If dark matter existed: wouldn't it slow down the orbital velocity of stars in galactic disks by dynamical friction more than it would accelerate them through additional mass? The original orbital momentum of the galaxy and the effect of its baryonic mass are only one-time effects while the presence of a dark matter halo and its dynamical friction exerted on orbiting stars would be permanent and abrasive.
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1$\begingroup$ "if it existed"? Is there much doubt? $\endgroup$– BarmarCommented Sep 1, 2022 at 14:28
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6$\begingroup$ @Barmar define dark matter, or for that matter, define existence. They're just words we all pretend mean something concrete. I would probably say that concrete exists, and if I had a better memory I'd remember what it was made of (or what concretions are in general) but dark matter is... a term in an equation, an explanation for the way stars move... it hasn't been isolated yet, so it's perfectly fine (with me at least) to say "If..." $\endgroup$– uhohCommented Sep 1, 2022 at 14:47
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10$\begingroup$ @uhoh I think you made a wrong turn, Philosophy is that way -> $\endgroup$– BarmarCommented Sep 1, 2022 at 15:00
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2$\begingroup$ @Barmar uhoh! :-) $\endgroup$– uhohCommented Sep 1, 2022 at 21:20
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2$\begingroup$ Dark matter is a hypothetical form of matter, whose presence is implied by certain observations that aren't compatible with current theories of gravity without the presence of additional mass. While "the scientific community generally accepts dark matter's existence," dark matter doesn't explain all observations well either; and there are alternative models proposed in an attempt to explain them better. (Source: Wikipedia.) So it's perfectly reasonable to ask a hypothetical question beginning with "If dark matter existed". $\endgroup$– LarsHCommented Sep 2, 2022 at 14:37
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2 Answers
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Dynamical friction is considered in the study of dark matter.
The timescale for dynamical friction to cause a significant loss of kinetic energy is roughly $$\tau \sim \frac{10^{5}}{\sqrt3 \ln \Lambda} \left(\frac{\sigma}{1 {\rm km/s}} \right) \left(\frac{r_0}{1 {\rm kpc}} \right)^2 \left(\frac{M}{M_\odot} \right)^{-1} \ \ \ {\rm Gyr}\ , $$ where $\sigma$ is the one-dimensional velocity dispersion of the dark matter, $r_0$ is like the core-radius of the dark matter and $M$ is the mass of the body being slowed down. $\ln \Lambda$ is the Coulomb logarithm and is a small factor of a few.
For dark matter in virial equilibrium at say the solar radius of 8 kpc and assuming an enclosed mass of $10^{11}M_\odot$, then $\sigma \sim 200$ km/s and the core radius would be a few kpc. Thus the dynamical friction timescale would be $\sim 10^{17}$ years - so ten million times older than the universe.
Where dynamical friction might be an issue is for more massive tracers of rotation curves (globular clusters $M\sim 10^5M_\odot$) in dwarf galaxies with $r_0 \sim 1$ kpc and $\sigma$ of a few km/s, where the dynamical friction timescale could be as short as a few Gyr (e.g. Cowsik et al. (2009)) but the estimates depend critically on how "cuspy" the dark matter distribution is and its velocity dispersion.
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2$\begingroup$ Excellent, thank you! Food for thought. Didn't think that DF turns out to be so weak given the permanence of the DM fields. $\endgroup$ Commented Sep 1, 2022 at 9:45
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In fact, dynamical friction is another aspect of dark matter than its mere gravitational pull, from which it was first discovered/postulated. Dynamical friction is one aspect of the exchange of energy as well as (linear and angular) momentum, and probes the inertia of the dark masses, not just their gravity.
Evidence for dynamical friction by dark matter would therefore bolster the dark-matter paradigm and exasperate alternative ideas of modified gravity. One promising avenue for gathering such evidence is from the friction of galactic bars, including that of the Milky Way, by the dark-matter halo. The transport of angular momentum from the bar to the dark halo via resonant dynamical friction is the thought to be the main driver for the slowdown and growth of galactic bars. Simulated bars w/o dark haloes grow much less and remain too small.
Another possible evidence comes from the efficiency of galaxy mergers and interactions, when the absorption of orbital energy and angular momentum into the dark halo via resonant dynamical friction binds the interacting objects more together and hence accelerates/enables the merger compared a situation w/o dark halo.
