Spectral Properties of Irradiated Circumbinary Disks around Binary Black Holes Governed by Hydrogen Opacities Dependent on Temperature and Density

TL;DR

This work develops a physically motivated, hydrogen-opacity–based model for irradiated circumbinary disks around BBHs, solving a 1D, azimuthally averaged energy balance with gas pressure and self-consistent ionization via the Saha equation. By comparing four opacity prescriptions (including a no-opacity baseline), it demonstrates that opacity strongly shapes the CBD midplane temperature and, especially in the irradiation-dominated outer disk, the IR/optical spectral energy distribution, with bound-free absorption (Model 3) enhancing IR reprocessing. The results show that the CBD+minidisk system typically yields a double-peaked SED, where the high-frequency peak comes from hot minidisks and the low-frequency IR peak from irradiated CBD layers; the IR component is most detectable for nearby sources with JWST/Subaru when using the most opacity-rich prescription. Observational prospects are discussed for JWST, Subaru, and Swift, and the study discusses LISA detectability across mass scales, highlighting the need for opacity-aware models and motivating the inclusion of metallicity-dependent opacities in future work to connect EM signatures with BBH coalescence events.

Abstract

We study the thermal and spectral properties of irradiated circumbinary disks (CBDs) around binary black holes (BBHs), using analytic, hydrogen-based opacity models that capture dependencies on temperature, density, and ionization. We solve the vertical hydrostatic equilibrium and energy balance, assuming gas pressure only, using Rosseland-mean opacities from free-free and bound-free absorption plus electron scattering, with ionization fractions given by the Saha equation. Four opacity models are considered, including a reference model with no physical opacity, constructed by Lee et al. (2024), and three physically motivated alternatives. The midplane temperature profiles show significant variation across models, while the surface temperature remains largely unchanged in regions dominated by viscous heating. Opacity effects become pronounced in the outer disk, where irradiation reprocessing shapes the IR-optical continuum. Bound-free opacity introduces flattening and a mid-frequency peak in the spectral energy distribution. We compute spectra of a triple disk system including the CBD and two accreting minidisks. The high-frequency peak arises from the hot minidisks, while the low-frequency excess originates from irradiated outer CBD layers. Comparing model spectra with detection limits of Subaru, JWST, and Swift, we find that BBH systems within ~10 Mpc can exhibit a detectable IR excess. Our results highlight the need for physically consistent opacity modeling to interpret electromagnetic (EM) signatures of BBHs approaching coalescence and support integration of metallicity-dependent opacity tables. Our opacity-informed framework for irradiated CBDs provides an EM template for identifying stellar- to intermediate-mass BBHs in a mass range sparsely sampled by LISA, thereby bridging the gravitational-wave-EM gap with testable IR/optical signatures.

Figures (10)

• Figure 1: Schematic illustration of an irradiated circumbinary disk (CBD) surrounding two minidisks orbiting the primary and secondary black holes. The minidisks, referred to as the circum-primary disk (CPD) and the circum-secondary disk (CSD), are gravitationally bound to the primary (BH1) and secondary (BH2) black holes, respectively. The yellow ochre, blue, and red shaded regions represent the CBD, CPD, and CSD, respectively. The two black circles at the center denote the black holes, with their common center of mass (CM) marked by a plus sign. The blue and red wavy arrows indicate the trajectories of irradiating photons emitted from the minidisks. The inner edge of the CBD is located at a radius $r_{\rm in} = C_{\rm gap} a$, where $C_{\rm gap}$ is a parameter characterizing the size of the gap between the CBD and the binary, and $a$ is the binary's semi-major axis.
• Figure 2: Analytic pure-hydrogen Rosseland-mean opacity $\kappa$ contributions as a function of the semi-major axis normalized by the Schwarzschild radius, $a/r_{\rm S}$. The opacities are evaluated for a pure-hydrogen CBD with $M=100\,M_\odot$, $Y=0.01$, and $\xi=10$. Colors denote the contributions from electron scattering multiplied by the ionization fraction ($x_e\kappa_{\rm es}$, black), free-free absorption ($\kappa_{\rm ff}$, red), and bound-free absorption ($\kappa_{\rm bf}$, blue). The black dashed curve shows the total opacity, $\kappa=x_{e}\kappa_{\rm es}+\kappa_{\rm ff}+\kappa_{\rm bf}$
• Figure 3: Radial temperature profiles of the CBD for the four opacity models in Table \ref{['tbl:opmodels']}. Panels (a) and (b) show the midplane temperature $T_{\mathrm c}$ and the surface temperature $T_{\mathrm s}$, respectively. Both quantities are plotted against the normalized radius $\xi$ on logarithmic axes. Solid curves correspond to Model 0 (black), Model 1 (blue), Model 2 (green), and Model 3 (red).
• Figure 4: SEDs of the CBD for the four opacity models listed in Table \ref{['tbl:opmodels']}. Panels (a)–(c) correspond to total binary masses of $100\,M_\odot$ (fiducial case), $10\,M_\odot$, and $1000\,M_\odot$, respectively. Each panel plots the normalized luminosity $\nu L_\nu/L_{\rm Edd}$ versus frequency on logarithmic axes. Solid curves indicate Model 0 (black), Model 1 (blue), Model 2 (green), and Model 3 (red); the dashed black curve reproduces Model 0 without external irradiation.
• Figure 5: Same format as Figure \ref{['fig:CBD_mass']} but for different outer disk radii, varying the outer radius $\xi_{\rm out}$ while keeping the binary mass fixed at $M=100\,M_\odot$. Panels (a)–(c) adopt $\xi_{\rm out}=10^{4}$ (fiducial case), $10^{3}$, and $10^{5}$, respectively; all other parameters are identical to those in Figure \ref{['fig:CBD_mass']}.