Temporal window effects and their deconvolution from solar oscillation spectra
Abstract
Long unbroken time series are a primary goal of observational helioseismology, but it is impossible to completely eliminate temporal gaps regardless of the adopted strategy. Here we report on a study of the effects of the gaps on the measurement of oscillation line parameters. We created observing windows described by a duty cycle, a gap periodicity, and a randomness factor. We then used a maximumlikelihood method to fit a simulated oscillation spectrum containing a single spectral line convolved with the window function. We find that frequent (less than 1.0 d apart) gaps have little or no effect on the oscillation parameters. Infrequent gaps (2 d apart) have more substantial effects on the measured oscillation line parameters, with the largest systematic deviations occurring for nearly periodic windows with low duty cycles. For these windows, the average gap length is a substantial fraction of the lifetime of the simulated mode. In this case, the deviations can be as high as 0.01 microHz in central frequency, 0.2 microHz in line width, with relative deviations of 15% in the energy and a factor of 5 in the background when compared to simulations with a perfect ungapped window. As the randomness of the window increases, we find that generally the systematic deviations decrease while the random errors increase. These results may well be different for a more realistic solarlike spectrum containing may spectral lines. We have tested a simple deconvolution method to remove the effects of the gaps from the oscillations spectrum. This procedure computes the deconvoluted spectrum from the ratio of the autocorrelation functions of the convolved signal and the window. The deconvolution alters the statistical distribution of the observations, and this effect must be accounted for in the fitting of the mode. We find that, in spectra with infrequent gaps and low duty cycles, this method can improve the estimate of the line width by as much as 40% and the estimate of the energy by 70%. However, the background is overestimated by as much as a factor of 30 in these cases.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 December 1993
 Bibcode:
 1993A&A...280..704L
 Keywords:

 Data Reduction;
 Helioseismology;
 Line Spectra;
 Observation;
 Solar Oscillations;
 Solar Spectra;
 Temporal Resolution;
 Autocorrelation;
 Convolution Integrals;
 Energy Spectra;
 Fourier Transformation;
 Maximum Likelihood Estimates;
 Solar Physics