Pulsation Physics

Why do stars pulsate?

Let's look at a normal star and squeeze it (a radial perturbation)

density and temperature and pressure increase
star "rebounds" and expands. But it will overshoot (like a swing) and go past equilibrium
now density and temperature and pressure are too low, so the star will fall back
etc

Okay, but we have ignored the role of opacity. In a normal star, when temperature increases, opacity decreases. So when we squeeze the star and it heats up, more of the stars heat can flow out of the star, relieving the excess pressure. Similarly when the star expands and temperature drops, more of the heat gets bottled up inside the star keeping it from collapsing back to far.

Opacity stabilizes stars against radial oscillations.

Under special conditions, however, opacity can work in the opposite direction.

Take a portion of a star where Helium is singly ionized. If the temperature rises, the Helium can become doubly ionized. So a temperature increase results in much of the radiative energy being absorbed during ionization. In a helium ionization zone, opacity rises as temperature rises.

Now squeeze the star

density and temperature and pressure increase
helium absorbs the energy in ionization
excess pressure can only be relieved via expansion -- and the star will now overshoot
density, temperature, and pressure decrease
helium recombines, opacity decreases
lack of thermal pressure is enhanced, as energy flows out of the star more easily.
star falls back too far
etc

The oscillation continues, driven by the helium ionization.

If stars are too cool, helium ionization occurs too far inside the star. If stars are too hot, helium ionization occurs too close to the surface. In the instability strip, the conditions are just right to drive the oscillation.