Magnetic and Spin History of Very Young Pulsars

Abstract

After Michel (1994) introduced a phenomenological picture of `rapid magnetization' of newly born neutron stars (NSs), Muslimov & Page (1995) suggested that the physical conditions accompanying the formation of a NS may result in the surface magnetic field of the NS having a low value (~ 10^8 - 10^9 G) while the bulk of the flux is submerged under the stellar surface. The subsequent growth of the surface magnetic field occurs owing to ohmic diffusion of a strong internal field (10^12-10^13 G) and proceeds over a time scale of 10^2-10^3 yrs, depending on the early thermal history of the NS, the initial distribution of magnetic flux and the electrical resistivity in the stellar crust, as well as on the details of the stellar structure. Referring to this suggestion, we perform numerical computations to demonstrate its possible relevance to young radio pulsars. In our calculations, we use different NS structures based on a model of dense matter presenting a phase transition to kaon condensation which implies both slow and fast neutrino cooling, depending on the stellar mass. We present sequences of secular evolution of the surface magnetic field, spin-down luminosity, spin period, `braking index', and spin-down age best matching the corresponding measured quantities for PSR 0531+21 (Crab), PSR 0540-69, and PSR 1509-58. We conclude that the effect under consideration reproduces remarkably well both the observed rotational characteristics and derived values of the surface magnetic field strength for these radio pulsars, the only ones having reliable measurements of the braking indices. In addition, our analysis suggests that the NSs in the Crab and PSR 0540-69 have experienced fast neutrino cooling while the NS in PSR 1509-58 has undergone slow cooling and hence has a mass below the critical mass.