The Neutron Star Census

The paucity of old isolated accreting neutron stars in ROSAT observations isused to derive a lower limit on the mean velocity of neutron stars at birth.The secular evolution of the population is simulated following the paths of astatistical sample of stars for different values of the initial kick velocity,drawn from an isotropic Gaussian distribution with mean velocity $0\leq \leq 550$ ${\rm km s^{-1}}$. The spin--down, induced by dipole losses and theinteraction with the ambient medium, is tracked together with the dynamicalevolution in the Galactic potential, allowing for the determination of thefraction of stars which are, at present, in each of the four possible stages:Ejector, Propeller, Accretor, and Georotator. Taking from the ROSAT All SkySurvey an upper limit of $\sim 10$ accreting neutron stars within $\sim 140$ pcfrom the Sun, we infer a lower bound for the mean kick velocity, $ < V>\gtrsim200-300$ ${\rm km s^{-1}},$ corresponding to a velocity dispersion$\sigma_V\gtrsim 125-190$ km s$^{-1}$. The same conclusion is reached for botha constant magnetic field ($B\sim 10^{12}$ G) and a magnetic field decayingexponentially with a timescale $\sim 10^9$ yr. Such high velocities areconsistent with those derived from radio pulsar observations. Present results,moreover, constrain the fraction of low velocity stars, which could haveescaped pulsar statistics, to less than 1%.Comment: 13 pages, 6 PostScript figures, accepted to Ap