Neutron Star Population Dynamics. I. Millisecond Pulsars

Abstract

We study the field millisecond pulsar population to infer its intrinsic distribution in spin period and luminosity and to determine its spatial distribution within the Galaxy. Our likelihood analysis on data from extant surveys (22 pulsars with periods < 20 ms) accounts for the following important selection effects: (1) the survey sensitivity as a function of direction, spin period, and sky coverage; (2) interstellar scintillation, which modulates the pulsed flux and causes a net increase in search volume ∼ 30%; and (3) errors in the pulsar distance scale.Adopting power-law models (with cutoffs) for the intrinsic distributions, the analysis yields a minimum period cutoff P min > 0.65 ms (99% confidence), a period distribution ∝ P −2.0±0.33 and a pseudo-luminosity distribution ∝ L −2.0±0.2 p (where L p = flux density × distance 2 , for L p ≥ 1.1 mJy kpc 2 ).We find that the column density of millisecond pulsars (uncorrected for beaming effects) is ∼ 50 +30 −20 kpc −2 in the vicinity of the solar system. For a Gaussian model the z scale height is 0.65 +0.16 −0.12 kpc, corresponding to local number density 29 +17 −11 kpc −3 . (For an exponential model the scale height becomes 0.50 +0.19 −0.13 kpc and the number density 44 +25 −16 kpc −3 .) Estimates of the total number of MSPs in the disk of the Galaxy and for the associated birthrate are given. The contribution of a diffuse halo-like component (tracing the Galactic spheroid, the halo or the globular cluster density profile) to the local number density of MSPs is limited to < ∼ 1% of the midplane value.We consider a kinematic model for the MSP spatial distribution in which objects in the disk are kicked once at birth and then orbit in a smooth Galactic potential, becoming dynamically well-mixed. The analysis yields a column density 49 +27 −17 kpc −2 (comparable to the above), a birth z kick velocity 52 +17 −11 km s −1 and a 3D velocity dispersion of ∼ 84 km s −1 . MSP velocities are smaller than those of young, long-period pulsars by about a factor of 5. The kinematic properties of the MSP population are discussed, including expected transverse motions, the occurrence of asymmetric drift, the shape of the velocity ellipsoid and the z scale height at birth. If MSPs are long-lived then a significant contribution to observed MSP z velocities owes to diffusive processes that increase the scale height of old stellar populations; our best estimate of

The Parkes multibeam pulsar survey – VII. Timing of four millisecond pulsars and the underlying spin-period distribution of the Galactic millisecond pulsar population

“…Uniform, power-law and Gaussian distributions are decisively ruled out in our likelihood analysis as being good descriptions to f (P ). We note that the strong preference for a log-normal model found here is in contrast to the power-law model proposed by Cordes & Chernoff (1997) based on a much smaller sample of MSPs. While the exponent of our power-law model tested here (-1.7) is consistent with theirs, the likelihood analysis strongly favors the lognormal model.…”

Population statistics study of radio and gamma-ray pulsars in the Galactic plane

“…We evolve a large number of neutron stars generated in our Monte Carlo simulation to determine the equilibrium spatial distribution of ms pulsars, which we then use in subsequent simulations. A scale height of 410 pc of the evolved ms pulsars is in good agreement with a scale height of 500 pc (exponential scale) of Cordes & Chernoff [4] and with a scale height of 410 pc of LMXBs [11].…”

“…For ms pulsars, we begin the evolution by using the magnetic field and supernova kick velocity distributions of Cordes & Chernoff [4]. Recent studies of low-mass Xray binary systems (LMXBs) have been able to determine the spins of the accreting neutron stars allowing for an estimate of their magnetic fields.…”

Accretion, ablation and propeller evolution in close millisecond pulsar binary systems

“…Because we examine only a subset of the binary MSP population the black widow rates are much less than previous binary MSP estimations which, instead, considered the total binary MSP population and ranged from 1 × 10 −6 − 4 × 10 −4 yr −1 (Lorimer 1995;Cordes & Chernoff 1997;Lorimer 2008;Hurley et al 2010).…”