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# Posts Tagged galaxy cluster

## Recent Postings from galaxy cluster

### X-ray line signal from 7 keV axino dark matter decay

Recently a weak X-ray emission around E ~ 3.5 keV is detected in the Andromeda galaxy and various galaxy clusters including the Perseus galaxy cluster but its source has been unidentified. Axino, the superpartner of axion, with a mass 2E is suggested as a possible origin of the line with R-parity violating decay into photon and neutrino.

### X-ray line signal from 7 keV axino dark matter decay [Cross-Listing]

Recently a weak X-ray emission around E ~ 3.5 keV is detected in the Andromeda galaxy and various galaxy clusters including the Perseus galaxy cluster but its source has been unidentified. Axino, the superpartner of axion, with a mass 2E is suggested as a possible origin of the line with R-parity violating decay into photon and neutrino.

### CLASH: Extending galaxy strong lensing to small physical scales with distant sources highly-magnified by galaxy cluster members

We present a strong lensing system in which a double source is imaged 5 times by 2 early-type galaxies. We take advantage in this target of the multi-band photometry obtained as part of the CLASH program, complemented by the spectroscopic data of the VLT/VIMOS and FORS2 follow-up campaign. We use a photometric redshift of 3.7 for the source and confirm spectroscopically the membership of the 2 lenses to the galaxy cluster MACS J1206.2-0847 at redshift 0.44. We exploit the excellent angular resolution of the HST/ACS images to model the 2 lenses in terms of singular isothermal sphere profiles and derive robust effective velocity dispersions of (97 +/- 3) and (240 +/- 6) km/s. The total mass distribution of the cluster is also well characterized by using only the local information contained in this lensing system, that is located at a projected distance of more than 300 kpc from the cluster luminosity center. According to our best-fitting lensing and composite stellar population models, the source is magnified by a total factor of 50 and has a luminous mass of about (1.0 +/- 0.5) x 10^{9} M_{Sun}. By combining the total and luminous mass estimates of the 2 lenses, we measure luminous over total mass fractions projected within the effective radii of 0.51 +/- 0.21 and 0.80 +/- 0.32. With these lenses we can extend the analysis of the mass properties of lens early-type galaxies by factors that are about 2 and 3 times smaller than previously done with regard to, respectively, velocity dispersion and luminous mass. The comparison of the total and luminous quantities of our lenses with those of astrophysical objects with different physical scales reveals the potential of studies of this kind for investigating the internal structure of galaxies. These studies, made possible thanks to the CLASH survey, will allow us to go beyond the current limits posed by the available lens samples in the field.

### Lensing Model of MACS J1149.5+2223 I: Cluster Mass Reconstruction

Measurements of the total logarithmic central slope of the mass profile in galaxy clusters constrain their evolution and assembly history and that of their Brightest Cluster Galaxies. We report the first full surface brightness distribution modelling of the inner region of the galaxy cluster MACS J1149.5+2223. We compare these results with a position-based modelling approach for which we employ more than twice the previously known positional constraints. This is the first time that the detailed lensed image configuration of two non-central cluster galaxies with Einstein rings has been mapped. Due to the extended radial coverage provided by the multiple images in this system, we are able to determine the slope $\partial \log{\kappa}/\partial \log{R} = -0.37$ of the total projected mass distribution from $8$ to $80 \mathrm{kpc}$. This is within the cluster-to-cluster scatter estimates from previous cluster measurements. Our reconstruction of the image surface brightness distribution of the large central spiral galaxy has a root mean square residual for all image pixels of $1.14 \sigma$, where $\sigma$ is the observational background noise. This corresponds to a reconstruction of the positions of bright clumps in the central galaxy with a rms of $0.063 \mathrm{arcseconds}$.

### Large scale gas sloshing out to half the virial radius in the strongest cool core REXCESS galaxy cluster, RXJ2014.8-2430

We search the cool core galaxy clusters in the REXCESS sample for evidence of large scale gas sloshing, and find clear evidence for sloshing in RXJ2014.8-2430, the strongest cool core cluster in the REXCESS cluster sample. The residuals of the surface brightness distribution from the azimuthal average for RXJ2014 show a prominent swirling excess feature extending out to an abrupt surface brightness discontinuity at 800 kpc from the cluster core (half the virial radius) to the south, which the XMM-Newton observations confirm to be cold, low entropy gas. The gas temperature is significantly higher outside this southern surface brightness discontinuity, indicating that this is a cold front 800 kpc from the cluster core. Chandra observations of the central 200 kpc show two clear younger cold fronts on opposite sides of the cluster. The scenario appears qualitatively consistent with simulations of gas sloshing due to minor mergers which raise cold, low entropy gas from the core to higher radius, resulting in a swirling distribution of opposing cold fronts at increasing radii. However the scale of the observed sloshing is much larger than that which has been simulated at present, and is similar to the large scale sloshing recently observed in the Perseus cluster and Abell 2142.

### Wide-Field Hubble Space Telescope Observations of the Globular Cluster System in NGC1399

We present a comprehensive high spatial-resolution imaging study of globular clusters (GCs) in NGC1399, the central giant elliptical cD galaxy in the Fornax galaxy cluster, conducted with HST/ACS. Using a novel technique to construct drizzled PSF libraries for HST/ACS data, we accurately determine the fidelity of GC structural parameter measurements from detailed artificial star cluster experiments. The measurement of rh for the major fraction of the NGC1399 GC system reveals a trend of increasing rh versus galactocentric distance, Rgal, out to about 10 kpc and a flat relation beyond. This trend is very similar for blue and red GCs which are found to have a mean size ratio of rh(red)/rh(blue)=0.82+/-0.11 at all galactocentric radii from the core regions of the galaxy out to ~40 kpc. This suggests that the size difference between blue and red GCs is due to internal mechanisms related to the evolution of their constituent stellar populations. Modeling the mass density profile of NGC1399 shows that additional external dynamical mechanisms are required to limit the GC size in the galaxy halo regions to rh~2 pc. We suggest that this may be realized by an exotic GC orbit distribution function, an extended dark matter halo, and/or tidal stress induced by the increased stochasticity in the dwarf halo substructure at larger Rgal. We match our GC rh measurements with radial velocity data from the literature and find that compact GCs show a significantly smaller line-of-sight velocity dispersion, <sigma(cmp)>=225+/-25 km/s, than their extended counterparts, <sigma(ext)>=317+/-21 km/s. Considering the weaker statistical correlation in the GC rh-color and the GC rh-Rgal relations, the more significant GC size-dynamics relation appears to be astrophysically more relevant and hints at the dominant influence of the GC orbit distribution function on the evolution of GC structural parameters.

### Measurement of the halo bias from stacked shear profiles of galaxy clusters

We present the observational evidence of the 2-halo term in the stacked shear profile of a sample of about 1200 optically selected galaxy clusters based on imaging data and the public shear catalog from the CFHTLenS. We find that the halo bias, a measure of the correlated distribution of matter around galaxy clusters, has amplitude and correlation with galaxy cluster mass in very good agreement with the predictions based on the LCDM standard cosmological model. The mass-concentration relation is flat but higher than theoretical predictions. We also confirm the close scaling relation between the optical richness of galaxy clusters and their mass.

### Discovery of large-scale diffuse radio emission and of a new galaxy cluster in the surroundings of MACSJ0520.7-1328

We report the discovery of large-scale diffuse radio emission South-East of the galaxy cluster MACS J0520.7-1328, detected through high sensitivity Giant Metrewave Radio Telescope 323 MHz observations. This emission is dominated by an elongated diffuse radio source and surrounded by other features of lower surface brightness. Patches of these faint sources are marginally detected in a 1.4 GHz image obtained through a re-analysis of archival NVSS data. Interestingly, the elongated radio source coincides with a previously unclassified extended X-ray source. We perform a multi-wavelength analysis based on archival infrared, optical and X-ray Chandra data. We find that this source is a low-temperature (~3.6 keV) cluster of galaxies, with indications of a disturbed dynamical state, located at a redshift that is consistent with the one of the main galaxy cluster MACS J0520.7-132 (z=0.336). We suggest that the diffuse radio emission is associated with the non-thermal components in the intracluster and intergalactic medium in and around the newly detected cluster. We are planning deeper multi-wavelength and multi-frequency radio observations to accurately investigate the dynamical scenario of the two clusters and to address more precisely the nature of the complex radio emission.

### A Free-Form Lensing Grid Solution for A1689 with New Mutiple Images

Hubble Space Telescope imaging of the galaxy cluster Abell 1689 has revealed an exceptional number of strongly lensed multiply-imaged galaxies, including high-redshift candidates. Previous studies have used this data to obtain the most detailed dark matter reconstructions of any galaxy cluster to date, resolving substructures ~25 kpc across. We examine Abell 1689 (hereafter, A1689) non-parametrically, combining strongly lensed images and weak distortions from wider field Subaru imaging, and we incorporate member galaxies to improve the lens solution. Strongly lensed galaxies are often locally affected by member galaxies, however, these perturbations cannot be recovered in grid based reconstructions because the lensing information is too sparse to resolve member galaxies. By adding luminosity-scaled member galaxy deflections to our smooth grid we can derive meaningful solutions with sufficient accuracy to permit the identification of our own strongly lensed images, so our model becomes self consistent. We identify 11 new multiply lensed system candidates and clarify previously ambiguous cases, in the deepest optical and NIR data to date from Hubble and Subaru. Our improved spatial resolution brings up new features not seen when the weak and strong lensing effects are used separately, including clumps and filamentary dark matter around the main halo. Our treatment means we can obtain an objective mass ratio between the cluster and galaxy components, for examining the extent of tidal stripping of the luminous member galaxies. We find a typical mass-to-light ratios of M/L_B = 21 inside the r<1 arcminute region that drops to M/L_B = 17 inside the r<40 arcsecond region. Our model independence means we can objectively evaluate the competitiveness of stacking cluster lenses for defining the geometric lensing-distance-redshift relation in a model independent way.

### A Free-Form Lensing Grid Solution for A1689 with New Mutiple Images [Replacement]

Hubble Space Telescope imaging of the galaxy cluster Abell 1689 has revealed an exceptional number of strongly lensed multiply-imaged galaxies, including high-redshift candidates. Previous studies have used this data to obtain the most detailed dark matter reconstructions of any galaxy cluster to date, resolving substructures ~25 kpc across. We examine Abell 1689 (hereafter, A1689) non-parametrically, combining strongly lensed images and weak distortions from wider field Subaru imaging, and we incorporate member galaxies to improve the lens solution. Strongly lensed galaxies are often locally affected by member galaxies, however, these perturbations cannot be recovered in grid based reconstructions because the lensing information is too sparse to resolve member galaxies. By adding luminosity-scaled member galaxy deflections to our smooth grid we can derive meaningful solutions with sufficient accuracy to permit the identification of our own strongly lensed images, so our model becomes self consistent. We identify 11 new multiply lensed system candidates and clarify previously ambiguous cases, in the deepest optical and NIR data to date from Hubble and Subaru. Our improved spatial resolution brings up new features not seen when the weak and strong lensing effects are used separately, including clumps and filamentary dark matter around the main halo. Our treatment means we can obtain an objective mass ratio between the cluster and galaxy components, for examining the extent of tidal stripping of the luminous member galaxies. We find a typical mass-to-light ratios of M/L_B = 21 inside the r<1 arcminute region that drops to M/L_B = 17 inside the r<40 arcsecond region. Our model independence means we can objectively evaluate the competitiveness of stacking cluster lenses for defining the geometric lensing-distance-redshift relation in a model independent way.

### An unidentified line in X-ray spectra of the Andromeda galaxy and Perseus galaxy cluster [Cross-Listing]

We identify a weak line at $E \sim 3.5$ keV in X-ray spectra of the Andromeda galaxy and the Perseus galaxy cluster — two dark matter-dominated objects, for which there exist deep exposures with the XMM-Newton X-ray observatory. Such a line was not previously known to be present in the spectra of galaxies or galaxy clusters. Although the line is weak, it has a clear tendency to become stronger towards the centers of the objects; it is stronger for the Perseus cluster than for the Andromeda galaxy and is absent in the spectrum of a very deep "blank sky" dataset. Although for individual objects it is hard to exclude the possibility that the feature is due to an instrumental effect or an atomic line of anomalous brightness, it is consistent with the behavior of a line originating from the decay of dark matter particles. Future detections or non-detections of this line in multiple astrophysical targets may help to reveal its nature.

### An unidentified line in X-ray spectra of the Andromeda galaxy and Perseus galaxy cluster

We identify a weak line at $E \sim 3.5$ keV in X-ray spectra of the Andromeda galaxy and the Perseus galaxy cluster — two dark matter-dominated objects, for which there exist deep exposures with the XMM-Newton X-ray observatory. Such a line was not previously known to be present in the spectra of galaxies or galaxy clusters. Although the line is weak, it has a clear tendency to become stronger towards the centers of the objects; it is stronger for the Perseus cluster than for the Andromeda galaxy and is absent in the spectrum of a very deep "blank sky" dataset. Although for individual objects it is hard to exclude the possibility that the feature is due to an instrumental effect or an atomic line of anomalous brightness, it is consistent with the behavior of a line originating from the decay of dark matter particles. Future detections or non-detections of this line in multiple astrophysical targets may help to reveal its nature.

### redMaPPer III: A Detailed Comparison of the Planck 2013 and SDSS DR8 RedMaPPer Cluster Catalogs

We compare the Planck Sunyaev-Zeldovich (SZ) cluster sample (PSZ1) to the Sloan Digital Sky Survey (SDSS) redMaPPer catalog, finding that all Planck clusters within the redMaPPer mask and within the redshift range probed by redMaPPer are contained in the redMaPPer cluster catalog. These common clusters define a tight scaling relation in the richness-SZ mass ($\lambda$–$M_{SZ}$) plane, with an intrinsic scatter in richness of $\sigma_{\lambda|M_{SZ}} = 0.266 \pm 0.017$. The corresponding intrinsic scatter in true cluster halo mass at fixed richness is $\approx 21\%$. The regularity of this scaling relation is used to identify failures in both the redMaPPer and Planck cluster catalogs. Of the 245 galaxy clusters in common, we identify three failures in redMaPPer and 36 failures in the PSZ1. Of these, at least 12 are due to clusters whose optical counterpart was correctly identified in the PSZ1, but where the quoted redshift for the optical counterpart in the external data base used in the PSZ1 was incorrect. The failure rates for redMaPPer and the PSZ1 are $1.2\%$ and $14.7\%$ respectively, or 9.8% in the PSZ1 after subtracting the external data base errors. We have further identified 5 PSZ1 sources that suffer from projection effects (multiple rich systems along the line-of-sight of the SZ detection) and 17 new high redshift ($z\gtrsim 0.6$) cluster candidates of varying degrees of confidence. Should all of the high-redshift cluster candidates identified here be confirmed, we will have tripled the number of high redshift Planck clusters in the SDSS region. Our results highlight the power of multi-wavelength observations to identify and characterize systematic errors in galaxy cluster data sets, and clearly establish photometric data both as a robust cluster finding method, and as an important part of defining clean galaxy cluster samples.

### CLASH-VLT: Constraints on the Dark Matter Equation of State from Accurate Measurements of Galaxy Cluster Mass Profiles

A pressureless scenario for the Dark Matter (DM) fluid is a widely adopted hypothesis, despite the absence of a direct observational evidence. According to general relativity, the total mass-energy content of a system shapes the gravitational potential well, but different test particles perceive this potential in different ways depending on their properties. Cluster galaxy velocities, being $\ll$c, depend solely on the gravitational potential, whereas photon trajectories reflect the contributions from the gravitational potential plus a relativistic-pressure term that depends on the cluster mass. We exploit this phenomenon to constrain the Equation of State (EoS) parameter of the fluid, primarily DM, contained in galaxy clusters. We use the complementary information provided by the kinematic and lensing mass profiles of the galaxy cluster MACS 1206.2-0847 at $z=0.44$, as obtained in an extensive imaging and spectroscopic campaign within the CLASH survey. The unprecedented high quality of our data-set and the properties of this cluster are well suited to determine the EoS parameter of the cluster fluid. Since baryons contribute at most $15\%$ to the total mass in clusters and their pressure is negligible, the EoS parameter we derive describes the behavior of the DM fluid. We obtain the most stringent constraint on the DM EoS parameter to date, $w=(p_r+2\,p_t)/(3\,c^2\rho)=0.00\pm0.15\mathrm{(stat)}\pm0.08\mathrm{(syst)}$, averaged over the radial range $0.5\,\mathrm{Mpc}\leq$$r$$\leq$$r_{200}$, where $p_r$ and $p_t$ are the radial and tangential pressure, and $\rho$ is the density. We plan to further improve our constraint by applying the same procedure to all clusters from the ongoing CLASH-VLT program.

### Mapping the large scale structure around a z=1.46 galaxy cluster in 3-D using two adjacent narrow-band filters

We present a novel method to estimate accurate redshifts of star-forming galaxies by measuring the flux ratio of the same emission line observed through two adjacent narrow-band filters. We apply this method to our NB912 and new NB921 data taken with Suprime-Cam on the Subaru Telescope of a galaxy cluster, XMMXCS J2215.9-1738, at z=1.46 and its surrounding structures. We obtain redshifts for 170 [OII] emission line galaxies at z~1.46, among which 41 galaxies are spectroscopically confirmed with MOIRCS and FMOS on the Subaru mainly, showing an accuracy of $\sigma$((z-z_spec})/(1+z_spec))=0.002. This allows us to reveal filamentary structures that penetrate towards the centre of the galaxy cluster and intersect with other structures, consistent with the picture of hierarchical cluster formation. We also find that the projected celestial distribution does not precisely trace the real distribution of galaxies, indicating the importance of the three dimensional view of structures to properly identify and quantify galaxy environments. We investigate the environmental dependence of galaxy properties with local density, confirming that the median colour of galaxies becomes redder in higher density region while the star-formation rate of star-forming galaxies does not depend strongly on local environment in this structure. This implies that the star-forming activity in galaxies is truncated on a relatively short time scale in the cluster centre.

### The XXL Survey: Detection of the Sunyaev-Zel'dovich effect of the Redshift 1.9 Galaxy Cluster XLSSU J021744.1-034536 with CARMA

We report the detection of the Sunyaev-Zel’dovich (SZ) effect of galaxy cluster XLSSU J021744.1-034536, using 30 GHz CARMA data. This cluster was discovered via its extended X-ray emission in the XMM-Newton Large Scale Structure survey, the precursor to the XXL survey. It has a photometrically determined redshift $z=1.91^{+0.19}_{-0.21}$, making it among the most distant clusters known, and nominally the most distant for which the SZ effect has been measured. The spherically integrated Comptonization is $Y_{500}=(5.8\pm1.0)\times10^{-12}$, a measurement which is largely independent of assumptions regarding the size and redshift of the cluster, as well as the background cosmology. Using a variety of locally calibrated cluster scaling relations extrapolated to $z\sim2$, we estimate a mass $M_{500}\sim(1$-$2)\times10^{14}$Msun from the X-ray flux and SZ signal. The measured properties of this cluster are in broad agreement with the extrapolation of an X-ray luminosity-SZ effect scaling relation calibrated from clusters discovered by South Pole Telescope at higher masses and lower redshifts. The complete XXL-CARMA sample will provide a more complete, multi-wavelength census of distant clusters in order to robustly extend the calibration of cluster scaling relations to these high redshifts.

### Gas bulk motion in the Perseus cluster measured with SUZAKU

We present the results from Suzaku observations of the Perseus galaxy cluster, which is relatively close, the brightest in the X-ray sky and a relaxed object with a cool core. A number of exposures of central regions and offset pointing with the X-ray Imaging Spectrometer cover a region within radii of 20′-30′. The central data are used to evaluate the instrumental energy-scale calibration with accuracy confirmed to within around 300 km/s, by the spatial and temporal variation of the instruments. These deep and well-calibrated data are used to measure X-ray redshifts of the intracluster medium. A hint of gas bulk motion, with radial velocity of about -(150-300) km/s, relative to the main system was found at 2-4 arcmin (45-90kpc) west of the cluster center, where an X-ray excess and a cold front were found previously. No other velocity structure was discovered. Over spatial scales of 50-100kpc and within 200kpc radii of the center, the gas-radial-velocity variation is below 300 km/s, while over scales of 400 kpc within 600 kpc radii, the variation is below 600 km/s. These X-ray redshift distributions are compared spatially with those of optical member galaxies for the first time in galaxy clusters. Based on X-ray line widths gas turbulent velocities within these regions are also constrained within 1000-3000 km/s. These results of gas dynamics in the core and larger scales in association with cluster merger activities are discussed and future potential of high-energy resolution spectroscopy with ASTRO-H is considered.

### How typical is the Coma cluster?

Coma is frequently used as the archetype z~0 galaxy cluster to compare higher redshift work against. It is not clear, however, how representative the Coma cluster is for galaxy clusters of its mass or X-ray luminosity, and significantly: recent works have suggested that the galaxy population of Coma may be in some ways anomolous. In this work, we present a comparison of Coma to an X-ray selected control sample of clusters. We show that although Coma is typical against the control sample in terms of its internal kinematics (substructure and velocity dispersion profile), it has a significantly high (~3sigma) X-ray temperature set against clusters of comparable mass. By de-redshifting our control sample cluster galaxies star-formation rates using a fit to the galaxy main sequence evolution at z < 0.1, we determine that the typical star-formation rate of Coma galaxies as a function of mass is higher than for galaxies in our control sample at a confidence level of > 99 per cent. One way to alleviate this discrepency and bring Coma in-line with the control sample would be to have the distance to Coma to be slightly lower, perhaps through a non-negligible peculiar velocity with respect to the Hubble expansion, but we do not regard this as likely given precision measurements using a variety of approaches. Therefore in summary, we urge caution in using Coma as a z~0 baseline cluster in galaxy evolution studies.

### Line-of-Sight Structure Toward Strong Lensing Galaxy Clusters

We present an analysis of the line-of-sight structure toward a sample of ten strong lensing cluster cores. Structure is traced by groups that are identified spectroscopically in the redshift range, 0.1 $\leq$ z $\leq$ 0.9, and we measure the projected angular and comoving separations between each group and the primary strong lensing clusters in each corresponding line of sight. From these data we measure the distribution of projected angular separations between the primary strong lensing clusters and uncorrelated large scale structure as traced by groups. We then compare the observed distribution of angular separations for our strong lensing selected lines of sight against the distribution of groups that is predicted for clusters lying along random lines of sight. There is clear evidence for an excess of structure along the line of sight at small angular separations ($\theta \leq 6′$) along the strong lensing selected lines of sight, indicating that uncorrelated structure is a significant systematic that contributes to producing galaxy clusters with large cross sections for strong lensing. The prevalence of line-of-sight structure is one of several biases in strong lensing clusters that can potentially be folded into cosmological measurements using galaxy cluster samples. These results also have implications for current and future studies — such as the Hubble Space Telescope Frontier Fields — that make use of massive galaxy cluster lenses as precision cosmological telescopes; it is essential that the contribution of line-of-sight structure be carefully accounted for in the strong lens modeling of the cluster lenses.

### Star formation in the cluster CLG0218.3-0510 at z=1.62 and its large-scale environment: the infrared perspective

The galaxy cluster CLG0218.3-0510 at z=1.62 is one of the most distant galaxy clusters known, with a rich muti-wavelength data set that confirms a mature galaxy population already in place. Using very deep, wide area (20×20 Mpc) imaging by Spitzer/MIPS at 24um, in conjunction with Herschel 5-band imaging from 100-500um, we investigate the dust-obscured, star-formation properties in the cluster and its associated large scale environment. Our galaxy sample of 693 galaxies at z=1.62 detected at 24um (10 spectroscopic and 683 photo-z) includes both cluster galaxies (i.e. within r <1 Mpc projected clustercentric radius) and field galaxies, defined as the region beyond a radius of 3 Mpc. The star-formation rates (SFRs) derived from the measured infrared luminosity range from 18 to 2500 Ms/yr, with a median of 55 Ms/yr, over the entire radial range (10 Mpc). The cluster brightest FIR galaxy, taken as the centre of the galaxy system, is vigorously forming stars at a rate of 256$\pm$70 Ms/yr, and the total cluster SFR enclosed in a circle of 1 Mpc is 1479$\pm$122 Ms/yr/Mpc2. We estimate a dust extinction of about 3 magnitudes by comparing the SFRs derived from [OII] luminosity with the ones computed from the 24um fluxes. We find that the in-falling region (1-3 Mpc) is special: there is a significant decrement (3.5x) of passive relative to star-forming galaxies in this region, and the total SFR of the galaxies located in this region is lower (130 Ms/yr/Mpc2) than anywhere in the cluster or field, regardless of their stellar mass. In a complementary approach we compute the local galaxy density, Sigma5, and find no trend between SFR and Sigma5. However, we measure an excess of star-forming galaxies in the cluster relative to the field by a factor 1.7, that lends support to a reversal of the SF-density relation in CLG0218.

### Star formation in the cluster CLG0218.3-0510 at z=1.62 and its large-scale environment: the infrared perspective [Replacement]

The galaxy cluster CLG0218.3-0510 at z=1.62 is one of the most distant galaxy clusters known, with a rich muti-wavelength data set that confirms a mature galaxy population already in place. Using very deep, wide area (20×20 Mpc) imaging by Spitzer/MIPS at 24um, in conjunction with Herschel 5-band imaging from 100-500um, we investigate the dust-obscured, star-formation properties in the cluster and its associated large scale environment. Our galaxy sample of 693 galaxies at z=1.62 detected at 24um (10 spectroscopic and 683 photo-z) includes both cluster galaxies (i.e. within r <1 Mpc projected clustercentric radius) and field galaxies, defined as the region beyond a radius of 3 Mpc. The star-formation rates (SFRs) derived from the measured infrared luminosity range from 18 to 2500 Ms/yr, with a median of 55 Ms/yr, over the entire radial range (10 Mpc). The cluster brightest FIR galaxy, taken as the centre of the galaxy system, is vigorously forming stars at a rate of 256$\pm$70 Ms/yr, and the total cluster SFR enclosed in a circle of 1 Mpc is 1161$\pm$96 Ms/yr. We estimate a dust extinction of about 3 magnitudes by comparing the SFRs derived from [OII] luminosity with the ones computed from the 24um fluxes. We find that the in-falling region (1-3 Mpc) is special: there is a significant decrement (3.5x) of passive relative to star-forming galaxies in this region, and the total SFR of the galaxies located in this region is lower (130 Ms/yr/Mpc2) than anywhere in the cluster or field, regardless of their stellar mass. In a complementary approach we compute the local galaxy density, Sigma5, and find no trend between SFR and Sigma5. However, we measure an excess of star-forming galaxies in the cluster relative to the field by a factor 1.7, that lends support to a reversal of the SF-density relation in CLG0218.

### Disentangling a group of lensed submm galaxies at z~2.9

MS$\,$0451.6$-$0305 is a rich galaxy cluster whose strong lensing is particularly prominent at submm wavelengths. We combine new SCUBA-2 data with imaging from Herschel SPIRE and PACS and HST in order to try to understand the nature of the sources being lensed. In the region of the "giant submm arc," we uncover seven multiply imaged galaxies (up from the previously known three), of which six are found to be at a redshift of $z\sim2.9$, and possibly constitute an interacting system. Using a novel forward-modelling approach, we are able to simultaneously deblend and fit SEDs to the individual galaxies that contribute to the giant submm arc, constraining their dust temperatures, far infrared luminosities and star formation rates. The submm arc first identified by SCUBA can now be seen to be composed of at least five distinct sources, four of these within the galaxy group at $z\sim2.9$. The total unlensed luminosity for this galaxy group is $(3.1\pm0.3) \times 10^{12}\,\mathrm{L}_\odot$, which gives an unlensed star formation rate of $(450\pm50)$ M$_\odot$ yr$^{-1}$. From the properties of this system, we see no evidence of evolution towards lower temperatures in the dust temperature versus far-infrared luminosity relation for high redshift galaxies.

### A Phenomenological Model for the Intracluster Medium that matches X-ray and Sunyaev-Zel'dovich observations [Replacement]

Cosmological hydrodynamical simulations of galaxy clusters are still challenged to produce a model for the intracluster medium that matches all aspects of current X-ray and Sunyaev-Zel’dovich observations. To facilitate such comparisons with future simulations and to enable realistic cluster population studies for modeling e.g., non-thermal emission processes, we construct a phenomenological model for the intracluster medium that is based on a representative sample of observed X-ray clusters. We create a mock galaxy cluster catalog based on the large collisionless N-body simulation MultiDark, by assigning our gas density model to each dark matter cluster halo. Our clusters are classified as cool-core and non cool-core according to a dynamical disturbance parameter. We demonstrate that our gas model matches the various observed Sunyaev-Zel’dovich and X-ray scaling relations as well as the X-ray luminosity function, thus enabling to build a reliable mock catalog for present surveys and forecasts for future experiments. In a companion paper, we apply our catalogs to calculate non-thermal radio and gamma-ray emission of galaxy clusters. We make our cosmologically complete multi-frequency mock catalogs for the (non-)thermal cluster emission at different redshifts publicly and freely available online through the MultiDark database (www.multidark.org).

### A Phenomenological Model for the Intracluster Medium that matches X-ray and Sunyaev-Zel'dovich observations

Cosmological hydrodynamical simulations of galaxy clusters are still challenged to produce a model for the intracluster medium that matches all aspects of current X-ray and Sunyaev-Zel’dovich observations. To facilitate such comparisons with future simulations and to enable realistic cluster population studies for modeling e.g., non-thermal emission processes, we construct a phenomenological model for the intracluster medium that is based on a representative sample of observed X-ray clusters. We create a mock galaxy cluster catalog based on the large collisionless N-body simulation MultiDark, by assigning our gas density model to each dark matter cluster halo. Our clusters are classified as cool-core and non cool-core according to a dynamical disturbance parameter. We demonstrate that our gas model matches the various observed Sunyaev-Zel’dovich and X-ray scaling relations as well as the X-ray luminosity function, thus enabling to build a reliable mock catalog for present surveys and forecasts for future experiments. In a companion paper, we apply our catalogs to calculate non-thermal radio and gamma-ray emission of galaxy clusters. We make our cosmologically complete multi-frequency mock catalogs for the (non-)thermal cluster emission at different redshifts publicly and freely available online through the MultiDark database (www.multidark.org).

### A Large Scale Structure at Redshift 1.71 in the Lockman Hole

We previously identified LH146, a diffuse X-ray source in the Lockman Hole, as a galaxy cluster at redshift 1.753. The redshift was based on one spectroscopic value, buttressed by seven additional photometric redshifts. We here confirm the previous spectroscopic redshift and present concordant spectroscopic redshifts for an additional eight galaxies. The average of these nine redshifts is 1.714 +/- 0.012 (error on mean). Scrutiny of the galaxy distribution in redshift and the plane of the sky shows that there are two concentrations of galaxies near the X-ray source. In addition there are three diffuse X-ray sources spread along the axis connecting the galaxy concentrations. LH146 is one of these three and lies approximately at the center of the two galaxy concentrations and the outer two diffuse X-ray sources. We thus conclude that LH146 is at the redshift initially reported but it is not a single virialized galaxy cluster as previously assumed. Rather it appears to mark the approximate center of a larger region containing more objects. For brevity we term all these objects and their alignments as large scale structure. The exact nature of LH146 itself remains unclear.

### Diffuse optical intracluster light as a measure of stellar tidal stripping: the cluster CL0024+17 at $z\sim$0.4 observed at LBT

We have evaluated the diffuse intracluster light (ICL) in the central core of the galaxy cluster CL0024+17 at $z\sim 0.4$ observed with the prime focus camera (LBC) at LBT. The measure required an accurate removal of the galaxies light within $\sim 200$ kpc from the center. The residual background intensity has then been integrated in circular apertures to derive the average ICL intensity profile. The latter shows an approximate exponential decline as expected from theoretical cold dark matter models. The radial profile of the ICL over the galaxies intensity ratio (ICL fraction) is increasing with decreasing radius but near the cluster center it starts to bend and then decreases where the overlap of the halos of the brightest cluster galaxies becomes dominant. Theoretical expectations in a simplified CDM scenario show that the ICL fraction profile can be estimated from the stripped over galaxy stellar mass ratio in the cluster. It is possible to show that the latter quantity is almost independent of the properties of the individual host galaxies but mainly depends on the average cluster properties. The predicted ICL fraction profile is thus very sensitive to the assumed CDM profile, total mass and concentration parameter of the cluster. Adopting values very similar to those derived from the most recent lensing analysis in CL0024+17 we find a good agreement with the observed ICL fraction profile. The galaxy counts in the cluster core have then been compared with that derived from composite cluster samples in larger volumes, up to the clusters virial radius. The galaxy counts in the CL0024+17 core appear flatter and the amount of bending respect to the average cluster galaxy counts imply a loss of total emissivity in broad agreement with the measured ICL fraction.

### Diffuse optical intracluster light as a measure of stellar tidal stripping: the cluster CL0024+17 at $z\sim$0.4 observed at LBT [Replacement]

We have evaluated the diffuse intracluster light (ICL) in the central core of the galaxy cluster CL0024+17 at $z\sim 0.4$ observed with the prime focus camera (LBC) at LBT. The measure required an accurate removal of the galaxies light within $\sim 200$ kpc from the center. The residual background intensity has then been integrated in circular apertures to derive the average ICL intensity profile. The latter shows an approximate exponential decline as expected from theoretical cold dark matter models. The radial profile of the ICL over the galaxies intensity ratio (ICL fraction) is increasing with decreasing radius but near the cluster center it starts to bend and then decreases where the overlap of the halos of the brightest cluster galaxies becomes dominant. Theoretical expectations in a simplified CDM scenario show that the ICL fraction profile can be estimated from the stripped over galaxy stellar mass ratio in the cluster. It is possible to show that the latter quantity is almost independent of the properties of the individual host galaxies but mainly depends on the average cluster properties. The predicted ICL fraction profile is thus very sensitive to the assumed CDM profile, total mass and concentration parameter of the cluster. Adopting values very similar to those derived from the most recent lensing analysis in CL0024+17 we find a good agreement with the observed ICL fraction profile. The galaxy counts in the cluster core have then been compared with that derived from composite cluster samples in larger volumes, up to the clusters virial radius. The galaxy counts in the CL0024+17 core appear flatter and the amount of bending respect to the average cluster galaxy counts imply a loss of total emissivity in broad agreement with the measured ICL fraction.

### Gravitational and distributed heating effects of a cD galaxy on the hydrodynamical structure of its host cluster [Replacement]

We investigate the effects of a cD galaxy’s gravity and AGN heating of the host galaxy cluster. We consider a standard prescription for the hydrodynamics, with the structures determined by mass continuity, momentum and energy conservation equations in spherical symmetry. The cluster comprises a dark matter halo (DM) and ionised X-ray emitting intracluster gas (ICM), which jointly determine the gravitational potential. The cD galaxy is an additive gravitational potential component. The DM assumes a polytropic equation of state (determined by its microphysics), which could be non-radiative self-interacting particles or more exotically interacting particles. The AGN provides distributed heating, counteracting radiative cooling. Stationary density and velocity dispersion profiles are obtained by numerically integrating the hydrodynamic equations with appropriate boundary conditions. The minimum gas temperature in the cluster core is higher when a cD galaxy is present than when it is absent. The solutions also yield a point-like mass concentration exceeding a minimum mass: presumably the AGN’s supermassive black hole (SMBH). Consistency with observed SMBH masses constrains the possible DM equations of state. The constraints are looser when a cD galaxy is present. Distributed (AGN) heating alters cluster global properties, and also reduces the lower limits for the central point-mass, for the preferred DM models in which the dark particles have greater heat capacity than point particles. Eluding these constraints would require dominant non-spherical or anisotropic effects (e.g. bulk rotation, non-radial streaming, asymmetric lumps, or a strong magnetic field).

### Gravitational and distributed heating effects of a cD galaxy on the hydrodynamical structure of its host cluster

We investigate the effects of a cD galaxy’s gravity and AGN heating of the host galaxy cluster. We consider a standard prescription for the hydrodynamics, with the structures determined by mass continuity, momentum and energy conservation equations in spherical symmetry. The cluster comprises a dark matter halo (DM) and ionised X-ray emitting intracluster gas (ICM), which jointly determine the gravitational potential. The cD galaxy is an additive gravitational potential component. The DM assumes a polytropic equation of state (determined by its microphysics), which could be non-radiative self-interacting particles or more exotically interacting particles. The AGN provides distributed heating, counteracting radiative cooling. Stationary density and velocity dispersion profiles are obtained by numerically integrating the hydrodynamic equations with appropriate boundary conditions. The minimum gas temperature in the cluster core is higher when a cD galaxy is present than when it is absent. The solutions also yield a point-like mass concentration exceeding a minimum mass: presumably the AGN’s supermassive black hole (SMBH). Consistency with observed SMBH masses constrains the possible DM equations of state. The constraints are looser when a cD galaxy is present. Distributed (AGN) heating alters cluster global properties, and also reduces the lower limits for the central point-mass, for the preferred DM models in which the dark particles have greater heat capacity than point particles. Eluding these constraints would require dominant non-spherical or anisotropic effects (e.g. bulk rotation, non-radial streaming, asymmetric lumps, or a strong magnetic field).

### Suzaku study of gas properties along filaments of A2744

Context: We present the results of Suzaku observations of a massive galaxy cluster A2744, which is an active merger at $z=0.308$. Aims: By using long X-ray observations of A2744, we aim to understand the growth of the cluster and the gas heating process through mass accretion along the surrounding filaments. Methods: We analyzed data from two-pointed Suzaku observations of A2744 to derive the temperature distribution out to the virial radius in three different directions. We also performed a deprojection analysis to study radial profiles of gas temperature, density, and entropy and compared the X-ray results with multi-wavelength data to investigate correlations with the surface density of galaxies and with radio relics. Results: The gas temperature was measured out to the virial radius $r_{200}$ in the north-east region and to about $1.5r_{200}$ in the north-west and south regions. The radial profile of the gas temperature is rather flat and the temperature is very high (even near $r_{200}$); it is comparable to the mean temperature of this cluster ($kT=9$ keV). These characteristics have not been reported in any other cluster. We find a hint of temperature jump in the northeast region whose location coincides with a large radio relic, indicating that the cluster experienced gas heating because of merger or mass accretion onto the main cluster. The temperature distribution is anisotropic and shows no clear positive correlation with the galaxy density, which suggests an inhomogeneous mass structure and a complex merger history in A2744.

### Spectroscopic Confirmation of the Rich z=1.80 Galaxy Cluster JKCS 041 Using the WFC3 Grism: Environmental Trends in the Ages and Structure of Quiescent Galaxies

We present HST/WFC3 imaging and grism spectroscopy of the distant galaxy cluster JKCS041. Our survey yields 98 redshifts whose precision is typically ~20x better than photometric estimates. We confirm that JKCS041 is a rich cluster and derive a redshift z=1.80 via the identification of 19 member galaxies, of which 15 are quiescent. These members are spatially aligned with diffuse X-ray emission seen by Chandra. As JKCS041 is the most distant known cluster with such a large and spectroscopically-confirmed quiescent population, it provides an unique opportunity to study the effect of the environment on galaxy properties at early epochs. We construct composite spectra of the quiescent members that clearly reveal Balmer and metallic absorption lines. From these, we infer that the more massive members (log M*>11) have a mean stellar age of 1.4+0.3-0.2 Gyr, whereas lower-mass examples (log M*=10.5-11) have a younger mean age of 0.9+0.2-0.1 Gyr. These ages agree closely with those inferred by Whitaker et al. for similarly-selected quiescent field galaxies, supporting the idea that the cluster environment is more efficient at truncating star formation while not having a strong effect on the mean epoch of quenching. In contrast to field samples, there is no sign of low-level Hbeta or [OIII] emission in our composite spectra. By comparing the ellipticity distribution of the quiescent members to coeval field galaxies drawn from the CANDELS survey, we find some evidence for a lower fraction of disk-like quiescent systems in JKCS041. Taking this into account, we do not detect a significant difference between the mass-radius relations of the quiescent JKCS041 members and our z~1.8 field sample. We review claims of environmentally-dependent size growth of z>1 quiescent galaxies, and we demonstrate how differences in morphological mixtures may complicate comparisons of sizes in different environments.

### X-ray Bright Active Galactic Nuclei in Massive Galaxy Clusters II: The Fraction of Galaxies Hosting Active Nuclei

We present a measurement of the fraction of cluster galaxies hosting X-ray bright Active Galactic Nuclei (AGN) as a function of clustercentric distance scaled in units of $r_{500}$. Our analysis employs high quality Chandra X-ray and Subaru optical imaging for 42 massive X-ray selected galaxy cluster fields spanning the redshift range of $0.2 < z < 0.7$. In total, our study involves 176 AGN with bright ($R <23$) optical counterparts above a $0.5-8.0$ keV flux limit of $10^{-14} \rm{erg} \ \rm{cm}^{-2} \ \rm{s}^{-1}$. When excluding central dominant galaxies from the calculation, we measure a cluster-galaxy AGN fraction in the central regions of the clusters that is $\sim 3$ times lower that the field value. This fraction increases with clustercentric distance before becoming consistent with the field at $\sim 2.5 r_{500}$. Our data exhibit similar radial trends to those observed for star formation and optically selected AGN in cluster member galaxies, both of which are also suppressed near cluster centers to a comparable extent. These results strongly support the idea that X-ray AGN activity and strong star formation are linked through their common dependence on available reservoirs of cold gas.

### Cold gas dynamics in Hydra-A: evidence for a rotating disk

We present multi-frequency observations of the radio galaxy Hydra-A (3C218) located in the core of a massive, X-ray luminous galaxy cluster. IFU spectroscopy is used to trace the kinematics of the ionised and warm molecular hydrogen which are consistent with a ~ 5 kpc rotating disc. Broad, double-peaked lines of CO(2-1), [CII]157 $\mu$m and [OI]63 $\mu$m are detected. We estimate the mass of the cold gas within the disc to be M$_{gas}$ = 2.3 $\pm$ 0.3 x 10$^9$ M$_{\odot}$. These observations demonstrate that the complex line profiles found in the cold atomic and molecular gas are related to the rotating disc or ring of gas. Finally, an HST image of the galaxy shows that this gas disc contains a substantial mass of dust. The large gas mass, SFR and kinematics are consistent with the levels of gas cooling from the ICM. We conclude that the cold gas originates from the continual quiescent accumulation of cooled ICM gas. The rotation is in a plane perpendicular to the projected orientation of the radio jets and ICM cavities hinting at a possible connection between the kpc-scale cooling gas and the accretion of material onto the black hole. We discuss the implications of these observations for models of cold accretion, AGN feedback and cooling flows.

### The Matryoshka Run: Eulerian Refinement Strategy to Study Statistics of Turbulence in Virialized Cosmic Structures [Replacement]

We study the statistical properties of turbulence driven by structure formation in a massive merging galaxy cluster at z=0. The development of turbulence is ensured as the largest eddy turnover time is much shorter than the Hubble time independent of mass and redshift. We achieve a large dynamic range of spatial scales through a novel Eulerian refinement strategy where the cluster volume is refined with progressively finer uniform nested grids during gravitational collapse. This provides an unprecedented resolution of 7.3 h^{-1} kpc across the virial volume. The probability density functions of various velocity derived quantities exhibit the features characteristic of fully developed compressible turbulence observed in dedicated periodic-box simulations. Shocks generate only 60% of the total vorticity within \rvir/3 region and 40% beyond that. We compute second and third order, longitudinal and transverse, structure functions for both solenoidal and compressional components, in the cluster core, virial region and beyond. The structure functions exhibit a well defined inertial range. The injection scale is comparable to the virial radius but increases towards the outskirts. Within \rvir/3, the spectral slope of the solenoidal component is close to Kolmogorov’s, but for the compressional component is substantially steeper and close to Burgers’; the flow is mostly solenoidal and statistically rigorously consistent with fully developed, homogeneous and isotropic turbulence. Small scale anisotropy appears due to numerical artifact. Towards the virial region, the flow becomes compressional, the structure functions flatter and modest genuine anisotropy appear. In comparison, mesh adaptivity based on Lagrangian refinement and the same finest resolution, leads to lack of turbulent power on small scale and excess thereof on large scales, and unreliable density weighted structure functions.

### The Matryoshka Run: Eulerian Refinement Strategy to Study Statistics of Turbulence in Virialized Cosmic Structures

We study the statistical properties of turbulence driven by structure formation in a massive merging galaxy cluster at redshift z=0. Turbulence develops as the largest eddy turnover time is much shorter than the Hubble time independent of mass and redshift. To achieve a sufficiently large dynamic range of spatial scales we employ a novel Eulerian refinement strategy where the cluster volume is refined with progressively finer uniform nested grids during gravitational collapse. This provides an unprecedented resolution of 7.3 h$^{-1}$ kpc across the virial volume. The probability density functions of various velocity derived quantities exhibit the same features characteristic of fully developed compressible turbulence as observed in dedicated periodic-box simulations. We apply Hodge-Helmholtz decomposition to the velocity field and compute second and third order, longitudinal and transverse, structure functions for both solenoidal and compressional components, in the cluster core, virial region and beyond. In general, the structure functions exhibit a well defined inertial range of turbulent cascade. The injection scale is comparable to the virial radius but increases towards the outskirts. In the inner Rvir/3, the spectral slope of the solenoidal component is close to Kolmogorov’s, but for the compressional component is substantially steeper and close to Burgers’. In addition, the flow is mostly solenoidal and statistically rigorously consistent with fully developed, homogeneous and isotropic turbulence. Small scale anisotropy appears due to numerical artifact. Towards the virial region, however, the flow becomes increasingly compressional, the structure functions flatter and modest genuine anisotropy appears particularly close to the injection scale.

### Constraining f(R) gravity with PLANCK data on galaxy cluster profiles

Models of $f(R)$ gravity that introduce corrections to the Newtonian potential in the weak field limit are tested at the scale of galaxy clusters. These models can explain the dynamics of spiral and elliptical galaxies without resorting to dark matter. We compute the pressure profiles of 579 galaxy clusters assuming that the gas is in hydrostatic equilibrium within the potential well of the modified gravitational field. The predicted profiles are compared with the average profile obtained by stacking the data of our cluster sample in the Planck foreground clean map SMICA. We find that the resulting profiles of these systems fit the data without requiring a dominant dark matter component, with model parameters similar to those required to explain the dynamics of galaxies. Our results do not rule out that clusters are dynamically dominated by Dark Matter but support the idea that Extended Theories of Gravity could provide an explanation to the dynamics of self-gravitating systems and to the present period of accelerated expansion, alternative to the concordance cosmological model.

### Constraining f(R) gravity with PLANCK data on galaxy cluster profiles [Cross-Listing]

Models of $f(R)$ gravity that introduce corrections to the Newtonian potential in the weak field limit are tested at the scale of galaxy clusters. These models can explain the dynamics of spiral and elliptical galaxies without resorting to dark matter. We compute the pressure profiles of 579 galaxy clusters assuming that the gas is in hydrostatic equilibrium within the potential well of the modified gravitational field. The predicted profiles are compared with the average profile obtained by stacking the data of our cluster sample in the Planck foreground clean map SMICA. We find that the resulting profiles of these systems fit the data without requiring a dominant dark matter component, with model parameters similar to those required to explain the dynamics of galaxies. Our results do not rule out that clusters are dynamically dominated by Dark Matter but support the idea that Extended Theories of Gravity could provide an explanation to the dynamics of self-gravitating systems and to the present period of accelerated expansion, alternative to the concordance cosmological model.

### Strong lensing in RX J1347.5-1145 revisited

We present a revised strong lensing mass reconstruction of the galaxy cluster RX J1347.5-1145. The X-ray luminous cluster at redshift z=0.451 has already been studied intensively in the past. Based on information of two such previous (strong-)lensing studies by Halkola et al. (2008) and Bradac et al. (2008), as well as by incorporating newly available data from the Cluster Lensing And Supernovae survey with Hubble (CLASH, Postman et al. 2012), we identified four systems of multiply lensed images (anew) in the redshift range 1.75 <= z <= 4.19. One multiple image system consists of in total eight multiply lensed images of the same source. The analysis based on a parametric mass model derived with the software glafic (Oguri 2010) suggests that the high image multiplicity is due to the source (z_phot = 4.19) being located on a so-called "swallowtail" caustic. In addition to the parametric mass model, we also employed a non-parametric approach using the software PixeLens (Saha and Williams 1997, 2004) in order to reconstruct the projected mass of the cluster using the same strong lensing data input. Both reconstructed mass models agree in revealing several mass components and a highly elliptic shape of the mass distribution. Furthermore, the projected mass inside, for example, a radius R ~35 arcsec ~200 kpc of the cluster for a source at redshift z=1.75 obtained with PixeLens exceeds the glafic estimate within the same radius by about 13 per cent. The difference could be related to the fundamental degeneracy involved when constraining dark matter substructures with gravitationally lensed arcs.

### A large-scale galaxy structure at z = 2.02 associated with the radio galaxy MRC0156-252

We present the spectroscopic confirmation of a structure of galaxies surrounding the radio galaxy MRC0156-252 at z = 2.02. The structure was initially discovered as an overdensity of both near-infrared selected z > 1.6 and mid-infrared selected z > 1.2 galaxy candidates. We use the VLT/FORS2 multi-object spectrograph to target ~80 high-redshift galaxy candidates; we obtain robust spectroscopic redshifts for more than half the targets. The majority of the confirmed sources are star-forming galaxies at z > 1.5. In addition to the radio galaxy, two of its close-by companions (< 6”) also show AGN signatures. Ten sources, including the radio galaxy, lie within |z – 2.020| < 0.015 (i.e., velocity offsets < 1500 km/s) and within 2Mpc comoving of the radio galaxy. Additional evidence suggest not only that the galaxy structure associated with MRC0156-252 is a forming galaxy cluster but also that this structure is most probably embedded in a larger scale structure.

### A large-scale galaxy structure at z = 2.02 associated with the radio galaxy MRC0156-252 [Replacement]

We present the spectroscopic confirmation of a structure of galaxies surrounding the radio galaxy MRC0156-252 at z = 2.02. The structure was initially discovered as an overdensity of both near-infrared selected z > 1.6 and mid-infrared selected z > 1.2 galaxy candidates. We use the VLT/FORS2 multi-object spectrograph to target ~80 high-redshift galaxy candidates; we obtain robust spectroscopic redshifts for more than half the targets. The majority of the confirmed sources are star-forming galaxies at z > 1.5. In addition to the radio galaxy, two of its close-by companions (< 6") also show AGN signatures. Ten sources, including the radio galaxy, lie within |z – 2.020| < 0.015 (i.e., velocity offsets < 1500 km/s) and within projected 2Mpc comoving of the radio galaxy. Additional evidence suggests not only that the galaxy structure associated with MRC0156-252 is a forming galaxy cluster but also that this structure is most probably embedded in a larger scale structure.

### Weak Lensing Galaxy Cluster Field Reconstruction [Replacement]

In this paper, we compare three methods to reconstruct galaxy cluster density fields with weak lensing data. The first method called FLens integrates an inpainting concept to invert the shear field with possible gaps, and a multi-scale entropy denoising procedure to remove the noise contained in the final reconstruction, that arises mostly from the random intrinsic shape of the galaxies. The second and third methods are based on a model of the density field made of a multi-scale grid of radial basis functions. In one case, the model parameters are computed with a linear inversion involving a singular value decomposition. In the other case, the model parameters are estimated using a Bayesian MCMC optimization implemented in the lensing software Lenstool. Methods are compared on simulated data with varying galaxy density fields. We pay particular attention to the errors estimated with resampling. We find the multi-scale grid model optimized with MCMC to provide the best results, but at high computational cost, especially when considering resampling. The SVD method is much faster but yields noisy maps, although this can be mitigated with resampling. The FLens method is a good compromise with fast computation, high signal to noise reconstruction, but lower resolution maps. All three methods are applied to the MACS J0717+3745 galaxy cluster field, and reveal the filamentary structure discovered in Jauzac et al. 2012. We conclude that sensitive priors can help to get high signal to noise, and unbiased reconstructions.

### Weak Lensing Galaxy Cluster Field Reconstruction

In this paper, we compare three methods to reconstruct galaxy cluster density fields with weak lensing data. The first method called FLens integrates an inpainting concept to invert the shear field with possible gaps, and a multi-scale entropy denoising procedure to remove the noise contained in the final reconstruction, that arises mostly from the random intrinsic shape of the galaxies. The second and third methods are based on a model of the density field made of a multi-scale grid of radial basis functions. In one case, the model parameters are computed with a linear inversion involving a singular value decomposition. In the other case, the model parameters are estimated using a Bayesian MCMC optimization implemented in the lensing software Lenstool. Methods are compared on simulated data with varying galaxy density fields. We pay particular attention to the errors estimated with resampling. We find the multi-scale grid model optimized with MCMC to provide the best results, but at high computational cost, especially when considering resampling. The SVD method is much faster but yields noisy maps, although this can be mitigated with resampling. The FLens method is a good compromise with fast computation, high signal to noise reconstruction, but lower resolution maps. All three methods are applied to the MACS J0717+3745 galaxy cluster field, and reveal the filamentary structure discovered in Jauzac et al. 2012. We conclude that sensitive priors can help to get high signal to noise, and unbiased reconstructions.

### The parameters of relaxation during the dark matter halo formation: how to fit observational data?

We show that moderate energy relaxation in the formation of dark matter haloes invariably leads to density profiles that match those observed in the central regions of galaxies. The density profile of the central region turns out to be universal and insensitive neither to the seed perturbation shape nor to the details of the relaxation process. The profile has a central core; multiplication of the central density on the core radius is almost independent of the halo mass, in accordance with observations. In the core area the density distribution behaves as an Einasto profile with small index ($n\sim 0.5$); at larger distances it has an extensive region with $\rho\propto r^{-2}$. This is exactly the shape that observations suggest for the central region of galaxies. On the other hand, this shape does not fit the galaxy cluster profiles. A possible explanation of this fact is that the relaxation is violent in the case of galaxy clusters; however, it is not violent enough when galaxies or smaller dark matter structures are considered. We discuss the reasons why it could be so.

### The parameters of relaxation during the dark matter halo formation: how to fit observational data? [Replacement]

We show that moderate energy relaxation in the formation of dark matter haloes invariably leads to density profiles that match those observed in the central regions of galaxies. The density profile of the central region turns out to be universal and insensitive neither to the seed perturbation shape nor to the details of the relaxation process. The profile has a central core; multiplication of the central density on the core radius is almost independent of the halo mass, in accordance with observations. In the core area the density distribution behaves as an Einasto profile with small index ($n\sim 0.5$); at larger distances it has an extensive region with $\rho\propto r^{-2}$. This is exactly the shape that observations suggest for the central region of galaxies. On the other hand, this shape does not fit the galaxy cluster profiles. A possible explanation of this fact is that the relaxation is violent in the case of galaxy clusters; however, it is not violent enough when galaxies or smaller dark matter structures are considered. We discuss the reasons why it could be so.

### Weighing "<NAME>" with a Pecision Scale: Hubble Space Telescope Weak-lensing Analysis of the Merging Galaxy Cluster ACT-CL J0102-4915 at z=0.87

(Abridged) We present a HST weak-lensing study of the merging galaxy cluster "<NAME>" (ACT-CL J0102-4915) at z=0.87 discovered by the Atacama Cosmology Telescope collaboration as the strongest SZ decrement in its ~1000 sq. deg survey. Our weak-lensing analysis confirms that ACT-CL J0102-4915 is indeed an extreme system consisting of two massive (~10^15 Msun each) subclusters with a projected separation of ~0.7 Mpc. This binary mass structure revealed by our lensing study is consistent with the cluster galaxy distribution and the dynamical study carried out with 89 spectroscopic members. We estimate the mass of ACT-CL J0102-4915 by simultaneously fitting two axisymmetric NFW profiles allowing their centers to vary. Our MCMC analysis shows that the masses of the northwestern (NW) and the southeastern (SE) components are M200c=(1.40+-0.31) x 10^15 Msun and (0.75+-0.17) x 10^15 Msun, respectively. The lensing-based velocity dispersions are consistent with their spectroscopic measurements. The centroids of both components are tightly constrained (~4") and close to the optical luminosity centers. The X-ray and mass peaks are spatially offset by ~13" (~100 kpc), which is significant at the ~3 sigma confidence level and confirms that the baryonic and dark matter in this cluster are disassociated. The dark matter peak, however, does not lead the gas peak in the direction expected if we are viewing the cluster soon after first core passage during a high speed merger. Under the assumption that the merger is happening in the plane of the sky, extrapolation of the two NFW halos to a radius r200a=2.4 Mpc yields a combined mass of M200a=(3.10+-0.70) x 10^15 Msun. This extrapolated total mass is consistent with our two-component-based dynamical analysis and previous X-ray measurements, projecting ACT-CL J0102-4915 to be the most massive cluster at z>0.6 known to date.

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text:
Journal of Formalized Mathematics
Volume 14, 2002
University of Bialystok
Copyright (c) 2002 Association of Mizar Users

## General Fashoda Meet Theorem for Unit Circle

<NAME>
Shinshu University, Nagano

### Summary.

Outside and inside Fashoda theorems are proven for points in general position on unit circle. Four points must be ordered in a sense of ordering for simple closed curve. For preparation of proof, the relation between the order and condition of coordinates of points on unit circle is discussed.

#### MML Identifier: JGRAPH_5

The terminology and notation used in this paper have been introduced in the following articles [1] [18] [11] [9] [17] [20] [8] [4] [5] [10] [2] [7] [12] [19] [16] [6] [3] [15] [14] [13]

#### Contents (PDF format)

1. Preliminaries
2. Fashoda Meet Theorems for Circle in Special Case
3. Properties of Fan Morphisms
4. Order of Points on Circle
5. General Fashoda Theorems

#### Bibliography

[1] <NAME>. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] <NAME>. Paracompact and metrizable spaces. Journal of Formalized Mathematics, 3, 1991.
[3] <NAME>. Binary operations. Journal of Formalized Mathematics, 1, 1989.
[4] <NAME>. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[5] <NAME>. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[6] <NAME> and <NAME>. Bounding boxes for compact sets in \$\calE^2\$. Journal of Formalized Mathematics, 9, 1997.
[7] <NAME>. Compact spaces. Journal of Formalized Mathematics, 1, 1989.
[8] <NAME>. Families of subsets, subspaces and mappings in topological spaces. Journal of Formalized Mathematics, 1, 1989.
[9] <NAME>. The Euclidean space. Journal of Formalized Mathematics, 3, 1991.
[10] <NAME> and <NAME>. Metric spaces as topological spaces --- fundamental concepts. Journal of Formalized Mathematics, 3, 1991.
[11] <NAME>. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[12] <NAME>, <NAME>, and <NAME>. Metric spaces. Journal of Formalized Mathematics, 2, 1990.
[13] <NAME>. Fan homeomorphisms in the plane. Journal of Formalized Mathematics, 14, 2002.
[14] <NAME> and <NAME>. A decomposition of simple closed curves and the order of their points. Journal of Formalized Mathematics, 9, 1997.
[15] <NAME> and <NAME>. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[16] <NAME> and <NAME>. Topological properties of subsets in real numbers. Journal of Formalized Mathematics, 2, 1990.
[17] <NAME>. <NAME> set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[18] <NAME>. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[19] <NAME> and <NAME>. Some properties of real numbers operations: min, max, square, and square root. Journal of Formalized Mathematics, 1, 1989.
[20] <NAME>. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

format: plain


text:
## Long descriptions for some figures in Formal Learning Theory

### Figure 1 description

A vertical arrow pointing up to the text “all ravens are black”. Along the arrow are three equidistant dots and to the left of each dot is a black raven and to the right a white raven. A gray fan linked to each dot has the text “not all ravens are black”. At the top of the arrow just before the arrowhead is an ellipsis.

A legend for the diagram depicts a dot with a black raven on the left and a white raven on the right and the explanation “at this point either a black or a nonblack raven is observed”.

### Figure 2 description

The two parts of this figure each contain as a base the image in figure 1. The legend for the whole is also from figure 1 and has in addition a question mark with the explanation “no conclusion yet”.

The left part which is captioned “the generalizing method” has to the left of each black raven the text “all ravens are black”.

The right part which is captioned “the skeptical method” has to the left of each black raven a question mark.

### Figure 3 description

The caption is “the conjecture of the natural projection rule”. The diagram is a a vertical arrow pointing up to a text stating “all emeralds are green”. This arrow has three equidistant dots on it.

For each dot on the vertical arrow, to the left and slight above is an outlined green emerald and to the left of that is the label “all green”; to the right and slightly below the dot is a solid blue emerald.

Also from each dot on the vertical arrow, a horizontal arrow points right with another dot just before its arrow head. Below each of these dots is a solid emerald. The text by the arrowhead of the lowest horizontal arrow is “all emeralds are grue(1)”. The next up horizontal arrow has “grue(2)” instead of “grue(1)” and the last has “grue(3)” instead. On the lowest horizontal arrow near the vertical line is the text “all grue(1)”; this is repeated on the same arrow just above its dot. The same on the second and third arrows with “grue(2)” and “grue(3)” substituting for “grue(1)”. In addition on the upper two arrows there is the text “First mind change” with a small arrow pointing to the first block of text.

The legend has

• “all grue$$(t)$$” = “all emeralds are grue$$(t)$$”
• “all green” = “all emeralds are green”
• a dot with to the left and slight above an outlined green emerald and with to the right and slightly below a solid blue emerald. The explanation is “At this stage, either a green or blue emerald may be observed”

### Figure 4 description

The figure shows the gruesome projection rule. The figure contains as a base the image in figure 3. The legend for the whole is also from the grue part of figure 3.

To the left of each of the three green diamonds, the three dots along the vertical arrow are labelled in order with the text items “all grue(2)”, “all grue(3)”, “all grue(4)”. The text items represent the sequence of conjectures made by the gruesome projection rule. The remainder of the figure is the same as figure 3.

### Figure 5 description

The figure illustrates how identifiable hypotheses are structured as disjunctions of refutable hypotheses. The caption of the Figure reads “Both swan hypotheses: Decomposition into refutable hypotheses.”

The left half of the figure shows the decomposition of the hypothesis “Almost all swans are black”. It shows three nested circles. The innermost circle contains one black swan to represent the hypothesis “at most one black swan” shown as a label. The middle circle contains two black swans to represent the hypothesis “at most two black swans” shown as a label. The outermost circle contains six black swans to represent the hypothesis “at most n black swans” shown as a label.

The right half of the figure shows the decomposition of the hypothesis “Almost all swans are white”. It shows three nested circles. The innermost circle contains one white swan to represent the hypothesis “at most one white swan” shown as a label. The middle circle contains two white swans to represent the hypothesis “at most two white swans” shown as a label. The outermost circle contains six white swans to represent the hypothesis “at most n white swans” shown as a label.

### Figure 6 description

The figure illustrates the decomposition into verirefutable hypotheses.

The caption of the left half of the figure is “Almost all swans are black”. It shows three disjoint boxes. The leftmost box contains one black swan to represent the hypothesis “exactly one black swan” shown as a label. The middle box contains two black swans to represent the hypothesis “exactly two black swans” shown as a label. The rightmost box contains four black swans to represent the hypothesis “exactly n black swans” shown as a label.

The caption of the right half of the figure is “Almost all swans are white”. It shows three disjoint boxes. The leftmost box contains one white swan to represent the hypothesis “exactly one white swan” shown as a label. The middle box contains two white swans to represent the hypothesis “exactly two white swans” shown as a label. The rightmost box contains four white swans to represent the hypothesis “exactly n white swans” shown as a label.

### Figure 7 description

The figure illustrates in a typical case how an unnatural projection rule may have to change its mind twice or more. The figure contains as a base the image in figure 3. We repeat some of the description for clarity and convenience.

The diagram is a a vertical arrow pointing up to a text stating “all emeralds are green”. This arrow has four equidistant dots on it.

For each dot on the vertical arrow, to the left and slight above is an outlined green emerald; to the right and slightly below the dot is a solid blue emerald. The four dots along the vertical arrow are labelled in order with the text items “all grue(3)”, “all grue(3)”, “all green”, and “all green”. The text items represent the sequence of conjectures made by an unnatural projection rule. For the third vertical dot, an arrow points from the text “first mind change” to the conjecture label “all green”.

Also from each dot on the vertical arrow, a horizontal arrow points right with another dot just before its arrow head. Below each of these dots is a solid emerald. The text by the arrowhead of the lowest horizontal arrow is “all emeralds are grue(1)”. The next up horizontal arrow has “grue(2)” instead of “grue(1)”. The third arrow has “grue(3)”, and the last has “grue(3)” also. On the lowest horizontal arrow near the vertical line is the text “all grue(1)”; this is repeated on the same arrow just above its dot. The same on the second and third arrows with “grue(2)” and “grue(3)” substituting for “grue(1)”. The fourth arrow also substitutes “grue(1)”. In addition on the fourth arrow there is the text “Second mind change” with a small arrow pointing to the first block of text.

The legend has the explanation “The conjectures of a reliable projection rule that fails to minimize mind changes.” In addition the legend repeats the information from figure 3 as follows.

• “all grue$$(t)$$” = “all emeralds are grue$$(t)$$”
• “all green” = “all emeralds are green”
• a dot with to the left and slight above an outlined green emerald and with to the right and slightly below a solid blue emerald. The explanation is “At this stage, either a green or blue emerald may be observed”

### Figure 8 description

A chance reversal corresponds to a failure to replicate a true result. A chance reversal is illustrated in the Figure above, where the chance of conjecturing the true hypothesis is smaller for 2 samples than for 3.

The figure is an $$x$$-$$y$$ plot. The $$x$$-axis is labelled “Sample Size”, the $$y$$-axis is labelled “Probability that Method conjectures true hypothesis that the coin is fair”. To the left of the origin the value 0% marks the minimum $$y$$-value. The top of the $$y$$-axis is labelled with the maximum value 100%. The $$x$$-axis is labelled with sample values $$x = 1, 2,3$$ evenly spaced out. The legend of the plot is “$$p=0.5$$”.

The body of the plot shows 5 dots, the first three at locations 1,2,3, followed by 2 more dots at roughly equal distance along the $$x$$-dimension. Along the $$y$$-dimension, the dot for $$x= 1$$ has the least $$y$$-value at roughly $$y= 10$$%. Dot 2 has a higher $$y$$-value than Dot 1 and Dot 3 has an intermediate $$y$$-value between Dot 1 and Dot 2. Dot 4 has a higher $$y$$-value than Dots 1 through 3 and Dot 5 the highest $$y$$-value of all dots. All successive dots are connected by directed arrows.


text:
# Persistent storage for packages

How can I implement persistent storage for packages/applications? For example, how can my package have settings which persist across sessions?

I have implemented this more than once in the past. This question is to share our solutions and keep them for future reference. This the kind of application where reliability is paramount because it is often used in packages that may be distributed to many people.

Things to pay attention to:

• Compatibility with different Mathematica versions. This is a typical requirement for packages. Solutions must be compatible with 10.0 and all later versions. Earlier version compatibility is even better, but I'm not asking for it because associations are too convenient ...

• Persistent storage is useful for package settings. Solutions presented here shouldn't stand in the way of changing the settings format in future versions of the package (adding or removing settings, changing the format, etc.)

• Corrupted storage files must be handled gracefully.

• Given that this is meant to be included in other packages, simple and short solutions are preferred.

• Anything else I didn't think of?

• What about Resourceobject? – rcollyer Nov 6 '16 at 15:32
• Could you expand on what you might use this persistent storage for? – <NAME> Nov 6 '16 at 16:13
• @ChrisK The main uses case I have in mind are persistent settings. E.g. MaTeX must store the location of the pdflatex executable permanently, so I use some persistent storage for this. MATLink also need to remember if it should try to use a 32-bit or 64-bit MATLAB. Another possible use case is caching certain information. I'm primarily interested in use cases where the data that needs to be stored is small. – Szabolcs Nov 6 '16 at 17:46
• What about CurrentValue[$FrontEnd, {TaggingRules, "MaTeX", "pdflatexpath"}] = ..., this is what I am doing (unles I missed the point) – Kuba Nov 7 '16 at 1:58 • @masterxilo OK, I'll post a solution myself, and I hope others will share theirs then. I won't be able to do it until tonight though. I prefer the file in $UserBaseDirectory/ApplicationData/PackageName, not in the package directory itself. The package directory may get removed when the package is updated. – Szabolcs Nov 9 '16 at 7:53

As stated in comments above, it does not meet all your requirements. Nevertheless I find it extremely useful and applicable in many situations.

That is to use CurrentValue[$FrontEnd, {TaggingRules, "MyApp", "setting1"}] to reference your package settings. Advantages: • no additional files Mathematica will automatically store them in init.m file. You don't even need to check whether your package is installed, which is very, very useful when it has a complex installation/autoload/updating scheme. • it is part of Mathematica setup, could it be more compatible? Tagging rules are there since V4 or something (not sure if this works there but should be no problem in V7, the earliest version I worked with) • it supports $FrontEndSession inheritance (see FrontEnd options)

so you don't need to worry about switching off something that was enabled temporarily

• automatically translates to nested rules:

CurrentValue[$FrontEnd, {TaggingRules, "MyApp", "param1"}] = True translates to: {..., "MyApp" -> {"param1" -> True}} with syntax that feels like using Associations • hard to corrupt that setup since it is done automatically • for missing entries there is an undocumented 3rd argument of CurrentValue It sets that value if you try to reference a missing key: CurrentValue[$FrontEnd, {TaggingRules}]

{..., "MyApp" -> {"param1" -> True}}

CurrentValue[
$FrontEnd, {TaggingRules, "MyApp", "param2"}, "defaultparam2" ] === "defaultparam2"  True CurrentValue[$FrontEnd, {TaggingRules}]

{..., "MyApp" -> {"param1" -> True, "param2" -> "defaultparam2"}}

Issues:


text:
# How do you write the mixed expression n^2+(n-1)/(n+4) as a rational expression?

May 2, 2017

$\frac{{n}^{3} + 4 {n}^{2} + n - 1}{n + 4}$

#### Explanation:

A rational expression is an algebraic fraction with a $\textcolor{b l u e}{\text{polynomial}}$ on the numerator and denominator.

$\text{before adding the mixed expression we require the terms}$

$\text{to have a "color(blue)"common denominator}$

$\text{multiply " n^2" by } \frac{n + 4}{n + 4}$

$\Rightarrow \frac{{n}^{2} \left(n + 4\right)}{n + 4} + \frac{n - 1}{n + 4}$

Now the 2 terms have a common denominator we can add the numerators leaving the denominator as it is.

$\Rightarrow \frac{{n}^{3} + 4 {n}^{2} + n - 1}{n + 4} \leftarrow \textcolor{red}{\text{ rational expression}}$


text:
Code covered by the BSD License

A MATLAB Script for Propagating Interplanetary Trajectories from Earth to Mars

Numerically integrate the orbital equations of motion of an Earth to Mars interplanetary trajectory.

pprop_e2m.m
```% pprop_e2m.m        April 15, 2013

% propagation of Earth-to-Mars interplanetary trajectories

% user-defined final condition choices

%  (1) Mars closest approach
%  (2) user-defined areocentric distance
%  (3) user-defined final epoch

% JPL ephemeris and NOVAS sidereal time

% Orbital Mechanics with MATLAB

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear all;

global aunit iephem km ephname dtr rtd

global emu smu xmu xmu_mars

global jdtdb_wrk

% ecliptic-to-equatorial transformation matrix

eq2000(1, 1) = 1.0d0;
eq2000(1, 2) = 0.0d0;
eq2000(1, 3) = 0.0d0;

eq2000(2, 1) = 0.0d0;
eq2000(2, 2) = 0.917482062069182d0;
eq2000(2, 3) = -0.397777155931914d0;

eq2000(3, 1) = 0.0d0;
eq2000(3, 2) = 0.397777155931914d0;
eq2000(3, 3) = 0.917482062069182d0;

% compute equatorial-to-ecliptic transformation matrix

eqwrk = eq2000';

% angular conversion factors

rtd = 180.0d0 / pi;

dtr = pi / 180.0d0;

% initialize JPL ephemeris

ephname = 'de421.bin';

iephem = 1;

km = 0;

% **************************************
% gravitational constants (au**3/day**2)
% DE 421 values
% **************************************

% sun

xmu(1) = 0.295912208285591100d-3;

% mercury

xmu(2) = 0.491254957186794000D-10;

% venus

xmu(3) = 0.724345233269844100D-09;

% earth - computed from user-defined value

% mars

xmu(5) = 0.954954869562239000D-10;

% jupiter

xmu(6) = 0.282534584085505000D-06;

% saturn

xmu(7) = 0.845970607330847800D-07;

% uranus

xmu(8) = 0.129202482579265000D-07;

% neptune

xmu(9) = 0.152435910924974000D-07;

% pluto

xmu(10) = 0.217844105199052000D-11;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% read simulation definition data file
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[filename, pathname] = uigetfile('*.in', 'Please select the input file to read');

[fid, r_tip, v_tip, jdtdb_tip, jdtdb_user, iptype, cmfile] = readdata(filename);

% sun gravitational constant (km**3/sec**2)

smu = xmu(1) * aunit^3 / 86400.0d0^2;

% earth gravitational constant (au**3/day**2)

xmu(4) = emu * 86400.0d0^2 / aunit^3;

% begin simulation

clc; home;

fprintf('\npprop_e2m - Earth-to-Mars trajectory propagation');
fprintf('\n------------------------------------------------\n');

fprintf('\nsimulation definition data file ==> ');

disp(filename);

fprintf('\nconstants data file ==> ');

disp(cmfile);

if (iptype == 1)

fprintf('\nMars closest approach\n');

end

if (iptype == 2)

fprintf('\nuser-defined areocentric distance\n');

end

if (iptype == 3)

fprintf('\nuser-defined final epoch\n');

end

fprintf('\nDE421 ephemeris\n');

fprintf('\n\ndeparture hyperbola characteristics');
fprintf('\n(Earth mean equator and equinox of J2000)');
fprintf('\n-----------------------------------------\n');

display1(jdtdb_tip, emu, r_tip, v_tip);

[c3, rla, dla] = rv2hyper (emu, r_tip, v_tip);

fprintf('\nspecific orbital energy     %12.6f  (km/sec)**2\n', c3);

fprintf('\nasymptote right ascension   %12.6f  degrees\n', rtd * rla);

fprintf('\nasymptote declination       %12.6f  degrees\n\n', rtd * dla);

fprintf('\nEarth heliocentric coordinates at departure');
fprintf('\n(Earth mean equator and equinox of J2000)');
fprintf('\n-----------------------------------------\n');

svearth = jplephem(jdtdb_tip, 3, 11);

rearth = svearth(1:3);

vearth = svearth(4:6);

display1(jdtdb_tip, smu, aunit * rearth, aunit * vearth / 86400.0d0);

fprintf('\nEarth heliocentric coordinates at departure');
fprintf('\n(Earth mean ecliptic and equinox of J2000)');
fprintf('\n-----------------------------------------\n');

recl = eqwrk * rearth;

vecl = eqwrk * vearth;

display1(jdtdb_tip, smu, aunit * recl, aunit * vecl / 86400.0d0);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% compute time and conditions at the SOI
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

jdtdb_wrk = jdtdb_tip;

% set up for ode45

options = odeset('RelTol', 1.0e-8, 'AbsTol', 1.0e-10, 'Events', @soi_event);

% define maximum search time (seconds)

tof = 25.0 * 86400.0;

[t, ysol, tevent, yevent, ie] = ode45(@geo_eqm, [0 tof], [r_tip v_tip], options);

jdtdb_soi = jdtdb_tip + tevent / 86400.0;

% spacecraft geocentric state vector at soi (km & km/sec)

rgeo_soi = yevent(1:3);

vgeo_soi = yevent(4:6);

% heliocentric state vector of the spacecraft at soi (au & au/day)

svsun = jplephem(jdtdb_soi, 3, 11);

rsun = svsun(1:3);

vsun = svsun(4:6);

for i = 1:1:3

rhelio_soi(i) = aunit * rsun(i) + yevent(i);

vhelio_soi(i) = aunit * vsun(i) / 86400.0d0 + yevent(i + 3);

end

fprintf('\ntime and geocentric conditions at Earth SOI');
fprintf('\n(Earth mean equator and equinox of J2000)');
fprintf('\n-----------------------------------------\n');

display1(jdtdb_soi, emu, rgeo_soi, vgeo_soi);

fprintf('\ntime and heliocentric conditions at Earth SOI');
fprintf('\n(Earth mean equator and equinox of J2000)');
fprintf('\n-----------------------------------------\n');

display1(jdtdb_soi, smu, rhelio_soi, vhelio_soi);

if (iptype == 1)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% find closest approach conditions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

jdtdb_wrk = jdtdb_soi;

ri = rhelio_soi / aunit;

vi = 86400.0d0 * vhelio_soi / aunit;

% compute closest approach conditions

[jdtdb_ca, rm2sc, vm2sc] = findca(jdtdb_soi, ri, vi);

fprintf('\ntime and conditions at Mars closest approach');
fprintf('\n(areocentric mean equator and IAU node of epoch)');
fprintf('\n------------------------------------------------\n');

display1(jdtdb_ca, xmu_mars, rm2sc, vm2sc);

% compute b-plane coordinates

[bplane, ibperr] = rv2bp2(xmu_mars, rm2sc, vm2sc);

% display results

fprintf('\nb-plane coordinates of incoming hyperbola');
fprintf('\n(areocentric mean equator and IAU node of epoch)');
fprintf('\n------------------------------------------------\n');

fprintf ('\nb-magnitude                %14.6f  kilometers', sqrt(bplane(7)^2 + bplane(8)^2));

fprintf ('\nb dot t                    %14.6f  kilometers', bplane(7));

fprintf ('\nb dot r                    %14.6f  kilometers', bplane(8));

fprintf ('\nb-plane angle              %14.6f  degrees', rtd * bplane(6));

fprintf ('\nv-infinity                 %14.6f  meters/second', 1000.0d0 * bplane(1));

fprintf ('\nr-periapsis                %14.6f  kilometers', bplane(5));

fprintf ('\ndecl-asymptote             %14.6f  degrees', rtd * bplane(2));

fprintf ('\nrasc-asymptote             %14.6f  degrees', rtd * bplane(3));

% flight path angle at entry interface

sfpa = rm2sc' * vm2sc /(norm(rm2sc) * norm(vm2sc));

fprintf('\n\nareocentric flight path angle     %12.10e  degrees\n\n', rtd * asin(sfpa));

fprintf('\nMars heliocentric coordinates at closest approach');
fprintf('\n(Earth mean equator and equinox of J2000)');
fprintf('\n-----------------------------------------\n');

svmars = jplephem(jdtdb_ca, 4, 11);

rmars = svmars(1:3);

vmars = svmars(4:6);

display1(jdtdb_ca, smu, aunit * rmars, aunit * vmars / 86400.0d0);

fprintf('\nMars heliocentric coordinates at closest approach');
fprintf('\n(Earth mean ecliptic and equinox of J2000)');
fprintf('\n------------------------------------------\n');

recl = eqwrk * rmars;

vecl = eqwrk * vmars;

display1(jdtdb_ca, smu, aunit * recl, aunit * vecl / 86400.0d0);

fprintf ('\nsequence of events summary');
fprintf ('\n--------------------------');

fprintf ('\n\ndeparture to SOI time         %12.6f  days', jdtdb_soi - jdtdb_tip);

fprintf ('\n\nSOI to closest approach time  %12.6f  days', jdtdb_ca - jdtdb_soi);

fprintf ('\n\nEarth to Mars transfer time   %12.6f  days\n', jdtdb_ca - jdtdb_tip);

end

if (iptype == 2)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% compute conditions at user-defined areocentric distance
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

jdtdb_wrk = jdtdb_soi;

ri = rhelio_soi / aunit;

vi = 86400.0d0 * vhelio_soi / aunit;

% compute areocentric distance conditions

[jdtdb_rm, rm2sc, vm2sc] = findrm(jdtdb_soi, ri, vi);

fprintf('\ntime and conditions at user-defined areocentric distance');
fprintf('\n(areocentric mean equator and IAU node of epoch)');
fprintf('\n------------------------------------------------\n');

display1(jdtdb_rm, xmu_mars, rm2sc, vm2sc);

fprintf('\nMars heliocentric coordinates at areocentric distance');
fprintf('\n(Earth mean equator and equinox of J2000)');
fprintf('\n-----------------------------------------\n');

svmars = jplephem(jdtdb_rm, 4, 11);

rmars = svmars(1:3);

vmars = svmars(4:6);

display1(jdtdb_rm, smu, aunit * rmars, aunit * vmars / 86400.0d0);

fprintf('\nMars heliocentric coordinates at areocentric distance');
fprintf('\n(Earth mean ecliptic and equinox of J2000)');
fprintf('\n------------------------------------------\n');

recl = eqwrk * rmars;

vecl = eqwrk * vmars;

display1(jdtdb_rm, smu, aunit * recl, aunit * vecl / 86400.0d0);

fprintf ('\nsequence of events summary');
fprintf ('\n--------------------------');

fprintf ('\n\ndeparture to SOI time         %12.6f  days', jdtdb_soi - jdtdb_tip);

fprintf ('\n\nSOI to areocentric distance   %12.6f  days', jdtdb_rm - jdtdb_soi);

fprintf ('\n\nEarth to Mars transfer time   %12.6f  days\n', jdtdb_rm - jdtdb_tip);

end

if (iptype == 3)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% compute conditions at user-defined final epoch
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% set up for ode45

options = odeset('RelTol', 1.0e-8, 'AbsTol', 1.0e-10);

% define propagation duration (days)

tof = jdtdb_user - jdtdb_soi;

%%%%%%%%%%%%%%%%%%%%%%%%%%%
% set up initial conditions
%%%%%%%%%%%%%%%%%%%%%%%%%%%

jdtdb_wrk = jdtdb_soi;

ri = rhelio_soi / aunit;

vi = 86400.0d0 * vhelio_soi / aunit;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% solve for final conditions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[t, ysol] = ode45(@hel_eqm, [0 tof], [ri vi], options);

% final heliocentric state vector (au and au/day)

rf = ysol(end,(1:3));

vf = ysol(end,(4:6));

% compute mars-centered state vector of the spacecraft
% (Mars mean equator and IAU node of epoch)

svmars = jplephem(jdtdb_user, 4, 11);

rmars = svmars(1:3);

vmars = svmars(4:6);

rm2sc = rf(1:3)' - rmars(1:3);

vm2sc = vf(1:3)' - vmars(1:3);

tmatrix = mme2000(jdtdb_user);

rsc = tmatrix * rm2sc;

vsc = tmatrix * vm2sc;

rm2sc = aunit * rsc;

vm2sc = aunit * vsc / 86400.0;

fprintf('\ntime and conditions at user-defined final epoch');
fprintf('\n(areocentric mean equator and IAU node of epoch)');
fprintf('\n------------------------------------------------\n');

display1(jdtdb_user, xmu_mars, rm2sc, vm2sc);

fprintf('\nMars heliocentric coordinates at final epoch');
fprintf('\n(Earth mean equator and equinox of J2000)');
fprintf('\n-----------------------------------------\n');

display1(jdtdb_user, smu, aunit * rmars, aunit * vmars / 86400.0d0);

fprintf('\nMars heliocentric coordinates at final epoch');
fprintf('\n(Earth mean ecliptic and equinox of J2000)');
fprintf('\n------------------------------------------\n');

recl = eqwrk * rmars;

vecl = eqwrk * vmars;

display1(jdtdb_user, smu, aunit * recl, aunit * vecl / 86400.0d0);

fprintf ('\nsequence of events summary');
fprintf ('\n--------------------------');

fprintf ('\n\ndeparture to SOI time         %12.6f  days', jdtdb_soi - jdtdb_tip);

fprintf ('\n\nSOI to final epoch            %12.6f  days', jdtdb_user - jdtdb_soi);

fprintf ('\n\nEarth to Mars transfer time   %12.6f  days\n', jdtdb_user - jdtdb_tip);

end

fprintf('\n\n');

close('all');

```

Contact us


text:
# A rectangular table is three times as long as it is wide. lf the area is 75 ft2, find the length and the width of the table?

Oct 27, 2016

Let the width be $x$ and the length be $3 x$.

$A = l \times w$

$75 = x \left(3 x\right)$

$75 = 3 {x}^{2}$

$25 = {x}^{2}$

$x = 5$

So, the width is $5$ feet and the length is $15$ feet.

Hopefully this helps!