The maximum rotation of a galactic disc

TL;DR

This paper derives a relation for the maximum rotation of galactic discs based on luminosity, surface brightness, and colour, highlighting the necessity of dark matter especially in low surface brightness galaxies.

Contribution

It introduces a new general relation for maximum disc rotation that accounts for luminosity, surface brightness, and colour, incorporating a fixed mass-to-light ratio based on population synthesis models.

Findings

Maximum disc rotation is about 63% of observed maximum rotation.

Dark matter is essential in the disc region, especially for LSB galaxies.

The relation is validated with observations of NGC 6503 and NGC 1560.

Abstract

The observed stellar velocity dispersions of galactic discs show that the maximum rotation of a disc is on average 63% of the observed maximum rotation. This criterion can, however, not be applied to small or low surface brightness (LSB) galaxies because such systems show, in general, a continuously rising rotation curve until the outermost measured radial position. That is why a general relation has been derived, giving the maximum rotation for a disc depending on the luminosity, surface brightness, and colour of the disc. As a physical basis of this relation serves an adopted fixed mass-to-light ratio as a function of colour. That functionality is consistent with results from population synthesis models and its absolute value is determined from the observed stellar velocity dispersions. The derived maximum disc rotation is compared with a number of observed maximum rotations, clearly demonstrating the need for appreciable amounts of dark matter in the disc region and even more so for LSB galaxies. Matters have been illustrated for two examples; the galaxy NGC 6503 and LSB galaxy NGC 1560.