Peaks and troughs in helioseismology: The power spectrum of solar oscillations

I present a matched-wave asymptotic analysis of the driving of solar oscill ations by a general localized source. The analysis provides a simple mathem atical description of the asymmetric peaks in the power spectrum in terms o f the relative locations of eigenmodes and troughs in the spectral response . It is suggested that the difference in measured phase function between th e modes and the troughs in the spectrum will provide a key diagnostic of th e source of the oscillations. I also suggest a form for the asymmetric line profiles to be used in the fitting of solar power spectra. Finally, I pres ent a comparison between the numerical and asymptotic descriptions of the o scillations. The numerical results bear out the qualitative features sugges ted by the asymptotic analysis but suggest that numerical calculations of t he locations of the troughs will be necessary for a quantitative comparison with the observations.