Accretion disks around binary black holes of unequal mass: General relativistic MHD simulations of postdecoupling and merger

We report results from simulations in general relativity of magnetized disks accreting onto merging black hole binaries, starting from relaxed disk initial data. The simulations feature an effective, rapid radiative cooling scheme as a limiting case of future treatments with radiative transfer. Here we evolve the systems after binary-disk decoupling through inspiral and merger, and analyze the dependence on the binary mass ratio with $q\equiv m_{\text{bh}}/M_{\mathrm{BH}}=1,1/2$, and $1/4$. We find that the luminosity associated with local cooling is larger than the luminosity associated with matter kinetic outflows, while the electromagnetic (Poynting) luminosity associated with bulk transport of magnetic field energy is the smallest. The cooling luminosity around merger is only marginally smaller than that of a single, nonspinning black hole. Incipient jets are launched independently of the mass ratio, while the same initial disk accreting on a single nonspinning black hole does not lead to a jet, as expected. For all mass ratios we see a transient behavior in the collimated, magnetized outflows lasting 2–5 $(M/10^8{M}_{\odot })$ days after merger: the outflows become increasingly magnetically dominated and accelerated to higher velocities, boosting the Poynting luminosity. These sudden changes can alter the electromagnetic emission across the jet and potentially help distinguish mergers of black holes in active galactic nucleus (AGNs) from single accreting black holes based on jet morphology alone.

Figure 1

Surface density $\mathrm{\Sigma }$ at decoupling (yellow solid lines) and immediately after merger, time averaged over $225M$ (corresponding to the initial binary orbital period) (black solid line with circles). $\mathrm{\Sigma }(r)$ is normalized to ${\mathrm{\Sigma }}_{0,\max }$—the maximum value of the surface density in the initial hydrostatic equilibrium solution used in [6]. In each panel the profile for the reference stationary single BH case is shown (gray solid line with dots).

Figure 2

Contours of rest-mass density ${\rho }_0$ normalized to the initial maximum ${\rho }_{\max }$ (log scale) in the equatorial plane corresponding to the time at decoupling (left), an intermediate time prior to merger (middle), and the moment following merger (right). Upper panels: Mass ratio $1:1$; ${\rho }_{\max }\simeq 2.1\times 10^{-11}(\frac{L_{\mathrm{b}}}{L_{\text{Edd}}}){(\frac{M}{10^8{M}_{\odot }})}^{-1}{(\frac{\epsilon }{0.13})}^{-1}\mathrm{g}{\mathrm{cm}}^{-3}$. Middle panels: Mass ratio $1:2$; ${\rho }_{\max }\simeq 4.2\times 10^{-11}(\frac{L_{\mathrm{b}}}{L_{\text{Edd}}}){(\frac{M}{10^8{M}_{\odot }})}^{-1}{(\frac{\epsilon }{0.08})}^{-1}\mathrm{g}{\mathrm{cm}}^{-3}$. Lower panels: Mass ratio $1:4$; ${\rho }_{\max }\simeq 3.75\times 10^{-11}(\frac{L_{\mathrm{b}}}{L_{\text{Edd}}}){(\frac{M}{10^8{M}_{\odot }})}^{-1}\mathrm{g}{\mathrm{cm}}^{-3}$. $L_{\mathrm{b}}=L_{\mathrm{EM}}+L_{\text{cool}}$ is the bolometric radiative luminosity at decoupling.

Figure 3

Total accretion rate, luminosities normalized to the single BH accretion rate, and GW strain ($+$ polarization) as functions of time. For ${\epsilon }_{\mathrm{EM}}$, ${\epsilon }_{\text{kin}}$, and $h^{+}$, $t$ is the retarded time. Red (dark grey in black and white) solid line: $1:1$; yellow (light grey in black and white) solid line: $1:2$; black solid line: $1:4$. The vertical lines indicate the corresponding merger times.

Figure 4

Contributions to the cooling luminosity $L_{\text{cool}}$ from various spherical regions. Left panel: $1:1$. Middle panel: $1:2$. Right panel: $1:4$.

Figure 5

Contours of $b^2/2{\rho }_0$ (log color scale) in a meridional slice, at merger (left panels), $100M$ after merger (middle panels), $400M$ after merger (right panels). Upper panels: $1:1$. Middle panels: $1:2$. Lower panels: $1:4$.

Figure 6

Volume rendering of rest-mass density, normalized to its initial maximum value ${\rho }_{0,\max }$ (see color coding), and magnetic field lines for the $1:1$ case. Left panels: Halfway through the inspiral $t-t_m=500M$. Right panels: Time $t-t_m\sim 100M$ after merger. Top panels: Global view out to $r/M\sim 150M$. Bottom panels: Close-up view within $r/M\sim 20M$. White field lines emanate from the BH apparent horizons. Green (black in black and white) field lines emanate from the disk. The blue (dark grey in black and white) background indicates densities less than $10^{-5}{\rho }_{0,\max }$. Incipient jets are launched above each BH, merge at larger radii, and further collimate shortly after merger.