Constrains on parameters of magnetic field decay for accreting isolated   neutron stars
  The influence of exponential magnetic field decay (MFD) on the spin evolution of isolated neutron stars is studied. The ROSAT observations of several X-ray sources, which can be accreting old isolated neutron stars, are used to constrain the exponential and power-law decay parameters. We show that for the exponential decay the ranges of minimum value of magnetic moment, $\mu_b$, and the characteristic decay time, $t_d$, $\sim 10^{29.5}\ge \mu_b \ge 10^{28} {\rm G} {\rm cm}^3$, $\sim 10^8\ge t_d \ge 10^7 {\rm yrs}$ are excluded assuming the standard initial magnetic moment, $\mu_0=10^{30} {\rm G} {\rm cm}^3$. For these parameters, neutron stars would never reach the stage of accretion from the interstellar medium even for a low space velocity of the stars and a high density of the ambient plasma. The range of excluded parameters increases for lower values of $\mu_0$.   We also show, that, contrary to exponential MFD, no significant restrictions can be made for the parameters of power-law decay from the statistics of isolated neutron star candidates in ROSAT observations.   Isolated neutron stars with constant magnetic fields and initial values of them less than $\mu_0 \sim 10^{29} {\rm G} {\rm cm}^3$ never come to the stage of accretion.   We briefly discuss the fate of old magnetars with and without MFD, and describe parameters of old accreting magnetars. 
S.B. Popov and M.E. Prokhorov (Sternberg Astronomical Institute)