I understand how galaxy rotation curves show the influence of dark matter, or something else that would produce similar behaviour, such as Modified Newtonian Dynamics (MOND). Do the orbits of satellite galaxies show the same influence?

In MOND terminology, the internal gravity of the satellite galaxy is not relevant to this question. The question would be if the gravitational effect of the host galaxy on the satellite was Newtonian or MOND?

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    $\begingroup$ +1 This is a really interesting question, and makes me wonder if the proper motion of satellite galaxies are even well determined from observations. $\endgroup$ – uhoh Jun 13 '20 at 23:31
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    $\begingroup$ Proper motions have actually been measured for more than 40 satellite galaxies, most recently with data from Gaia. $\endgroup$ – Peter Erwin Jun 16 '20 at 8:14
  • $\begingroup$ In fact, there is even a -- rather uncertain -- proper motion measurement for M31; see here. $\endgroup$ – Peter Erwin Jun 16 '20 at 9:54

The short answer is "Yes, the orbits of satellite galaxies definitely show the influence of dark matter (or something like MOND, if you prefer)." For galaxies outside the Local Group, you can only measure their radial velocities from Doppler shifts (i.e., velocities along our line of sight to the galaxy), but you can still look at the distribution of these velocities for satellites around some central galaxy and work out the approximate amount of mass required for the satellites to remain bound -- and thus you need dark matter. (The first hints of dark matter, going back in the 1930s, were from a larger-scale version of this: Zwicky and others measured the radial velocities of galaxies in galaxy clusters and found they were too high to be explained by the visible mass of the galaxies in the clusters.[*])

For satellites of our own galaxy, it has become possible, in the last twenty-five years or so, to measure proper motions (motions across the sky, perpendicular to the line of sight) as well as their radial velocities and so we can measure their actual 3D space velocities. This paper by Fritz et al. (2020) uses proper motions from Gaia observations for 45 satellite galaxies to estimate the mass of the Milky Way's dark-matter halo. They find this to be about $1.5 \times 10^{12} M_{\odot}$, consistent with other measurements.[**] (Note that unlike the case for measurements of gas clouds orbiting in a disk -- the original data indicating dark matter in spiral galaxies -- you can't assume the orbits of satellites are circular, so the calculations involved are more complicated, but they still give roughly the same answers.)

[*] Later observations with X-ray satellites demonstrated that galaxy clusters contain significant amounts of normal baryonic matter in between the galaxies, in the form of very hot, dilute, X-ray-emitting gas. However, even when you add this to the stellar mass in the galaxies, you still don't have enough mass in the cluster to explain the radial velocities.

[**] This value can be compared with a baryonic mass for the Milky Way of about $5 \times 10^{10} M_{\odot}$ in the form of stars, plus maybe another $1 \times 10^{10} M_{\odot}$ in the form of gas.


I conflated your question with "do satellite galaxies show the influence of dark matter in general...ie. Do they HAVE dark matter?", but I think I answered your question at the bottom regarding orbits and velocity dispersion as you mention.

Tidal dwarf galaxies (TDGs) are typically observed to lack dark matter. TDGs are different from “regular” dwarf galaxies which are typically dark matter-dominated and likely of primordial origin and are thought to have formed in their own dark matter halo and have distinct evolutionary histories from a TDG.

TDGs form through galaxy collisions/interactions and they do not accrete dark matter through this process. The dark matter in the halo from the parent galaxy is too dynamically hot to be accreted and only baryons are accreted. This result does fit in with the dark matter paradigm (not specific to MOND but doesn't necessarily exclude it), as these galaxies are NOT primordial in origin. What DOES challenge Lambda-CDM (cold dark matter) and may support MOND is as follows:

So we know Lambda-CDM predicts isotropic distributions and random kinematics for satellite systems, but we don’t observe this. Instead, we find that dwarf satellite galaxies exist on a disk or plane that likely co-rotates with the main galaxy. We see this occur in the Milky Way, Andromeda, and Centaurus A. TDGs fit into this puzzle because phase-space coherence may make better sense if the satellite galaxies were initially TDGs. In the work by Muller et al. 2018, 14 of the 16 satellites with kinematic data follow a coherent velocity pattern aligned with the long axis of their spatial distribution.

With the data we have on satellite galaxies and their massive host galaxies, it’s getting more difficult to state that we just can’t see the dwarf satellite galaxies (known as the missing satellite problem which LCDM doesn't explain). It seems the simulations that predict a halo-like distribution of satellite galaxies have some serious flaws. Perhaps there is something not being accounted for or the idea of dark matter is incorrect. In any case, being able to predict the distributions of satellites remains a problem.

Most astronomers still "vote" for LCDM because dark matter is "needed" to explain the large structure we see today and the gravitational mass density exceeds the baryon density. The problem is we still don't know what dark matter is and are running out of options. I am personally agnostic until we have more data.

MOND predicts that the velocity dispersion will vary from the Newtonian regime when the external field of the host exceeds the internal field of the dwarf satellite (external field dominant quasi-newtonian regime). To confidently discriminate between Newtonian dynamics and MOND in the velocity dispersions of satellite galaxies requires extraordinarily high accuracy, which is unlikely at the current time. See http://astroweb.case.edu/ssm/mond/EFE.html for more details and equations.

  • $\begingroup$ I've clarified the question. $\endgroup$ – John Dallman Jun 16 '20 at 8:17
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    $\begingroup$ This is very interesting, but I'm not sure it actually answers the question, which, I think, is asking whether the orbits of dwarf galaxies can be explained simply by the baryonic mass of their host galaxy (and Newtonian gravity or GR) or whether, like stars, they seem to orbit too rapidly for that? $\endgroup$ – Steve Linton Jun 16 '20 at 8:37

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