Issue |
A&A
Volume 411, Number 2, November IV 2003
|
|
---|---|---|
Page(s) | 215 - 220 | |
Section | Stellar structure and evolution | |
DOI | https://doi.org/10.1051/0004-6361:20031318 | |
Published online | 17 November 2003 |
The ratio of small to large separations of acoustic oscillations as a diagnostic of the interior of solar-like stars
1
Astronomy Unit, Queen Mary, University of London, Mile End Road, London E1 4NS, UK
2
LESIA, Observatoire de Paris, place Jules Janssen, 92195 Meudon, France
3
Institute of Physics of the Earth, B Gruzinskya 10, Moscow 123810, Russia
Corresponding author: I. W. Roxburgh, Roxburgh@qmul.ac.uk
Received:
7
May
2003
Accepted:
14
August
2003
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 we define the
internal phase shift
through the relation
. The
are almost independent of acoustic radius
outside the
stellar core and can be determined as a continuous functions of ω
from partial wave solutions for the interior – that is solutions
of the oscillation equations for any ω that satisfy the Laplace
boundary condition at a sufficiently large acoustic radius tf outside
the stellar core. If the ω are eigenfrequencies then they satisfy
the Eigenfrequency Equation
where
is the
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
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 μHz) from the upcoming space missions MOST, COROT
and Eddington.
Key words: stars: oscillations
© ESO, 2003
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