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ASTR 5610, Majewski [SPRING 2016]. Lecture Notes

ASTR 5610 (Majewski) Lecture Notes


The Instability Strip and Pulsational Variables

All stars have oscillations to some degree (e.g., solar turbulence from convection), but stars with large amplitude, coherent oscillations have had a profound influence on stellar populations studies (as we have already seen).

p-mode oscillations (pressure fluctuations) are the most relevant here:

Physics of Pulsation

The opacity mechanism (κ-mechanism) (identified by Eddington) is the instability that drives large-amplitude pulsations.

Instability Strip

There is an instability strip slicing through the HR diagram in which the opacity law can undergo the inversion and stars become unstable to p-mode instability and the stars become pulsational variables.

Why is there this limited zone that expresses the pulsational instability?
Phase Lag

Pulsational variables are brightest and bluest right after passing through minimum radius.

The phase lag between maximum radius and maximum luminosity has to do with delaying action of the H partial ionization zone.

Period-Luminosity Relationship

The pulsational period of a variable should be of order the time it takes for a sound wave to propagate through the star.

The period luminosity relationship is a result of the fact that the instability strip lies at approximately constant effective temperature.

Types of Pulsational Variables

The instability strip crosses various evolutionary phases of different mass (and density) stars, and each produces a class of pulsational variable.

Each class of variable has a characteristic period and can be attributed to a typical mass of progenitor.

Note also that because stars of lower luminosity have higher density, by the period-density relation, lower luminosity pulsational variables have shorter periods, as may be seen by the above table, for stars in the classical instability strip.

Long Period Variables (Miras)

Classical (Population I) Cepheids
Type I or classical Cepheid light curve for δ Cephei.
Type II or W Virginis Cepheid, showing the contrast in shapes that distinguish them from classical Cepheids. Figures from

Population II Cepheids (W Virginis Stars)
Anomalous Cepheids
RR Lyrae Stars
ZZ Ceti Stars
Pulsational Variables as Population Tracers

Obviously, through the PL relationship, pulsational variables are incredibly important standard candles.

But they are also important tracers of the star formation history of galaxies and the structure of specific stellar populations.

Summary of Oscillating Stars and Oscillation Modes

The types of oscillations generally seen in typical stars are:

In sun-like stars p-modes dominate, g-modes confined to core by convection zone.

HR-diagram showing different classes of oscillating stars, including radial and non-radial pulsators. Figure from Favata, Roxburfg, Christensen-Dalsgaard (2000, Eddington: A mission to map stellar evolution through oscillations and to find habitable planets). From
Non-radial pulsations:


Asteroseismology studies the internal structure of stars by the interpretation of spectra of oscillation modes (similar to earh seismology).

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All material copyright © 2003,2006,2008,2010,2012,2014,2016 Steven R. Majewski. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 551 and Astronomy 5610 at the University of Virginia.