Brightening of an Accretion Disk due to Viscous Dissipation of Gravitational Waves during the Coalescence of Supermassive Black Holes

Mergers of supermassive black hole binaries release peak power of up to $\sim {10}^{57}\mathrm{erg}{\mathrm{s}}^{-1}$ in gravitational waves (GWs). As the GWs propagate through ambient gas, they induce shear and a small fraction of their power is dissipated through viscosity. The dissipated heat appears as electromagnetic (EM) radiation, providing a prompt EM counterpart to the GW signal. For thin accretion disks, the GW heating rate exceeds the accretion power at distances farther than $\sim {10}^3$ Schwarzschild radii, independently of the accretion rate and viscosity coefficient.

Figure 1

The radiative diffusion time, $t_{\mathrm{diff}}$, over the geometric light travel time, $r/c$, as a function of radius for various $\alpha$-models with $\alpha =0.3$. The solid and dashed curves correspond to $\dot{m}=0.1$ and 1, respectively. Two sets of curves are shown for $M_7=1$ and 10, respectively, with the lower mass corresponding to the lower curves.

Figure 2

The excess luminosity curve before ($t<0$) and after ($t>0$) the binary coalescence event, relative to the luminosity of the punctured disk. The time axis is shown on a logarithmic scale at both negative and positive values (in units of $r_S$ at the bottom or ‘$M_7$ days’ at the top). The solid and dashed curves correspond to cases where the accretion disk is face on or edge on, respectively. The top curve applies if the cooling time is shorter than the geometrical delay $r/c$ at each radius, while the bottom curve show the case where disk cooling is limited by photon diffusion. The dotted curve depicts $L_{-3}^{\mathrm{GW}}(t)$ for reference. The $y$ axis is normalized by the luminosity of the punctured disk for a cavity radius, $r_{\min }={10}^2{r}_{\min ,2}{r}_S$.