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 <20 ms) accounts for important selection effects. We infer a minimum period cutoff P(min) > 0.65 ms (99% confidence), a period distribution proportional to P^{-2.0 +- 0.33} and a pseudo-luminosity distribution proportional to L_p^{-2.0 +- 0.2} (where L_p = flux density times distance^2, for L_p >= 1.1 mJy kpc^2). We find a vertical scale height 0.65{+0.16,-0.12} kpc. We use our results to estimate the total number and birthrate of MSPs in the disk of the Galaxy. We limit the density contribution of a diffuse halo-like component to <1% of the midplane value. The MSP velocity dispersion is smaller that that of young, long-period pulsars by about a factor of 5. Our best estimate of the 1D velocity kick that is unique to MSP evolution is approximately 40 km s^-1. We discuss the evolutionary relationship of MSPs and low-mass X-ray binaries and prospects for future searches for MSPs.