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Radiatively inefficient accretion flows induced by gravitational-wave emission before massive black hole coalescence

We study an accretion flow during the gravitational-wave driven evolution of binary massive black holes. After the binary orbit decays due to an interaction with a massive circumbinary disk, the binary is decoupled from the circumbinary disk because the orbital-decay timescale due to emission of gravitational wave becomes shorter than the viscous timescale evaluated at the inner edge of circumbinary disk. During the subsequent evolution, the accretion disk, which is truncated at the tidal radius because of the tidal torque, also shrinks as the orbital decay. Assuming that the disk mass changed by this process is all accreted, the disk becomes radiatively inefficient when the semi-major axis is several hundred Schwarzschild radii. The high-energy radiations, in spite of a low bolometric luminosity, are emitted from an accretion disk around each black hole long before the black hole coalescence as well as the gravitational wave signals. The synchrotron process can notably produce potentially observable radio emissions at large distances if there is a strong, dipole magnetic field around each black hole. In unequal mass-ratio binaries, step-like light variations are seen in the observed light curve because the luminosity is higher and its duration time are shorter in the radio emission by the disk around the secondary black hole than those of the primary black hole. Such a precursor would be unique to not a single black hole system but a binary black hole system, and implies that binary black holes finally merge without accretion disks.