How long do high-redshift massive black hole seeds remain outliers in black hole vs. host galaxy relations?

The existence of $10^9\ {\rm M_\odot}$ supermassive black holes (SMBHs) within the first billion years of the universe remains a puzzle in our conventional understanding of black hole formation and growth. Several suggested formation pathways for these SMBHs lead to a heavy seed, with an initial black hole mass of $10^4-10^6~{\rm M_\odot}$. This can lead to an overly massive BH galaxy (OMBG), whose nuclear black hole's mass is comparable to or even greater than the surrounding stellar mass: the black hole to stellar mass ratio is $M_{\rm bh}/M_* \gg 10^{-3}$, well in excess of the typical values at lower redshift. We investigate how long these newborn BHs remain outliers in the $M_{\rm bh}-M_{*}$ relation, by exploring the subsequent evolution of two OMBGs previously identified in the \texttt{Renaissance} simulations. We find that both OMBGs have $M_{\rm bh}/M_* > 1$ during their entire life, from their birth at $z\approx 15$ until they merge with much more massive haloes at $z\approx 8$. We find that the OMBGs are spatially resolvable from their more massive, $10^{11}~{\rm M_\odot}$, neighboring haloes until their mergers are complete at $z\approx 8$. This affords a window for future observations with {\it JWST} and sensitive X-ray telescopes to diagnose the heavy-seed scenario, by detecting similar OMBGs and establishing their uniquely high black hole-to-stellar mass ratio.