Measuring amplitudes of harmonics and combination frequencies in variable stars

TL;DR

This paper introduces a robust method for measuring harmonic and combination frequencies in variable stars, addressing challenges caused by complex spectra and noisy data, and provides a heuristic algorithm for accurate amplitude estimation.

Contribution

It presents a new, more robust light curve fitting method and proves the amplitude measurement problem is NP-hard, offering a practical heuristic solution.

Findings

The new method reduces ringing artifacts in light-curve fits.

The amplitude measurement problem is NP-hard.

The heuristic algorithm provides quick and accurate amplitude estimates.

Abstract

Discoveries of RR Lyrae and Cepheid variable stars with multiple modes of pulsation have increased tremendously in recent years. The Fourier spectra of these stars can be quite complicated due to the large number of combination frequencies that can exist between their modes. As a result, light-curve fits to these stars often suffer from undesirable ringing effects that arise from noisy observations and poor phase coverage. These non-physical overfitting artifacts also occur when fitting the harmonics of single-mode stars as well. Here we present a new method for fitting light curves that is much more robust against these effects. We prove that the amplitude measurement problem is very difficult (NP-hard) and provide a heuristic algorithm for solving it quickly and accurately.