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Is there such as thing as the viscosity of stars in a galaxy, along the lines of gravitational attraction between stars changing the dynamics.

If so, how is that put in terms of the Virial Theorem?

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Yes. Since the gravitational force is long-range, one star traveling through a star field tends to leave behind a slightly denser "wake" of stars that moved slightly towards its previous locations. This increased density acts to pull backwards on the fast-moving star, creating a sort of fluid friction, or viscosity. The Virial Theorem is based on a fully-randomized distribution of positions and velocities, so it absolutely requires some kind of viscosity effect to smooth out the initial distribution of positions and velocities, whatever it happens to be.

On a more technical note, a frequently used synonym for randomized is "thermalized," leaning heavily on the parallel between the statistical physics of a large number of gravitating bodies interacting and a large number of atoms or molecules interacting electromagnetically. The gravitational viscosity can be considered to use up "mechanical energy," i.e. kinetic energy that stands out from purely random motion and therefore could be used to do work without the constraints of thermodynamics, from the point of view of stars as particles. Gravitational viscosity would therefore produce "heat," or randomized particle motion, only usable for doing bulk work under the constraints of thermodynamics, like the Carnot Efficiency.

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Great answer. I used to know that stuff back when I was a grad student. :) Haven't used it since then and it was sitting back in some dusty corner of my brain. –  dagorym Jul 1 '11 at 14:27
    
Understood, from what you wrote, does that mean Maxwell–Boltzmann statistics can be used for galaxies or at least nebulae? –  metzgeer Jul 1 '11 at 14:31
    
@dagorym-Funny. Here it is, my fondest dream in life to stop being a grad student as soon as possible. @metzgeer-Um, I'm going back and forth on this. I think a MB distribution is assumed to be confined, while a cluster or galaxy is free to expand into the vacuum but is bound by its own mutual attraction. From the bare intuitive point of view, it's hard to equate an evenly distributed gas with a highly concentrated and organized globular cluster at the level of obeying the same statistics, rather than analogous statistics. (Statistical and thermo were definitely not my concentration.) –  Andrew Jul 1 '11 at 23:35
    
@Andrew: I didn't say I wanted to be a grad student again, it's just that I've forgotten so much from when I was. :) –  dagorym Jul 2 '11 at 3:00
    
+1 on wanting to stop being a grad student soon. Regarding @metzgeer's question, I believe the question is "no". I might be wrong, but I seem to remember from Binney & Tremaine that the dynamic friction and hence the viscosity term in Dark Matter is so low (that is, DM particles so weakly interacting) that the thermalization time for galaxies should be several times the current age of the Universe. –  Thriveth Jun 9 '13 at 12:47
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