A new method to determine the asymptotic eigenfrequency equation of low-degree acoustic modes

Details A new method to determine the asymptotic eigenfrequency equation of low-degree acoustic modes A new method to determine the asymptotic eigenfrequency equation of low-degree acoustic modes

Mar 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001mnras.321..615l&link_type=abstract

Monthly Notices of the Royal Astronomical Society, Volume 321, Issue 4, pp. 615-624.

Astronomy and Astrophysics

Astronomy

5

Sun: Interior, Sun: Oscillations, Stars: Interiors, Stars: Oscillations, Sun: Interior, Sun: Oscillations, Stars: Interiors, Stars: Oscillations

Scientific paper

The high accuracy of the observed solar spectra obtained from the space experiments GOLF and VIRGO has motivated us to develop a more precise asymptotic analysis of low-degree acoustic modes. Therefore we present a phase method to build an asymptotic solution to the equation of motion of acoustic oscillations. The principle consists of describing the oscillatory motion by a system of two first-order non-linear differential equations for the phase and amplitude. The equations are coupled only in the amplitude equation, leaving a single phase equation to determine the eigenfrequencies. We illustrate also the deficiency in the accuracy of standard asymptotic methods to determine the eigenfrequency, and highlight the advantages of this new method. The strength of this new technique is based on an accurate description of the phase dependence on the background state rather than on the wavefunction, as is done in standard asymptotic methods. This allows us to obtain a new asymptotic eigenvalue equation for low-degree acoustic modes, which is more accurate than the usual ones. In this case, the eigenfrequency equation is obtained without making the so-called Cowling approximation, i.e., by neglecting the Eulerian perturbation of the gravitational field. This allows us to obtain a new expression for the small separation, valid for the global acoustic modes of high and low radial orders.

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