Re: why are cepheid variables variable?

The bottom line is that Cepheids vary in magnitude because they pulsate.  
In fact, all stars oscillate at some level - a star, to first 
approximation, is a large spherical gas cloud, and can vibrate or 
oscillate in many different ways.  In Cepheids these oscillations are 
unusually large, and correspond to simple radial pulsations of alternating 
phases of expansion and contraction.

How does this produce variations in magnitude?  It turns out there are two 
competing effects here.  Firstly, when the Cepheid is at its maximum size, 
the surface area is large, which tends to lead it to emit more radiation 
and appear brighter.  However, the second effect is that as the Cepheid 
is compressed during the contraction phase its temperature rises, again 
leading to an increase in the total radiation emitted.  As it happens, the 
temperature effect is most important in its influence on the optical 
luminosity, whereas the surface area effect is more important in the 
infrared (the net result is that when a Cepheid is brightest in optical 
light, it is not at the maximum of the infrared light).

This still leaves one question: why are Cepheids particularly prone to 
such large pulsations?  The answer relates to their structure, and in 
particular to the existence of a zone a little below the surface of the 
star, in which (mainly) Helium atoms are partially ionized.  The 
properties of this zone are that as it is compressed, further ionization 
occurs, and the opacity (its tendency to block the passage of light 
photons from the interior) increases.  This has an effect rather like that 
of putting a lid on a saucepan - the pressure builds up, and the whole 
star expands.  As it does so, the ionization decreases, the star becomes 
more transparent, and so the pressure drops again (analogous to the lid 
lifting up briefly, and letting some steam escape!).  When the pressure 
drops, gravity pulls in on the outer layers of the star, leading again to 
contraction, hence completing the cycle.