Electromagnetic variability from circumbinary discs around binary black holes during their post-decoupling epoch

TL;DR

The paper addresses whether electromagnetic signatures, especially lump-driven variability in circumbinary discs around binary black holes, survive the post-decoupling epoch. It combines 2D general-relativistic hydrodynamics in an approximate near-zone spacetime with post-Newtonian inspiral trajectories and general-relativistic ray-tracing to produce synthetic UV/optical emission. A key finding is that the overdense lump, a dominant non-axisymmetric CBD feature, persists up to the end of the simulations for mass ratios $q\in\{0.3,1\}$, with an effective CBD viscosity $α_{\rm eff}\sim10^{-3}$–$2×10^{-2}$ and a lump-modulation period $P_{\rm lump}\sim6\,P_{\rm orb}$, amplified by relativistic beaming. The results imply potential UV signatures for LISA sources and offer a plausible origin for long-term optical periodicity in some PTA/optical BBH candidates, contingent on the disc viscosity.

Abstract

We present general-relativistic hydrodynamical simulations of inviscid circumbinary discs (CBDs) around near equal-mass binary black holes (BBH) in the binary-disc post-decoupling epoch. We use an approximate BBH spacetime with a post-Newtonian inspiral motion trajectory from ${\sim}80 (M/10^7 \mathrm{M_\odot}) \, \mbox{days}$ (separation of ${\sim}\,30$ gravitational radii) to ${\sim}100 (M/10^7 \mathrm{M_\odot}) \, \mbox{minutes}$ before merger. Initial data for the inspiral runs are produced from circular-orbits runs covering the formation timescale of the overdense {\lq}lump{\rq}, orbiting the CBD inner edge. The CBD non-axisymmetries (spiral waves and lump) lead to non-negligible angular momentum transport with effective viscosity ${α_\mathrm{eff} \, {\sim} \, 10^{-3}{- 2\times 10}^{-2}}$. We post-process these simulations with a general-relativistic ray-tracing code to obtain synthetic observations in thermal emission. We find the lump and its associated electromagnetic (EM) modulation, already reported in the pre-decoupling epoch, to survive post-decoupling up until the end of the simulation. For LISA sources, our findings point to an active EM signature in UV during optimal gravitational wave source localization. For PTA sources and current BBH candidates detected through their optical periodicity: the lump{ in a low-viscosity CBD is a possible, though not unique, origin} for the observed periodicity.

Figures (7)

• Figure 1: Temporal evolution of the orbital separation ${r_{12}}(t)$, in units of $M$. The $x-$axis indicates the time to merger for the inspiral runs, chosen to be the same for $q\, {=} \, 1$ and $q\, {=} \, 0.3$.
• Figure 2: Radial profile of the time-averaged effective kinematic (top panel, Eq. \ref{['eq:nueff']}) and $\alpha$ (bottom panel, Eq. \ref{['eq:alphaeff']}) viscosities (see the main text for the two different methods of calculation) at the time of starting the inspiral. The vertical dotted line is located at $r \, {=} \, 3\, r_{12,0}$ to help locating the bulk of the CBD.
• Figure 3: Density maps in the inspiral runs at ${\sim} 70 (M/10^7M_\odot)\, \hbox{days}$ (left column) and less than $1 (M/10^7M_\odot)\, \hbox{day}$ (near the end of the run, ${r_{12}} \, {=} \, 8\mathrm{M}$; right column) before merger for $q\, {=} \, 1$ (top) and $q\, {=} \, 0.3$ (bottom). Density contours are overplotted in gray. From the left to the right column, one can see how the grid inner boundary moves inward. The BH size is increased by $10$ for visibility.
• Figure 4: Azimuthally-averaged density profile at the start (dashed line) and end (full line) of the inspiral runs, for $q \, {=} \, 1$ (left) and $q \, {=} \, 0.3$ (right).
• Figure 5: Radius-time map of the density at $\phi \, {=} \, 0$ to show the evolution of non-axisymmetries post-decoupling, for $q\, {=} \, 0.3$. The gray curve indicates $2 \, r_{12}(t)$.