Why use velocity dispersion in Faber Jackson relation

[Ron19932017]

Hi all,

Recently I am reading some online material about Tully-Fisher relation and Faber-Jackson relation
which is describing the dynamical constrain on the mass of spiral/elliptical galaxies.

In spiral galaxy, TF relation suggest Luminsoty ≈ (some const) (Vmax)^4
while in elliptical galaxy the Vmax term become the σ, which is the velocity dispersion.

I know that the assumptions behind are a little bit different. For example in TF relation we assume (L/M) ratio is independent of M while in FJ relation it is not. I also understand that in reality stars in elliptical galaxy just move in random direction rather than systematically move in a disk.

Therefore in the case of elliptical galaxies we can only talk about velocity dispersion σ, rather than just velocity itself. However I don't know why is the TF and FJ relation looks so similar. Are they by coincidence? Or there is physical justification behind replacing the V by σ in TF relation and you get the FJ relation?

Thanks for your patience and help. :)

 

[stefan r]

I believe we just measure the width of a characteristic peak. If the galaxy is a point source you would get photons from a random selection of stars.

My analytic chemistry professor told me that they used to cut out the peak with scissors. Then they would weight the paper. This was before computers were around to do the integration.