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I know that we have measured the rate a lot of stars and galaxies move away from us using the doppler shift, and I know that the further a star / galaxy is the faster they accelerate away from us due to space inflation. I'm wondering, did anyone categorise which star / galaxy is moving towards us / away from us the fastest? How fast are they going in relation to our solar system?

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    $\begingroup$ Another way to ask this question might be "What object has the highest observed cosmological redshift z?" $\endgroup$ – uhoh Jul 9 at 7:04
  • $\begingroup$ I would assume the stars at the very edge of the observable universe are moving away the fastest, if indeed the farther they are from us they are moving away faster $\endgroup$ – user17915 Jul 10 at 0:20
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    $\begingroup$ The closer a galaxy is to satisfying your criterion, the more difficult it is to detect. Given any object that is currently the one with the greatest cosmological redshift, we are essentially guaranteed that there are others with a greater cosmological redshift, which is why we can't detect them. the faster they accelerate away from us due to space inflation. The quantity to talk about in Hubble's law is velocity, not acceleration, and none of this has anything to do with inflation, which is a different phenomenon. We actually don't know for sure whether inflation happened. $\endgroup$ – Ben Crowell Jul 10 at 3:19
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When a galaxy recedes from us, the light we see from it is redshifted. For galaxies at cosmological distances, this redshift is fundamentally different from a Doppler shift; whereas the latter is due to a velocity difference between the emitter and the receiver, a cosmological redshift is due to photons traveling through an expanding space$^\dagger$.

Hence, as @uhoh comments, your question is equivalent to asking "Which galaxy has the highest measured redshift?". Redshift is arguably the single most important concept in astronomy, and indeed we do catalogue the redshift of all galaxies, if possible. For our adopted cosmological model, the cosmological redshift can be translated to both a recession velocity, a distance, and an age of the Universe when the light was emitted.

The answer is GN-z11 (Oesch et al. 2016) which has a redshift of $z=11.09$. This corresponds to a distance of $d = 32.2\,\mathrm{Glyr}$ (i.e. billion light-years), and hence, by Hubble's law, to a recession velocity of $$ v = H_0\,d = 670\,000\,\mathrm{km}\,\mathrm{s}^{-1}, $$ or more than twice the speed of light. Furthermore, the light we see today was emitted when the Universe was only 410 Myr (i.e. million years), or 3% of its current age.

You may think that "twice the speed of light" violates the theory of relativity, but this velocity is not a velocity through space. Both our galaxy (the Milky Way) and GN-z11 move through space at modest velocities of a few 100 km/s. The recession is merely due to space expanding, and space is allowed to expand at whatever rate is wishes.


$^\dagger$A hypothetical scenario that emphasizes the difference between the two types of redshifts is the following: If an emitter and an observer are stationary wrt. each other when the emitter emits a photon, then start moving away from each other while the photon is traveling, then stops again before the observer receives the photon, the observer would measure zero redshift. On the other hand, if space were static when the emitter emits the photon, then while the photon is traveling suddenly expanded by a factor of, say, four, and then were static again when the observer receives the photon, the observer would measure a redshift of $z+1 = 4$.

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    $\begingroup$ Wouldn't there be some unknown number of galaxies beyond the cosmological horizon that are receding even faster? All one could answer of course is the galaxy receding fastest among all known galaxies. $\endgroup$ – nasch Jul 9 at 16:28
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    $\begingroup$ @nasch Oh yes, definitely! Unless our understanding of the Universe is severely flawed, it looks (on average) the same everywhere and in all directions. I'm only describing the most distant one observed, and when we observe the distant Universe we're looking to the past, so we see GN-z11 as it looked more than 13 Gyr ago. More galaxies are "almost surely" beyond GN-z11, and even beyond the edge of the observable Universe. The Universe may even be infinite, in which case their is no limit to how fast a galaxy recedes. $\endgroup$ – pela Jul 9 at 20:40
  • $\begingroup$ Both our galaxy (the Milky Way) and GN-z11 move through space at modest velocities of a few 100 km/s. This is not quite right. GR reduces to SR at small scales, and SR says there is no way to define how fast something is moving "through space." I think what you probably mean is that 100 km/s is the speed relative to the Hubble flow, which is basically just the average state of motion of nearby matter. $\endgroup$ – Ben Crowell Jul 10 at 3:15
  • $\begingroup$ @BenCrowell You're right that it's relative to the Hubble flow. It's also relative to most other sensible inertial frames you can think of, unless you choose the inertial frame of some individual, fast-moving particle. I think it makes sense to say that galaxies, stars, and bicycles move through space. You're of course free to choose some reference frame where a galaxy, or a bike, doesn't move, but then you just make other galaxies, or bikes, move at a somewhat different velocity. $\endgroup$ – pela Jul 10 at 7:32
  • $\begingroup$ So if the recession velocity from a galaxy is greater than the speed of light, we will be unable to ever see the photons emitted from that galaxy right now? $\endgroup$ – NotTelling Jul 10 at 11:02
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From what I know I don't think they have categorized that this specific galaxy, for example, is the fastest one moving away from the Milky Way Galaxy. There are two reasons for this:

  • First of all, this isn't really that important. Measuring which galaxy is moving that fastest away from us can have some implications but not a whole lot. Scientists are however interested in the fastest speed any galaxy can move away from us. That does not, of course, violate the Theory of Relativity. And that speed is faster than the speed of light. Here is some extra info:

The Hubble constant is the measure of how fast the Universe is expanding today and its value has been measured to be 70 km/s per Megaparsec (a parsec is just a unit of distance equal to about 3.26 light-years, and a Megaparsec is a million parsecs). This means that on average, for every Megaparsec two galaxies are separated by, they are moving away from each other by 70 km/s. Therefore, to be moving away from each other at the speed of light, two galaxies would need to be separated by a distance of about 4,300 million parsecs. This is smaller than the radius of the observable Universe, therefore not only are there galaxies in the Universe that are moving away from us faster than light, but we can still see them!

Source: http://curious.astro.cornell.edu/legal-information/104-the-universe/cosmology-and-the-big-bang/expansion-of-the-universe/1066-can-two-galaxies-move-away-from-each-other-faster-than-light-intermediate

  • Second, we can't really be sure even if we research really hard, because every day we detect new objects circulating in our solar system, and for galaxies, we are talking about mega-big distances.

Conclusion: So it is possible, but it is really time-consuming and abstract in a way, so it isn't something scientists are looking into today. But if you want some galaxies which are moving really fast away from us you can search the internet or read some books and you will find a lot. Of course, there is this certain galaxy which at the moment is categorized as the fastest or most-redshifted (if you understand what I'm saying) that we have detected (remark: detected) and it is GN-Z11. It is the most distant found galaxy in the whole observable universe, so the fact that it is the fastest moving away from us makes sense.

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  • $\begingroup$ Something more, @pela, also puts the speed of GN-Z11 which is nice. Good work, @pela! $\endgroup$ – Gaurav Mall Jul 9 at 7:40
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    $\begingroup$ Hi Guarav. Thanks! You're right that velocity is not really an important concept for cosmological distances, but it's not true that we don't know, nor that it's abstract. It might be time-consuming, but redshift is such an important concept that it's worthwhile. An once we know its redshift, we know exactly the recession velocity of a galaxy (although of course there is some uncertainty in the value of the Hubble constant used to calculate the velocity). $\endgroup$ – pela Jul 9 at 7:45
  • $\begingroup$ Thanks, @pela for the reply. Yes, I should have used different words there, like not in interest I think. Anyways I agree with your point about the redshift :) $\endgroup$ – Gaurav Mall Jul 9 at 7:47
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    $\begingroup$ Also, for low-redshift objects, it's actually quite normal to quote velocity rather than redshift (because peculiar velocities may dominate cosmological). $\endgroup$ – pela Jul 9 at 7:47
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    $\begingroup$ You're welcome! Actually, right now I'm drinking coffee with the guy who found GN-z11 :) $\endgroup$ – pela Jul 9 at 9:44

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