Light, heavy, primordial: exploring the diversity of black hole seeding and growth mechanisms in the JWST era

The James Webb Space Telescope (JWST) has revealed a puzzling population of massive black holes in the first billion years, many of which are over-massive compared to their hosts (obese black holes), and reside in metal-poor hosts, posing a challenge for theoretical models at these early epochs. In this work, we compare the observational properties of astrophysically-seeded black holes using the DELPHI semi-analytic model and cosmologically-seeded primordial black holes (PBHs) using the PHANES analytic model. We explore the growth of light ($\sim 100M_{\odot }$) and heavy ($\sim {10}^{3-5}{M}_{\odot }$) seeds through mergers and accretion (both Eddington-limited and at super-Eddington rates) in the astrophysical scenario; PBHs (seeded between ${10}^{0.5-6}{M}_{\odot }$) only grow through accretion at sub-Eddington rates. Comparing to observables at $z\sim 5-10$, the only model that can be ruled out is the one where we allow Eddington-limited accretion onto light seeds. The observed high values of the black hole mass-stellar mass relation ($0.3-1$) can be reproduced by both PBHs and heavy seeds accreting at super-Eddington rates. However, only the PBH and Eddington-limited heavy seeding models can simultaneously reproduce the observed black hole masses (${\mathrm{M}}_{\mathrm{b}\mathrm{h}}$), stellar masses ($M_{\ast }$), and extremely low host metallicities ($Z\le 0.01Z_{\odot }$) inferred at $z\sim 7-10$. Crucially, we find PBHs show decrease in the black hole mass-stellar mass ratio with increasing halo mass at all redshifts, contrary to any astrophysical black hole model. Selecting systems at $z\sim 7$ with ${\mathrm{M}}_{\mathrm{b}\mathrm{h}}\mathrm{/}{M}_{\ast }>0.1$ and bolometric luminosities $\sim {10}^{44-46}\mathrm{e}\mathrm{r}\mathrm{g}{\mathrm{s}}^{-1}$ that show a negative black hole to stellar mass ratio and reside in ${10}^{9-11}{M}_{\odot }$ halos offer a promising clustering-based discriminant of PBH seeding models.