On the Determination of Michelson Doppler Imager High‐Degree Mode Frequencies

Abstract

The characteristics of the solar acoustic spectrum are such that mode lifetimes get shorter and spatial leaks get closer in frequency as the degree of a mode increases for a given order. A direct consequence of this property is that individual p-modes are resolved only at low and intermediate degrees and that at high degrees individual modes blend into ridges. Once modes have blended into ridges, the power distribution of the ridge defines the ridge central frequency, and it will mask the true underlying mode frequency. An accurate model of the amplitude of the peaks that contribute to the ridge power distribution is needed to recover the underlying mode frequency from fitting the ridge. We present the results of fitting high-degree power ridges (up to l = 900) computed from several 2-3 month long time series of full-disk observations taken with the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory between 1996 and 1999. We also present a detailed discussion of the modeling of the ridge power distribution, and the contribution of the various observational and instrumental effects on the spatial leakage, in the context of the MDI instrument. We have constructed a physically motivated model (rather than some ad hoc correction scheme) that we believe results in a methodology that can produce an unbiased determination of high-degree modes once the instrumental characteristics are well understood. Finally, we present preliminary estimates of changes in high-degree mode parameters with epoch and thus solar activity level and discuss their significance. These estimates are preliminary because they rely on a simple—if not simplistic—ridge-to-mode correction scheme to account for errors in the plate scale used for the spherical harmonic decomposition. Such a correction scheme produced residual systematics that, as we show, are not always constant with time. These cannot be properly corrected without reprocessing the data back to the level of the spherical harmonic decomposition.