Adaptation of the phase distance correlation periodogram to account for measurement uncertainties

¹ Porter School of the Environment and Earth Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 6997801, Israel
e-mail: avrahambinn@gmail.com
² Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel

Received: 19 August 2023
Accepted: 2 April 2024

Abstract

We present an improvement of the phase distance correlation (PDC) periodogram to account for uncertainties in the time-series data. The PDC periodogram introduced in our previous papers is based on the statistical concept of distance correlation. By viewing each measurement and its accompanying error estimate as a probability distribution, we are able to use the concept of energy distance to design a distance function (metric) between measurement-uncertainty pairs. We used this metric as the basis for the PDC periodogram, instead of the simple absolute difference. We demonstrate the periodogram’s performance using both simulated and real-life data. This adaptation makes the PDC periodogram much more useful, demonstrating it can be helpful in the exploration of large time-resolved astronomical databases, ranging from Gaia radial velocity and photometry data releases to those of smaller surveys, such as APOGEE and LAMOST. We have made a public GitHub repository available, with a Python implementation of the new tools available to the community.