= Faber-Jackson relation
{c}
{title2=$L\propto\sigma^4$}
{wiki}
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 $M\propto\sigma^2R$, 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.
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