Period distribution of old accreting isolated neutron stars

In this paper we present calculations of period distribution for old accreting isolated neutron stars (INSs). After few billion years of evolution low velocity INSs come to the stage of accretion. At this stage INS's period evolution is governed by magnetic braking and angular momentum accreted. Since the interstellar medium is turbulized accreted momentum can either accelerate or decelerate spin of an INS, therefore the evolution of period has 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 INS's spatial velocity, its magnetic field and density of the surrounding medium). Such periods are much longer than the values measured by {\emph ROSAT} for 3 radio-silent isolated neutron stars. Due to long periods INSs should have high spin up/down rates, $\dot p$, which should fluctuate on a time scale of $\sim 1$ yr.