# How to calculate the mass of a star using redshift?

• LachyP

#### LachyP

Hi everyone,

Is there a simple formula/equation for calculating the mass of a star simply by measuring it's redshift. I know there is a way to do it, but have been unable to find any clues on the web..

This depends on what you mean by redshift. There can be several sources of redshift, including cosmological, doppler, and gravitational.

If you know or can neglect the effects of the other contributions, you can use the gravitational red shift to compute the mass of the star (or rather M/R, gravitational redshift depends on this quantity).

Let's say it is gravitational redshift.. If you can, could you please also explain for the other two types of redshift?

The amount of red-shift is computed by looking at the position of spectral lines and comparing to the proper frequencies of these lines. You can then compute the gravitational mass using the predicted gravitational redshift and equaling it to the observed redshift. For details on how to compute the gravitational redshift, I recommend reading an introductory text on general relativity. There are several conceptual pitfalls and it really requires more careful writing than you will generally find in a forum. The same goes for cosmological redshift, while doppler shift is essentially a special relativistic effect. Neither the cosmological shift or doppler shift depend on the mass of the star. If you do not have access to an introductory textbook, I suggest starting at Wikipedia.

The amount of red-shift is computed by looking at the position of spectral lines and comparing to the proper frequencies of these lines. You can then compute the gravitational mass using the predicted gravitational redshift and equaling it to the observed redshift. For details on how to compute the gravitational redshift, I recommend reading an introductory text on general relativity. There are several conceptual pitfalls and it really requires more careful writing than you will generally find in a forum. The same goes for cosmological redshift, while doppler shift is essentially a special relativistic effect. Neither the cosmological shift or doppler shift depend on the mass of the star. If you do not have access to an introductory textbook, I suggest starting at Wikipedia.
I've been working on it, and I think this may work, M = z(rc^2)/G , where "z" is the redshift, do you think this would work, it seems to be giving around the correct result, but I would much prefer someone wiser to review and correct...

Yes, this is true under some assumptions. Mainly, the Schwarzschild metric must be a good description of the space-time around the star and the radius of the star must be much larger than the Schwarzschild radius of an object with the same mass. For normal stars, this is generally a pretty good approximation.

Yes, this is true under some assumptions. Mainly, the Schwarzschild metric must be a good description of the space-time around the star and the radius of the star must be much larger than the Schwarzschild radius of an object with the same mass. For normal stars, this is generally a pretty good approximation.
OK thank you for the help and advice :)

I've been working on it, and I think this may work, M = z(rc^2)/G , where "z" is the redshift, do you think this would work, it seems to be giving around the correct result, but I would much prefer someone wiser to review and correct...
And note you are actually getting M/r, not M, by observing z. That wouldn't work so well for giant stars, because M/r is very small and hard to detect, and it's not that helpful for main-sequence stars, because they all tend to have a similar M/r so you'd need to detect z very precisely to distinguish them, but the z would only be about 1 part in 100,000. But it is very handy for white dwarfs, because white dwarfs have a mass-radius relationship, such that r is proportional to M-1/3, so M/r is proportional to M4/3, so M is proportional to z to the 3/4, and z is much larger and easier to detect. So it's used as a good way to get the mass of a white dwarf.