On the orbital evolution of binaries with polar circumbinary disks

Binaries occur in many astrophysical systems, from young protostellar binaries in star forming regions to supermassive black hole binaries in galaxy centers. In many cases, a circumbinary disk of gas forms around the binary with an orbit that may be misaligned to the binary plane. Misaligned disks around nearly circular binaries evolve into disks that are either aligned or counteraligned with the binary orbit. However, if the binary is sufficiently eccentric, then it can be more likely that the disk ends up in a polar-aligned configuration in which the disk angular momentum vector aligns with the binary eccentricity vector. We use Smoothed Particle Hydrodynamics simulations, evolved to an approximate steady state under mass injection, to determine the orbital evolution of a binary with a polar-aligned disk for a range of binary-disk parameters. We find that, in all of the cases we have simulated, the binary shrinks with time. The decay rate is larger than for binaries surrounded by aligned or retrograde disks with matched disk parameters. The rate of shrinkage is largely unaltered by the size of the sink radii employed for the binary stars, but for small enough sink radii some of the models exhibit long-lived polar circumprimary disks, which are continually fed mass from the circumbinary disk. We discuss our results in the contexts of planet formation in young polar-aligned disks and merging supermassive black holes in galaxy centers.