A simple toy model for the electromagnetic variability of lump-dominated circumbinary disks around binary black holes

TL;DR

This paper introduces a simple toy model to predict electromagnetic variability in circumbinary disks around binary black holes, aiding observational efforts by providing a computationally inexpensive alternative to complex simulations.

Contribution

The paper presents a novel, simplified toy model for electromagnetic variability in circumbinary disks, capturing key features and compatible with detailed simulations, useful for observational testing.

Findings

The model reproduces main lightcurve features observed in simulations.

Lump modulation at a few times the orbital period is detectable with current telescopes.

Detectability of lump modulation depends on black hole mass and observation duration.

Abstract

The electromagnetic detection of circumbinary disks around pre-merger binary black holes (BBHs) relies on theoretical predictions. These are generally obtained through expensive numerical simulations, but simple or fast toy models are lacking to unleash the potential of these theoretical advances for observational purposes. We aim to present a simple toy model to compute the electromagnetic variability of circumbinary disks around circular-orbit BBHs at relativistic separations, focusing on the impact of disk non-axisymmetries. We assume that the disk is threaded by spiral arms and hosts a hotspot linked to an overdense structure (the {\lq}lump{\rq}) preferably reported in binaries close to equal mass. We build a simple temperature distribution, and estimate its thermal emission, perceived by a distant observer, via a ray-tracing code in a BBH approximate metric. We propose a toy model reproducing the main lightcurve features and show it is consistent with 2D general-hydrodynamical simulations under the assumption of compressional heating and expansional cooling except for purely dynamical effects such as the binary-lump beat. The lightcurve exhibits a main modulation at the lump's period (i.e. a few times the orbital period), due to relativistic Doppler effect, and a shorter one at the orbital-like period, due to spiral arms or the beat. These are more prominent in the optical/UV band for a total binary mass $M\, {=} \, 10^{4-10}\mathrm{M_\odot}$, where the disk energy spectrum peaks. For $M=10^{9}\mathrm{M_\odot}$, a $4\%$-amplitude lump modulation is detectable with the Vera Rubin Observatory after six months of observation, up to $z\, {=}\, 0.5$. We proposed a new, simple toy model that can be used, for instance, to test the compatibility of the periodicity of BBH candidate sources with a circumbinary disk origin.