What is the recession speed of a galaxy based on the wavelengths of two stars?

[NebulaBilly]

I have been having a conversation with a few friends, and we have been discussing the speed of stars in a galaxy base of the wave lengths. We have 2 stars measuring wave lengths 494.6nm and 494.2nm. At rest the wavelength is 486.1nm. From this we managed to deduce that the speed of both stars using Doppler shift is 4011 km/s and 4999 km/s. We then wanted to take this further and calculate the distance of this galaxy but to do this we need to know the recession speed of the galaxy, and we are just not sure how to get that answer, hopefully somebody here can shed abit of light onto it.

 

[mfb]

The recession speed of the galaxy will be somewhat close to the speed of these stars. A better estimate would need more measurements of stars at different points of the galaxy.

 

[JMz]

If you know where those 2 stars lie in the galaxy, and you know that the galaxy is a disk, that could help you make a better estimate. (If it's not a disk, it's not clear that anything other than the average is a reasonable estimate, without a lot more information about it.)

For example, if they lie on opposite sides of its center, by equal apparent distances, then their mean is probably as good an estimate as you can hope for. Conversely, if one of them is much closer to the center, then that star's speed alone may be a better estimate than their average.

 

[NebulaBilly]

Hi thanks for your reply, i thought maybe a good way would be to calculate the redshift, then x it by speed of light, this gave me around 900km/s

 

[JMz]

Hi thanks for your reply, i thought maybe a good way would be to calculate the redshift, then x it by speed of light

Yes, that is what you presumably did in your OP. But you asked about the galaxy's recession speed (and then its distance), so my answer was to help you get the galaxy's speed from the stars' speeds. (You could just as well average the redshifts themselves by the procedure I described, and multiply afterward by the speed of light -- the distributivity property of multiplication. ;-)

this gave me around 900km/s

Why 900 here vs. 4011 & 4999 in your OP?

 

[NebulaBilly]

Hi JMz yeah 900 but i think its because we did it incorrectly. If i do the mean like you suggest as the stars are opposite side of galaxy so mean would work, the recession speed would be 4,505km/s and then we would get a distance of 60.1 MPC

 

[JMz]

Souds good. I imagine this galaxy already has a published distance somewhere. Did you check if 60 Mpc is about right?

 

[NebulaBilly]

All looks good atleast can see how they got there now, sometimes the simplest way seems the most difficult.