Galactic center, could also contribute to pericenter precessing of the S2, but in the opposite direction \cite{Nucita_07,gill09a}. Progress in monitoring bright stars near the Galactic Center have been made recently \cite{gill09a}. With the Keck 10 m telescope, the several stars orbiting the black hole in Galactic Center have been monitored, and in some cases almost entire orbits, as, for example, that of the S2 star, have been observed, allowing an unprecedented description of the Galactic Center region \cite{gill09a}. The astrometric limit for S2 star orbit is today around 10 mas and within that limit one can not say for sure that S2 star orbit really deviates from the Newtonian case. In the future, it will be possible to measure the positions of some stars with astrometric errors several times smaller than errors of current observations and that is why we will consider here even smaller astrometric limits. Capozziello et al. \cite{capo07} investigated the possibility that the observed flatness of the rotation curves of spiral galaxies is not evidence for the existence of dark matter (DM) haloes, but rather a signal of the breakdown of General Relativity (GR). They found a very good agreement between the theoretical rotation curves and the data using only stellar disc and interstellar gas when the slope $n$ of the gravity Lagrangian is set to the value $n$ = 3.5 (giving $\beta$ = 0.817), obtained by fitting the Type Ia supernova Hubble diagram with the assumed power-law $f(R)$ model and without dark matter \cite{capo07}. Frigerio Martins and Salucci \cite{fms07} have also investigated the possibility of fitting the rotation curves of spiral galaxies with the power-law fourth-order theory of gravity, without the need for dark matter. They show that, in general, the power law {\bf $f(R)$} version could fit the observations well, with reasonable values for the mass model. Recently, gravitational microlensing has been investigated in the framework of the weak field limit of fourth order gravity theory \cite{zakh06}. The solar system data (i.e. planetary periods) and light bending due to microlensing can be used to put strong constraints on the parameters of this class of gravity theories. In paper \cite{zakh06} it was found that these parameters must be very close to those corresponding to the Newtonian limit of the theory. In paper \cite{zakh07} the authors discuss the constraints that can be obtained from the orbit analysis of stars (as S2 and S16) moving inside the DM concentration. In particular, consideration of the S2 star apoastron shift may allow improving limits on the DM mass and size. Rubilar and Eckart \cite{rubi01} investigated the properties of stellar orbits close to central mass and the corresponding connection with current and (near) future observational capabilities. They showed that the orbital precession can occur due to relativistic effects, resulting in a prograde shift, and due to a possible extended mass distribution, producing a retrograde shift. Both, prograde relativistic and retrograde Newtonian periastron shifts will result in rosette shaped orbits. Weinberg et al. \cite{wein05} discuss physical experiments achievable via the monitoring of stellar dynamics near the massive black hole at the Galactic Center with a diffraction-limited, next-generation, extremely large telescope (ELT). They demonstrate that the lowest order relativistic effects, such as the prograde precession, will be detectable if the astrometric precision become less then 0.5 mas. In this paper we continue to investigate constraints on the parameters of this class of gravity theories using S2-like star orbits under uncertainty of 10 mas. In Section \S2 the type of used gravitational potential is given. In Section \S3 we present the S2-like stars orbits, gravity parameters and angles of orbital precession, and also compared theoretical results with observations. The main conclusions are pointed out in \S4. \begin{figure*}[ht!] \centering \includegraphics[width=0.85\textwidth]{fig1.eps} \caption{The orbits of an S2-like star around massive black hole in $R^n$ gravity (blue solid line) and in Newtonian gravity (red dashed line) for $r_c$ = 100 AU and for these nine values of parameter $\beta$: 0.005, 0.01, 0.015, 0.02, 0.025, 0.03, 0.035, 0.04, 0.0475. The black hole with mass $M_{BH}=3.4\times 10^6\ M_\odot$ is assumed to be located at coordinate origin, and mass of S2-like star is taken to be $M_\star=1\ M_\odot$.} \label{fig01} \end{figure*} \begin{figure*}[ht!] \centering \includegraphics[width=0.85\textwidth]{fig2.eps} \caption{The distances between the S2-like star and black hole as a function of time for the same values of parameters $r_c$ and $\beta$ as in the Fig. \ref{fig01}.} \label{fig02} \end{figure*} \begin{figure*}[ht!] \centering \includegraphics[width=0.85\textwidth]{fig3.eps} \caption{The parameter space for $R^n$ gravity under the constraint that, during one orbital period, S2-like star orbits in $R^n$ gravity differ less than $\varepsilon$ from the corresponding orbits in Newtonian gravity, for the following 10 values of parameter $\varepsilon$: 0.001, 0.002, 0.003, 0.004, 0.005, 0.006, 0.007, 0.008, 0.009 and 0$''$.01.} \label{fig03} \end{figure*} \begin{figure*}[ht!] \centering \includegraphics[width=0.85\textwidth]{fig4.eps} \caption{The same as in Fig. \ref{fig03} but for the following 12 values of parameter $\varepsilon$: 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.11 and 0$''$.12.} \label{fig04} \end{figure*} \begin{figure*}[ht!] \centering \includegraphics[width=0.40\textwidth]{fig5a.eps} \hspace*{1cm} \includegraphics[width=0.40\textwidth]{fig5b.eps} \caption{The dependence of the maximal value of parameter $\beta$ on precision $\varepsilon$ ranging from 0 to 0$''$.3 (\emph{left}) and from 0 to 0$''$.1 (\emph{right}).} \label{fig05} \end{figure*} \begin{figure*}[ht!] \centering \includegraphics[width=0.40\textwidth]{fig6a.eps} \hspace*{1cm} \includegraphics[width=0.40\textwidth]{fig6b.eps} \caption{The dependence of the $r_c^{max}$ on precision $\varepsilon$ ranging from 0 to 0$''$.3 (\emph{left}) and from 0 to 0$''$.1 (\emph{right}).} \label{fig06} \end{figure*} \begin{figure*}[ht!] \centering \includegraphics[width=0.40\textwidth]{fig7a.eps} \hspace*{1cm} \includegraphics[width=0.40\textwidth]{fig7b.eps} \caption{The orbits of S2-like star around massive black hole in $R^n$ gravity (blue solid line) and in Newtonian gravity (red dashed line) for $r_c$ = 100 AU and $\beta$ = 0.02 during 0.8 periods (\emph{left}) and 10 periods (\emph{right}).} \label{fig07} \end{figure*} \begin{figure*}[ht!] \centering \includegraphics[width=0.85\textwidth]{fig8.eps} \caption{The orbital precession of an S2-like star around massive black hole located at coordinate origin in $R^n$ gravity for $r_c$ = 100 AU and these nine values of parameter $\beta$: 0.005, 0.01, 0.015, 0.02, 0.025, 0.03, 0.035, 0.04, 0.0475.} \label{fig08} \end{figure*} \begin{figure}[ht!] \centering \includegraphics[width=0.45\textwidth]{fig9.eps} \caption{The exact expression for precession angle $\Delta \theta$ in $R^n$ gravity (in degrees) as a function of the parameter $\beta$ (black solid line) and two its approximations: for $\beta \approx$ 0 (blue dash-dotted line) and for $\beta \approx$ 1 (red dotted line). The other parameters correspond to the case of S2-like star: $a = $ 919 AU, $e = 0.87$ and $r_c$ = 100 AU.} \label{fig09} \end{figure} \begin{figure*}[ht!] \centering \includegraphics[width=0.45\textwidth]{fig10a.eps} \hspace*{0.8cm} \includegraphics[width=0.45\textwidth]{fig10b.eps} \caption{The fitted orbit of S2 star around massive black hole in $R^n$ gravity for $r_c$ = 100 AU and $\beta$ = 0.01 (black solid lines in both panels). The NTT/VLT astrometric observations are presented in the left panel by blue circles, while the Keck measurements are denoted by red circles in the right panel.} \label{fig10} \end{figure*} \begin{figure*}[ht!] \centering \includegraphics[width=0.49\textwidth]{fig11a.eps} \includegraphics[width=0.49\textwidth]{fig11b.eps} \caption{Comparison between the fitted (black solid lines) and measured (open circles) distances of the S2 star from black hole in the case of NNT/VLT (left) and Keck (right) observations.} \label{fig11} \end{figure*} \begin{figure}[ht!] \centering \includegraphics[width=0.49\textwidth]{fig12.eps} \caption{Comparison between the fitted (black solid line) and measured radial velocities for the S2 star. Measured velocities are labeled with open circles (VLT data) and open rhombuses (Keck data).} \label{fig12} \end{figure}
|
In this paper S2-like star orbit has been investigated in the framework of fourth order gravity theory. Using the observed positions of S2 star we put new constraints on the parameters of this class of gravity theories. We confirmed that these parameters must be very close to those corresponding to the Newtonian limit of the theory. For parameter $\beta$ approaching to zero, we recover the value of the Keplerian orbit for S2 star. Also, we performed two-body calculations of its orbit in the $R^n$ potential. The obtained results showed that, in contrast to General Relativity, $R^n$ gravity gives retrograde direction of the precession of the S2 orbit, like in the case when it is caused by an extended matter concentration in Newtonian potential. Despite the excellent agreement between theoretical and observed rotation curves obtained by Capozziello and coworkers \cite{capo07} for $R^n$ parameter $\beta$ (the slope $n$ of the gravity Lagrangian is set to the value $n$ = 3.5 giving $\beta$ = 0.817), our findings indicate that for $\varepsilon$ = 0$''$.01 maximal value of $\beta$ is 0.0475, i.e. $\beta$ is less or equal than 0.0475, and our fitting indicated that optimal value for $\beta$ is around 0.01. Therefore, $R^n$ gravity in this form may not represent a good candidate to solve both the dark energy problem on cosmological scales and the dark matter one on galactic scales using the same value of parameter $\beta$. But this theory has its own benefits in explaining orbits of the stars and solar system data. For today astrometric limit of around 10 mas for S2 star orbit, within that limit one can not say for sure that S2 star orbit really deviates from the Newtonian case, i.e. we have to stress that at the moment observations are in agreement with the Newtonian point-like potential for the Galactic Center. Therefore the observations and their theoretical analysis give us one of the best cases to discuss departures from the standard GR plus stellar cluster and dark matter (as it was done in our papers and papers of other authors) or to analyze an opportunity to get constraints on alternative theories observing trajectories of S2-like stars. The newest astrometric data for the star S2 of NTT/VLT measurements and Keck measurements show the Keplerian orbit fits for the respective data set, do not yield closed ellipses. Maybe this represents really small deviation of S2 star orbit from the Newtonian case and for more sure conclusion we need astrometric errors several times smaller than these errors, but we compared these data with S2 star orbit obtained using $R^n$ gravity potential. We can conclude that additional term in $R^n$ gravity compared to Newtonian gravity has a similar effect like extended mass distribution and produce a retrograde shift, that results in rosette shaped orbits.
| 12 | 6 |
1206.0851
|
1206
|
1206.1142.txt
|
We have worked out simple analytical formulae that accurately approximate the relationship between the position of the source with respect to the lens center and the amplification of the images, hence the lens cross section, for realistic lens profiles. We find that, for essentially the full range of parameters either observationally determined or yielded by numerical simulations, the combination of dark matter and star distribution can be very well described, for lens radii relevant to strong lensing, by a simple power-law whose slope is very weakly dependent on the parameters characterizing the global matter surface density profile and close to isothermal in agreement with direct estimates for individual lens galaxies. Our simple treatment allows an easy insight into the role of the different ingredients that determine the lens cross section and the distribution of gravitational amplifications. They also ease the reconstruction of the lens mass distribution from the observed images and, vice-versa, allow a fast application of ray-tracing techniques to model the effect of lensing on a variety of source structures. The maximum amplification depends primarily on the source size. Amplifications larger than $\approx 20$ are indicative of compact source sizes at high-$z$, in agreement with expectations if galaxies formed most of their stars during the dissipative collapse of cold gas. Our formalism has allowed us to reproduce the counts of strongly lensed galaxies found in the H-ATLAS SDP field. While our analysis is focussed on spherical lenses, we also discuss the effect of ellipticity and the case of late-type lenses (showing why they are much less common, even though late-type galaxies are more numerous). Furthermore we discuss the effect of a cluster halo surrounding the early-type lens and of a supermassive black hole at its center.
|
\label{sect:intro} \setcounter{footnote}{0} The discovery rate of strong galaxy-scale lens systems has increased dramatically in recent years mostly thanks to spectroscopic lens searches and, most recently, to surveys of sub-millimeter galaxies. Spectroscopic searches, such as the Sloan Lens Advanced Camera for Surveys (SLACS) survey (Bolton et al. 2006, 2008; Auger et al. 2009) or the BOSS (Baryon Oscillation Spectroscopic Survey) Emission-Line Lens Survey (BELLS; Brownstein et al. 2012) or the optimal line-of-sight (OLS) lens survey (Willis et al. 2006) or the Sloan WFC (Wide Field Camera) Edge-on Late-type Lens Survey (SWELLS; Treu et al. 2011), rely on the detection of multiple background emission lines in the residual spectra found after subtracting best-fit galaxy templates to the foreground-galaxy spectrum. Sub-millimeter surveys were predicted (Blain 1996; Perrotta et al. 2002, 2003; Negrello et al. 2007), and demonstrated (Negrello et al. 2010), to be an especially effective route to efficiently detect strongly lensed galaxies at high redshift because the extreme steepness of number counts of unlensed high-$z$ galaxies implies a strong magnification bias so that they are easily exceeded by those of strongly lensed galaxies at the bright end. Also, gravitational lensing effects are more pronounced for more distant sources. But high-$z$ galaxies are frequently in a dust-enshrouded active star formation phase and therefore are more easily detected at far-IR/sub-mm wavelengths, while they are very optically faint. Negrello et al. (2007) predicted that about 50\% of galaxies with $500\,\mu$m flux densities above $\approx 100\,$mJy would be strongly lensed, with the remainder easily identifiable as local galaxies or as radio-loud Active Galactic Nuclei (AGNs). This prediction was supported by the mm-wave South Pole Telescope (SPT) counts (Vieira et al. 2010). But a spectacular confirmation came with the results of the \textsl{Herschel} Astrophysical Terahertz Large Area Survey\footnote{http://www.h-atlas.org/} (H-ATLAS; Eales et al. 2010) for the Science Demonstration Phase (SDP) field covering about $14.4$ deg$^2$. Five out of the 10 extragalactic sources with $S_{500\,\mu\rm m}\ga 100\,$mJy were found to be strongly lensed high-$z$ galaxies, four are $z<0.1$ spiral galaxies and one is a flat-spectrum radio quasar (Negrello et al. 2010). Gonzalez-Nuevo et al. (2012) presented a simple method, the \textsl{Herschel}-ATLAS Lensed Objects Selection (HALOS), aimed at identifying fainter strongly lensed galaxies. This method gives the prospect of reaching a surface density of $\sim 2$ deg$^{-2}$ for strongly lensed candidates, i.e., the detection of $\sim 1000$ high-$z$ strongly lensed galaxies over the full H-ATLAS survey area ($\approx 550$ deg$^{2}$; Eales et al. 2010). It should be noted that the (sub-)mm selected lensed galaxies are very faint in the optical, while most foreground lenses are passive ellipticals (Auger et al. 2009; Negrello et al. 2010), essentially invisible at sub-mm wavelengths. This means that the foreground lens is `transparent' at (sub-)mm wavelengths, i.e. does not confuse the images of the background source. Therefore, the (sub-)mm selection shares with spectroscopic searches the capability of detecting lensing events with small impact parameters and has the advantage that, in most cases, there is no need to subtract the lens contribution to recover the source images within the effective radii of the lenses. Also, compared to the optical selection, the (sub-)mm selection allows us to probe earlier phases of galaxy evolution which have typically higher lensing optical depths. This makes this technique ideal for tracing the mass density profiles of elliptical galaxies over a broad redshift range and for probing their evolution with cosmic time. Samples of strongly lensed galaxies are further enriched by the, to some extent complementary, imaging surveys (Cabanac et al. 2007; Faure et al. 2008; Kubo \& Dell' Antonio 2008; Ruff et al. 2011) which look for arc-like features, and by radio surveys (Browne et al. 2003). All that holds the promise of a fast increase of the number of known strongly lensed sources, fostered by the forthcoming large area optical (e.g., Oguri \& Marshall 2010) and radio (SKA, Square Kilometer Array) surveys (e.g., Koopmans, Browne, \& Jackson 2004). A simple, efficient, analytical tool applicable to the analysis of large samples of galaxy-scale lenses is therefore warranted. In this paper we work out exact and approximate solutions of the lens equation based on a realistic model for the mass density profile of the lens (\S\,\ref{sect:lens_eq}) and exploit them to reckon the lensing probability as a function of the source redshift (\S\,\ref{sect:lens_prob}). As an application of these results, following on the study of the high-$z$ luminosity function of galaxies measured by the H-ATLAS survey (Lapi et al. 2011), we compute, in \S\,\ref{sect:counts}, the number counts of strongly lensed sub-mm galaxies implied by the physical model of galaxy formation and evolution formulated by Granato et al. (2004) and further developed by Lapi et al. (2006) and Mao et al. (2007). The model counts are compared with the observational estimates by Negrello et al. (2010) and by Gonzalez-Nuevo et al. (2012). While our study is focussed on early-type lenses, assumed to be circularly symmetric, the cases of late-type lenses, of ellipticity, of the presence of a super-massive black hole in the galactic nucleus, and of super-galactic structures are discussed in \S\,\ref{sect:disc}. Finally, our main results are summarized in \S\,\ref{sect:concl}. Throughout the paper we adopt the standard flat $\Lambda$CDM cosmology (see Komatsu et al. 2011) with current matter density parameter $\Omega_{\rm M}=0.27$ and Hubble constant $H_0=72$ km s$^{-1}$ Mpc$^{-1}$.
|
\label{sect:concl} In view of the large samples of strongly lensed galaxies that are being/will be provided by large area sub-mm (Serjeant 2011; Negrello et al. 2010; Gonz\'alez-Nuevo et al. 2012), optical (e.g., Oguri \& Marshall 2010) and radio (SKA) surveys (e.g., Koopmans et al. 2004) we have worked out simple analytical formulae that accurately approximate the relationship between the position of the source with respect to the lens center and the amplification of the images and hence the cross section for lensing (see Fig.~\ref{fig:solutions}). The approximate relationships are based on a lens matter density profile appropriate for early-type galaxies, that comprise most of the lenses found with different selection criteria. The adopted profile is a combination of a S\'ersic profile, describing the distribution of stars, with a NFW profile for the dark matter. We find that, for essentially the full range of parameters either observationally determined (for the S\'ersic profile) or yielded by numerical simulations (for the NFW profile), the combination can be very well described, for lens radii relevant for strong lensing, by a simple power law. Remarkably, the power law slope is very weakly dependent on the parameters characterizing the matter distribution of the lens (the dark matter to stellar mass ratio, the S\'ersic index, the concentration of NFW profile). For the most common parameter choices, the slope is slightly sub-isothermal if we consider the projected profile and slightly super-isothermal if we consider the 3-dimensional profile, in good agreement with the results of detailed studies of individual lens galaxies (e.g. Koopmans et al. 2009; Spiniello et al. 2011; Barnab\'e et al. 2011; Ruff et al. 2011; Grillo 2012; Bolton et al. 2012). Our approach implies slightly steeper slopes of the total matter density profile for the least massive systems (see Table~\ref{tab:fits}); evidence in this direction has been reported by Barnab\'e et al. (2011). Table~\ref{tab:fits} shows that, if the source and lens redshifts are measured and the halo mass of the lens is reliably estimated, the factor $[2\,\Sigma_0/(2-\eta)\,\Sigma_c]^{1/\eta}$, and hence $\theta_E$ [see Eq.~(\ref{eq:thetaE})], varies by no more than $20-30\%$ for conceivable variations of the parameters of the lens mass distribution. Such small variance paves the way to the possibility of exploiting gravitational lensing as a probe of cosmological parameters (Grillo et al. 2008). Our simple analytic solutions provide an easy insight into the role of the different ingredients that determine the lens cross section and the distribution of gravitational amplifications. The maximum amplification depends primarily on the source size. Amplifications larger than $\approx 20$, as found for some sub-mm and optical sources (Belokurov et al. 2007; Negrello et al. 2010; Swinbank et al. 2010; Brownstein et al. 2012), are indicative of compact source sizes at high-$z$, in agreement with expectations if most of the stars formed during dissipative collapse of cold gas. Similarly, analytic formulae highlight in a transparent way the role of parameters characterizing the lens mass profile ($M_{\rm H}$, $M_{\rm H}/M_\star$ ratio, concentration of the DM component, S\'ersic index of the stellar component), and of the source and lens redshifts. They also allow a fast application of ray-tracing techniques to model the effect of lensing on a variety of source structures. We have investigated, in particular, the cases of a point-like or of an extended source with a smooth profile, and of a source comprising various emitting clumps (as frequently found for high-$z$ active star-forming galaxies). Our formalism has allowed us to reproduce the counts of strongly lensed galaxies found in the H-ATLAS SDP field. While our analysis is focussed on spherical lenses, we have also discussed the case of disk galaxies (showing why they are much less common, even though late-type galaxies are more numerous) and the effect of ellipticity. Furthermore we have discussed the effect of a cluster halo surrounding the early-type lens and of a supermassive BH at its center.
| 12 | 6 |
1206.1142
|
1206
|
1206.0126_arXiv.txt
|
We study plasma flows along selected coronal loops in NOAA Active Region 10926, observed on 3 December 2006 with \textit{Hinode's EUV Imaging Spectrograph} (EIS). From the shape of the loops traced on intensity images and the Doppler shifts measured along their length we compute their three-dimensional (3D) shape and plasma flow velocity using a simple geometrical model. This calculation was performed for loops visible in the \feviii\ 185~\AA, \fex 184~\AA, \fexii\ 195~\AA, \fexiii\ 202~\AA, and \fexv\ 284~\AA\ spectral lines. In most cases the flow is unidirectional from one footpoint to the other but there are also cases of draining motions from the top of the loops to their footpoints. Our results indicate that the same loop may show different flow patterns when observed in different spectral lines, suggesting a dynamically complex rather than a monolithic structure. We have also carried out magnetic extrapolations in the linear force-free field approximation using SOHO/MDI magnetograms, aiming toward a first-order identification of extrapolated magnetic field lines corresponding to the reconstructed loops. In all cases, the best-fit extrapolated lines exhibit left-handed twist ($\alpha < 0$), in agreement with the dominant twist of the region.
|
\label{sec:Introduction} Solar telescopes provide us with two-dimensional projections of coronal structures on the plane of the sky. The measure of the 3D geometry of coronal loops is important for understanding these structures. Reconstructions of a loop's true shape have been attempted via a variety of methods, such as stereoscopy or models that make assumptions for the loop shape, flow etc \cite{Loughhead1983,Berton1985,Aschwanden1999,Nitta1999}. Moreover, the STEREO space mission, with its twin telescopes in two different positions in space, is dedicated to the solar coronal stereoscopy by combining simultaneous EUV images from two different lines of sight \cite{Aschwanden09,Aschwanden11}. The 3D geometry of active-region loops, computed with STEREO images, was used to constrain the magnetic field topology computed with non-linear force-free extrapolation methods \cite{DeRosa2009}. \begin{figure} \centerline{ \includegraphics[width=0.7\textwidth]{mdireadfulldisk.ps} } \caption{Full disk image recorded by SOHO/MDI on 3 December 2006, at 20:51~UT. EIS rasters 1 and 2 field of views are represented with dark frames around AR 10926. The white frame shows the part of the MDI magnetogram used for the magnetic field extrapolation.} \label{fig:MDIfulldisk} \end{figure} To interpret the active-region Doppler maps computed with the data from instruments such as \textit{Hinode}/EIS and to understand the plasma flows along coronal loops, one also needs to know the loops' 3D geometry. \inlinecite{DelZanna2008}, using \textit{Hinode}/EIS observations of NOAA AR 10926, studied the behavior of the line of sight velocity, along loops and weak emission regions of the active region, at different plasma temperatures. In this work we analyze the same active region and we study the flows along selected loops for which we were able to reconstruct their 3D geometry. Our method, introduced by \opencite{Alissandrakis2008} (Paper~I) also uses the Doppler shifts measured along coronal loops in this reconstruction. Based on the analysis of Paper~I we extend the study to more loops and a wider range of formation temperatures in this work.
|
We reconstructed the 3D geometry of six loops observed by the \textit{Hinode}/EIS spectrograph in five spectral lines during two rasters of the instrument, a total of 17 cases. All loops correspond to NOAA AR 10926. All reconstructed loops have large inclinations with respect to the vertical, in the range of $-60\degr$ to $-75\degr$ and they are all projected to the South of the bright central part of the active region. Moreover, due to pressure scale height effects, large inclinations lead to denser and brighter plasma near the loop top, hence the entire loop stands clearly above the background level. The flows calculated for all loops were subsonic in all spectral lines that validates the loops description using their hydrostatic scale. The best-studied loop is Loop 1, successfully reconstructed in nine images. We find that this loop is {\it not a monolithic } structure, as the flows deduced in different spectral lines vary from unidirectonal flow from East to West in the low-temperature \feviii\ line, to draining motion from the top to the footpoints in the intermediate-temperature \fex\ line, to unidirectional flow from West to East in the high-temperature lines. This being said, the computed inclination is very similar in all images, namely $63\degr \pm 3\degr$, that strengthens our assessment of internal structure in the loop in different temperature ranges. An independent comparison between the reconstructed loops and extrapolated field lines by means of a linear force-free extrapolation implemented on a case-by-case basis give results that call for additional investigation. We have been able to closely model the height of the loops' apices and we have noticed best-fit lines with a consistent (left-handed in this case) twist in the AR, but extrapolated field lines are consistently less inclined than reconstructed loops. This discrepancy may be due to drawbacks in the reconstruction method, weaknesses in the extrapolation and/or the extrapolated boundary, or a combination of both. Aiming to validate our technique as reliably as possible, we intend to carry out similar investigations in future works, relying on larger statistical samples of reconstructed coronal loops. \begin{acks} This research was supported by research grant 200/740 of the Academy of Athens. CHIANTI is a collaborative project involving researchers at NRL (USA) RAL (UK), and the Universities of: Cambridge (UK), George Mason (USA), and Florence (Italy). We would also like to thank the anonymous referee for the valuable comments which improved our paper, as well as the editor for a careful reading of the manuscript. \end{acks}
| 12 | 6 |
1206.0126
|
1206
|
1206.1911_arXiv.txt
|
We investigate the interacting agegraphic dark energy in Brans-Dicke theory and introduce a new series general forms of dark sector coupling. As examples, we select three cases involving a linear interaction form (Model I) and two nonlinear interaction form (Model II and Model III). Our conclusions show that the accelerated scaling attractor solutions do exist in these models. We also find that these interacting agegraphic dark energy modes are consistent with the observational data. The difference in these models is that nonlinear interaction forms give more approached evolution to the standard $\Lambda$CDM model than the linear one. Our work implies that the nonlinear interaction forms should be payed more attention. \PACS{ 95.36.+x\and98.80.-k\and98.80.Es}
|
\label{sec:introduction} Recent astronomical observations have provided strong evidence that our universe is undergoing an accelerated expansion due to an exotic energy component with negative pressure which is called dark energy \cite% {Perlmutter-99,Bennett-03,Tegmark-04,Allen-04}. By far a leading candidate of dark energy model is the Einstein's cosmological constant model ($\Lambda$% CDM) which is consistent with the late-time observational data. However, it is confronted with the so-called ``cosmological constant problem" and ``coincidence problem" \cite{Weinberg-05}. Therefore, many dynamical dark energy models \cite{Copeland-06}, such as quintessence \cite{quintessence}, phantom \cite{phantom}, quintom \cite{quintom}, tachyon \cite{tachyon}, generalized Chaplygin gas \cite{Chaplygin}, etc, have also been taken into account. The cosmological constant problem may be essentially an issue of quantum gravity problem, since the cosmological constant is commonly considered as the vacuum expectation value of some quantum fields. Although a complete theory of quantum gravity has not been established, according to some principles of quantum gravity, one can make some attempts to probe the nature of dark energy model. The holographic dark energy model is just an appropriate and interesting example. This model is based on the holographic principle of quantum gravity theory \cite{Hooft-93}, and is derived from the relationship between the ultraviolet (UV) and the infrared (IR) cutoffs proposed by Cohen {\emph{et al.}} in ref. \cite{Nelson-99}. According to the limit set of the formation of a black hole, the UV-IR relationship gives an upper bound on the zero point energy density $\rho_q=3L^{-2}/8\pi G$, which means that the maximum entropy of the system is of the order of $S^{3/4}_{BH} $, where $L$ is the scale of IR cutoff and $S_{BH}$ is the entropy of the black hole. Compared with the holographic dark energy model and based on the K$\acute{a}$rolyh$\acute{a}$zy relation \cite{time-energy uncertainty}, the so-called agegraphic dark energy model was proposed, where the age of the universe $T=\int dt$ is used as the IR cutoff $L$ \cite{Cai-07}. Furthermore, in ref.\cite{Cai-09}, the interacting agegraphic dark energy has been introduced and investigated. It was shown that the equation of state of interacting agegraphic dark energy can cross the phantom division. The interacting agegraphic dark energy model also has been extended to the universe with spatial curvature in ref. \cite{Sheykhi-09}. Recently, using the phase space analysis, it was shown that the accelerated scaling attractor solutions of the interacting agegraphic dark energy in the Einstein universe did exist and the results agree with the observations \cite{Lemets-10}. On the other side, scalar-tensor theories of gravity have been widely applied to cosmology \cite{V.Faraoni-04}. The simplest alternative to Einstein's general relativity which includes a scalar field in addition to the tensor field is Brans-Dicke theory. This theory is more consistent with the Mach's principle and less reliant on absolute properties of space \cite% {Brans-Dicke-65}. It got a new impetus in recent years because it arises naturally as the low energy limit of many theories of quantum gravity such as super string theory or Kaluza-Klein theory. Noticing that the holographic dark energy density belongs to a dynamical cosmology constant, it is more natural for a dynamical frame to replace the Einstein's general gravity. Therefore, it is worthwhile to investigate the holographic dark energy model within the framework of Brans-Dicke theory \cite% {Y.G.Gong-04,Y.G.Gong-08,Ahmad Sheykhi-09,J.Liu-10}. The extended holographic dark energy model with Hubble horizon in Brans-Dicke theory has been proposed and it is found that the model is not a viable dark energy model unless the Brans-Dicke scalar field has a potential. So it is a very interesting attempt to deeply investigate the agegraphic dark energy model in the framework of Brans-Dicke theory . Considering that dark energy (DE) and dark matter (DM) contribute to the most fraction of the content of the universe, it is natural to look into the possibility of the interaction between DE and DM, which has been widely discussed \cite{D-D interaction}. It has been argued that the coupling between DE and DM can provide a mechanism to alleviate the coincidence problem and lead to an accelerated scaling attractor solution with similar energy densities in the dark sector today \cite{D-D interaction,Pavon-05,Boehmer-08,Chen Wang Jing-08}. Noticing that there is no fundamental theory which can be used to select a specific interacting dark energy model, any interacting dark energy model will necessarily be phenomenological. There are two criterions to determine whether the model is correct and feasible. One is the observations, the other is to examine whether the interacting model can lead to the accelerated scaling attractor solutions, which is a decisive way to achieve similar energy densities in dark sector and alleviate the coincidence problem. In this work, we firstly introduce a new series of interacting agegraphic dark energy models including linear and nonlinear forms. Using the phase-plane analysis, it is found that the accelerated scaling attractor solutions do exist in these models. What's more, these agegraphic dark energy models are in accordance with the late-time observational data. Our paper is organized as follows. In section \ref{Sec2}, the agegraphic dark energy models in Brans-Dicke theory is constructed and a series of dark sector coupling forms are introduced. In section \ref{Sec3}, using the phase-plane analysis, the accelerated scaling attractor solutions are discussed in these models. In section \ref{Sec4}, using the newly released Hubble parameter data \cite% {Hubble..expand..Jimenez,Hubble..expand..Simon,Hubble..expand..Stern,Hubble..parameter..MaCong}% , these agegraphic dark energy models are tested. Some conclusions will be presented in section \ref{Sec5}.
|
\label{Sec5} Holographic dark energy model is an interesting attempt to investigate the nature of dark energy in the framework of quantum gravity. Considering that the simplest alternative to Einstein's general relativity which includes a scalar field in addition to the tensor field is Brans-Dicke theory and the holographic bound can be satisfied for both the $k=0$ and $k=-1$ universe in the Brans-Dicke cosmology\cite{Gongprd60}, it is natural to extend the research to the holographic dark energy models of this theory. In this paper, we have investigated the interacting agegraphic dark energy in the flat ( $k=0$ ) Brans-Dicke cosmology. Firstly, a series of new general forms of dark sector coupling are introduced and the accelerated scaling attractor solutions have been found. Moreover, using the newly released Hubble parameter data, we have also tested these interacting agegraphic dark energy models. The interacting term can be selected as a function of $H$, the density of dark energy, and the density of the dark matter. According to this requirement, we have proposed the general interacting agegraphic dark energy models. Three cases including a linear interaction form (Model I) and two nonlinear interaction forms (Model II and Model III) have been investigated. Using the phase-plane analysis, the dynamical behavior of these models has been investigated and it was found that the accelerated scaling attractor solutions did exist in these models. This can alleviate the coincidence problem. Afterwards, using the newly released Hubble parameter data, we tested these dynamical dark energy models. These interacting agegraphic dark energy modes have given a series of reasonable pictures of the cosmic evolution and they were consistent with the late-time observational data. In particular, we found the nonlinear interaction forms (Model II and Model III) gave more approached evolution to the standard $\Lambda$CDM model than the linear one (Model I). Our work show that we should pay more attention to the nonlinear interaction forms rather than the linear form. This deserves further investigations.
| 12 | 6 |
1206.1911
|
1206
|
1206.4828_arXiv.txt
|
We present the results of a comprehensive analysis of the structure and kinematics of six Galactic globular clusters. By comparing the results of the most extensive photometric and kinematical surveys available to date with suited dynamical models, we determine the stellar and dynamical masses of these stellar systems taking into account for the effect of mass segregation, anisotropy and unresolved binaries. We show that the stellar masses of these clusters are on average smaller than those predicted by canonical integrated stellar evolution models because of the shallower slope of their mass functions. The derived stellar masses are found to be also systematically smaller than the dynamical masses by $\sim$ 40\%, although the presence of systematics affecting our estimates cannot be excluded. If confirmed, this evidence can be linked to an increased fraction of retained dark remnants or to the presence of a modest amount of dark matter.
|
Among the stellar system zoo there is a widely recognized discrepancy between the photon-emitting mass (constituted by stars and gas) and dynamical mass (including the contribution of dark matter). From galaxy clusters to dwarf galaxies the mass of the baryonic component, estimated through the conversion of light in mass, has been found to be significantly smaller than that estimated via kinematical considerations (see Tollerud et al. 2011 for a recent review). The commonly accepted solution to this problem invokes the presence of a large amount of dark, non-baryonic matter driving the kinematics of these systems without contributing to their luminosity. Within this framework, globular clusters (GCs) are considered a notable exception: although they are the next step down from the smallest stellar systems containing dark matter (the Ultra Compact Dwarf galaxies; Mieske et al. 2008) and brighter than the most dark matter dominated systems (the Ultra Faint Galaxies; Simon et al. 2011) they are not believed to contain dark matter (Baumgardt et al. 2009). This conclusion is mainly justified by the evidence that dynamical mass-to-light (M/L) ratios of GCs are $\sim$25\% {\it smaller} than those predicted by simple stellar population models that assume a canonical Initial Mass Function (IMF; McLaughlin \& van der Marel 2005; Strader et al. 2009, 2011). However, these models do not account for dynamical effects such as the preferential loss of low-mass stars due to energy equipartition which alters the shape of the present-day mass function (PDMF) and consequently the stellar M/L ratio. In fact, all the past determinations of PDMFs in GCs derived slopes shallower than that of a canonical (e.g. Kroupa 2001) IMF (Piotto \& Zoccali 1999; Paust et al. 2010; De Marchi et al. 2010). In a recent paper Kruijssen \& Mieske (2009) modeled the evolution of the mass function of 24 GCs including the effects of dynamical dissolution, low-mass star depletion, stellar evolution and stellar remnants finding a substantial agreement between the prediction of their model and the dynamical M/L ratio estimated through the cluster kinematics. They conclude that dynamical effects are likely responsible for the observed discrepancy between stellar and dynamical masses. The flood of available data from deep photometric and spectroscopic surveys make now possible to test this issue observationally at an higher level, sampling the mass function of GCs down to the hydrogen burning limit (Paust et al. 2010) and their velocity dispersion profile up to many half-mass radii (Lane et al. 2010a). This gives the unprecedented opportunity to derive stellar masses from direct star counts instead of converting light in mass, obtaining an estimate which does not require the assumption of a $M/L$ ratio. In this paper we compare the results of deep Hubble Space Telescope (HST) photometric observations and wide-field radial velocities available from recent public surveys with a set of dynamical models with the aim of deriving the amount of stellar and dynamical mass in a sample of six Galactic GCs.
|
By comparing the most extensive photometric and spectroscopic surveys with suitable dynamical models we derived the global binary fraction, the PDMF of six Galactic GCs as well as their stellar and dynamical masses. The approach adopted here has the advantage to not require an a priori assumption of the $M/L$ ratio to estimate the stellar mass (as usually done in previous works; e.g. McLaughlin \& van der Marel 2005) which is instead estimated via direct star counts in the CMD. We confirm the anticorrelation between binary fraction and cluster mass already found in previous studies (Milone et al. 2008, 2012; Sollima et al. 2010) and explained as the consequence of the increased efficiency of the binary ionization process in massive clusters. Indeed, in massive clusters both the number of collisions and the mean kinetic energy of stellar encounters is larger resulting in a higher probability of ionization of multiple systems (Sollima 2008). The PDMFs of the six clusters are well-represented by single power laws, although we cannot exclude a turnover at masses $M<0.2~M_{\odot}$, because of the uncertainty in the relative fraction of the least massive stars. The stellar masses derived for these clusters are on average smaller than those predicted by population synthesis models. This is a consequence of the fact that the IMF adopted by these models is steeper that the actual PDMF of the considered clusters. This has been previously predicted by Kruijssen \& Mieske (2009) as the result of the preferential loss of low-mass stars during the cluster evolution. We found a discrepancy between the stellar and dynamical masses of five clusters. In particular, dynamical masses are on average $\sim$40\% larger than stellar ones. Such a discrepancy is statistically significant when considering the entire sample of six clusters and could not be detected by previous studies because of the overestimate of the stellar mass mentioned above. Unfortunately, we cannot exclude that such a discrepancy is due to the presence of systematics affecting our estimates. In particular, a possible source of systematics is constituted by the inhomogeneity of the surface brightness profiles sample of Trager et al. (1995). However, if the detected difference would be real, a number of physical interpretations could be given. After a careful test on the effect of various assumptions and physical processes we found that a significant spurious increase of the estimated dynamical masses is given by the tidal heating which can reduce (but not eliminate) the observed discrepancy. On the other hand, the assumption on the distribution and retention of dark remnant has the largest impact on the estimated stellar masses. Part (up to 75\%) of the observed mass difference can be indeed explained assuming that most the remnants, including the most massive neutron stars and black holes, are retained. This could be the case if the cluster mass at the moment of the SNe II explosion was large enough to trap the remnants, whose kinetic energy has been increased by the velocity kick following the explosion. The mass necessary to retain the majority of massive remnants is of $\sim10^{7}~M_{\odot}$ (see Fig. 1 of Kruijssen 2009). Such a large mass is comparable with the initial mass predicted by D'Ercole et al. (2008) to ignite the self-enrichment process observed in most GCs (see Carretta et al. 2009b). Moreover, massive remants are expected to be more resistant to tidal stripping since tend to sink toward in the cluster core as a result of mass segregation. It is however worth noting that a retention fraction larger than 80\% would require initial masses and an early mass loss history quite extreme, which has indeed been proposed in theoretical works to be the result of severe tidal shocking in the primordial environment of GCs (Elmegreen 2010; Kruijssen et al. 2012). An even larger effect is provided by the slope of the high-mass end of the IMF of the precursors which can drastically increase the amount of non-luminous mass. In this regard, a recent analysis by Marks et al. (2012) suggests that the slope of the IMF in the range $M>M_{\odot}$ could be actually shallower than the canonical Salpeter (1955) and Kroupa (2001) values with a dependence on density and metallicity. In this case, a slope $\alpha \simeq -1.5$ (instead of $\alpha=-2.3$ by Kroupa 2001) could account for the entire difference between the estimated stellar and dynamical masses. Such a variation would have strong implications on the evolution of the GC MF: in fact, while the largest mass contribution would be due to the increased number of white dwarfs, the consistent increase of the fraction of massive remnants (black holes and neutron stars) makes these objects the main drivers of the MF evolution. It is not clear if such IMF could actually evolve in the PDMF observed in these clusters. Another possibility is that GCs contain a modest fraction of non-baryonic dark matter. In this case, it is possible that what we see now is the remnant of a larger halo lost during the interaction with the Milky Way (see Saitoh et al. 2006). Some amount of dark matter is also expected if some GCs are the remnants of past accretion events, as previously suggested by Freeman \& Bland-Hawthorn (2002). However, given the involved uncertainties, all these hypotheses are merely speculative. Further studies will be needed to verify the above possibilities.
| 12 | 6 |
1206.4828
|
1206
|
1206.4705_arXiv.txt
|
A fundamental problem of cosmic ray (CR) physics is the determination of the average properties of Galactic CRs outside the Solar system. Starting from COS-B data in the 1980's, gamma-ray observations of molecular clouds in the Gould Belt above the Galactic plane have been used to deduce the Galactic CR energy spectrum. We reconsider this problem in view of the improved precision of observational data which in turn require a more precise treatment of photon production in proton-proton scatterings. We show that the spectral shape $dN/dp\propto p^{-2.85}$ of CR protons as determined by the PAMELA collaboration in the energy range $80\,{\rm GeV}<p{\rm c}<230$\,GeV is consistent with the photon spectra from molecular clouds observed with Fermi-LAT down to photon energies $E\sim 1$--2\,GeV. Adding a break of the CR flux at 3\,GeV, caused by a corresponding change of the diffusion coefficient, improves further the agreement in the energy range 0.2--3\,GeV.
|
The propagation of cosmic ray (CR) protons and nuclei with energies $E/Z\lsim 10^{18}$\,eV in the turbulent component of the Galactic magnetic field resembles a random walk and can be described in general by the diffusion approximation~\cite{diff}. Therefore the Galactic disk should be filled with a well-mixed ``sea'' of CRs whose properties are summarized by the differential diffuse intensity $I(E)$ or the differential number density $n(E)=4\pi\, I(E)/v$. Excluding the regions close to recent CR sources, the gradient $\vec\nabla \ln[n(E)]$ induced by the small current of CRs diffusing out of the disc and its extended CR halo is small. Most of our knowledge about Galactic CRs is obtained via observations in our local environment. Despite of the diffusive propagation of CRs, the CR intensity deduced locally may differ from the one averaged over the Galactic disc: At low energies, the influence of the Solar wind on measurements of the CR energy spectrum and the total CR energy density has to be corrected based on current understanding of the heliospheric modulation and direct CR measurements at different heliospheric distances and at different modulation levels. Clearly, such a correction is model-dependent and can introduce uncertainties. Moreover, the Sun is close to a region with increased star-formation and thus supernova rate. Other reasons for local deviations include stochastic re-acceleration in the local interstellar turbulence or local sources as old supernova shocks, winds and flares of massive stars. Therefore, the CR density close to the Solar system may deviate from the average Galactic one. A way to obtain independent information on the average ``sea'' Galactic CRs is the observation of suitable molecular clouds far from CR accelerating regions~\cite{review}: These clouds serve as a target for CRs producing gamma-rays mainly through decays of neutral pions created as secondaries in CR-gas collisions. Suitable clouds should be located away from the Galactic plane in order to test the ``sea'' CR spectrum, excluding the directions towards the inner and outer Galaxy. Assuming that gamma-ray production in hadronic interactions is sufficiently well-understood, the observed gamma-ray flux $\F_\gamma(E)$ from these clouds can be inverted to obtain the differential CR number density $n(E)$. Previous works used observations of molecular clouds in the Gould Belt, in particular of Orion A and B, performed first by COS-B~\cite{1980A&A....91L...3C}, then EGRET~\cite{1995ApJ...441..270D,1999ApJ...520..196D}, and most recently Fermi-LAT to derive the spectral shape of Galactic CRs. During this period, the quality of experimental data has been hugely improved: On the observational side, the data from Fermi-LAT have a much reduced error compared to its predecessor EGRET and extend now up to photon energies $E_\gamma\sim 100$\,GeV, corresponding to typical energies of CR primaries $E\sim 1$\,TeV. Moreover, the PAMELA collaboration determined the slope $\beta_{\rm CR}$ of the CR spectrum $dN/dp\propto p^{-\beta_{\rm CR}}$ with an accuracy of $\Delta\beta_{\rm CR}=\pm 0.05$ in the energy range $80\,{\rm GeV}<p{\rm c}<230$\,GeV~\cite{pamela}. Thus the prediction of the secondary photon spectrum requires either similar precise photon fragmentation functions, or at least an estimate of their error. Finally, there are new results on photon yields from HERA~\cite{HERA} as well as from LHC~\cite{LHCf} on the accelerator side, restricting theoretical models for photon fragmentation functions. In view of the improved precision of the experimental data, we reconsider this problem, paying special attention to the treatment of photon production in proton-proton scatterings. We find that several commonly used parametrisations for the photon fragmentation function as the ones of Refs.~\cite{kamae07,kelner} deviate substantially from experimental data at high energies. These differences diminuish considering the photon yield produced by CRs with a power-law momentum distribution. In this case, we find a relatively good agreement concerning the shape of the photon spectra, while the absolute photon yield differs by $\sim 20$\%. As our main result, we show that the spectral shape $dN/dp\propto p^{-2.85}$ of CR protons as determined by PAMELA in the energy range $80\,{\rm GeV}<p{\rm c}<230$ GeV~\cite{pamela} is consistent with the photon spectra from molecular clouds observed by Fermi-LAT down to energies $E\sim 1$--2\,GeV. The agreement is further improved, if the CR spectrum exhibits a break around 3\,GeV, as suggested by radio data~\cite{low2}. This work is structured as follows: We compare first in Sec.~\ref{sec:Model-approaches} several models used for the calculation of photon production in hadronic collisions to experimental data. We conclude that a combination of the parametrization of Ref.~\cite{kamae07} for nondiffractive processes below $E_{{\rm thr}}=50$\,GeV with the QGSJET-II model~\cite{ost11} at higher energies gives a satisfactory description of experimental data. Then we calculate in Sec.~\ref{sec:gamma-ray spectra} the photon spectra expected from molecular clouds for a given CR flux. In the appendix, we describe the use of the photon and antiproton fragmentation functions employed by us which are available from \url{http://sourceforge.net/projects/ppfrag}.
|
We have reconsidered the problem of determining the average properties of Galactic CRs using gamma-ray observations of molecular clouds. The largely improved quality of the observational data requires a careful treatment of the photon fragmentation function. Comparing photon fragmentation functions calculated in different approaches at high energies, we have argued that a combination of the Kamae parametrisation and QGSJET-II provides the most reliable results. As our main result, we obtained that the spectral shape of CR protons as determined by PAMELA is consistent with the photon spectra from molecular clouds observed by Fermi-LAT down to energies $E\sim 1$--2\,GeV. The agreement is improved further, if the CR spectrum exhibits a break around 3\,GeV. This gives additional evidence for a change of the diffusion coefficient around 3\,GeV, which was previously suggested on theoretical grounds~\cite{Ptuskin:2005ax} and supported by observations~\cite{low2}.
| 12 | 6 |
1206.4705
|
1206
|
1206.6700_arXiv.txt
|
Gamma ray burst (GRBs) can be used to constrain cosmological parameters from medium up to very high redshift. These powerful systems could be the further reliable distance indicators after SNeIa supernovae. We consider GRBs samples to achieve the luminosity distance to redshift relation and derive the values of the cosmographic parameters considering several possible scaling relations. GRBs, if calibrated by SNeIa, seem reliable as distance indicators and give cosmographic parameters in good agreement with the $\Lambda$CDM model. GRBs correlations with neutrino and gravitational wave signals are also investigated in view of high energy neutrino experiments and gravitational wave detectors as LIGO-VIRGO. A discussion on the GRB afterglow curve up to the visible and radio wavelengths is developed considering the possibility to use the Square Kilometer Array (SKA) telescope to achieve the first GRB-radio survey.
|
Observational data collected in the last fifteen years, as the anisotropy and polarization spectra of the cosmic microwave background radiation (CMBR) \cite{Boom00,QUAD09,WMAP7}, the large scale structure of galaxy redshift surveys \cite{D02,P02,Sz03,H03}, the measurements of Baryonic Acoustic Oscillations (BAO, \cite{Eis05,P10}) and the Hubble diagram derived from Supernovae Type Ia (SNeIa) \cite{Union,H09,SNeIaSDSS}), strongly support the cosmological picture of a spatially flat universe with a subcritical matter content $(\Omega_M \sim 0.3)$ undergoing an accelerated phase of expansion. While the observational overview is now firmly established, the search for the motivating theory is, on the contrary, still dawning despite of several efforts and the abundance of models proposed during these years. The question is not the lack of a well established theory, but the presence of too many viable candidates, ranging from the classical cosmological constant \cite{CPT92,SS00}, to scalar fields \cite{PR03,Copeland06} and higher order gravity theories \cite{CF08,FS08,ND08,dFT10,report,francaviglia}, all of them being more or less capable of fitting the available data. As usual, adding further reliable data is the best strategy to put order in the confusing abundance of theoretical models. In particular, the extension of the observed Hubble Diagram (HD) to higher redshift $z$, would allow to trace the universe background evolution up to the transition regime from the accelerated dark energy era to the decelerated matter dominated phase. Moreover, being the distance modulus related to the luminosity distance and depending on the dark energy equation of state, one should go to large $z$ in order to discriminate among different models when these predict similar curves at lower redshift. Unfortunately, SNeIa are not well suitable for this aim since their current Hubble diagram go back to $z_{max} \sim 1.4\div1.7$ and does not extend further than $z \simeq 2$ even for excellent space based experiments such as SNAP \cite{SNAP}. Unlike GRBs, due to their enormous, almost instantaneous energy release, stand out as ideal candidates to explore further redshift, the farthest one today detected at $z = 8.3$ \cite{Salvaterra2009}. The wide range spanned by their peak energy makes them everything but standard candles; anyway the existence of many observationally motivated correlations between redshift dependent quantities and rest frame properties \cite{Amati08,FRR00,G04,liza05} offers the intriguing possibility of turning GRBs into standardizable objects as SNeIa. Many attempts to use GRBs as cosmological distance indicators tools have been already performed (see, {\it e.g.}, \cite{fir06,L08,LWZ09,QiLu09,Izzo08,Izzo09} and refs. therein) showing the potentiality of GRBs as cosmological probes. It is mandatory to remind that the possibility offered by GRBs to track the HD deep into the matter dominated epoch does not come for free. Two main problems are actually still to be fully addressed. First, missing a local GRBs sample, all the possible correlations have to be calibrated assuming a fiducial cosmological model to estimate the redshift dependent quantities. As a consequence, the so called {\it circularity problem} comes out, that is to say one wants to use GRBs scaling relations to constrain the basic cosmology, but needs the basic cosmology to get the scaling relations \cite{perillo}. A well behaved distance indicator should be not only visible to high $z$ and characterized by scaling relations with as small as possible intrinsic scatter, but its physics should be well understood from a theoretical point of view. Presently, there is no full understanding of the GRBs scaling relations so that, as a dangerous drawback, one cannot anticipate whether the calibration parameters are redshift dependent or not. Since we cannot refer to specific theoretical models, one tries to address this problem in a phenomenological way. This review, without claim of completeness, is an attempt in this direction. We will try to summarize some scaling relations and interesting features (most of them already present in literature) that could result useful to standardize GRBs in view of cosmology. The paper is organized as follows. The main features of GRB phenomena are sketched in Sec.2. The so called {\it fireball model} is shortly reviewed in Sec.3. Cosmology with GRBs is widely discussed in Sec.4. Here we recall the main scaling relations that could be useful in order to figure out GRBs as possible standard cosmological indicators. In particular, we discuss the correlation analysis in view of testing cosmological models. Implication for particle astrophysics (i.e. high energy neutrinos) and gravitational radiation are taken into account in Sec.5. Sec.6 is devoted to the GRB radio emission which could be extremely important to accomplish the luminosity curve of these objects in the whole electromagnetic spectrum. Conclusions are drawn in Sec.7.
|
GRBs are flashes of $\gamma$-rays associated with extremely energetic explosions that have been observed in distant galaxies. As discussed, they can be roughly separated into two classes \cite{Weeeks}, long GRBs (with T$_{90}$ $\gtrsim2$s), associated to gravitational collapse of very massive stars, and short GRBs (with T$_{90}$ $\lesssim2$s), associated to mergers of compact objects. GRBs have recently attracted a lot of attention as promising standardizable objects candidates to describe the Hubble diagram up to very high $z$, deep into the matter dominated era thus complementing SNeIa which are, on the contrary, excellent probes for the dark energy epoch. However, still much work is needed in order to be sure that GRBs can indeed hold this promise. Searching for a relation similar to that used to standardize SNeIa has lead to different empirically motivated scaling relations for GRBs. Anyway there are still open issues related to the use of GRBs in cosmology: \begin{itemize} \item the low number of events: the samples of GRBs which can be used to constrain cosmological parameters through the discussed correlations are not so rich; \item the absence of GRBs at low redshift does not allow to calibrate the correlations and requires to adopt methods to fit the cosmological parameters in order to avoid the circularity problem. \end{itemize} Moreover, the lack of theoretical interpretation for the physics of these correlations represents a still open issue. The increase of the number of bursts which can be used to measure the cosmological parameters, and the possible calibration of the correlations would greatly improve the constraints that are presently obtained with few events and non-calibrated correlations. In order to use GRBs as a cosmological tools, through the above correlations, three fundamental parameters, {\it i.e.} $E_{peak}$, $E_\gamma$ and $\theta_{jet}$, should be accurately measured. On the other hand the $L_{iso}-E_{peak}-T_{0.45}$ does not require the knowledge of the afterglow emission because it completely relies on the prompt emission observables. The need to know the cosmological model to infer the luminosity distance for each GRB contrasts with the desire to constrain that same cosmological model (circularity problem). In the attempt to overcome this problem, one can take into account scaling relations and derive the Hubble diagram by different methods in order to estimate the luminosity distance \cite{perillo}. Moreover, GRBs are powerful sources of high-energy neutrinos emitted in different phases according to the fireball model . A mechanism leading to higher (GeV) energy neutrinos in GRB is due to inelastic nuclear collisions. Proton-neutron inelastic collisions are expected, at much lower radii than radii where shocks occur, due to the decoupling of neutrons and protons in the fireball or jet phases. If the fireball has a substantial neutron/proton ratio, as expected in most GRB progenitors, the collisions become inelastic and their rate peaks where the nuclear scattering time becomes comparable to the expansion time. Inelastic neutron/proton collisions then lead to charged pions, GeV muon and electron neutrinos. The typical GRBs neutrino energies range from multi-GeV to EeV, and can yield interesting physical information about fundamental interactions, about (ultra-high energy) cosmic rays, and about the nature of GRBs and their environment. The GRBs neutrino signals may be detected in the coming years by current and forthcoming experiments such as Ice-Cube, RICE, and KM3NeT \cite{KM3NeT}. While the $\pi$ interactions leading to $>100 $TeV energy neutrinos provide a direct probe of the internal shock acceleration process, as well as of the MeV photon density associated with them, the $>10$ PeV neutrinos would probe the reverse external shocks, as well as the photon energies and energy density there. In the very recent years several neutrino telescopes are performing a systematic search for neutrinos emission from GRBs with different analysis methods. Up to now, no signal in excess over the background rate has been observed. The leading models for the ultimate energy source of GRBs are stellar collapse or compact stellar mergers, and these are expected to be sources of GWs. If some fraction of GRBs are produced by double neutron star or neutron star-black hole mergers, the gravitational wave chirp signal of the in-spiral phase should be detectable by the advanced LIGO-VIRGO, associated with the GRB electromagnetic signal. Although the waveforms of the gravitational waves produced in the break-up, merger and/or bar instability phase of collapsars are not known, a cross-correlation technique can be used making use of two co-aligned detectors. The understanding of GRB physics is today rapidly advancing since the discovery of long-lived "afterglow" emission is giving a great insight into the problem. Radio afterglow studies have become an integral part of this field, providing complementary and sometimes unique diagnostics on GRB explosions, their progenitors, and their environments. The reason for this is that the radio part of the spectrum is phenomenologically rich, but also difficult to investigate because only $20\%$ of GRBs observed so far have been seen at radio-wavelength. A GRB radio-survey requires a very high sensitivity that only few radio telescopes can reach. The forthcoming Square Kilometers Array (SKA) could be of extreme interest in this effort.
| 12 | 6 |
1206.6700
|
1206
|
1206.3852_arXiv.txt
|
{In de Sitter spacetime there exists an absolute minimum for the mass of a spin-2 field set by the Higuchi bound $m^2 \ge 2H^2$. We generalize this bound to arbitrary spatially flat FRW geometries in the context of the recently proposed ghost-free models of Massive Gravity with an FRW reference metric, by performing a Hamiltonian analysis for cosmological perturbations. We find that the bound generically indicates that spatially flat FRW solutions in FRW massive gravity, which exhibit a Vainshtein mechanism in the background as required by consistency with observations, imply that the helicity zero mode is a ghost. In contradistinction to previous works, the tension between the Higuchi bound and the Vainshtein mechanism is equally strong regardless of the equation of state for matter.}
|
Theories that attempt to modify General Relativity (GR) have a long and rich history. Their study in most recent years has been further motivated by the observational finding on the Supernova data \cite{Perlmutter:1998np,Riess:1998cb} which points to acceleration in the current expansion of the Universe. If GR is correct, then there must be a \textit{dark energy} density of $\rho\sim 10^{-29}\rm{g/cm^3}$. If this value is due to the cosmological constant $\Lambda$, it will enforce an extremely small number for $\Lambda$, very far from the value that arises from quantum field theory considerations \cite{Weinberg:1988cp}. On the other hand, if one is willing to modify GR, it has been shown in different \textit{modified gravity} theories \cite{Deffayet:2000uy}-\cite{DeFelice:2010aj} that there exist self-accelerating solutions \cite{Carroll:2003wy,Carroll:2004de} which might explain the current acceleration of the Universe without resorting to dark energy. A ubiquitous issue in theories of gravity, such as the smallness of the cosmological constant, can have different manifestations in different theories. A much desired feature of such theories would be a mechanism by which the smallness of the parameter $\Lambda$ (or whatever parameter takes its place) is technically natural. Quite generally, if setting to zero a small parameter in a theory results in an additional symmetry, it is reasonable to expect that quantum corrections to that parameter will be of the same order of the parameter itself as they are protected by the initial symmetry; if this is the case, the parameter is said technically natural. Take for example massive gravity (MG): at large distances MG weakens with respect to GR, the potential reads $\sim e^{-m r}/r$. This results in the possibility of an accelerated expansion without dark energy. Observations force one to assume a very small $m$ and again, the fine tuning issue reappears in the ratio $m/M_{\rm Pl}$. Interestingly though, one notices here how the $m=0$ theory, GR, has an additional gauge symmetry that is broken by the massive term and so there is indeed room for a technically natural small value of the parameter $m$. Departing from GR comes with a heavy baggage: since the pioneering proposal of Fierz and Pauli \cite{FP}, theories of massive gravity have been plagued with continuity issues \cite{vDVZ1,vDVZ2,Vain}, instabilities (ghosts) \cite{BD}, and with a hierarchy of scales which has made it hard to make sense of the theory \cite{ArkaniHamed:2002sp}. A lot has been done in recent years to make the prospect of a massive theory of gravity more intriguing and, possibly, more predictive. This effort \cite{Kurtrev} culminated \cite{deRham:2010ik,deRham:2010kj} in the formulation of a theory of massive gravity (which we shall refer to as dRGT from now on) which is free of ghosts at the fully non linear level \cite{Hassan:2011hr,Hassan:2011ea,deRham:2011rn,deRham:2011qq,Mirbabayi:2011aa, Hassan:2012qv,Golovnev:2011aa,Kluson:2011rt}. This theory is endowed with a benevolent hierarchy of scales which neatly splits the linear regime, the non-linear one and the regime where quantum effects must be taken into account. Having such a young theory at one's disposal, there is no shortage of aspects in need of careful investigation \cite{,Gumrukcuoglu:2011zh,Burrage:2011cr,Alberte:2011ah,Berezhiani:2011mt,Brihaye:2011aa,Vakili:2012tm,Tasinato:2012mf,Baccetti:2012bk}. The more cosmologically inclined might for example opt for a study of realistic cosmological solutions for dRGT, this has recently been done in \cite{massivec}. The analysis we present here shares some features with the work \cite{massivec} in that it points towards the same direction. In this manuscript we study the classical stability of the scalar sector of dRGT theory up to quadratic order in perturbations when the reference metric is taken to be FRW. We probe several cases according to the background value of the dynamical metric $g_{\mu\nu}$ and the reference metric $f_{\mu\nu}$. Matter content besides the cosmological constant is also considered. Such a study has been performed in the past for theories which were known to have ghosts \cite{Deser,Grisa}. In this context the so called \textit{Higuchi bound} \cite{Higuchi} on the mass of the graviton was introduced. It is a strong lower bound on $m$, $m^2\ge 2H^2$, and arises from the requirement that the kinetic term for the helicity zero mode, i.e. the scalar cosmological perturbations, is positive definite. Things do not necessarily improve when one includes matter because a similar bound must hold over the different cosmological epochs \cite{Grisa}, as we will see. We show that, even if in dRGT there is more room to accommodate for such a bound (e.g. dRGT has 2 free parameters) and even if we employ at full the freedom on the reference metric, once observations are taken into account the bound remains quite stringent. We hint to a possible resolution in the \textit{Conclusions}. Our final bound is give by \be \tilde{m}^2(H) =m^2 \frac{H}{H_0} \left( (3+3\alpha_3+\alpha_4) -2(1+2 \alpha_3+\alpha_4)\frac{H}{H_0}+(\alpha_3+\alpha_4) \frac{H^2}{H_0^2}\right)\ge 2 H^2. \nonumber \ee where $H$ is the Hubble rate of the dynamical metric and $H_0$ that of the reference (non-dynamical) metric, and $\alpha_3$ and $\alpha_4$ are the two free parameters in the dRGT model \cite{deRham:2010kj}. This should be compared with the associated Friedmann equation \bea H^2&=&\frac{1}{3 \mpl^2} \rho -(6+4\alpha_3+\alpha_4)\frac{m^2}{3}+(3+3\alpha_3+\alpha_4)m^2 \frac{H}{H_0}-\nonumber \\ &&(1+2\alpha_3+\alpha_4)m^2 \frac{H^2}{H_0^2} + (\alpha_3+\alpha_4)\frac{m^2}{3}\frac{H^3}{H_0^3}. \nonumber \eea In this paper the background metrics studied are both homogeneous and isotropic, a natural next step would then be to consider introducing inhomogeneities at the background level. There is more to support further work in this direction: in \cite{massivec}, it was shown that there exist no truly homogeneous and isotropic cosmological solutions in dRGT theory with a Minkowski reference metric, for the very same reasons that guarantee no Boulware-Deser ghost is present in such a theory. On the other hand, there are approximate solutions that well describe observations and yet evade this no-go theorem. We will expand upon this in a forthcoming work \cite{paper3}. This paper is organized as follows: in the first \textit{Section} we briefly introduce dRGT theory. In \textit{Section 2} we report the details of the theory at second order in perturbation for the scalar sector. In \textit{Section 3} we briefly introduce the Higuchi bound and summarize previous work on the subject. In \textit{Section 4} we present the analysis for the theory when both metrics are de Sitter. In \textit{Section 5} we add matter content and consider FRW solutions. In the \textit {Conclusions} section we elaborate on our findings and future work. Although in this work we concentrate on quite specific aspects of the theory, it is important to appreciate that this model of massive gravity seems to enjoy properties and structures that are ubiquitous in current analysis of, for example, alternative models to inflation \cite{galileon1,galileon2,burrage,Bartolo,galileon3}. This theory as a whole also appears to be part of a larger family of massive theories of gravity \cite{Paulos} some of which first emerged in the study of $\rm{AdS}_{3}/\rm{CFT}_2$ correspondence.
| 12 | 6 |
1206.3852
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.