The Influences of the Velocity Distribution and the Thickness Effect of Galactic Disk on the Z-distribution of Normal Pulsars

Based on the gravitational potential of an undisturbed finitely-thick disk derived by Peng et al. (1978), 3-D Monte Carlo simulations of 4 × 105 pulsars are made for the four combinations of the two parameters of gravitational potential (hz1 = 0.001 kpc, hz2 = 0.325 kpc) and two parameters of initial velocity distribution (σv1 = 115 km/s, σv2 = 200 km/s). The 4 × 105 pulsars are divided into 20 age-groups and the fraction of “escaped” pulsars is calculated for each group. The “not escaped” pulsars in each group, whose simulated projective positions on the Galactic plane lie in the two radial ranges 0 < r < 25 kpc and 5 < r < 11 kpc, are selected to construct the |z|-distribution and derive the segmental and cumulative scale heights. The evolution characteristics of the segmental and cumulative scale heights of the “not escaped” pulsars in these two regions are studied. The segmental scale height of the “not escaped” pulsars varies with the time irregularly while the cumulative scale height varies smoothly. For a relatively long time (>108yr), the Galactic disk thickness has an obvious and complex effect on the evolution of the pulsar's cumulative scale height, but for a relatively short time (< 2 × 107), the effect is very small and the time dependence of the cumulative scale height is linear. Over a long period, the initial velocity distribution also has an obvious influence on the cumulative scale height. In the condition hz2 = 0.325 kpc and σv2 = 200 km/s, the simulated cumulative scale height is 0.596 ± 0.005 kpc in the radial range 5 < r < 11 kpc and at the time t = 9.22 × 106 yr.