Simple Fit of Data Relating Supermassive Black Hole Mass to Galaxy Pitch Angle

TL;DR

This paper proposes a simple linear model relating supermassive black hole mass to the cotangent of galaxy pitch angle, offering an elegant alternative to complex double power law fits and potentially clarifying the underlying correlation.

Contribution

It introduces a straightforward linear fit between black hole mass and the cotangent of pitch angle, simplifying previous complex models and enhancing understanding of their relationship.

Findings

The linear model fits the data within error margins.

It matches the accuracy of the more complex double power law.

The approach offers a more elegant and interpretable correlation.

Abstract

Seigar, et al, have recently demonstrated a new, tight correlation between galactic central supermassive black hole (BH) mass and the pitch angle of the spiral arm in disc galaxies which they attribute to other indirect correlations. They fit a double power law, governed by five parameters, to the BH mass as a function of pitch. Noting the features of their fitted curve, we show that a simple linear proportion of the BH mass to the cotangent of the pitch angle can obtain the same fit, within error. Such a direct, elegant fit may help shed light on the nature of the correlation.