Abstract
We use astrometric, distance, and spindown data on pulsars to (1) estimate three-dimensional velocity components, birth distances from the Galactic plane, and ages of individual objects; (2) determine the distribution of space velocities and the scale height of pulsar progenitors; (3) test spindown laws for pulsars; (4) test for correlations between space velocities and other pulsar parameters; and (5) place empirical requirements on mechanisms than can produce high-velocity neutron stars. Our approach incorporates measurement errors, uncertainties in distances, deceleration in the Galactic potential, and differential Galactic rotation. We focus on a sample of proper motion measurements of young (<10 Myr) pulsars whose trajectories may be accurately and simply modeled. This sample of 49 pulsars excludes millisecond pulsars and other objects that may have undergone accretion-driven spinup. We estimate velocity components and birth z distance on a case-by-case basis assuming that the actual age equals the conventional spindown age for a braking index n = 3, no torque decay, and birth periods much shorter than present-day periods. Every sample member could have originated within 0.3 kpc of the Galactic plane while still having reasonable present-day peculiar radial velocities. For the 49 object sample, the scale height of the progenitors is ~0.13 kpc, and the three-dimensional velocities are distributed in two components with characteristic speeds of 175−24+19 km s-1 and 700−132+300 km s-1, representing ~86% and ~14% of the population, respectively. The sample velocities are inconsistent with a single-component Gaussian model and are well described by a two-component Gaussian model but do not require models of additional complexity. From the best-fit distribution, we estimate that about 20% of the known pulsars will escape the Galaxy, assuming an escape speed of 500 km s-1. The best-fit, dual-component model, if augmented by an additional, low-velocity (<50 km s-1) component, tolerates, at most, only a small extra contribution in number, less than 5%. The best three-component models do not show a preference for filling in the probability distribution at speeds intermediate to 175 and 700 km s-1 but are nearly degenerate with the best two-component models. We estimate that the high-velocity tail (>1000 km s-1) may be underrepresented (in the observed sample) by a factor ~2.3 owing to selection effects in pulsar surveys. The estimates of scale height and velocity parameters are insensitive to the explicit relation of chronological and spindown ages. A further analysis starting from our inferred velocity distribution allows us to test spindown laws and age estimates. There exist comparably good descriptions of the data involving different combinations of braking index and torque decay timescale. We find that a braking index of 2.5 is favored if torque decay occurs on a timescale of ~3 Myr, while braking indices ~4.5 ± 0.5 are preferred if there is no torque decay. For the sample as a whole, the most probable chronological ages are typically smaller than conventional spindown ages by factors as large as 2. We have also searched for correlations between three-dimensional speeds of individual pulsars and combinations of spin period and period derivative. None appears to be significant. We argue that correlations identified previously between velocity and (apparent) magnetic moment reflect the different evolutionary paths taken by young, isolated (nonbinary), high-field pulsars and older, low-field pulsars that have undergone accretion-driven spinup. We conclude that any such correlation measures differences in spin and velocity selection in the evolution of the two populations and is not a measure of processes taking place in the core collapse that produces neutron stars in the first place. We assess mechanisms for producing high-velocity neutron stars, including disruption of binary systems by symmetric supernovae and neutrino, baryonic, or electromagnetic rocket effects during or shortly after the supernova. The largest velocities seen (~1600 km s-1), along with the paucity of low-velocity pulsars, suggest that disruption of binaries by symmetric explosions is insufficient. Rocket effects appear to be a necessary and general phenomenon. The required kick amplitudes and the absence of a magnetic field-velocity correlation do not yet rule out any of the rocket models. However, the required amplitudes suggest that the core collapse process in a supernova is highly dynamic and aspherical and that the impulse delivered to the neutron star is larger than existing simulations of core collapse have achieved.
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