Constraints from dwarf galaxies on black hole seeding and growth models with current and future surveys

Dwarf galaxies are promising test beds for constraining models of supermassive and intermediate-mass black holes (MBH) via their black hole occupation fraction (BHOF). Disentangling seeding from the confounding effects of mass assembly over a Hubble time is a challenging problem, that we tackle in this study with a suite of semi-analytical models (SAMs). We show how measured BHOF depends on the lowest black hole mass or AGN luminosity achieved by a survey. To tell seeding models apart, we need to detect or model all AGN brighter than $10^{37}\ \rm{erg \ s^{-1}}$ in galaxies of $M_* \sim 10^{8-10} \ \rm{M_{\odot}}$. Shallower surveys, like eRASS, cannot distinguish between seed models even with the compensation of a much larger survey volume. We show that the AMUSE survey, with its inference of the MBH population underlying the observed AGN, strongly favors heavy seed models, growing with either a power-law Eddington Ratio Distribution Function (ERDF) or one in which black hole accretion is tagged to the star-formation rate (AGN-MS). These two growth channels can then be distinguished by the AGN luminosity function at $> 10^{40}\ \rm{erg \ s^{-1}}$, with the AGN-MS model requiring more accretion than observed at z $\sim$ 0. Thus, current X-ray observations favour heavy seeds whose Eddington ratios follow a power-law distribution. The different models also predict different radio scaling relations, which we quantify using the fundamental plane of black hole activity. We close with recommendations for the design of upcoming multi-wavelength campaigns that can optimally detect MBHs in dwarf galaxies.