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Summary: PASJ: Publ. Astron. Soc. Japan 64, 1??, 2012 August 25
c 2011. Astronomical Society of Japan.
Mode Classification of Linear Adiabatic Oscillations of Spherically Symmetric
Stars
Masao Takata
Department of Astronomy, School of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033
takata@astron.s.u-tokyo.ac.jp
and
Kavli Institute for Theoretical Physics, Kohn Hall, University of California, Santa Barbara, CA 93106-4030, USA
(Received 2011 October 18; accepted 2011 December 21)
Abstract
We propose a mathematical scheme to classify the eigenmodes of linear adiabatic oscillations of spherically
symmetric stars, with fully taking account of the perturbation to the gravitational potential. The scheme allows
us to allocate a unique and continuous integral index (the radial order) to each eigenmode with a positive squared
eigenfrequency of any stellar structure, which is invariant against any continuous change in the equilibrium structure.
Based on this index, we can unambiguously define the three kinds of eigenmodes of adiabatic stellar oscillations, p
modes, g modes, and f modes.
Key words: stars: oscillations--Sun: oscillations--methods: analytical
1. Introduction
The eigenmode analysis is one of the most fundamental
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