Bence Kocsis, Zoltan Haiman, Abraham Loeb
Many astrophysical binaries, from planets to black holes, exert strong torques on their circumbinary accretion disks, and are expected to significantly modify the disk structure. Despite the several decade long history of the subject, the joint evolution of the binary + disk system has not been modeled with self-consistent assumptions for arbitrary mass ratios and accretion rates. Here we solve the coupled binary-disk evolution equations analytically in the strongly perturbed limit, treating the azimuthally-averaged angular momentum exchange between the disk and the binary and the modifications to the density, scale-height, and viscosity self-consistently, including viscous and tidal heating, diffusion limited cooling, radiation pressure, and the orbital decay of the binary. We find a solution with a central gap and a migration rate similar to those previously obtained for Type-II migration, applicable for large masses and binary separations, and near-equal mass ratios. However, we identify a distinct new regime, applicable at smaller separations and masses, and mass ratio in the range 0.001< q < 0.1. For these systems, gas piles up outside the binary's orbit, but rather than creating a cavity, it continuously overflows as in a porous dam. The disk profile is intermediate between a weakly perturbed disk (producing Type-I migration) and a disk with a gap (with Type-II migration). However, the migration rate of the secondary is typically slower than both Type-I and Type-II rates. We term this new regime "Type-I.5" migration.
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http://arxiv.org/abs/1205.4714
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