An empirical Bayesian analysis applied to the globular cluster pulsar population

We describe an empirical Bayesian approach to determine the most likely size of an astronomical population of sources of which only a small subset are observed above some limiting flux density threshold. The method is most naturally applied to astronomical source populations at a common distance (e.g.,stellar populations in globular clusters), and can be applied even to populations where a survey detects no objects. The model allows for the inclusion of physical parameters of the stellar population and the detection process. As an example, we apply this method to the current sample of radio pulsars in Galactic globular clusters. Using the sample of flux density limits on pulsar surveys in 94 globular clusters published by Boyles et al., we examine a large number of population models with different dependencies. We find that models which include the globular cluster two-body encounter rate, $\Gamma$, are strongly favoured over models in which this is not a factor. The optimal model is one in which the mean number of pulsars is proportional to $\exp(1.5 \log \Gamma)$. This model agrees well with earlier work by Hui et al. and provides strong support to the idea that the two-body encounter rate directly impacts the number of neutron stars in a cluster. Our model predicts that the total number of potentially observable globular cluster pulsars in the Boyles et al. sample is 1070$^{+1280}_{-700}$, where the uncertainties signify the 95% confidence interval. Scaling this result to all Galactic globular clusters, and to account for radio pulsar beaming, we estimate the total population to be 2280$^{+2720}_{-1490}$.Comment: 8 pages, 6 figures, 3 tables, corrected a few minor formatting errors which have also been submitted as an erratum to MNRA

Why the distance of PSR J0218+4232 does not challenge pulsar emission theories

Recent VLBI measurements of the astrometric parameters of the millisecond pulsar J0218+4232 by Du et al. have suggested this pulsar is as distant as 6.3 kpc. At such a large distance, the large {\gamma}-ray flux observed from this pulsar would make it the most luminous {\gamma}-ray pulsar known. This luminosity would exceed what can be explained by the outer gap and slot-gap pulsar emission models, potentially placing important and otherwise elusive constraints on the pulsar emission mechanism. We show that the VLBI parallax measurement is dominated by the Lutz-Kelker bias. When this bias is corrected for, the most likely distance for this pulsar is 3.15(+0.85/-0.60) kpc. This revised distance places the luminosity of PSR J0218+4232 into a range where it does not challenge any of the standard theories of the pulsar emission mechanism.Comment: 3 pages, 2 figures, 1 table. Accepted for publication in MNRA

Isolated pulsar spin evolution on the P-Pdot Diagram

We look at two contrasting spin-down models for isolated radio pulsars and, accounting for selection effects, synthesize observable populations. While our goal is to reproduce all of the observable characteristics, in this paper we pay particular attention to the form of the spin period vs. period derivative (P-Pdot) diagram and its dependence on various pulsar properties. We analyse the initial spin period, the braking index, the magnetic field, various beaming models, as well as the pulsar's luminosity. In addition to considering the standard magnetic dipole model for pulsar spin-down, we also consider the recent hybrid model proposed by Contopoulos & Spitkovsky. The magnetic dipole model, however, does a better job of reproducing the observed pulsar population. We conclude that random alignment angles and period dependent luminosity distributions are essential to reproduce the observed P-Pdot diagram. We also consider the time decay of alignment angles, and attempt to reconcile various models currently being studied. We conclude that, in order to account for recent evidence for the alignment found by Weltevrede & Johnston, the braking torque on a neutron star should not depend strongly on the inclination. Our simulation code is publically available and includes a web-based interface to examine the results and make predictions for yields of current and future surveys.Comment: 9 pages, 4 figure

Lutz-Kelker bias in pulsar parallax measurements

Lutz & Kelker showed that parallax measurements are systematically overestimated because they do not properly account for the larger volume of space that is sampled at smaller parallax values. We apply their analysis to neutron stars, incorporating the bias introduced by the intrinsic radio luminosity function and a realistic Galactic population model for neutron stars. We estimate the bias for all published neutron star parallax measurements and find that measurements with less than ~95% certainty, are likely to be significantly biased. Through inspection of historic parallax measurements, we confirm the described effects in optical and radio measurements, as well as in distance estimates based on interstellar dispersion measures. The potential impact on future tests of relativistic gravity through pulsar timing and on X-ray--based estimates of neutron star radii is briefly discussed.Comment: 9 pages, 3 tables, 1 figure. Accepted for publication in MNRA

Gravitational wave background from rotating neutron stars

The background of gravitational waves produced by the ensemble of rotating neutron stars (which includes pulsars, magnetars and gravitars) is investigated. A formula for \Omega(f) (commonly used to quantify the background) is derived, properly taking into account the time evolution of the systems since their formation until the present day. Moreover, the formula allows one to distinguish the different parts of the background: the unresolvable (which forms a stochastic background) and the resolvable. Several estimations of the background are obtained, for different assumptions on the parameters that characterize neutron stars and their population. In particular, different initial spin period distributions lead to very different results. For one of the models, with slow initial spins, the detection of the background can be rejected. However, other models do predict the detection of the background by the future ground-based gravitational wave detector ET. A robust upper limit for the background of rotating neutron stars is obtained; it does not exceed the detection threshold of two cross-correlated Advanced LIGO interferometers. If gravitars exist and constitute more than a few percent of the neutron star population, then they produce an unresolvable background that could be detected by ET. Under the most reasonable assumptions on the parameters characterizing a neutron star, the background is too faint. Previous papers have suggested neutron star models in which large magnetic fields (like the ones that characterize magnetars) induce big deformations in the star, which produce a stronger emission of gravitational radiation. Considering the most optimistic (in terms of the detection of gravitational waves) of these models, an upper limit for the background produced by magnetars is obtained; it could be detected by ET, but not by BBO or DECIGO.Comment: 25 pages, 15 figure

Low-Mass X-Ray Binaries, Millisecond Radio Pulsars, and the Cosmic Star Formation Rate

We report on the implications of the peak in the cosmic star-formation rate (SFR) at redshift z ~ 1.5 for the resulting population of low-mass X-ray binaries(LMXB) and for that of their descendants, the millisecond radio pulsars (MRP). Since the evolutionary timescales of LMXBs, their progenitors, and their descendants are thought be significant fractions of the time-interval between the SFR peak and the present epoch, there is a lag in the turn-on of the LMXB population, with the peak activity occurring at z ~ 0.5 - 1.0. The peak in the MRP population is delayed further, occurring at z < 0.5. We show that the discrepancy between the birthrate of LMXBs and MRPs, found under the assumption of a stead-state SFR, can be resolved for the population as a whole when the effects of a time-variable SFR are included. A discrepancy may persist for LMXBs with short orbital periods, although a detailed population synthesis will be required to confirm this. Further, since the integrated X-ray luminosity distribution of normal galaxies is dominated by X-ray binaries, it should show strong luminosity evolution with redshift. In addition to an enhancement near the peak (z ~ 1.5) of the SFR due to the prompt turn-on of the relatively short-lived massive X-ray binaries and young supernova remnants, we predict a second enhancement by a factor ~10 at a redshift between ~ 0.5 and ~ 1 due to the delayed turn-on of the LMXB population. Deep X-ray observations of galaxies out to z ~ 1 by AXAF will be able to observe this enhancement, and, by determining its shape as a function of redshift, will provide an important new method for constraining evolutionary models of X-ray binaries.Comment: 13 pages, including 1 figure. Accepted for publication in ApJ Letter

The Arecibo 430-MHz Intermediate Galactic Latitude Survey: Discovery of Nine Radio Pulsars

We have used the Arecibo Radio Telescope to search for millisecond pulsars in two intermediate Galactic latitude regions (7 deg < | b | < 20 deg) accessible to this telescope. For these latitudes the useful millisecond pulsar search volume achieved by Arecibo's 430-MHz beam is predicted to be maximal. Searching a total of 130 square degrees, we have discovered nine new pulsars and detected four previously known objects. We compare the results of this survey with those of other 430-MHz surveys carried out at Arecibo and of an intermediate latitude survey made at Parkes that included part of our search area; the latter independently found two of the nine pulsars we have discovered. At least six of our discoveries are isolated pulsars with ages between 5 and 300 Myr; one of these, PSR J1819+1305, exhibits very marked and periodic nulling. We have also found a recycled pulsar, PSR J2016+1948. With a rotational period of 65 ms, this is a member of a binary system with a 635-day orbital period. We discuss some of the the properties of this system in detail, and indicate its potential to provide a test of the Strong Equivalence Principle. This pulsar and PSR J0407+16, a similar system now being timed at Arecibo, are by far the best systems known for such a test.Comment: Accepted for publication in ApJ Referee format: 22 pages, 7 figure

X-ray Timing of PSR J1852+0040 in Kesteven 79: Evidence of Neutron Stars Weakly Magnetized at Birth

The 105-ms X-ray pulsar J1852+0040 is the central compact object (CCO) in SNR Kes 79. We report a sensitive upper limit on its radio flux density of 12 uJy at 2 GHz using the NRAO GBT. Timing using XMM and Chandra over a 2.4 yr span reveals no significant change in its spin period. The 2 sigma upper limit on the period derivative leads, in the dipole spin-down formalism, to an energy loss rate E-dot < 7e33 ergs/s, surface magnetic field strength B_p < 1.5e11 G, and characteristic age tau_c = P/2P-dot > 8 Myr. This tau_c exceeds the age of the SNR by 3 orders of magnitude, implying that the pulsar was born spinning at its current period. However, the X-ray luminosity of PSR J1852+0040, L(bol) ~ 3e33(d/7.1 kpc)^2 ergs/s is a large fraction of E-dot, which challenges the rotation-powered assumption. Instead, its high blackbody temperature, 0.46+/-0.04 keV, small blackbody radius ~ 0.8 km, and large pulsed fraction, ~ 80%, may be evidence of accretion onto a polar cap, possibly from a fallback disk made of supernova debris. If B_p < 1e10 G, an accretion disk can penetrate the light cylinder and interact with the magnetosphere while resulting torques on the neutron star remain within the observed limits. A weak B-field is also inferred in another CCO, the 424-ms pulsar 1E 1207.4-5209, from its steady spin and soft X-ray absorption lines. We propose this origin of radio-quiet CCOs: the B-field, derived from a turbulent dynamo, is weaker if the NS is formed spinning slowly, which enables it to accrete SN debris. Accretion excludes neutron stars born with both B_p 0.1 s from radio pulsar surveys, where B_p 40 Myr) or recycled pulsars. Finally, such a CCO, if born in SN 1987A, could explain the non-detection of a pulsar there.Comment: 8 pages, 3 figures, to appear in The Astrophysical Journa

New limits on the population of normal and millisecond pulsars in the Large and Small Magellanic Clouds

We model the potentially observable populations of normal and millisecond radio pulsars in the Large and Small Magellanic Clouds (LMC and SMC) where the known population currently stands at 19 normal radio pulsars. Taking into account the detection thresholds of previous surveys, and assuming optimal period and luminosity distributions based on studies of Galactic pulsars, we estimate there are (1.79 +/- 0.20) x 10^4 and (1.09 +/- 0.16) x 10^4 normal pulsars in the LMC and SMC respectively. When we attempt to correct for beaming effects, and the fraction of high-velocity pulsars which escape the clouds, we estimate birth rates in both the LMC and SMC to be comparable and in the range 0.5--1 pulsar per century. Although higher than estimates for the rate of core-collapse supernovae in the clouds, these pulsar birth rates are consistent with historical supernova observations in the past 300 yr. A substantial population of active radio pulsars (of order a few hundred thousand) have escaped the LMC and SMC and populate the local intergalactic medium. For the millisecond pulsar (MSP) population, the lack of any detections from current surveys leads to respective upper limits (at the 95% confidence level) of 15,000 for the LMC and 23,000 for the SMC. Several MSPs could be detected by a currently ongoing survey of the SMC with improved time and frequency resolution using the Parkes multibeam system. Giant-pulse emitting neutron stars could also be seen by this survey.Comment: 5 pages, 2 figures, accepted for publication in MNRAS Letter