Neutron Star Population Dynamics. I. Millisecond Pulsars

We study the field millisecond pulsar (MSP) 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 less than 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 of ~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 Pmin > 0.65 ms (99% confidence), a period distribution proportional to P-2.0?0.33, and a pseudoluminosity distribution proportional to L$−2.0{±}0.2p$ --> (where Lp is the product of the flux density and the square of the distance, for Lp ? 1.1 mJy kpc2). We find that the column density of MSPs (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 the 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 three-dimensional 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 is the result of diffusive processes that increase the scale height of old stellar populations; our best estimate of the one-dimensional velocity kick that is unique to MSP evolution is ~40 km s-1 if such diffusion is taken into account. The scale heights of millisecond pulsars and low-mass X-ray binaries are consistent, suggesting a common origin and that the primary channel for forming both classes of objects imparts only low velocities. Binaries involving a common envelope phase and a neutron star-forming supernova explosion can yield such objects, even with explosion asymmetries like those needed to provide the velocity distribution of isolated, nonspun-up radio pulsars. Future searches for MSPs may be optimized using the model results. As an example, we give the expected number of detectable MSPs per beam area and the volumes of the Galaxy sampled per beam area for a hypothetical Green Bank Telescope all sky survey. Estimates for the volume that must be surveyed to find a pulsar faster than 1.5 ms are given. We also briefly discuss how selection effects associated with fast binaries influence our results.