Three Dimensional MHD Simulation of Circumbinary Accretion Disks: Disk   Structures and Angular Momentum Transport
  We present the first three-dimensional magnetohydrodynamic (MHD) simulations of a circumbinary disk surrounding an equal mass binary. The binary maintains a fixed circular orbit of separation $a$. As in previous hydrodynamical simulations, strong torques by the binary can maintain a gap of radius $\simeq 2a$. Streams curve inward from $r \simeq 2a$ toward the binary; some of their mass passes through the inner boundary, while the remainder swings back out to the disk. However, we also find that near its inner edge the disk develops both a strong $m=1$ asymmetry and growing orbital eccentricity. Because the MHD stresses introduce more matter into the gap, the total torque per unit disk mass is $\simeq 14$ times larger than found previously. The inner boundary accretion rate per unit disk mass is $\simeq 40$ times greater than found from previous hydrodynamical calculations. The implied binary shrinkage rate is determined by a balance between the rate at which the binary gains angular momentum by accretion and loses it by gravitational torque. The large accretion rate brings these two rates nearly into balance, but in net, we find that $\dot a/a < 0$, and its magnitude is about 2.7 times larger than predicted by the earlier hydrodynamic simulations. If the binary comprises two massive black holes, the accretion rate may be great enough for one or both to be AGN, with consequences for the physical state of the gas both in the disk body and in its inner gap. 
Ji-Ming Shi, Julian H. Krolik, Stephen H. Lubow, and John F. Hawley
astro-ph.HE astro-ph.GA