Application of the Continuous Orthonormalization and Adjoint Methods to the Computation of Solar Eigenfrequencies and Eigenfrequency Sensitivities
Abstract
Existing numerical techniques in helioseismology are applied in new ways to compute two sets of basic quantities: solar eigenfrequencies, computed via the continuous orthonormalization (CON) method, and their sensitivities with respect to changes in the solar equilibrium model, computed via the adjoint method. The CON method integrates an eighth-order nonlinear system of ordinary differential equations (ODEs) which defines the linear adiabatic nonradial oscillation modes of the sun. The adjoint method integrates a related eighth-order linear inhomogeneous system of ODEs. From the resultant solution, an eigenfrequency's partial derivatives with repsect to an extensive set of solar model parameters may be computed simultaneously. Numerical tests confirm the validity of the two methods. Eigenfrequencies obtained via the CON method agree with the corresponding eigenfrequencies obtained via finite-difference or mesh approaches. Eigenfrequency sensitivities for the three different types of modes (pressure, gravity, and fundamental) obtained via the adjoint method are presented.
- Publication:
-
The Astrophysical Journal Supplement Series
- Pub Date:
- September 1991
- DOI:
- 10.1086/191600
- Bibcode:
- 1991ApJS...77...97R
- Keywords:
-
- Computational Astrophysics;
- Helioseismology;
- Solar Oscillations;
- Eigenvalues;
- Orthonormal Functions;
- Solar Interior;
- Solar Physics;
- NUMERICAL METHODS;
- SUN: INTERIOR;
- SUN: OSCILLATIONS