# Mass of a galaxy via luminosity

Is there a general formula for calculating the mass of a galaxy, or even a nebula from the luminosity? Or, is there a way of calculating the total mass of a galaxy from its energy output?

Is there a Hertzsprung–Russell diagram equivalent for galaxies?

I know about gravitational lensing or velocity dispersion via the virial equation, and the Schechter function, and using doppler spread to calculate a mass.

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It sounds like you already have a pretty comprehensive answer in hand, but I would mention that galactic clusters are often classified by the mass or luminosity of their Nth-biggest or brightest member, where N is a smallish integer like 5. The idea is that the biggest couple might be weird outliers, but by the time you get down to the "rank and file" galaxies in a cluster, you should have a good handle on how big the cluster is. The strength of that scheme is that it can be difficult to determine if every galaxy in your image is actually a member, so that it is difficult to arrive at a good estimate of total mass directly. ...And you only have to take detailed data on a handful of the easiest galaxies anyway.

EDIT: I knew there was another, more direct answer, but I couldn't remember the authors' names. The Tully-Fisher Relation and the Faber-Jackson Relation describe empirically the relation between galactic luminosity and velocity-dispersion for spiral and elliptical galaxies, respectively. It is usually used to infer the former from the latter, but if for some reason you had luminosity in-hand already, velocity dispersion is related to the strength of the gravitational field of the galaxy and thus its mass.

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Now I understand, different types of galaxies have different relations Tully-Fisher for spiral galaxies, and Faber–Jackson relation for elliptical galaxies. But I haven't found a luminosity-mass relation for spherical galaxies. Which is odd, as I would have thought a spherical system would be easier to formulate. –  metzgeer Jul 8 '11 at 0:01
Spherical is only a special case of elliptical- E0. The Faber-Jackson relation should work for those; I didn't see anything about anisotropy of the galaxy on the Wiki page. –  Andrew Jul 8 '11 at 0:53