USuRPER: Unit-sphere representation periodogram for full spectra

Abstract

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.

TESS cycle 1 observations of roAp stars with 2-min cadence data

“…Pulsational variability was discovered in the cores of hydrogen lines and in doubly-ionized Pr, Nd, and Dy lines. Recently, the same 102 HARPS spectra were analysed by Binnenfeld et al (2020) by using the unit-sphere representation periodogram (USuRPER), finding the same period.…”

New periodograms separating orbital radial velocities and spectral shape variation

“…Distance correlation also provides a measure of dependence between random variables of different dimensions. Building on this attribute, Binnenfeld et al (2020) extended the use of distance correlation, by introducing USuRPER-a novel method to detect periodic variation in a time series of astronomical spectra. The novelty of USuRPER is that it enables the detection of periodic variations of the overall spectral shape, without extracting specific scalar quantities such as RV or activity indicators from the spectrum.…”

“…The third is the spectral shape, s i . The s distance matrix is computed as defined by Binnenfeld et al (2020), using the metric…”

“…The novelty of the presented method is its ability to separate and distinguish periodic signals that originate from Doppler shift from those that originate from line deformation. It is an extension of the phase distance correlation (PDC) concept (Zucker 2018) and the recently introduced unit-sphere representation periodogram (USuRPER) presented in Binnenfeld et al (2020).…”

A Transiting Warm Giant Planet around the Young Active Star TOI-201

“…We find a stronger signal at the 53 day period in the PDC periodogram than in a comparison GLS periodogram, as expected for eccentric orbits, as shown in Figure 6. We also ran the recent PDC extension, the USuRPER (Binnenfeld et al 2020), which is designed to account for fluctuations in the entire spectral shape. A prominent peak is visible in the USuRPER low-frequency region (Figure 6).…”