Jaffe profile

The Jaffe profile (or Jaffe model) is a mathematical function that is used to describe the distribution of mass or light in elliptical galaxies and the bulges of spiral galaxies. It was proposed by Walter Jaffe in 1983.^[1] Its usefulness derives from the fact that it accurately reproduces a de Vaucouleurs profile when projected onto the sky.

The density in the Jaffe model is given by

$\rho (r) = {\rho_0\over 4\pi}\left({r\over r_0}\right)^{-2} \left(1%2B{r\over r_0}\right)^{-2}.$

In this equation, $\rho_0$ and $r_0$ are parameters that can be varied to fit the observed density.

Jaffe described how he arrived at his model: ^[1]

[The formula] was derived heuristically from the observation that the brightness profiles of spherical galaxies seem to run as $r^{-3}$ and $r^{-1}$ in at least some parts of their envelopes and cores, respectively. This would imply that the spatial density runs as $r^{-4}$ and $r^{-2}$ .

Variations on Jaffe's law include the Hernquist profile, the Dehnen profile and the NFW profile, which have a similar functional form as Jaffe's law but which use different values for the two exponents.

References

^ ^a ^b Jaffe, Walter (March 15, 1983). "A simple model for the distribution of light in spherical galaxies". Royal Astronomical Society, Monthly Notices 202: 995–999. Bibcode 1983MNRAS.202..995J.