Estimate the distance and mass of a galaxy

[Junji]

Hi!

I want to estimate the distance and mass of a galaxy by given values.

The center of an inclined galaxy sends out light of a certain wavelength (f.ex. the HI line) out to a certain radius r.
At the outer edges of the galaxy the emitted line has a wavelength of l +/- dl

At first, I thought the distance is calculated by using the redshift principle. However, this would mean that one edge has a redshift whereas the other one has a blueshift, so the galaxy plane would be rotating. Can this be possible?
Yet, I don't know why else there are observed different wavelengths at the edges and why the center wavelength is observed out to a radius r. Any ideas?

If my first thought was right, I get to the following equation:
The formula for the redshift is given as c*z = H*d , with redshift z = dl/l and Hubble constant H.
So the distance for the more distance edge would be d = c*(dl/l)/H, right?

However, I don't have any ideas so far, how to estimate the mass of a galaxy.
Is there some relation between the emitted wavelengths and its mass at all?

Thank you in advance!

Junji

 

[AndyW]

Hi Junji,

Thank you for your question. Estimating the distance and mass of a galaxy can be a complex task, but there are some methods that can help us make these estimations.

First, let's address the issue of redshift and blueshift. You are correct that the redshift principle can be used to estimate the distance to a galaxy. However, in an inclined galaxy, the rotation of the galaxy can cause the light from one edge to be redshifted while the light from the other edge is blueshifted. This is known as the rotation curve of the galaxy and it is a common phenomenon in spiral galaxies.

To estimate the distance to the galaxy, we can use a modified version of the redshift equation you mentioned. Instead of using the Hubble constant, we can use the rotational velocity of the galaxy at its outer edges. This is known as the Tully-Fisher relation and it is often used to estimate the distance to spiral galaxies. The equation is v = R x H, where v is the rotational velocity, R is the distance to the galaxy, and H is a constant that depends on the type of galaxy. By measuring the rotational velocity at the outer edges of the galaxy, we can estimate the distance to the galaxy.

As for estimating the mass of the galaxy, there are a few different methods that can be used. One method is to use the rotation curve of the galaxy to calculate the mass distribution within the galaxy. This can give us an estimate of the total mass of the galaxy.

Another method is to use the velocity dispersion of stars in the galaxy. The velocity dispersion is the spread of velocities of stars in the galaxy, and it is related to the mass of the galaxy through the Virial theorem.

There are also other techniques, such as measuring the gravitational lensing effect of the galaxy, that can help us estimate its mass.

I hope this helps answer your question. Good luck with your calculations!