 Faber–Jackson relation

The Faber-Jackson relation is an empirical correlation between luminosity and stellar velocity dispersion for elliptical galaxies, approximately $L\propto {\sigma }^4$ in its classical form. Slope, scatter, sample and band matter. A heuristic combines $M\propto {\sigma }^{2}R$, common mass-to-light ratio, and common characteristic surface brightness $L/R^2$. The luminosity-dispersion correlation alone does not imply those auxiliary assumptions, and extrapolation to a dwarf spheroidal galaxy is not guaranteed.

The Faber–Jackson relation is an empirical relationship in astrophysics and cosmology that describes the correlation between the luminosity of a galaxy and the velocity dispersion of its stars, particularly in elliptical galaxies. This relation suggests that brighter galaxies tend to have a higher velocity dispersion, which is a measure of how fast the stars within the galaxy move.