Eccentricity of supermassive black hole binaries coalescing from gas rich mergers

Angular momentum loss to circumbinary gas provides a possible mechanism for overcoming the `last parsec' problem and allowing the most massive black hole binaries formed from galactic mergers to coalesce. Here, we show that if gas disks also catalyze the merger of the somewhat lower mass binaries detectable with the Laser Interferometer Space Antenna (LISA), then there may be a purely gravitational wave signature of the role of gas in the form of a small but finite eccentricity just prior to merger. Numerical simulations suggest that eccentricity, excited by the interaction between the binary and surrounding gas disk, is only partially damped during the final phase of gravitational radiation-driven inspiral. We estimate that the typical eccentricity at one week prior to coalescence is of the order of 0.01. Higher terminal eccentricities, which can approach 0.1, are possible if the binary has an extreme mass ratio. The detection of even a small eccentricity prior to merger by LISA provides a possible discriminant between gas-driven inspirals and those effected by stellar processes.