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

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 key dependencies on temperature, density, and ionization. We solve the vertically hydrostatic energy balance equations with Rosseland mean opacities from free-free absorption, bound-free absorption, and electron scattering processes, combined with ionization fractions derived 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. Inclusion of bound-free opacity introduces a noticeable flattening and a mid-frequency peak in the spectral energy distribution. We also 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. By comparing model spectra with detection limits of Subaru, JWST, and Swift, we find that systems within $\sim10$ Mpc may show detectable IR excess from the CBD. Our results highlight the need for accurate opacity modeling to interpret electromagnetic signatures of black hole mergers and support future integration of opacity tables with metallicity.