Dynamical response of the solar corona. I. Basic formulations.
Abstract
The dynamic response of the corona to finiteamplitude perturbations in the presence of a spherically symmetric adiabatic singlefluid solar wind is analyzed to illustrate the proper method of specifying such perturbations in a subsonic flow regime for a mixed initial and boundaryvalue problem. Basic equations are presented which form a system of hyperbolic partial differential equations. It is shown that information traveling toward the sun must be accounted for when introducing finiteamplitude perturbations at a boundary in a subsonic flow regime to simulate solar events, and that this information leads to a compatibility relation that must be satisfied by the perturbation variables at the boundary. A procedure for introducing this relation in numerical simulations is outlined, and numerical examples are used to demonstrate that discontinuities may be formed at the boundary if the perturbations do not satisfy the compatibility relation. It is found that erroneous conclusions regarding the relationship between solar events and interplanetary disturbances may be inferred if the perturbations are not located in the subsonic flow region and if the compatibility relation is neglected.
 Publication:

The Astrophysical Journal
 Pub Date:
 July 1976
 DOI:
 10.1086/154493
 Bibcode:
 1976ApJ...207..296N
 Keywords:

 Boundary Value Problems;
 Digital Simulation;
 Perturbation Theory;
 Solar Corona;
 Solar Wind;
 Subsonic Flow;
 Adiabatic Equations;
 Critical Point;
 Eigenvalues;
 Hyperbolic Differential Equations;
 Matrices (Mathematics);
 Numerical Analysis;
 Partial Differential Equations;
 Shock Waves;
 Solar Physics