Astronomy and Astrophysics – Astrophysics
Scientific paper
Nov 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003a%26a...411..215r&link_type=abstract
Astronomy and Astrophysics, v.411, p.215-220 (2003)
Astronomy and Astrophysics
Astrophysics
85
Stars: Oscillations
Scientific paper
By considering stellar models with the same interior structure but different outer layers we demonstrate that the ratio of the small to large separations of acoustic oscillations in solar-like stars is essentially independent of the structure of the outer layers, and is determined solely by the interior structure. Defining the scaled Eulerian pressure perturbation psil (omega ,t) = r p' /(rho c)1/2 we define the internal phase shift deltal (omega ,t) through the relation omega psi /(dpsi /dt)=tan (omega t -pil /2 + deltal ). The deltal are almost independent of acoustic radius t=int dr/c outside the stellar core and can be determined as a continuous functions of omega from partial wave solutions for the interior - that is solutions of the oscillation equations for any omega that satisfy the Laplace boundary condition at a sufficiently large acoustic radius tf outside the stellar core. If the omega are eigenfrequencies then they satisfy the Eigenfrequency Equation omega T=(n+l/2) pi +alpha (omega )-deltal (omega ) where alpha (omega ) is the l independent surface phase shift (Roxburgh & Vorontsov 2000). Using this result we show that the ratio of small to large separations is determined to high accuracy solely by the internal phase shifts deltal (omega ) and hence by the interior structure alone. The error in this result is estimated and shown to be smaller than that associated with the errors in the determination of the frequencies (~0.1-0.3 mu Hz) from the upcoming space missions MOST, COROT and Eddington.
Roxburgh Ian W.
Vorontsov Sergei V.
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