Faber–Jackson relation

The Faber -Jackson relation is an observed correlation between luminosity L and the velocity dispersion in elliptical galaxies. The luminosity depends proportionally by a power of the velocity dispersion from:

This connection was first discovered by Robert Earl Jackson and Sandra M. Faber in 1976. Nowadays it is widely used to infer the velocity dispersion of the galaxy.

Derivation

One can easily estimate that the Faber -Jackson relation under certain idealizing assumptions. This leads to the exponent of the relationship. The actually observed exponent depends on the shape of the density and the mass-luminosity ratio and differs from the theoretical value more or less sharply.

The potential energy of a selbstgravitierenden mass distribution of radius R and mass M

The total kinetic energy is

Using the virial theorem () follows

If mass and luminosity are proportional to each other, M can be replaced and still has

A relationship between R and the velocity dispersion:

With a constant surface brightness

Follows

And finally the sought relation between luminosity and velocity dispersion:

Swell

• Original work of Faber and Jackson (English )