1999ApJ...526..327Z

We study statistical properties of the Galactic population of X-ray pulsars with ages of less than 10⁶ yr using the Monte Carlo method. Combining the initial magnetic field and spatial and velocity distributions of neutron stars at birth (which are obtained from radio pulsar statistical studies) with either the X-ray pulsar model proposed by Cheng & Zhang or the expected X-ray flux obtained by the empirical formula proposed by Becker & Trümper, we obtain the distance, period, period derivative, and X-ray energy flux distributions of those X-ray pulsars whose X-ray and radio fluxes are above the detectable threshold fluxes. Our simulated results indicate that (1) the distance, period, period derivative, and X-ray energy flux distributions of simulated X-ray pulsars in both models are consistent with those of the known X-ray pulsars observed by ROSAT if the minimum detectable X-ray energy flux is 2x10^–14 ergs.cm^–2.s^–1, and (2) the expected X-ray pulsar numbers in both models are different; the ratio of expected X-ray pulsars in our model to those in Becker & Trümper's model is about 0.6. Moreover, as the minimum detectable X-ray energy flux decreases, the simulated distributions from the two models obviously differ except in the distance distributions, and especially so for the simulated distributions of the period and period derivative. As the minimum detectable X-ray energy flux decreases, those X-ray pulsars with long periods and small period derivatives become detectable. The next generation of X-ray satellites, e.g., XMM, may differentiate our model from that of Becker & Trümper.