From a posting to vsnet-chat
> Can anybody tell me why and how pulsating star pulsate??
Most of the pulsations are considered to be caused by the kappa-mechanism. "kappa" is for opacity.
In most of the inside of stars, the opacity of stellar gas decreases as temperature increases. However, there are some regions where this tendency gets weak, or even gets reverse. For example, in the hydrogen and helium ionization zones, opacity increases as temperature increases. These zones, especially helium ionization zones are considered to be the exciting regions of the classical Cepheids, RR Lyrae etc. Recently, a small bump of the opacity caused by metals is recognized. This bump is considered to be responsible for the beta Cephei type and some higher effective temperature pulsators.
Let's consider that the gas in the ionization zone is compressed by a perturbation. The density and temperature of this zone increases and the opacity also increases. Then, the energy flux from inside of the star decreases because of the increase of opacity. This energy flux decrease causes the extra heat energy comparing with the adiabatic change. Then, this region obtains extra restoring force by this extra heat energy.
When the gas in this region is expanded, opacity decreases. This decrease causes the extra energy loss and again obtains extra restoring force.
The region where there is an opacity bump is unstable to the pulsation. However, most of the stellar envelope is stable. If the effect of destabilization is larger than that of stabilization a star will pulsate as a whole.
Please remark that above described kappa mechanism works when the most of the energy flux is transferred by radiation. When the convective transfer becomes dominant process, the pulsation will not occur. This is considered to be the origin of the red edge of the pulsation in the HR diagram.
If the effective temperature of a star is high enough, the density of ionization region is too low, and the destabilizing effect is too small. This is considered to be the origin of the blue edge.
> why a variable star can pulsate periodically??
Actually, there are some pulsating stars which pulsate not strictly periodic. For examples, Mira stars are relatively regular pulsators, however their cycle length between successive light maxima indicate some variations. The magnitudes at maxima also changes cycle by cycle. There are more irregular pulsators and they are classified as semi-regulars and irregulars. RV Tauri type stars also shows some irregularity.
Considering other post into account, you seems to intend to ask about the cause of the pulsation. If so, I write some abstract of the present situation of the research in the earlier part of this e-mail. However, under above mentioned situation, your question sounds as the following question to me.
Why a star can pulsate periodically, ( and why some others cannot) ?
In some stars, even though more than two pulsation modes are unstable from theoretical consideration and it more than two periodicities are possible to appear, only one period appears. The other modes are suppressed by some reason. This is called as mode selection, and seems to be caused by the nonlinear interaction between some pulsation modes.
Recently, there are some attempts to interpret irregularities in pulsating stars as chaos. In some stars, there is a sign that the observed variation seems to be caused by chaos. However, it seems still not clear, which type of pulsating stars can be interpreted by chaos and which cannot.
Anyway, we need nonlinear pulsation theory to make an answer to the above question, which is still on it's way to develop.
For more details, there is a monograph on stellar pulsation.
J.P. Cox, Theory of Stellar Pulsation, Princeton Ser in Ap, ISBN 0-691-08252-9 = hardcover, ISBN 0-691-08253-7 = paperback
Its contents are somewhat out of date, especially where related to observational facts, but the basics concerning the mechanism of the periodic pulsation will be still useful. However, it may be out of print now. If so, I can't remind the other book now. There are some proceedings dedicated to related problems, however, I'm afraid that fundamentals are not included in such a proceedings.
You can also find out some more shorter description about pulsating stars in the books about the variable stars in general.