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(was: Is redshift unique for a galaxy? see Note (a) )

The question makes sense for middle distance galaxies, far enough that individual stars cannot be resolved (but perhaps not exactly the most far-away that we see as just a few pixels on a CCD sensor).

We have catalogues with thousands (perhaps more) of galaxies and I assume each entry would show one unique redshift.

It must be some rule / standard practice / requirement specifying where precisely one points the telescope at (when measuring / computing the redshift).

Galactic bulge would make sense. How about if we could zoom-in selecting different regions of this bulge, would we see different redshift? Can we even do that? [Edit: Seems like this very question (Bold after Edit) should have been given proper emphasis in the initial formulation (b)]

So, in fewer words, I'd say the essence of my question is: Is there a difference between the redshift measured at a central location and the redshift measured somewhere else? [Edit: somewhere else, still in the bulge if the bulge can be clearly identified from the rest of the "nebula")

Notes (later Edit):

(a) The initial Title was changed as suggested in Meta channel; "there are good answers then question should fit them".

(b) At the time the question was initially formulated my naive assumption was that one can point the instrument at some exact point in the sky (say within the bulge) and read a redshift value. In the meantime it has became more clear that at least for galaxies that are not the closest to us (as OP specifies) redshift is mostly the result of heavy post-processing and averaging. See ProfRob's comments "We cannot resolve the regions you seem to be wanting to talk about, and even if we could, the bulge of the galaxy is in the way."

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    $\begingroup$ Note that some galaxies are irregular. So much that it would be challenging to define a bulge or central location for them. $\endgroup$ Commented Mar 23, 2025 at 22:11

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Yes! Zoom in!

With a sufficiently high resolution observation, you can do much better than a single redshift measurement of a galaxy.

Galaxies are large enough that many have a non-trivial angular size when observed with a powerful enough telescope. And since redshift is a function of spectra, and spectra can be measured at any apparent point (basically one "pixel" of a broad-spectrum image), you can therefore produce a map of redshift of every visible point of a galaxy, which can then be interpreted as a relative velocity map of its stars.

For example, this is such a map of M31 (Andromeda Galaxy):

Stellar radial velocity map of M31

source

If the apparent size of the galaxy is more than one pixel in your data, then technically you can produce such a map. The method requires spatially resolving different parts of the galaxy to detect Doppler shifts across its structure, then comparing to the average.

Note that measuring the angular velocity of the stars relative to the center of the galaxy requires some statistical modelling - it's not quite as simple as comparing to a single measurement at the galactic center. But the average redshift of the entire galaxy is certainly still of interest, because it gives us an idea of how the entire galaxy is moving relative to us.

For example, this has even been done for extremely distant galaxies, such as REBELS-25 (light travel distance of 13 billion ly!):

Cropped image of velocity field map of REBELS-25

source

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  • $\begingroup$ Well argued technique of measuring redshift in a point and Impressive image of Andromeda with so many different measured values. But this shows the kinematic / Doppler component of redshift and that's not what I'm interested in. That's why I said middle distance galaxies (not the closest nor 13y). The central location (BH) is crucial here. $\endgroup$ Commented Mar 25, 2025 at 13:36
  • $\begingroup$ Having said that, I realise now that maybe the REBELS-25 example is still useful, I didn't expect that these extremely distant galaxies could provide so many individual measurement points. Still @Wyck can you explain how the velocity is only in the hundreds km/s? I suspect this is not redshift (what I'm interested in). But how else can you measure velocity if not from spectrum? $\endgroup$ Commented Mar 25, 2025 at 14:23
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    $\begingroup$ Those measurements are in the hundreds of km/s because they are relative to the target center, not to Earth. $\endgroup$ Commented Mar 25, 2025 at 15:35
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    $\begingroup$ (Not sure if "how else can you measure velocity if not from spectrum?" was rhetorical, but I'll take it seriously.) Measuring velocity without redshift is extremely difficult, and although doing so is very inconvenient (it's like bobbing for apples with both hands tied behind your back) we still do it because confirming measurements without redshift is an important way we build up the extragalactic distance ladder. One such way is VLBI Monitoring of Water Maser Emission. $\endgroup$ Commented Mar 25, 2025 at 15:39
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Yes. Galaxies rotate, so if you can resolve different parts of a galaxy then you would measure different redshifts.

But, for context, rotation speeds are measured in hundreds of km/s, whereas a small redshift of $z=0.01$ already implies a cosmological redshift of 3000 km/s.

The redshifts quoted for nearby galaxies would be some attempt to estimate the average redshift, ignoring internal motions.

However, the internal motions of galaxies are a small perturbation, and really quite negligible once you get to modest redshifts.

Your comment mentions gravitational redshift. The bulge of a galaxy might have a radius of say $R=1000$ pc and an enclosed mass of $M=10^{10}M_\odot$. This would have a gravitational redshift of $$ z \sim \frac{GM}{Rc^2} = 4\times 10^{-7}\ , $$ so just looking at the bulge has an utterly negligible effect on a measured cosmological redshift.

However, if you can look right to the central regions around a supermassive black hole then [perhpas you do see something different. The light from the central regions would come from an accretion disk orbiting the black hole. The orbital radii would range from a few to hundreds and thousands of Schwarzschild radii. There would be a negligible gravitational redshift for the latter, although the orbital speeds can reach $\sim 1000$ km/s, which causes a broadening of spectral lines (but no change in the average redshift).

You can however focus on the very inner regions, where the gas is extremely hot, using an X-ray telescope. Here you do see some evidence of General Relativistic effects in the profiles of X-ray emission lines. Blue-shifted material (approaching the observer) is Doppler-boosted in intensity, whilst redshifted material is diminished. Both are subject to a gravitational redshift (see Ilic & Popovich 2014). The net effect depends on viewing angle and the black hole spin. None of this is relevant to measured and quoted redshifts of galaxies, which usually arise from either optical or infrared spectra that are incapable of separating out emission from the very central regions from the general bulge emission, even in relatively nearby galaxies.

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    $\begingroup$ Very good point showing how the cosmological component of redshift makes the rotation (Doppler?) insignificant. That's very close to what I'm after, even more interesting would be to compare to the gravitational component of redshift, that's why I suggested the central location (BH). $\endgroup$ Commented Mar 25, 2025 at 13:42
  • $\begingroup$ R=1000pc for the bulge of a typical SMBH? Am I right saying that the BH itself would be R a million times smaller? therefore the z=0.4 would not be that negligible? and that R is the Schwarzschild radius, isn't the BH mass actually within an even smaller space? My point is z at the very centre vs somewhere else in the bulge (if we can separate these measurements... part of my question) $\endgroup$ Commented Mar 25, 2025 at 18:41
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    $\begingroup$ @adsp42 you need to start asking what you want to know in your question. What do you mean by the "bulge of a SMBH"? Black holes are not mentioned in your question at all. And what do you mean by "z at the very centre"? Light is required to measure a redshift. We cannot resolve the regions you seem to be wanting to talk about, and even if we could, the bulge of the galaxy is in the way. $\endgroup$ Commented Mar 25, 2025 at 19:50
  • $\begingroup$ You are right that we have diverged from the main question, surely the title seems not very relevant now. I meant "Bulge of a typical {1E10 solar masses galaxy that has a} SMBH at its centre like in your example, sorry for shortening in a comment. And "z at the very centre" wants to imply we are able to point the instrument very precisely at the BH itself... Perhaps that's where I'm making assumptions that don't stand. Your point "we cannot resolve the regions" seems to answer No to my OP "Can we even do that?". I need to think what "bulge is on the way" means, perhaps rephrase ... $\endgroup$ Commented Mar 25, 2025 at 20:34

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