Evolution of Isolated Neutron Stars

In this paper we briefly review our recent results on evolution and properties of isolated neutron stars (INSs) in the Galaxy. As the first step we discuss stochastic period evolution of INSs. We briefly discuss how an INS's spin period evolves under influence of interaction with turbulized interstellar medium. To investigate statistical properties of the INS population we calculate a {\it census} of INSs in our Galaxy. Then we show that for exponential field decay the range of minimum value of magnetic moment, $\mu_b$: $\sim 10^{29.5}\ge \mu_b \ge 10^{28} {\rm G} {\rm cm}^3$, and the characteristic decay time, $t_d$: $\sim 10^8\ge t_d \ge 10^7 {\rm yrs}$, can be excluded assuming the standard initial magnetic momentum, $\mu_0=10^{30} {\rm G} {\rm cm}^3$, if accreting INSs are observed. It is shown that old accreting INSs become more abundant than young cooling INSs at X-ray fluxes below $\sim 10^{-13}$ erg cm$^{-2}$ s$^{-1}$. The weak {\it ROSAT} sources, associated with INSs, can be young cooling objects, if the NSs birth rate in the solar vicinity during the last $\sim 10^6$ yr was much higher than inferred from radiopulsar observations.