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.
