Systematics-insensitive periodic signal search with K2

From pulsating stars to transiting exoplanets, the search for periodic signals in K2 data, Kepler's 2-wheeled extension, is relevant to a long list of scientific goals. Systematics affecting K2 light curves due to the decreased spacecraft pointing precision inhibit the easy extraction of periodic signals from the data. We here develop a method for producing periodograms of K2 light curves that are insensitive to pointing-induced systematics; the Systematics-Insensitive Periodogram (SIP). Traditional sine-fitting periodograms use a generative model to find the frequency of a sinusoid that best describes the data. We extend this principle by including systematic trends, based on a set of 'Eigen light curves', following Foreman-Mackey et al. (2015), in our generative model as well as a sum of sine and cosine functions over a grid of frequencies. Using this method we are able to produce periodograms with vastly reduced systematic features. The quality of the resulting periodograms are such that we can recover acoustic oscillations in giant stars and measure stellar rotation periods without the need for any detrending. The algorithm is also applicable to the detection of other periodic phenomena such as variable stars, eclipsing binaries and short-period exoplanet candidates. The SIP code is available at https://github.com/RuthAngus/SIPK2

Loose Ends for the Exomoon Candidate Host Kepler-1625b

The claim of an exomoon candidate in the Kepler-1625b system has generated substantial discussion regarding possible alternative explanations for the purported signal. In this work we examine in detail these possibilities. First, the effect of more flexible trend models is explored and we show that sufficiently flexible models are capable of attenuating the signal, although this is an expected byproduct of invoking such models. We also explore trend models using X and Y centroid positions and show that there is no data-driven impetus to adopt such models over temporal ones. We quantify the probability that the 500 ppm moon-like dip could be caused by a Neptune-sized transiting planet to be < 0.75%. We show that neither autocorrelation, Gaussian processes nor a Lomb-Scargle periodogram are able to recover a stellar rotation period, demonstrating that K1625 is a quiet star with periodic behavior < 200 ppm. Through injection and recovery tests, we find that the star does not exhibit a tendency to introduce false-positive dip-like features above that of pure Gaussian noise. Finally, we address a recent re-analysis by Kreidberg et al (2019) and show that the difference in conclusions is not from differing systematics models but rather the reduction itself. We show that their reduction exhibits i) slightly higher intra-orbit and post-fit residual scatter, ii) $\simeq$ 900 ppm larger flux offset at the visit change, iii) $\simeq$ 2 times larger Y-centroid variations, and iv) $\simeq$ 3.5 times stronger flux-centroid correlation coefficient than the original analysis. These points could be explained by larger systematics in their reduction, potentially impacting their conclusions.Comment: 21 pages, 4 tables, 11 figures. Accepted for publication in The Astronomical Journal, January 202

Fast and scalable Gaussian process modeling with applications to astronomical time series

The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose but, since the computational cost scales, in general, as the cube of the number of data points, their application has been limited to small datasets. In this paper, we present a novel method for Gaussian Process modeling in one-dimension where the computational requirements scale linearly with the size of the dataset. We demonstrate the method by applying it to simulated and real astronomical time series datasets. These demonstrations are examples of probabilistic inference of stellar rotation periods, asteroseismic oscillation spectra, and transiting planet parameters. The method exploits structure in the problem when the covariance function is expressed as a mixture of complex exponentials, without requiring evenly spaced observations or uniform noise. This form of covariance arises naturally when the process is a mixture of stochastically-driven damped harmonic oscillators -- providing a physical motivation for and interpretation of this choice -- but we also demonstrate that it can be a useful effective model in some other cases. We present a mathematical description of the method and compare it to existing scalable Gaussian Process methods. The method is fast and interpretable, with a range of potential applications within astronomical data analysis and beyond. We provide well-tested and documented open-source implementations of this method in C++, Python, and Julia.Comment: Updated in response to referee. Submitted to the AAS Journals. Comments (still) welcome. Code available: https://github.com/dfm/celerit