M-sigma vs. M-M_bulge relationship

[Veles]

Why is the M-sigma relationship so tight, but the M-M_bulge relationship much looser?

Don't the theories that black hole growth and star formation are coupled only explain why M_BH would be correlated with M_bulge? We might expect sigma to follow to an extent due to the stars having roughly Keplerian orbits, but why would it be more strongly correlated?

 

[lippyka]

The M-sigma relationship is so tight because the two quantities are closely related to each other. Supermassive black holes at galactic centers are thought to be the main source of the observed velocity dispersion. As the mass of the black hole increases, the galaxy's gravitational potential deepens, increasing the velocity dispersion of its stars. Therefore, the tighter correlation between M_BH and sigma reflects the physical processes that control the behavior of the stars in the galaxy. The M-M_bulge relationship is looser because the bulge mass is not directly connected to the supermassive black hole. Instead, it is a measure of the stellar mass contained in the central region of the galaxy. While there may be a correlation between bulge mass and black hole mass due to theories that black hole growth and star formation are coupled, it is not as strong as the correlation between M_BH and sigma. This is likely because the formation and evolution of galaxies is a complex process that involves many different factors, such as gas accretion, mergers, and feedback from supermassive black holes. The looser correlation between M_BH and M_bulge reflects this complexity.