Constraints on dynamically formed massive black holes in little red dots from X-ray non-detections

The existence of extremely massive and compact galaxies, also called little red dots (LRDs), at z greater than or similar to 2 challenges models of early structure formation, suggesting extremely rapid stellar and black hole (BH) assembly. These galaxies are efficient environments for rapid BH growth, but several LRDs show no evidence of strong emission from the active galactic nuclei in X-rays. Our work uses a subsample of X-ray non-detected LRDs to determine whether the collision-based BH formation scenario is compatible with the non-detections and to constrain the physical parameters (e.g., metallicity) and observational parameters (e.g., column density). Our results show that LRDs might be ideal birthplaces for the formation of massive BHs, particularly in the case of a mass-radius relation R-gal proportional to M-gal(0.6) (similar to spiral galaxies in the local Universe). Given the high stellar densities, collision-based models suggest seed masses greater than those observed in the local Universe, and these are compatible with the mass-radius relation of high-redshift BHs. We modeled the BH seed formation and subsequent X-ray emission to investigate the physical and observational parameter space to compare with the observed X-ray upper limits in the soft (0.3 - 2 keV) and hard band (2 - 7 keV). We found that exponents in the mass-radius relation above 0.55 favor the collision-based scenario, but consistency with the stacked X-ray analysis requires specific combinations of accretion and obscuration parameters. Additionally, we found that constant or increasing star formation rate scenarios assuming high Eddington ratios and long duty cycles are feasible, but require higher column densities and/or a higher level of metal enrichment in the shielding columns. Alternatively, moderate sub-Eddington accretion rates seem to be sufficient to reconcile the massive seeds with their final observed masses, consistent with the observed X-ray weakness. Overall, we conclude that even if LRDs were initially starburst galaxies, they should evolve into an active galactic nucleus.