Stochastic spin evolution of neutron stars

In this paper we present calculations of period distribution for old accreting isolated neutron stars (INSs). At the age about a few billions years low velocity INSs come to the stage of accretion. At that stage their period evolution is governed by magnetic breaking and accreted angular momentum. Due to turbulence of the interstellar medium (ISM) accreted momentum can both accelerate and decelerate rotation of an INS and spin evolution has chaotic character. Calculations show that for constant magnetic fields INSs have relatively long spin periods, $\ge 10^4$--$10^5$ s, depending on parameters of INSs and an ISM. Due to long periods INSs have high spin up/spin down rates, which should fluctuate on a time scale about a few years.