Disks around merging binary black holes: From GW150914 to supermassive black holes

We perform magnetohydrodynamic simulations in full general relativity of disk accretion onto nonspinning black hole binaries with mass ratio $q=29/36$. We survey different disk models which differ in their scale height, total size and magnetic field to quantify the robustness of previous simulations on the initial disk model. Scaling our simulations to LIGO GW150914 we find that such systems could explain possible gravitational wave and electromagnetic counterparts such as the Fermi GBM hard x-ray signal reported 0.4 s after GW150915 ended. Scaling our simulations to supermassive binary black holes, we find that observable flow properties such as accretion rate periodicities, the emergence of jets throughout inspiral, merger and postmerger, disk temperatures, thermal frequencies, and the time delay between merger and the boost in jet outflows that we reported in earlier studies display only modest dependence on the initial disk model we consider here.

Figure 1

Plots of surface density profile $\mathrm{\Sigma }(R)$ and disk scale height $H/R$ vs cylindrical coordinate radius $R$ for the three disk models. These initial disk models belong to a one-parameter family of models in which the parameter that varies is the specific angular momentum parameter ($l_{\mathrm{in}}$) at the disk inner edge, whose initial radius we fix at $20M$. For cases A–C we have $l_{\mathrm{in}}=5.25M$ (solid lines), $l_{\mathrm{in}}=5.15M$ (dashed lines), and $l_{\mathrm{in}}=5.05M$ (dot-dashed lines), respectively (see Table 2).

Figure 2

Top row: Contours of the ${\lambda }_{\mathrm{MRI}}$-quality factor $Q={\lambda }_{\mathrm{MRI}}/dx$ in the equatorial plane at $t=0$ for all cases. Bottom row: Rest-mass density contours (color coded) on a meridional slice, and ${\lambda }_{\mathrm{MRI}}/2$ (black solid line) at $t/M=0$ for all cases. The left column plots correspond to case A, the middle column to case B and the right column to case C. These plots demonstrate that with our grid choices we resolve the fastest growing MRI mode by $\gtrsim 10$ points in the bulk of the disks (the blue ring stems from the extremely small values of ${\lambda }_{\mathrm{MRI}}$ where the vertical component of the B field changes sign). The plots also demonstrate that ${\lambda }_{\mathrm{MRI}}/2$ mostly fits within the disks.

Figure 3

Volume rendering of rest-mass density, normalized to its initial maximum value ${\rho }_{0,\max }$ (see color coding), magnetic field lines (solid white curves), and velocity vectors (green arrows) at select times during the inspiral, merger and postmerger. Case A corresponds to the left column, case B to the middle column, and case C to the right column.

Figure 4

Volume rendering of magnetic-to-rest-mass energy density $\log (b^2/2{\rho }_0)$ for case B. The white lines indicate the magnetic field lines corresponding to the B field measured by a normal observer.

Figure 5

The Poynting luminosity $L_{\mathrm{EM}}$ and accretion rate $\dot{M}$ vs time for all cases and the strain of the “plus” polarization of the gravitational waveform $h_{+}$. The GWs are computed as described in [78]. The dotted-dashed lines on the top panel indicate the expected Blandford-Znajek luminosity from a single BH with the same mass, spin and quasistationary polar magnetic field strength as found for each case. The normalization ${\dot{M}}_{\mathrm{eq}}$ in each panel is the time-averaged accretion rate onto the postmerger remnant black hole over the last 500M of the evolution. The displacements in the dashed vertical merger line in the luminosity and GW plots with respect to the merger lines in the accretion plots accounts for the light travel time between the BH and the radiation extraction radii.

Figure 6

GBM flux vs time for each case assuming the source lies at redshift $z=0.09$. The dashed vertical line is the time at which the binary merges as measured by the observer. The horizontal line shows the sensitivity of Fermi GBM.