Implications of the Eccentric Kozai-Lidov Mechanism for Stars Surrounding Supermassive Black Hole Binaries

An enhanced rate of stellar tidal disruption events (TDEs) may be an important characteristic of supermassive black hole (SMBH) binaries at close separations. Here we study the evolution of the distribution of stars around a SMBH binary due to the eccentric Kozai-Lidov (EKL) mechanism, including octupole effects and apsidal precession caused by the stellar mass distribution and general relativity. We identify a region around one of the SMBHs in the binary where the EKL mechanism drives stars to high eccentricities, which ultimately causes the stars to either scatter off the second SMBH or get disrupted. For SMBH masses 10^7 Msun and 10^8 Msun, the TDE rate can reach 10^{-2} yr and deplete a region of the stellar cusp around the secondary SMBH in ~0.5 Myr. As a result, the final geometry of the stellar distribution between 0.01 and 0.1 pc around the secondary SMBH is a torus. These effects may be even more prominent in nuclear stellar clusters hosting a supermassive and an intermediate mass black hole.