Abstract
ABSTRACT There are increasing interests in binary supermassive black holes (SMBHs), but merging binaries with separations smaller than $\sim 1\,$ light-days ($\sim 10^{2}\,$ gravitational radii for 108 M⊙), which are rapidly evolving under control of gravitational waves, are elusive in observations. In this paper, we discuss fates of mini-discs around component SMBHs for three regimes: (1) low rates (advection-dominated accretion flows: ADAFs); (2) intermediate rates; (3) super-Eddington accretion rates. Mini-discs with intermediate rates are undergoing evaporation through thermal conduction of hot corona forming a hybrid radial structure. When the binary orbital periods are shorter than sound propagation time-scales of the evaporated mini-discs, a new instability, denoted as sound instability, arises because the discs will be highly twisted so that they are destroyed. We demonstrate a critical separation of Acrit(∼102Rg) from the sound instability of the mini-discs and the cavity is full of hot gas. For those binaries, component SMBHs are accreting with Bondi mode in the ADAF regime, showing periodic variations resulting from Doppler boosting effects in radio from the ADAFs due to orbital motion. In the mean while, the circumbinary discs (CBDs) are still not hot enough (ultraviolet deficit) to generate photons to ionize gas for broad emission lines. For slightly super-Eddington accretion of the CBDs, Mg ii line appears with decreases of UV deficit, and for intermediate super-Eddington Balmer lines appear, but C iv line never unless CBD accretion rates are extremely high. Moreover, if the CBDs are misaligned with the binary plane, it is then expected to have optical periodical variations with about ten times radio periods.
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