Fourier Analysis of Gapped Time Series: Improved Estimates of Solar and Stellar Oscillation Parameters - AstrophysicsReportar como inadecuado

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Abstract: Quantitative helio- and asteroseismology require very precise measurements ofthe frequencies, amplitudes, and lifetimes of the global modes of stellaroscillation. It is common knowledge that the precision of these measurementsdepends on the total length T, quality, and completeness of the observations.Except in a few simple cases, the effect of gaps in the data on measurementprecision is poorly understood, in particular in Fourier space where theconvolution of the observable with the observation window introducescorrelations between different frequencies. Here we describe and implement arather general method to retrieve maximum likelihood estimates of theoscillation parameters, taking into account the proper statistics of theobservations. Our fitting method applies in complex Fourier space and exploitsthe phase information. We consider both solar-like stochastic oscillations andlong-lived harmonic oscillations, plus random noise. Using numericalsimulations, we demonstrate the existence of cases for which our improvedfitting method is less biased and has a greater precision than when thefrequency correlations are ignored. This is especially true of lowsignal-to-noise solar-like oscillations. For example, we discuss a case wherethe precision on the mode frequency estimate is increased by a factor of five,for a duty cycle of 15%. In the case of long-lived sinusoidal oscillations, aproper treatment of the frequency correlations does not provide any significantimprovement; nevertheless we confirm that the mode frequency can be measuredfrom gapped data at a much better precision than the 1-T Rayleigh resolution.

Autor: Thorsten Stahn, Laurent Gizon


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