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

Abstract

Context. 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 a star reliably shows 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. Aims. In this paper we develop a procedure based on the autocorrelation of the seismic Fourier spectrum that is capable of providing measurements of the large and small frequency separations. The performance of the autocorrelation method needs to be assessed and quantified. We therefore searched for criteria able to predict the output that one can expect from the analysis by autocorrelation of a seismic time series. Methods. First, the autocorrelation is properly scaled to take into account the contribution of white noise. Then we use the null hypothesis H 0 test to assess the reliability of the autocorrelation analysis. Calculations based on solar and CoRoT time series are performed to quantify the performance as a function of the amplitude of the autocorrelation signal. Results. We obtain an empirical relation for the performance of the autocorrelation method. We show that the precision of the method increases with the observation length, and with the mean seismic amplitude-to-background ratio of the pressure modes to the power 1.5 ± 0.05. We propose an automated determination of the large separation, whose reliability is quantified by the H 0 test. We apply this method to analyze red giants observed by CoRoT. We estimate the expected performance for photometric time series of the Kepler mission. We demonstrate that the method makes it possible to distinguish = 0 from = 1 modes. Conclusions. The envelope autocorrelation function (EACF) 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.

Seismic and spectroscopic characterization of the solar-like pulsating CoRoT target HD 49385

“…It then seems reasonable to identify the ridges as follows: neighboring ridges A and B correspond to = 2 and = 0 modes, respectively, and ridge C to = 1 modes. We note that Mosser & Appourchaux (2009) and Bedding & Kjeldsen (2010) obtained the same identification for the degrees of the ridges using different approaches. The following analysis is based on this identification.…”

The universal red-giant oscillation pattern

“…The measurement of the large separation is performed in two steps. First, an initial-guess value Δν guess of the large separation is computed by an automated pipeline (Mosser & Appourchaux 2009). This is used to form the initial synthetic template to correlate with the real spectrum.…”

“…Unfortunately, the methods currently used to determine the global oscillation parameters suffer from various sources of uncertainty (Hekker et al 2009;Huber et al 2009;Mathur et al 2010). First, the stochastic excitation of the modes gives rise to variability in the amplitudes, resulting in an apparently irregular comb structure; second, the finite mode lifetime blurs the estimates of the eigenfrequencies; third, estimates are affected by the stellar noise and Article published by EDP Sciences L9, page 1 of 4 granulation signal superimposed on the oscillations (Mosser & Appourchaux 2009). In fact, simulations have shown that the impact of realization noise on the measurement of the large separation Δν, can be much stronger than the background noise for red giants .…”

Detection of solar-like oscillations in relics of the Milky Way: asteroseismology of K giants in M4 using data from the NASA K2 mission

“…Estimates of the large spacing were first provided by the autocorrelation function (Mosser & Appourchaux 2009), with the requirement that the null hypothesis be rejected at the 95 % confidence level. These values were then refined with the method of Mosser et al (2011).…”