Re: why in a cephied variable star in the helium ionization layer does opacity

The causes behind the oscillations in RR Lyrae
and other variables are well understood, but are a
bit subtle.

The key thing is that the helium ionization zone is
a partial ionization zone.  Gases of more than one
ionization state can exist together.

There are typically two ionization zones in
most stars.  The hydrogen partial ionization
zone contains neutral and ionized hydrogen (i.e.,
protons).  The helium ionization zone, which is mainly
responsible for the oscillations, contains both the
first and second ionization states of helium (i.e.,
helium with one and zero electrons, respectively).

The opacity in the partial ionization zone depends
on two factors: the temperature and the density.

Depending on the temperature of the star, the
ionization zones can exist right at the surface,
at some intermediate depth, or way down deep in
the interior.  For pulsating stars, these zones
contain enough material to act as a piston for the
oscillations but are not so deep that they can't rise
against the outer layers.

You are absolutely right that ionized gasses typically
have lower opacity than neutral ones.  Normally hotter
gasses have lower opacity, too.

Suppose there is some sort of compression in the gas
to start things off....

Then what happens is that much of the energy available
from the compression goes into ionizing the gas
(actually increasing the fraction that is ionized)
rather than strongly raising the overall temperature.
The rise in density increases the opacity to a greater
effect than the reduction of opacity from the higher
ionization.

Then the higher opacity produces an outward pressure
on the partially ionized layers, and the stuff
rises up.

During the expansion, energy is released.
The temperature does not go down much, but there
is still a big release of energy as the electrons
recombine with the atoms to produce more atoms in the
next lower ionization state.  As the stuff rises,
it expands and the density goes down and with it
the opacity.  But the effect of the density changes
is larger than the effect of the ionization changes,
and the opacity declines.

This is called the Zhevakin opacity mechanism.