Studying the influence of bars on the $M$–$\sigma$ correlation

To examine the evolution of galaxies and their supermassive black holes, we look at the relationship between black hole mass, $M$, and the central velocity dispersion of stars, $\sigma$, commonly referred to as the $M$–$\sigma$ correlation. Using data from the cosmological TNG100 simulation, we compare the results of the most popular $\sigma$ calculation methods when applied to disk galaxies with varying bar strength. We also compare each $\sigma$ method to the kinetic energy of the stars in the central bulge and make the recommendation that $\sigma$ measurements which consider both line-of-sight dispersion and mean line-of-sight velocity get closest to accurately representing the galaxy. From here, we move on to analyzing $M$–$\sigma$ and find that TNG100 systematically overestimates $M$ when compared to observational data. However, we can still note differences between barred and unbarred galaxies, indicating that a more accurate relation can be obtained after separating galaxies by bar strength. Finally, we examine $M$–$\sigma$ for samples at increasing redshifts, $z$, and find that they differ from the correlation at $z=0$. This implies that if TNG100 represents reality, the $M$–$\sigma$ relationship in disk galaxies at $z=0$ cannot be used to predict $M$ at higher redshifts.