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

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.