A PHENOMENOLOGICAL MODEL FOR THE INTERACTION OF SOLAR P-MODES WITH ACTIVE REGIONS

We adopt a phenomenological approach to study the interaction of solar p-mode waves with magnetic regions. We assume that the interaction ca n be described by a complex index of refraction. The modification of t he index of refraction due to magnetic fields is defined as a complex interaction parameter, which results in a change of the p-mode wave am plitude and phase shift. The effect of the complex index of refraction appears as a source term in the wave equation, which is a function of the interaction parameter. The wave equation with the source is solve d with a method of Green's functions and the Born approximation to obt ain the scattered waves, if the interaction parameter is small. In gen eral, an incident mode would be converted into the degenerate modes, w hich have the same frequency as the incident mode but different wavenu mbers, after interacting with a magnetic region. Since the incident wa ves consist of many modes, there is coupling between different inciden t modes through the interaction with the sunspot. The coupling is the greatest for the adjacent modes. The range of coupling depends on the distribution of sigma. This mode coupling would complicate the calcula tion of the absorption coefficient and phase shift of each mode from a model, since all incident modes within the coupling range would contr ibute to the outgoing mode. The mode coupling would also make the comp arison of the computed absorption coefficients and phase shifts with t he observed values difficult. For uniform axisymmetric sunspots, the m ode coupling is small, and the absorption coefficient and phase shift of each mode can be calculated with a given interaction parameter. We use a solar model to calculate absorption coefficients and phase shift s for several horizontally uniform axisymmetric sunspots. The comparis on of observed values with computed values suggests that (1) the horiz ontal size of the regions responsible for the absorption and phase shi ft does not change much with depth (2) the overall size of an active r egion does not change much with depth, though the size of each small f lux tube might decrease with depth over a few pressure scale heights, and (3) the regions responsible for the absorption and phase shift pro bably have a depth of about 15-40 Mm.