  We have carried out a numerical study of the effect of large scale magnetic
fields on the rate of accretion from a uniform, isothermal gas onto a
resistive, stationary point mass. Only mass, not magnetic flux, accretes onto
the point mass. The simulations for this study avoid complications arising from
boundary conditions by keeping the boundaries far from the accreting object.
Our simulations leverage adaptive refinement methodology to attain high spatial
fidelity close to the accreting object. Our results are particularly relevant
to the problem of star formation from a magnetized molecular cloud in which
thermal energy is radiated away on time scales much shorter than the dynamical
time scale. Contrary to the adiabatic case, our simulations show convergence
toward a finite accretion rate in the limit in which the radius of the
accreting object vanishes, regardless of magnetic field strength. For very weak
magnetic fields, the accretion rate first approaches the Bondi value and then
drops by a factor ~ 2 as magnetic flux builds up near the point mass. For
strong magnetic fields, the steady-state accretion rate is reduced by a factor
~ 0.2 \beta^{1/2} compared to the Bondi value, where \beta is the ratio of the
gas pressure to the magnetic pressure. We give a simple expression for the
accretion rate as a function of the magnetic field strength. Approximate
analytic results are given in the Appendixes for both time-dependent accretion
in the limit of weak magnetic fields and steady-state accretion for the case of
strong magnetic fields.
