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 cavity 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 10 ^ { -3 } \lesssim q \lesssim 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-1.5 ” migration .