Lecture Notes on Stellar Oscillations
The purpose of the present set of notes is to provide the
technical background for the study of stellar pulsation,
particularly as far as the oscillation frequencies are concerned.
Thus the notes are heavily biased towards the use of
oscillation data to study the interior of stars;
also, given the importance of the study of solar
oscillations, a great deal of emphasis is given to
the understanding of their properties.
In order to provide this background, the notes go into
considerably more detail on derivations and properties of
equations than is common, e.g., in review papers on this topic.
However, in a course on stellar pulsations
they must be supplemented with other texts
that consider the application of these techniques to, for example,
More general background information about stellar
pulsation can be found in the books by Unno et al. (1989)
and Cox (1980).
An excellent description of the theory of stellar pulsation,
which in many ways has yet to be superseded, was given
by Ledoux & Walraven (1958).
Cox (1967) (reprinted in Cox & Giuli 1968) gave a very clear
physical description of the instability of Cepheids, and
the reason for the location of the instability strip.
The notes were originally written for a course in helioseismology
given in 1985, and they were substantially revised in the Spring of
1989 for use in a course on pulsating stars.
I am grateful to the students who attended these courses
for their comments.
This has led to the elimination of some, although surely not all,
errors in the text.
Further comments and corrections are most welcome.
Preface to 3rd edition
The notes have been very substantially revised and extended in this edition,
relative to the previous two editions.
Thus Chapters 6 and 9 are essentially new, as are Sections 2.4,
the present Section 5.1, Section 5.3.2, Section 5.5 and Section 7.6.
Some of this material has been adopted from various reviews,
particularly Christensen-Dalsgaard & Berthomieu (1991).
Also, the equation numbering has been revised.
It is quite plausible that additional errors have crept in during
this revision; as always, I should be most grateful to be told about them.
Preface to 4th edition
In this edition three appendices have been added,
including a fairly extensive set of student problems in Appendix C.
Furthermore, Chapter 10, on the excitation of oscillations, is new.
The remaining revisions are relatively minor, although new material
and updated results have been added throughout.
Preface to 5th edition
The present edition has been extensively revised.
New material includes a presentation of the recent data on
solar-like oscillations in distant stars, which mark the beginning of a new
era of asteroseismology.
Also, the discussion of asymptotic eigenfunctions of stellar oscillations,
and of stochastic excitation of solar-like oscillations, has been
Unlike previous editions, the present one
has been typeset using LaTeX, leading
to substantial changes in appearance and changes to the equation numbering.
I am grateful to Ross Rosenwald for his
careful reading of the 4th edition, which uncovered
a substantial number of misprints, and to Frank Pijpers for
comments on a draft of the present edition.
I thank Sarbani Basu, Francois Bouchy, Bill Chaplin, Yvonne Elsworth,
Hans Kjeldsen, Jesper Schou and Steve Tomczyk for help with figures or
This edition replaces the 4th edition first made available on the
Internet in February 1998. The 4th edition is still available on
the Internet, at
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Sunday, 1 June, 2003 at 19:28