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Re: Plasma



A couple of days ago I contributed this piece which I did expect to be
provocative:

There was a mention of plasma in outer space. There is a considerable
mass of gas in intergalactic space that is nearly completely ionized.
Diffuse X-rays detected from rich clusters of galaxies show that they
often include gas (mostly hydrogen and helium) in that state. It is
thought that the ionization is due to gravitational interaction, that
the virial theorem applies for galaxies and ions alike. Of course
this process of virialization does not reach an equilibrium state in
rich clusters, but the high temperatures inferred cannot be accounted
for by any other process.

Ludwik Kowalski responded:

In my mind ionization is associated with inelastic collisions
(nuclear reactions, scattering of electrons or photons, etc).
An atom traversing a layer of a stationary material can
loose all of its electrons if its speed is much higher than
the orbiting speed of its innermost electrons. Am I the only
one who does not know how a "gravitational interaction"
can ionize an atom? Is it something that is theoretically
expected from general relativity (which I never studied)?

It's fun to be back on phys-l. Ludwik, your principal interest used to
be in nuclear reactions. Is it not true that the great majority of
nuclear reactions taking place in the universe are driven by gravity?

An inelastic collision between two neutral hydrogen atoms having more
than 12.6 eV of kinetic energy in their center of mass frame can result
in ionization of one of the atoms. In a box of hydrogen in thermal
equilibrium at a given temperature and pressure there is a calculable
frequency of occurrence of such collisions. (Of course at room
temperature at least one of the participants in such a collision will
come from way out on the wings of the Maxwell speed distribution.) The
degree of ionization in the box will depend upon the frequency of
ionizing collisions and the frequency of recombinations of the ions.

The easiest way to treat the problem of determining the degree of
ionization given temperature and pressure (or particle density) is by
using statistical thermodynamics. The result of this calculation is
surprisingly simple; it is called the Saha equation (q.v.). That is,
however, not relevant to the question Ludwik asked, nor is general
relativity germane here.

In the case of cluster gas, the box is provided by the gravitational
potential inside the rich cluster of galaxies. Ultimately the high
speeds of the ions are derived at the expense of the kinetic energies
of the galaxies in the cluster through their mutual gravitational
interaction. These ion energies are much higher than the ionization
potentials of the atoms in the plasma because the gravitational
potential wells inside rich clusters are so deep. One of the several
"dark matter" or "missing mass" problems concerns clusters of galaxies.
If one looks at the luminous mass in a cluster and (by their redshifts)
the peculiar velocities of the galaxies in the cluster, it appears that
a cluster should discorporate in much less time than the age of the
universe because so many of the galaxies possess speeds greater than
escape velocity. Cluster gas can account for more than the luminous
mass of the galaxies in a cluster in many cases, at least partially
accounting for the missing mass.

Leigh