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 centre of galaxies, and the stellar mass of the host galaxies at $z\gtrsim 5$. In this work, we apply the method of extreme-value statistics to calculate the distributions of extreme black hole and stellar mass for the redshift range $3.5\lesssim z\lesssim 8.5$. We sample these distributions to obtain a prediction for the black hole to stellar mass ratio of $\sim 0.24$ over this redshift range, with the median in each bin varying in the range $0.18-0.35$. Our predictions are consistent with the highest observed values of the ratio from JWST observations of high-redshift galaxies.