Diagnosing the massive-seed pathway to high-redshift black holes: statistics of the evolving black hole to host galaxy mass ratio

Supermassive black holes (SMBHs) with masses of similar to 10(9) M-circle dot within the first billion year of the universe challenge our conventional understanding of black hole formation and growth. One pathway to these SMBHs proposes that supermassive stars born in pristine atomic cooling haloes yield massive seed BHs evolving to these early SMBHs. This scenario leads to an overly massive BH galaxy (OMBG), in which the BH to stellar mass ratio is initially M-bh/M-* >= 1, well in excess of the typical values of similar to 10(-3) at low redshifts. Previously, we have investigated two massive seed BH candidates from the Renaissance simulation and found that they remain outliers on the M-bh-M-* relation until the OMBG merges with a much more massive halo at z = 8. In this work, we use Monte-Carlo merger trees to investigate the evolution of the M-bh-M-* relation for 50 000 protogalaxies hosting massive BH seeds, across 10 000 trees that merge into a 10(12) M-circle dot halo at z = 6. We find that up to 60 per cent (depending on growth parameters) of these OMBGs remain strong outliers for several 100 Myr, down to redshifts detectable with JWST and with sensitive X-ray telescopes. This represents a way to diagnose the massive-seed formation pathway for early SMBHs. We expect to find similar to 0.1-1 of these objects per JWST Near Infrared Camera (NIRCam) field per unit redshift at z greater than or similar to 6. Recently detected SMBHs with masses of similar to 10(7) M-circle dot and low-inferred stellar-mass hosts may be examples of this population.