# The Redshift Evolution of the $M_\bullet-M_\star$ Relation for JWST's Supermassive Black Holes at $z > 4$

**Authors:** Fabio Pacucci, Abraham Loeb  
**arXiv:** [2401.04159](https://arxiv.org/abs/2401.04159)  
**Date:** 2024-01-08  
**Summary page:** https://www.summarizepaper.com/en/paper/2401.04159v1/

## Key points

- The James Webb Space Telescope (JWST) has discovered overmassive galactic systems at redshifts greater than 4
- These systems have black hole masses (M_bullet) that are 10 to 100 times larger than expected based on local relations and the stellar mass of their host galaxies (M_star)
- A model is proposed to explain these overmassive systems by suggesting that the mass of the black hole is the primary driver behind the quenching of star formation at high redshifts
- Supermassive black holes (SMBHs) have a global impact on their host galaxies at redshifts greater than 4
- Black hole mass growth is regulated by quasars, while stellar mass growth is suppressed by it and not correlated with overall properties of the host halo
- The ratio between M_bullet and M_star determines the average star formation efficiency, with a threshold value given by a complex equation involving gas density, cooling efficiency, Eddington fraction, baryon density parameter, matter density parameter, and halo mass
- Once this threshold ratio is surpassed, a runaway process occurs bringing these initially overmassive systems closer to the local relation between black hole mass and stellar mass (M_bullet - M_star)
- This relation evolves with redshift as proportional to (1+z)^(5/2), with an overmassive factor of around 55 found at a redshift of approximately 5
- Extending observations to higher redshifts and lower masses will help test this model and enhance our understanding of early co-evolution between black holes and galaxies.

## Summary

The James Webb Space Telescope (JWST) has made a significant discovery, detecting numerous overmassive galactic systems at redshifts greater than 4. These systems exhibit black hole masses (M_bullet) that are 10 to 100 times larger than expected based on local relations and the stellar mass of their host galaxies (M_star). In this study, the authors propose a model to explain these overmassive systems in the high-redshift universe by suggesting that the mass of the black hole is the primary driver behind the quenching of star formation at high redshifts. Supermassive black holes (SMBHs) have a global impact on their host galaxies due to their small size and duty cycles close to unity at redshifts greater than 4. The authors assume that while black hole mass growth is regulated by the output of quasars, stellar mass growth is suppressed by it and is not correlated with overall properties of the host halo. The ratio between M_bullet and M_star plays a crucial role in determining the average star formation efficiency. If this ratio exceeds a certain threshold value given by 8 x 10^18 multiplied by (n * Lambda / f_edd) multiplied by [(\Omega_b * M_h) / (\Omega_m * M_star) - 1], where n represents gas density, Lambda represents cooling efficiency, f_edd represents Eddington fraction, \Omega_b represents baryon density parameter, \Omega_m represents matter density parameter, and M_h represents halo mass; then the galaxy becomes inefficient in forming stars. Once this threshold ratio is surpassed, a runaway process occurs that brings these initially overmassive systems closer to the local relation between black hole mass and stellar mass (M_bullet - M_star). Furthermore, it is found that this relation evolves with redshift as proportional to (1+z)^(5/2). At a redshift of approximately 5, the authors find an overmassive factor of around 55, which is in excellent agreement with current JWST data and the high-redshift relation inferred from it. The authors suggest that extending observations of black holes to even higher redshifts and lower masses will help test this model and enhance our understanding of the early co-evolution between black holes and galaxies. This study provides valuable insights into the relationship between black hole mass, stellar mass, and star formation efficiency in the high-redshift universe.