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

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.