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In recent numerical simulations \citep{matsubayashi07,lockmann08}, it hasbeen found that the eccentricity of supermassive black hole(SMBH) -intermediate black hole(IMBH) binaries grows toward unity through interactionswith stellar background. This increase of eccentricity reduces the mergingtimescale of the binary through the gravitational radiation to the value wellbelow the Hubble Time. It also gives the theoretical explanation of theexistence of eccentric binary such as that in OJ287 \citep{lehto96,valtonen08}. In self-consistent N-body simulations, this increase ofeccentricity is always observed. On the other hand, the result of scatteringexperiment between SMBH binaries and field stars \citep{quinlan96} indicated noincrease of eccentricity. This discrepancy leaves the high eccentricity of theSMBH binaries in $N$-body simulations unexplained. Here we present astellar-dynamical mechanism that drives the increase of the eccentricity of anSMBH binary with large mass ratio. There are two key processes involved. Thefirst one is the Kozai mechanism under non-axisymmetric potential, whicheffectively randomizes the angular momenta of surrounding stars. The other isthe selective ejection of stars with prograde orbits. Through these twomechanisms, field stars extract the orbital angular momentum of the SMBHbinary. Our proposed mechanism causes the increase in the eccentricity of mostof SMBH binaries, resulting in the rapid merger through gravitational waveradiation. Our result has given a definite solution to the "last-parsecproblem".

Eccentric evolution of SMBH binaries