THE ABSORPTION OF P-MODES BY SUNSPOTS - VARIATIONS WITH DEGREE AND ORDER

The absorption of solar p-modes by an isolated sunspot is investigated by means of a spherical harmonic decomposition of the p-modes into inward and outward propagating waves. We find, in close agreement with the results of Braun, Duvall, & LaBonte (BDL), that the absorption coefficient (averaged over frequency and azimuthal order) increases with increasing horizontal wavenumber k (i.e., with increasing spherical harmonic degree l) over the range 0 less-than-or-equal-to k less-than-or-equal-to 0.8 Mm-1. However, for larger horizontal wavenumbers, in the range 0.8 less-than-or-equal-to k less-than-or-equal-to 1.5 Mm-1, we find that the absorption coefficient decreases with increasing k, whereas BDL find little if any decrease in absorption over this range. The high spatial resolution and high signal-to-noise ratio of our data allow us to measure the variation of the absorption along individual p-mode ridges for radial orde up to n = 5. The absorption along each ridge tends to peak at an intermediate value of the spherical harmonic degree l in the range 200 less-than-or-equal-to l less-than-or-equal-to 400. The highest absorption is found along the p1 ridge, and the absorption decreases with increasing radial order n. There is also an apparent sinusoidal-like variation of the absorption with increasing degree l along each ridge. Repeating our analysis for a field of view containing only quite Sun, we find no net frequency-integrated absorption. However, the quiet-Sun data show apparent acoustic emission along the p1 ridge for precisely the same range of degrees (400 less-than-or-equal-to l less-than-or-equal-to 600) where the sunspot shows its maximum absorption of p1. This curious result can be understood by taking into account the decrease in the lifetime and spatial range of the p-modes with increasing degree 1.