[vsnet-chat 2947] Re: (fwd) reason for variable star to pulsate periodically

[Toshihito Ishida <ishida@nhao.go.jp>]

Dear Mr. Tan, 

Sorry for my reply is so late.  I have been very busy in these days 
and could not have no time to make a reply. 

Kato-san wrote in the message received on Fri, 5 May 2000 10:53(JST). 
Subject: [vsnet-chat 2894] (fwd) reason for variable star to pulsate periodically
> (fwd) reason for variable star to pulsate periodically
> 
>    Forwarded query.  Could anyone help?  (Ishida-san, please?)

OK. I will try it now.  

In  [vsnet-chat 2914] 
> 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. 

> From: "jitchun tan" <jcjit@hotmail.com>
> Date: Thu, 04 May 2000 23:56:27 MYT
> Subject: reason for variable star to pulsate periodically
> 
> 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

It's 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.  

If my reply does not answer to your question properly, please feel 
free to ask me more.  

Sincerely, 

---
% 石田　俊人
% Tel: 0790-82-3886 ext.142 Fax: 0790-82-3514
% e-mail: ishida@nhao.go.jp(office) HQA01560@nifty.ne.jp(private)
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