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Twenty-One Millisecond Pulsars in Terzan 5 Using the Green Bank Telescope

We have discovered 21 millisecond pulsars (MSPs) in the globular cluster Terzan 5 using the Green Bank Telescope, bringing the total of known MSPs in Terzan 5 to 24. These discoveries confirm fundamental predictions of globular cluster and binary system evolution. Thirteen of the new MSPs are in binaries, of which two show eclipses and two have highly eccentric orbits. The relativistic periastron advance for the two eccentric systems indicates that at least one of these pulsars has a mass>1.68 Msun at 95% confidence. Such large neutron star masses constrain the equation of state of matter at or beyond the nuclear equilibrium density.

We have discovered 21 millisecond pulsars (MSPs) in the globular cluster Terzan 5 using the Green Bank Telescope, bringing the total of known MSPs in Terzan 5 to 24. These discoveries confirm fundamental predictions of globular cluster and binary system evolution. Thirteen of the new MSPs are in binaries, of which two show eclipses and two have highly eccentric orbits. The relativistic periastron advance for the two eccentric systems indicates that at least one of these pulsars has a mass >1.68 M ⊙ at 95% confidence. Such large neutron star masses constrain the equation of state of matter at or beyond the nuclear equilibrium density.
The extremely high stellar densities (10 4 −10 6 pc −3 ) in the cores of globular clusters (GCs) result in stellar interactions which produce and destroy binary systems as well as exchange their members (1). Formed by the death of massive stars early in a cluster's history, neutron stars unblocked aperture of the GBT, the wide bandwidth provided by the Spigot and S-band receiver, and the move to higher observing frequencies together provided an increase in sensitivity over the Parkes searches (21) by factors of ∼5 for typical recycled pulsars and by > ∼ 10 for MSPs with spin periods P psr < ∼ 2 ms (26). We searched the observation by de-dispersing the raw data into 40 separate time series with DMs ranging from 230−250 pc cm −3 and spaced by 0.5 pc cm −3 . We Fourier-transformed the full 5.9-hr time series as well as 10-, 20-and 60-min sections and searched them using Fourierdomain acceleration search techniques (27) in a manner similar to that described in Ransom et al. (28) in order to maintain sensitivity to pulsars in compact binary systems. In that first observation we discovered 14 new pulsars, Ter 5 E−R (29). Using eight more observations taken between July and November 2004, we found seven additional pulsars and determined the basic orbital parameters of 10 of the 13 new binaries ( Fig. 1 and Table 1). In general, the uncalibrated flux densities of the pulsars (as computed by comparing the integrated signal from a pulsar to the predicted total system noise level) were constant to within a level of < ∼ 50% between these observations implying that diffractive scintillation will not largely affect pulsar measurements for Terzan 5 at these observing frequencies. Several additional binary pulsar candidates from these data remain unconfirmed but may reappear in future observations at more fortuitous orbital phases. Since the volume enclosed by the GBT beam at 1950 MHz out to a distance of 10 kpc is ∼10 −3 kpc 3 and it has been estimated (30) that there are roughly 10 5 observable MSPs within the Galaxy (with volume ∼10 2 −10 3 kpc 3 ), it is possible that a detectable foreground MSP is within our beam. However, given that the DM towards Terzan 5 is known to within ∼5%, the probability of that MSP having a similar DM is much smaller, and hence we are confident that all of the new pulsars are members of Terzan 5. Positions with < ∼ 1 ′′ accuracy of the new MSPs from pulsar timing will solidify the associations.
The New Pulsar Population With our initial discovery data, the ensemble of pulsars all have measured DMs with errors < ∼ 0.1 pc cm −3 , flux densities S 1950 with fractional errors of ∼30%, and precisely determined spin periods P psr . These measurements allow us to compare the new systems with known MSPs such as those in 47 Tuc. Once precise positions and pulsar spin period derivatives have been determined from timing observations over the next year (the positions of the new pulsars are currently known only to within the 6. ′ 5 primary beam of the GBT), a variety of tests of the gravitational potential and internal dynamics of Terzan 5 will be possible, in addition to estimates of the ages and magnetic field strengths of many of the pulsars (31).
The DMs for the pulsars in Terzan 5 are distributed with a central Gaussian-like component with an average and standard deviation of 237.8 ± 1.4 pc cm −3 , and five outliers having higher and lower DMs ( Table 1). The overall spread in DM, 9.5 pc cm −3 (13 times larger than what is observed for 47 Tuc), is the largest known for any GC and is likely due to the large average DM for Terzan 5 and irregularities in the ISM along the differing sight-lines toward its pulsars. The Gaussian-like component of the DM distribution likely corresponds to a group of centrally concentrated pulsars near the cluster core. The position of Ter 5 C, which has an average DM, is about 10 ′′ or one core radius (9) north of the cluster center and supports such a notion. Likewise, pulsars with outlying DMs, such as Ter 5 D and J, are probably more offset like Ter 5 A, which has a high DM and is located 36 ′′ from the center (20).
The VLA radio imaging of Terzan 5 (17) revealed numerous point sources within 30 ′′ of the cluster center, as well as ∼2 mJy of diffuse emission at 1400 MHz within ∼10 ′′ . The central emission was attributed to 60−200 unresolved pulsars assuming D=7.1 kpc, a standard luminosity distribution, and a minimum pulsar luminosity (L 1400 ≡ S 1400 × D 2 ) of L 1400,min =0.3 mJy kpc 2 . A distance to Terzan 5 of D=8.7 kpc (16), would increase the number of unresolved pulsars by ∼50%. For a typical pulsar radio spectral index of −1.6 (32), and omitting the flux densities of Ter 5 A and C which are located outside the region of diffuse emission (20), the integrated measured flux density from the other 22 pulsars at 1400 MHz is ∼1.3 mJy. If the five pulsars with outlying DMs reside outside the cluster core, the total flux density from the remaining pulsars is only ∼1 mJy. None of the new pulsars can individually (or in combination with nearby Ter 5 C) account for the bright (1.42 mJy) point source "N" located 12 ′′ north of the cluster center (17). However, given its very wide pulse profile, lack of a flat off-pulse baseline, and positional coincidence (20), Ter 5 C could possibly emit significant unpulsed emission like the MSP J0218+4232 (33) and thereby account for all of the flux density of source N.
The differential luminosity distribution of the new pulsars resembles that of the 47 Tuc (4), M15 (5), and the Galactic disk (34) populations by following the normal d log N = −d log L relation, with no sign of a downturn at the low luminosity end (L 1400 ∼1−2 mJy kpc 2 ). This implies that we have not reached the lowest luminosities of the intrinsic pulsar distribution in Terzan 5, nor have we yet reached the sensitivity limit of the observing system (35). It is likely that tens of less-luminous pulsars remain to be discovered in Terzan 5, and possibly even several bright ones (e.g. the source N). Such bright pulsars may remain undetected if they are members of very compact or massive binaries due to eclipsing or excessive Doppler accelerations or if they have extremely fast spin periods (P psr ≪1.5 ms). Detailed searches using more advanced search techniques may yet uncover these systems.
The 24 known pulsars in Terzan 5 and the 22 in 47 Tuc appear to have different spin period distributions. The 47 Tuc pulsars are a homogeneous population with periods 2.1−7.6 ms (3), while those in Terzan 5 have a flatter distribution that includes six pulsars slower than 7.6 ms and the four fastest pulsars known in GCs (P psr =1.67, 1.73, 2.05, and 2.07 ms). A Kolmogorov-Smirnov test suggests that these samples are drawn from different parent distributions at 85% confidence. These differences may be related to the dynamical states of the cluster cores [i.e. just pre-or just post-core collapse for Terzan 5 (16)], different epochs of MSP creation, or the occurrence of unusual evolutionary mechanisms that only manifest themselves at very high (i.e. >10 5 pc −3 ) stellar densities.

Individual Pulsars
The binaries Ter 5 E and W have orbital periods of P orb ∼60 days and ∼4.9 days, respectively. In the dense stellar environment of a GC, such wide binaries have large cross-sections for stellar encounters which can disrupt them, eject them from the cluster core, or after multiple collisions, induce significant eccentricities (36) in their initially circular orbits (31). For these pulsars, the measured eccentricities are e∼0.02, significantly larger than predicted for binary MSPs with helium WD companions in the Galaxy (31). If they are located near the cluster center, where the stellar densities are > ∼ 10 5 pc −3 (25), the time scale for interactions to produce such eccentricities is 10 8 −10 9 yr (36), consistent with the > ∼ 10 9 yr ages of most cluster pulsars. However, the 60-day orbit of Ter 5 E implies a time scale near the low end of that range, possibly too short for MSP lifetimes. This may indicate that it resides further from the center of Terzan 5: >10 9 yr spent in the core could result in many interactions which would either destroy the binary or induce much larger eccentricities. The eccentricities of Ter 5 I and J are too large to have been produced by this method, especially given the relatively compact nature of their orbits, indicating that they were formed by a different mechanism.
At least two of the new binary pulsars, Ter 5 O and P, have been observed to eclipse, although given the factor of 10 difference in the inferred companion masses (m 2 > ∼ 0.036 M ⊙ for Ter 5 O and > ∼ 0.38 M ⊙ for Ter 5 P) and eclipse durations (∼0.05P orb for Ter 5 O and > ∼ 0.5P orb for Ter 5 P), the systems are unalike. Ter 5 O, the third fastest MSP known, is similar to the Black-Widow eclipsing MSP B1957+20 (37) with a very low-mass companion and an eclipse duration (∼15−20 min) corresponding to a physical size (∼0.03 R ⊙ ) much larger than the companion star's Roche lobe. Such systems are common in GCs (38). Ter 5 P, the fourth fastest MSP known, is unusual and most similar to the binary MSP NGC 6397 A, whose peculiar red straggler or sub-subgiant companion causes irregular and long-duration eclipses of the radio pulses (8). Ter 5 P's eclipses are also irregular and correspond to an eclipsing region of several solar radii in size, indicating the companion is likely a peculiar evolved star as well. If so, the system may have been created after at least one exchange encounter where the MSP's original companion (which had spun up the pulsar) was ejected and replaced by a main sequence star. Such an encounter might eject the system from the core of the cluster as has been observed for NGC 6397 A [although alternative formation scenarios for this pulsar have been proposed as well (39)].
The pulsars Ter 5 I and J are in highly eccentric orbits with companions of at least 0.24 and 0.38 M ⊙ , respectively (Fig. 2). The companions are not sufficiently massive to be NSs unless the systems have improbably low inclination angles i (i.e. are almost face-on). If they were mainsequence or giant stars, eclipses would likely be observed for a variety of inclinations given the compactness of the orbits (orbital separations of ∼5R ⊙ ). Additionally, the orbital circularization time scales would be of order 10 5 yr for both pulsars and so no eccentricity should currently be observed (40). The companions are therefore probably WDs. However, the pulsar recycling scenario generates MSP−WD binaries in nearly circular orbits due to tidal interactions during mass-transfer and therefore did not produce these eccentric systems. A possible scenario involves the off-center collision of a NS with a red giant which would disrupt the giant's envelope and leave the core (now the WD) in an eccentric orbit about the NS (41). An alternative scenario involves the exchange of an initially isolated WD into a binary consisting of an MSP and the lowmass WD that recycled it. However, the observed pulsars are only mildly recycled. Furthermore, the multiple exchanges required in this scenario imply that the system was created near the core, where due to mass segregation the isolated WDs would be more massive than the observed companions to Ter 5 I and J. We therefore regard the collision scenario as more likely.
The high eccentricities of both orbits permitted us to measure their advances of the angle of periastron,ω = 0.255±0.001 • yr −1 for I and 0.327±0.004 • yr −1 for J, which are likely due to general-relativistic modification of the Keplerian elliptical orbit. Under this assumption, the total mass can be derived for each system: 2.17±0.02 M ⊙ for I and 2.20±0.04 M ⊙ for J. Together with the measured Keplerian mass functions, in both cases this implies that the most likely NS masses are >1.7 M ⊙ (Fig. 2). However, classical contributions toω from tidal or rotational quadrupole mass moments in the companion star must also be considered (42,43). Tidal deformation is insignificant for a WD companion (42), but rotationally induced quadrupoles are possible if the WD is rapidly rotating, as there is no reason to expect the spin axis of the companion to be aligned with the orbital angular momentum.
The predicted contributions toω for Ter 5 I and J due to a rotationally induced quadrupole arė ω rot ∼0.01−0.02 • yr −1 times angular and stellar structure factors (42,43,44). One of the stellar structure factors, α 6 , can range up to 15 for WDs (42), makingω rot a potentially significant contribution to the measuredω. A significantω rot , however, will produce changes in i and hence in the projected semi-major axis x ≡ a 1 sin(i)/c. The size of this effect may be written aṡ ω rot ∼ẋ rot /x times a trigonometric factor usually of order unity that depends on i, the angle between the WD rotation axis and the orbital angular momentum vector, and the phase of the orbital precession (43). For random choices of these angles the trigonometric factor is <10, ∼80% of the time. By incorporating detections from Parkes search observations taken in 1998 and 2000 (21) using the now known orbital ephemerides, we have upper limits onẋ which imply thatω rot is < ∼ 0.003 • yr −1 times the trigonometric factor for both systems. The magnitudes of these rotational-quadrupole contributions are comparable to our current measurement uncertainties foṙ ω. We emphasize that this result does not depend on the type of companion and is equally valid for main-sequence stars and WDs. Therefore, unless the orientations of the orbital and rotational angular momentum vectors are fine-tuned for both systems, theω measurements are well-described by general relativity. Under this assumption, one or both of these NSs are likely to be unprecedentedly massive: calculation of the joint probabilities (Fig. 2) indicates that at least one of the pulsars is more massive than 1.48, 1.68, or 1.74 M ⊙ at 99%, 95% and 90% confidence levels, respectively. A strict upper limit to the masses of both pulsars is 1.96 M ⊙ . Similar but slightly less stringent evidence from pulsar timing for a massive NS in the Galactic low-mass WD−MSP binary J0751+1807 has been presented (45). It is an intriguing question whether the large masses for Ter 5 I and J resulted from the collision formation mechanism, possibly during a short period of hypercritical accretion which partially or completely spun-up the pulsars (41). GBT observations over the next 1−3 yr will measure the varying delays due to gravitational redshift and time dilation as Ter 5 I moves in its orbit, which together are known as γ (the measurement of γ for Ter 5 J will take 5−10 yr due to the relatively slow spin period of the pulsar). This parameter, along with general relativity and the already well measuredω, will provide a precise mass for the pulsar and will likely rule out several soft equations of state for matter at nuclear densities (46).  (18). Pulsars listed without orbital parameters are likely isolated systems while those marked with an e are eclipsing systems. The errors on the dispersion measures (DMs) range from 0.01−0.1 pc cm −3 and the errors on the measured flux densities are ∼30%. The flux densities for the eclipsing pulsars include only the times when the pulsar is not eclipsed. The light travel time across the projected pulsar semi-major axis is defined as x ≡ a 1 sin(i)/c. Eccentricities listed as "0" are too small to measure at present and have been set to zero for orbital parameter fitting. The minimum companion mass m 2 was calculated assuming a pulsar mass m 1 of 1.4 M ⊙ and i=90 • except for Ter 5 I and J (Fig. 2). All measured parameters were determined using the TEMPO software package (47). All but Ter 5 A, C, and D are newly discovered (18). Each profile is the weighted average of the best detections of that pulsar and is a measure of the relative flux density as a function of rotational phase. Asterisks indicate that the pulsar is the member of a binary system, and the length of the horizontal error bar (0.3 ms) is the effective system time resolution. The grey vertical band shows the range of precisely measured NS masses from relativistic binary radio pulsars (46). In both cases the median pulsar mass (indicated by the vertical line in the marginal distribution) lies significantly above 1.7 M ⊙ , implying that one or both of these pulsars is considerably more massive than the NSs that have been well measured to date. A strict upper limit to the masses of both pulsars is 1.96 M ⊙ .