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 Chi^2 2-degrees-of-freedom 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, nu_max. 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 cataloged nu_max values with an average precision of 2.7% for 99.4% of the stars with 4 years of Kepler photometry. Our method produces false positives for <1% of dwarf stars with nu_max 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 catalog as part of our characterization of the Kepler light curves of APOKASC-2 targets.