Modeling Solar Oscillation Power Spectra. I. Adaptive Response Function for Doppler Velocity Measurements

Abstract

Improving the accuracy and resolution of helioseismic inversions calls for more accurate modeling of the observational p-mode power spectra from which the solar oscillation frequencies are traditionally measured. We present a new technique of calculating the response function ( leakage matrix) for Doppler velocity measurements that is based largely on an analytical description of the relevant instrumental and physical effects. The computational efficiency of the new approach allows us to implement the response function in an adaptive manner: i.e., the compensation for instrumental or optical distortions of unknown magnitude can be performed as a part of the spectral fitting procedure.

Effects of differential rotation and meridional circulation in solar oscillations of high degree l

“…Therefore, the effects of meridional flows in the observational power spectra of solar oscillations are of the order of v 2 mer , if small spatial leaks with imaginary amplitudes (e.g. those coming from a small CCD tilt; Vorontsov & Jefferies 2005) are neglected.…”

“…To recover the underlying mode parameters, we need an accurate response function (leakage matrix; see e.g. Vorontsov & Jefferies 2005), an accurate model of the acoustic line profiles (e.g. Jefferies, Vorontsov & Giebink 2006) and an accurate physical description of the mode‐coupling effects induced by internal velocity fields, effects which become strong at high degree l .…”

eSDO algorithms, data centre and visualization tools

“…Once a target mode's times series and power spectrum have been produced, the eSDO algorithm can calculate the mode's frequency, linewidth and power amplitude parameters. First, the static and dynamic components of the target mode's response function, or "leakage matrix", are computed with the adaptive response function method developed by Vorontsov & Jefferies (2005). Next, the total leakage matrix is used in conjunction with a table of p-mode frequencies and the target mode's degree, azimuthal order, and order to determine the optimal spherical harmonics coefficients.…”

The autocorrelation function of stellar p-mode measurements and its diagnostic properties

“…Measurements with MDI data can be expected to be more accurate because the sensitivity coefficients are known with better accuracy [we used sensitivity coefficients resulting from leakage matrix calculations described in Vorontsov & Jefferies (2005)].…”