Studies in Astronomical Time Series Analysis: The Double Lomb-Scargle Periodogram and Super Resolution

Abstract: Multiple-frequency periodograms -- based on time series models consisting of two or more independent sinusoids -- have long been discussed. What is new here is the presentation of a practical, simple-to-use computational framework implementing this concept. Our algorithms have super resolution that evades the Rayleigh criterion, as well as provision for statistical weighting and tapering. They can be used for essentially any time series (e.g. time-tagged events or point measurements) with arbitrary sampling -- even or uneven. Examples of super resolution of synthetic data, sunspot numbers, and the rich pulsations of white dwarf J0135+5722, demonstrate practical applications. Appendices derive generalized periodograms using an arbitrary number of arbitrary basis functions (following Bretthorst, 1988)and define several examples of non-sinusoidal bases for these ``omnigrams.'' Application beyond the frequency domain is demonstrated with an autoregressive model exhibiting super resolution in the time domain. A GitHub repository containing omnigram code, and symbolic algebra scripts for generating it, will soon be available.