USuRPER: Unit-sphere representation periodogram for full spectra

We introduce an extension of the periodogram concept to time-resolved spectroscopy. USuRPER, the unit-sphere representation periodogram, is a novel technique that opens new horizons in the analysis of astronomical spectra. It can be used to detect a wide range of periodic variability of the spectrum shape. Essentially, the technique is based on representing spectra as unit vectors in a multidimensional hyperspace, hence its name. It is an extension of the phase-distance correlation periodogram we had introduced in previous papers, to very high-dimensional data such as spectra. USuRPER takes the overall shape of the spectrum into account, which means that it does not need to be reduced into a single quantity such as radial velocity or temperature. Through simulations, we demonstrate its performance in various types of spectroscopic variability: single-lined and double-lined spectroscopic binary stars, and pulsating stars. We also show its performance on actual data of a rapidly oscillating Ap star. USuRPER is a new tool to explore large time-resolved spectroscopic databases such as APOGEE, LAMOST, and the RVS spectra of Gaia. We have made a public GitHub repository with a Python implementation of USuRPER available to the community, to experiment with it and apply it to a wide range of spectroscopic time series.