The $M_{*}-M_{\rm BH}$ Relation Evolution from z $\sim$ 6 to the Present Epoch

The ratio between the stellar mass of a galaxy, $M_{*}$, and that of its central supermassive black hole (SMBH), $M_\bullet$, the ``Magorrian'' relationship, traces their coevolution. JWST observations have suggested significant evolution in $M_\bullet/M_{*}$ relative to local scaling relationships both in low-mass galaxies and in quasars at z $\ge$ 4. We test this possibility by (1) determining the preferred $M_\bullet/M_{*}$ scaling relation among those proposed locally; and (2) providing uniform host galaxy stellar mass estimates. These steps reduce the prominence of the reported evolution. We then apply Monte Carlo simulations to account for observational biases. We still find a significant increase over the local scaling relation in $M_\bullet/M_{*}$ for z $\ge$ 4 SMBHs in very low-mass galaxies ($\log(M_*/M_{\odot})<10$). However, similarly high values of $M_\bullet/M_{*}$ are also found in low mass galaxies at $z \sim$ 0.5 to 3 that may be common at cosmic noon. Nonetheless, galaxies with similar behavior are rare locally and not accounted for in the local scaling relations. In contrast, z $\sim$ 6 quasars can have $M_\bullet/M_{*}$ well above the local relation value, but they can be explained as extreme cases still within the scaling relation for their higher mass host galaxies. Black holes in some of them and in the low-mass systems may be undergoing very high accretion episodes that result in high $M_\bullet/M_{*}$ but that will be followed by quiescent periods when growth of the host drives the systems toward more typical $M_\bullet/M_{*}$ values.