Coefficients of variation for detecting solar-like oscillations

Abstract

Detecting the presence and characteristic scale of a signal is a common problem in data analysis. We develop a fast statistical test of the null hypothesis that a Fourier-like power spectrum is consistent with noise. The null hypothesis is rejected where the local 'coefficient of variation' (CV) - the ratio of the standard deviation to the mean - in a power spectrum deviates significantly from expectations for pure noise (CV ≈ 1.0 for a χ2 2-degrees-offreedom distribution). This technique is of particular utility for detecting signals in power spectra with frequency-dependent noise backgrounds, as it is only sensitive to features that are sharp relative to the inspected frequency bin width. We develop a CV-based algorithm to quickly detect the presence of solar-like oscillations in photometric power spectra that are dominated by stellar granulation. This approach circumvents the need for background fitting to measure the frequency of maximum solar-like oscillation power, vmax. In this paper, we derive the basic method and demonstrate its ability to detect the pulsational power excesses from the well-studied APOKASC-2 sample of oscillating red giants observed by Kepler. We recover the catalogued vmax values with an average precision of 2.7 per cent for 99.4 per cent of the stars with 4 yr of Kepler photometry. Our method produces false positives for < 1 per cent of dwarf stars with vmax well above the long-cadence Nyquist frequency. The algorithm also flags spectra that exhibit astrophysically interesting signals in addition to single solar-like oscillation power excesses, which we catalogue as part of our characterization of the Kepler light curves of APOKASC-2 targets.