Is gravitational redshift taken into account in Hubble's Law?

[m.w.lever]

From what I understand:

1. The more massive the object, the stronger the gravitational field. This leads to the light being emitted from the surface to shift down in frequency.
2. The rate of expansion of the universe causes a redshift proportional its distance away.

I'm new to this, but let's give it a shot:

In general, how are the Hubble's Law measurements different for let's say, a very large galaxy and a small one, i.e., how are the two shifts differentiated?

P.S.

Thanks!

 

[Matterwave]

You probably couldn't really differentiate the two redshifts; however, there are 2 probable solutions. First, gravitational redshift should not depend on distance. On average, the universe is homogeneous and isotropic so that there shouldn't be more massive galaxies the farther out you look. Therefore, on average, the gravitational redshift should not present anything more than a small systematic error.

Second, I think the gravitational redshift is not large enough to be too much a problem. I'm not 100% on this second statement; however. I don't have any concrete numbers. Perhaps someone more knowledgeable can provide them. =)

 

[m.w.lever]

You probably couldn't really differentiate the two redshifts; however, there are 2 probable solutions. First, gravitational redshift should not depend on distance. On average, the universe is homogeneous and isotropic so that there shouldn't be more massive galaxies the farther out you look. Therefore, on average, the gravitational redshift should not present anything more than a small systematic error.

Second, I think the gravitational redshift is not large enough to be too much a problem. I'm not 100% on this second statement; however. I don't have any concrete numbers. Perhaps someone more knowledgeable can provide them. =)

That answer is more than enough. If I am understanding it correctly, the size of the gravitational redshift is too small to really worry about, but it would be hard to tell the difference between them if we really needed to?

 

[nicksauce]

We actually do measure gravitational redshifts from galaxies in a way. The late time integrated Sachs-Wolfe effect (see http://en.wikipedia.org/wiki/Sachs–Wolfe_effect) accounts for the change in energy of CMB photons as they move through gravitational potentials.

 

[Matterwave]

That answer is more than enough. If I am understanding it correctly, the size of the gravitational redshift is too small to really worry about, but it would be hard to tell the difference between them if we really needed to?

Observationally, all we would see if a red-shift. Since these galaxies are so far out, we can't really pinpoint their mass, nor their speed using some other method, so I don't see how we could tell the two apart (other than saying v=Hd and w/e deviations from there you attribute to "other" factors).

Don't quote me on the size of the gravitational redshift though, I actually don't have very good numbers for those. That statement is more of a guess on my part.

 

[m.w.lever]

We actually do measure gravitational redshifts from galaxies in a way. The late time integrated Sachs-Wolfe effect (see http://en.wikipedia.org/wiki/Sachs–Wolfe_effect) accounts for the change in energy of CMB photons as they move through gravitational potentials.

I never knew how much the two were related. They really seem inseparable now!
Thanks nicksauce for the extra info.

 

[marcus]

That answer is more than enough. If I am understanding it correctly, the size of the gravitational redshift is too small to really worry about, but it would be hard to tell the difference between them if we really needed to?

Don't quote me on the size of the gravitational redshift though, I actually don't have very good numbers for those. That statement is more of a guess on my part.

One way to get a handle is the square of the circular orbit speed of stars in the galaxy.

That shows how small it is. Rough order of magnitude.

z_grav is approximately (v_circ/c)²

The circular orbit speed of stars in a spiral galaxy seen edge-on is easy to get by doppler and is commonly around 300 km/s or less. Milkyway it's about 250 km/s, so less.
And as a fraction of c that is 1/1000.

So the square is 1/1000000, a millionth. That is about what grav redshift is for light leaving Milkyway from roughly where we are.

And the redshift on what leaves the source galaxy can be somewhat balanced by the blueshift the light acquires coming into a target galaxy of roughly the same mass and dimensions.

If you want equations, z_grav is approx GM/(c²r)

But the circular orbit speed is about sqrt(GM/r) at distance r from galaxy center with mass M inside the orbit.

So expressing that as a fraction of c, and squaring it, we get that the square of the circular orbit speed ("beta" i.e. as fraction of c) is

GM/(c²r)

for the light from stars you have to make assumptions about the star. If it is very dense etc etc. But as a rule of thumb you can convince yourself that the grav redshift is almost always negligible compared with the Hubblelaw distance redshift

 

[Matterwave]

great, seems like my intuition was correct haha.