Extreme Values of Black Hole to Stellar Mass Ratio for High-Redshift Galaxies

Abstract

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 $\sim0.24$ 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.

Figures (3)

• Figure 1: Plots of the black hole mass function (top) from Taylor2024 and the stellar mass function (bottom) from Navarro-Carrera24. The black hole mass function is given in a single redshift bin $z\sim4-8$, whereas the stellar mass function is given in the binned redshift range $z = 3.5- 8.5$. Both are Schechter functions of the form given in Eq. \ref{['schechter']}.
• Figure 2: Plot of the EVS prediction for the extreme ratio $M_{BH}/M_*$ for redshift bins in the range $z = 3.5 - 8.5$. The values for $M_{BH}$ and $M_*$ are calculated using the extreme-value modelling of the mass functions from Taylor2024 and Navarro-Carrera24 respectively. The solid black line corresponds to the median, whilst the darker/lighter shaded area corresponds to the $95^{th}$/$99^{th}$ percentile. (See values in Table \ref{['table']}.) The data points are from mattheeyuekokorev, showing consistency with our EVS-derived estimates.
• Figure 3: Plot of black hole mass against stellar mass. the blue dashed line corresponds to the calculated ratio $M_{\,\textrm{BH}}/M_*$ for the redshift range $5.5\lesssim z \lesssim 6.5$, where we plot the median value of $M_{\,\textrm{BH}}/M_* \sim 0.35$. The ellipses show the distribution of the calculated extreme masses, providing an upper bound on both black hole and stellar mass. We include the data points from yue in this redshift range, along with their provided error bars.