Expert: Philip Stahl - 7/13/2009

Question
I was reading about galaxies in Wikipedia. In the section entitled "Future trends" towards the bottom, there is mention of gravitational relaxation. I have never heard of this before and could not find any information elsewhere to satisfy my curiousity.
Would you happen to be able to enlighten me in this area?
Thank you very much.

Answer
Hello,

Generally, in reference to astrodynamic systems, when one refers to "gravitational relaxation" s/he is referring to a particular condition which may best be described as collisional. (As opposed to a collisionless regime).

What this means in terms of a system like a galaxy, is that one has to take care to distinguish between individual orbits of component masses inside it, from collective dynamics which describes much more complex global (and often more chaotic) behavior.

What this implies is that strong aberrations from what one might expect in a self-gravitating system can emerge.

For example, while a "mean gravitational field" can be used to define the collective system, there are still going to be wild variations in the orbits, especially when any deviations from axial symmetry occur (e.g. in the global configuration, say going from a spherical to an extremely irregular shape that radically redistributes the mass).

In a collisional system there will be many more collisions and a general dissipation of (gravitational potential) energy. meanwhile, all astrodynamic (stellar) systems display a natural tendency to collapse because of what is called "self-gravity".

Meanwhile, in collisionless (dissipation-free) systems, if an equilibrium configuration emerges (more or less equivalent forces acting in tandem) then the tendency to collapse can be opposed even with random motions.


Given all the preceding, it should not surprise you to learn that some of the same equations employed in plasma physics are also employed for galaxies, in modeling both collisional and collisionless models.

IN respect to the first, one uses e.g. the Boltmann eqn.:  

@f/ @t + v*grad f + F/m*@f/@t = (@f/@t)_C

where @ denotes partial derivative, and (@f/@t)_C  is the time rate of change in f (the velocity distribution function) due to *collisions*.

So, the same equation that can be used to describe collisions in a plasma is often applied to galactic systems too.

In the collisionless domain, one would use the Vlasov equation - which is just the Boltzmann eqn. minus the collisional (RHS) expression, viz.

f/@t + v*grad f + q/m (E + v X B)*@f/@t = 0


for which the force F is denoted as the Lorentz force.

You certainly pick some esoteric areas with which to whet your curiosity! Have you had much advanced mathematical training?