A&A 411, 215-220 (2003)

DOI: 10.1051/0004-6361:20031318

## The ratio of small to large separations of acoustic oscillations as a diagnostic of the interior of solar-like stars

**I. W. Roxburgh**

^{1, 2}and S. V. Vorontsov^{1, 3}^{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

(Received 7 May 2003 / Accepted 14 August 2003)

** Abstract **

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
from *partial wave* solutions for the interior - that is solutions
of the oscillation equations for any
that satisfy the Laplace
boundary condition at a sufficiently large acoustic radius
*t*_{f} outside
the stellar core. If the
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
Hz) from the upcoming space missions MOST, COROT
and *Eddington*.

**Key words:**stars: oscillations

Offprint request: I. W. Roxburgh, Roxburgh@qmul.ac.uk

**©**

*ESO 2003*