Synthetic Spectral Library of Optically Thick Atmospheres for Little Red Dots

Little Red Dots (LRDs) challenge conventional models of active galactic nuclei. At rest-optical-to-near-infrared (IR) wavelengths, these compact extragalactic objects show blackbody-like continuum emission and spectral features reminiscent of stars, motivating models with an optically thick atmosphere at $T_{\text{\hspace{0.17em}⁣}\mathrm{e}\mathrm{f}\mathrm{f}}\sim 4000-5000\mathrm{K}$. We develop (and publicly release) a synthetic spectral library of optically thick atmospheres with gas conditions tailored for LRDs, parameterized by effective temperature $T_{\text{\hspace{0.17em}⁣}\mathrm{e}\mathrm{f}\mathrm{f}}$ and surface gravity $g$. Given the uncertain dynamical structure of LRDs, we interpret $g$ most directly as a photospheric density ${\rho }_{\text{\hspace{0.17em}⁣}\mathrm{p}\mathrm{h}}$. We show that blackbodies are only crude approximations to the emission from LRD-like atmospheres. Spectral features are abundant, many of which are sensitive diagnostics of photospheric density, including the overall curvature of the spectral energy distribution, the rest-$1.6\mu \mathrm{m}$ spectral ‘‘kink’’ from ${\mathrm{H}}^{-}$ opacity, and the Ca II triplet (CaT) absorption at rest-8500 $\text{unicode}x212B$. When compared against a local LRD, \egg, all three features consistently indicate a low photospheric density of ${\rho }_{\text{\hspace{0.17em}⁣}\mathrm{p}\mathrm{h}}\sim {10}^{-11}\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$ ($g\sim {10}^{-3}\mathrm{c}\mathrm{m}{\mathrm{s}}^{-2}$ in our library). This disfavors hydrostatic configurations and suggests a mass within the photosphere (black hole plus gas) of ${10}^4{M}_{\odot }$, with an Eddington ratio ${\lambda }_{\mathrm{E}\mathrm{d}\mathrm{d}}\gtrsim 20$, if the CaT width traces turbulent support at the photosphere in spherical symmetry; the inferred mass could be higher depending on the geometry and the radius probed by CaT. For higher redshift LRDs, we advocate for rest-near-IR spectroscopic surveys and high-resolution spectra of potential absorption lines as a test of the optically thick atmosphere scenario and as a unique probe of the central engine mass.