Extreme Values of Black Hole to Stellar Mass Ratio for High-Redshift Galaxies
With recent data from the \emph{James Webb Space Telescope} (JWST), it is possible to calculate the mass of the supermassive black holes at the center of galaxies, and the stellar mass of the host galaxies at redshift $z \gtrsim 5$. In this work, we apply extreme-value statistics to calculate the distributions of extreme black-hole and stellar masses for galaxies in the redshift range $3 \lesssim z \lesssim 8$. We show that under certain assumptions about the stellar and black-hole mass functions, a high ratio of $M_\text{BH}/M_*\sim0.3-0.5$ can be obtained without invoking additional black-hole growth physics. Nevertheless, surveying a range of extreme-value methodologies, we find predictions of the extreme ratio $M_\text{BH}/M_*$ to still be in slight tension with the high values observed by JWST.