Limiting eccentricity of subparsec massive black hole binaries surrounded by self-gravitating gas discs

Abstract

We study the dynamics of supermassive black hole binaries embedded in circumbinary gaseous discs, with the smoothed particle hydrodynamics code gadget-2. The subparsec binary (of total mass M and mass ratio q= 1/3) has excavated a gap and transfers its angular momentum to the self-gravitating disc (Mdisc= 0.2M). We explore the changes of the binary eccentricity, e, by simulating a sequence of binary models that differ in the initial eccentricity e0 only. In initially low-eccentric binaries, the eccentricity increases with time, while in high-eccentric binaries e declines, indicating the existence of a limiting eccentricity ecrit that is found to fall in the interval [0.6, 0.8]. We also present an analytical interpretation for this saturation limit. An important consequence of the existence of ecrit is the detectability of a significant residual eccentricity eLISA by the proposed gravitational wave detector Laser Interferometer Space Antenna (LISA). It is found that at the moment of entering the LISA frequency domain eLISA~ 10-3-10-2, a signature of its earlier coupling with the massive circumbinary disc. We also observe large periodic inflows across the gap, occurring on the binary and disc dynamical time-scales rather than on the viscous time. These periodic changes in the accretion rate (with amplitudes up to ~100 per cent, depending on the binary eccentricity) can be considered a fingerprint of eccentric subparsec binaries migrating inside a circumbinary disc. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.