  The radiation magnetohydrodynamics (RMHD) system couples the ideal
magnetohydrodynamics equations with a gray radiation transfer equation. The
main challenge is that the radiation travels at the speed of light while the
magnetohydrodynamics changes with fluid. The time scales of these two processes
can vary dramatically. In order to use mesh sizes and time steps that are
independent of the speed of light, asymptotic preserving (AP) schemes in both
space and time are desired. In this paper, we develop an AP scheme in both
space and time for the RMHD system. Two different scalings are considered, one
results in an equilibrium diffusion limit system, while the other results in a
non-equilibrium system. The main idea is to decompose the radiative intensity
into three parts, each part is treated differently. The performances of the
semi-implicit method are presented, for both optically thin and thick regions,
as well as for the radiative shock problem. Comparisons with the semi-analytic
solution are given to verify the accuracy and asymptotic properties of the
method.
