TEMPORAL WINDOW EFFECTS AND THEIR DECONVOLUTION FROM SOLAR OSCILLATION SPECTRA

Long unbroken time series are a primary goal of observational heliosei smology, but it is impossible to completely eliminate temporal gaps re gardless of the adopted strategy. Here we report on a study of the eff ects of the gaps on the measurement of oscillation line parameters. We created observing windows described by a duty cycle, a gap periodicit y, and a randomness factor. We then used a maximum-likelihood method t o fit a simulated oscillation spectrum containing a single spectral li ne convolved with the window function. We find that frequent (less tha n 1.0 d apart) gaps have little or no effect on the oscillation parame ters. Infrequent gaps (2 d apart) have more substantial effects on the measured oscillation line parameters, with the largest systematic dev iations occurring for nearly periodic windows with low duty cycles. Fo r these windows, the average gap length is a substantial fraction of t he lifetime of the simulated mode. In this case, the deviations can be as high as 0.01 muHz in central frequency, 0.2 muHz in line width, wi th relative deviations of 15% in the energy and a factor of 5 in the b ackground 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. Thes e results may well be different for a more realistic solar-like spectr um containing many spectral lines. We have also tested a simple deconv olution method to remove the effects of the gaps from the oscillation spectrum. This procedure computes the deconvolved spectrum from the ra tio of the autocorrelation functions of the convolved signal and the w indow. The deconvolution alters the statistical distribution of the ob servations, and this effect must be accounted for in the fitting of th e mode. We find that, in spectra with infrequent gaps and low duty cyc les, 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.