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 χ 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, ν max . In this paper, we derive the basic method and demonstrate its ability to detect the pulsational power excesses from the wellstudied APOKASC-2 sample of oscillating red giants observed by Kepler. We recover the cataloged ν 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 ν 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.

A Hot Saturn Orbiting an Oscillating Late Subgiant Discovered by TESS

“…To extract oscillation parameters characterizing the average properties of the power spectrum, we used several automated analysis methods (e.g., Huber et al 2009;Mathur et al 2010;Benomar et al 2012;Kallinger et al 2012;Mosser et al 2012a;Corsaro & De Ridder 2014;Lundkvist 2015;Stello et al 2017;Campante 2018;Bell et al 2019), many of which have been extensively tested on Kepler data (e.g., Hekker et al 2011;Verner et al 2011). In most of these analyses, the power contributions due to granulation noise and stellar activity were modeled by a combination of power laws and a flat contribution due to shot noise, and then corrected by dividing the power spectrum by the background model.…”

A Hot Saturn Orbiting An Oscillating Late Subgiant Discovered by TESS

“…To extract oscillation parameters characterizing the average properties of the power spectrum, we used several automated analysis methods (e.g. Huber et al 2009;Mathur et al 2010;Mosser et al 2012a;Benomar et al 2012;Kallinger et al 2012;Corsaro & De Ridder 2014;Lundkvist 2015;Stello et al 2017;Campante 2018;Bell et al 2019), many of which have been extensively tested on Kepler data (e.g. Hekker et al 2011;Verner et al 2011).…”

Determining the Best Method of Calculating the Large Frequency Separation For Stellar Models

“…To obtain another set of ν max and ∆ν measurements for our data we also determined the seismic parameters using a more efficient technique. The recent work of Bell et al (2019) has shown that ν max can be quickly determined using what is called the coefficient of variation, or CV. The coefficient of variation is the ratio of the standard deviation to the mean of the power spectrum.…”

“…It should be noted that our implementation of the CV method is not identical to that of Bell et al (2019). This is necessary because the Bell et al (2019) CV method was designed for red giant stars, using long-cadence light curves, while our sample also contains main sequence and subgiant stars that have short-cadence data.…”

“…It should be noted that our implementation of the CV method is not identical to that of Bell et al (2019). This is necessary because the Bell et al (2019) CV method was designed for red giant stars, using long-cadence light curves, while our sample also contains main sequence and subgiant stars that have short-cadence data. For example, Bell et al (2019) use 2000 overlapping bins spaced evenly in log-frequency (for their "oversampled" spectrum) while we implement the moving window overlapping by an amount based on the previous window size.…”