Testing the BH$^*$ Model: a UV-to-Optical Spectral Fitting of The Cliff

Abstract

In the black hole star (BH*) model, the characteristic "V"-shaped SED of LRDs is produced by an accreting BH embedded in a dense neutral-gas envelope with a near-unity covering factor. This envelope reprocesses radiation and emits as a ~5,000K blackbody, producing the optical continuum. Meanwhile, the UV is powered by a low-mass, dust-free, metal-poor host. The BH* scenario is promising, but it has yet to undergo detailed testing; conducting a self-consistent UV-to-optical spectral-fitting analysis of LRDs would provide a robust assessment of the model. In this work, we test the BH* scenario by fitting the full JWST/NIRSpec PRISM spectrum of The Cliff ($z_{spec}=3.55$), an LRD that played a pivotal role in the development of this model. A Bagpipes fit that allows stellar, nebular, AGN, and blackbody components naturally yields a BH*-like solution for The Cliff, even with broad priors. Our method allows us to characterize its host, despite remaining unresolved in JWST imaging. From the continuum, we infer the host to be low-mass (log $M_\star/M_\odot$~7.7), star-forming, metal-poor, affected by non-negligible dust attenuation ($A_V$~0.5 mag) acting on both stellar and nebular components. Larger $M_\star$ (up to log $M_\star/M_\odot$~8.1) and attenuations (up to $A_V$~1 mag) are obtained depending on the assumed dust attenuation law. Modest AGN UV leakage is consistently allowed by the code, but remains weak and not robustly constrained, with both AGN+host and host-dominated UV scenarios yielding equivalent fits. The star formation history of the host is relatively smooth, with the galaxy already assembling log $M_\star/M_\odot$~7 about 200 Myr before $z_{spec}=3.55$. The BH-to-$M_\star$ ratio exceeds the values expected from BH-host scaling relations, especially at recent times. This tension may indicate either inaccurate estimates of the BH properties or non-coeval BH-host evolution.