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