The period distribution of old accreting isolated neutron stars

In this paper we present calculations of the period distribution for old accreting isolated neutron stars (INSs). After a few billion years of evolution low velocity INSs come to the stage of accretion. At this stage the INS period evolution is governed by magnetic braking and the accreted angular momentum. Since the interstellar medium is turbulent the accreted momentum can either accelerate or decelerate the spin of an INS, therefore the evolution of the period has a chaotic character. Our calculations show that in the case of constant magnetic field accreting INSs have relatively long spin periods (some hours and more, depending on the spatial velocity of the INS, its magnetic field and the density of the surrounding medium). Such periods are much longer than the values measured by ROSAT for 3 radio-silent isolated neutron stars. Due to their long periods INSs should have high spin up/down rates, (p) over dot, which should fluctuate on a time scale of similar to1 yr.