Authors: Toropina O.D., Romanova M.M., Toropin Yu.M.,  Lovelace R.V.E., 

Isolated old neutron stars (IONS) moving through the interstellar medium capture matter gravitationally. If the star is unmagnetized the captured matter  accretes to the surface of the star. However, the stars are expected to be magnetized. Moreover, some of the stars may be in the ``propeller" stage of evolution. Both the magnetic field and the rotation act to decrease the accretion rate to the surface of the star. Here, we consider stars which are past the propeller stage so that rotation is unimportant. The influence of the magnetic field on the accretion rate to the star's surface is investigated using axisymmetric, resistive magnetohydrodynamic (MHD) simulations.  Matter is taken to inflow at the Bondi rate for a nonmagnetized star, and we verify that stationary Bondi accretion flows occur in the absence of a magnetic field. For a  magnetized star we find that an outward propagating shock wave forms, and that a new stationary, subsonic accretion flow is set up inside this shock as first pointed out  by Toropin et al. (1999). Accretion to the surface of the star dM/dt occurs along two columns aligned with the magnetic axis of the star. The flow is subsonic except at the ``throat'' or critical point of the flow near the surface of the star where it is sonic. Only a fraction of the Bondi flux dMB/dt accretes to the surface of the star. The empirical dependences we find are (dM/dt / dMB/dt) ~ (R* / RA)5 for RA / R* ~ 6-10, where RA is the Alfven radius. In terms of the star's magnetic moment m, we find (dM/dt / dMB/dt) ~m-3.  The accretion rate decreases as the magnetic diffusivity of the plasma hm decreases,  dM/dt ~hm 0.6. We conclude that even a very small residual  magnetic field ~ 10(6-8) G may significantly reduce the accretion rate to the surface of the star and thereby make the accretion luminosity undetectable. The possibility of enhanced accretion owing to three-dimensional instabilities remains to be investigated. The results presented here may also be applicable to wind-fed X-ray stars in binary systems.

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