Abstract
In recent years, astronomers have witnessed major progresses in the field of stellar physics. This was made possible thanks to the combination of a solid theoretical understanding of the phenomena of stellar pulsations and the availability of a tremendous amount of exquisite space-based asteroseismic data. In this context, this chapter reviews the basic theory of stellar pulsations, considering small, adiabatic perturbations to a static, spherically symmetric equilibrium. It starts with a brief discussion of the solar oscillation spectrum, followed by the setting of the theoretical problem, including the presentation of the equations of hydrodynamics, their perturbation, and a discussion of the functional form of the solutions. Emphasis is put on the physical properties of the different types of modes, in particular acoustic (p-) and gravity (g-) modes and their propagation cavities. The surface (f-) mode solutions are also discussed. While not attempting to be comprehensive, it is hoped that the summary presented in this chapter addresses the most important theoretical aspects that are required for a solid start in stellar pulsations research.
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Notes
- 1.
Here the term that would dominate in the case of atmospheric gravity waves is being neglected, as those will not be discussed in these lectures.
- 2.
In a real stellar atmosphere there can be partial reflection of the wave energy even when ω > ω c . Accounting for that would require modifying the atmospheric model and, thus, the outer boundary condition accordingly.
- 3.
For a more general case in which these assumptions are not made, see Gough (1993).
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Acknowledgements
I am grateful to Ângela Santos for producing Fig. 1 and to Jørgen Christensen-Dalsgaard for producing Fig. 8. This work was supported by Fundação para a Ciência e a Tecnologia (FCT) through national funds (UID/FIS/04434/2013) and by FEDER through COMPETE2020 (POCI-01-0145-FEDER-007672), as well as through the Investigador FCT Contract No. IF/00894/2012/CP0150/CT0004. This work has received funding from EC, under FP7, through the grant agreement FP7-SPACE-2012-312844.
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Cunha, M.S. (2018). Theory of Stellar Oscillations. In: Campante, T., Santos, N., Monteiro, M. (eds) Asteroseismology and Exoplanets: Listening to the Stars and Searching for New Worlds. Astrophysics and Space Science Proceedings, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-319-59315-9_2
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