Testing the BH* model: A UV-to-optical spectral fitting of The Cliff
In the BH* framework, the 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 the radiation and emits as a ~5,000 K blackbody, producing the optical continuum. Meanwhile, the UV is powered by a low-mass, dust-free, metal-poor host. The BH* model is promising but 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 tested 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 it 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, and affected by non-negligible dust attenuation ($A_V$~0.5 mag) acting on both stellar and nebular components. Higher $M_\star$ (up to log $M_\star/M_\odot$~8.1) and attenuations (up to $A_V$~1 mag) are obtained depending on the assumed dust law. Modest AGN UV leakage is consistently allowed-and sometimes preferred-by the code but remains weak and not robustly constrained, with both AGN+host and host-dominated UV scenarios yielding statistically equivalent fits. The SFH of the host is relatively smooth, with the galaxy already assembling log $M_\star/M_\odot$~7 about 200 Myr before $z=3.55$. The BH-to-$M_\star$ ratio consistently 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 in this LRD.