Radiation Magnetohydrodynamic Simulation of sub-Eddington Circumbinary Disk in a 10:1 Massive Black Hole Binary

TL;DR

This work presents a global RMHD simulation of a sub-Eddington circumbinary disk around a $2\times10^{7}\,M_{\odot}$ MBHB with mass ratio $q=0.1$ at $a=100\,r_g$, comparing to an equivalent MHD run and an equal-mass RMHD case. Radiation makes the CBD thinner, denser, and more filamentary, while reducing inner-edge eccentricity and lowering the overall accretion rate. The unequal-mass configuration yields significantly brighter and more variable far-UV/soft X-ray emission, with a light-curve modulation near twice the binary orbital frequency, in contrast to the equal-mass case. The results underscore the importance of radiation in shaping CBD structure and EM signatures, and they lay groundwork for EM counterpart templates to LISA precursors and heavier PTA binaries.

Abstract

We present a global three-dimensional radiation magnetohydrodynamic (RMHD) simulation of a circumbinary disk (CBD) around a massive black hole binary (MBHB) with a total mass $2 \times 10^7\,M_{\odot}$ and mass ratio $0.1$, separated by $100\, GM_{\rm tot}/c^2$. The inclusion of radiation makes the disk thinner, denser, less eccentric at the inner edge, and more filamentary when compared to an otherwise identical locally isothermal MHD disk. The RMHD disk has accretion rate $\sim 0.23\,\dot{M}_{\mathrm{Edd}}$ and produces thermal emission peaking in the near-UV/optical with a luminosity of $\sim 1\, \% L_{\rm {Edd }}$. Compared with an equal-mass binary with the same total mass, the thermal emission of the CBD around the unequal-mass binary is several orders of magnitude brighter and much more variable at far-UV/soft X-rays frequencies. Similarly, we find that the light curve associated with the $0.1$ mass ratio binary exhibits dominant periodicity corresponding to 2 binary orbits, compared to the equal-mass binary that shows periodicity at 2.5-5 binary orbits. Our results highlight the importance of radiation for the structure and observational properties of MBHB circumbinary disks and have implications for detecting electromagnetic counterparts to LISA gravitational wave precursors and for the heavier binaries targeted by the Pulsar Timing Arrays.

Figures (8)

• Figure 1: Top: Gas density in the mid-plane of the disk for the MHD and the RMHD run, showing the denser and more filamentary nature of the disk when radiation is included. Bottom: Vertical slice showing density in the MHD and RMHD runs. The RMHD disk is visibly thinner than the isothermal MHD disk. Both snapshots correspond to a time of approximately 80 binary orbits.
• Figure 2: Top: The time and shell-averaged radial disk eccentricity profile for the MHD run (in blue) and the RMHD run (orange). The time averaging was done over the time window of 75-80 binary orbits. Bottom: The time evolution of the inner edge eccentricity in the radial range of $170\,r_g$ to $370\,r_g$ for the MHD (blue) and the RMHD (orange) runs.
• Figure 3: Top Left: The total mass accretion rate through the inner edge of the simulation domain at $r=100\,r_{\rm g}$ from 60-80 binary orbits for the MHD run (blue) and the RMHD run (orange). Bottom Left: The power spectral density of the mass accretion rate for the MHD and the RMHD simulations calculated in the same time window. Top Right: Luminosity curves calculated on the hemispheres located at $r/r_{\rm g}$ = 150, 200, 300 in the RMHD run. Bottom Right: Power spectral density calculated after normalizing the light curves showing a prominent mode at $\approx$ 0.5 $\Omega_{\rm bin}$.
• Figure 4: Left: Mass accretion rate onto the primary (green) and the secondary (purple) scaled by the individual MBHs Eddington limit for the MHD run. Right: Same as the left panel but for the RMHD run, showing that the secondary accretes at a super-Eddington rate, as in the MHD run.
• Figure 5: Ratio of mass accretion rates onto the MBHs ($\dot{M}_2/\dot{M}_1$) for MHD (blue) and RMHD (blue) simulations. The horizontal gray line marks $\dot{M}_2/\dot{M}_1$=1.