On detecting the large separation in the autocorrelation of stellar oscillation times series

Abstract

The observations carried out by the space missions CoRoT and Kepler provide a large set of asteroseismic data. Their analysis requires an efficient procedure first to determine if the star is reliably showing solar-like oscillations, second to measure the so-called large separation, third to estimate the asteroseismic information that can be retrieved from the Fourier spectrum. We develop in this paper a procedure, based on the autocorrelation of the seismic Fourier spectrum. We have searched for criteria able to predict the output that one can expect from the analysis by autocorrelation of a seismic time series. First, the autocorrelation is properly scaled for taking into account the contribution of white noise. Then, we use the null hypothesis H0 test to assess the reliability of the autocorrelation analysis. Calculations based on solar and CoRoT times series are performed in order to quantify the performance as a function of the amplitude of the autocorrelation signal. We propose an automated determination of the large separation, whose reliability is quantified by the H0 test. We apply this method to analyze a large set of red giants observed by CoRoT. We estimate the expected performance for photometric time series of the Kepler mission. Finally, we demonstrate that the method makes it possible to distinguish l=0 from l=1 modes. The envelope autocorrelation function has proven to be very powerful for the determination of the large separation in noisy asteroseismic data, since it enables us to quantify the precision of the performance of different measurements: mean large separation, variation of the large separation with frequency, small separation and degree identification.