Connections between Quasi-periodicity and Modulation in Pulsating Stars

TL;DR

This paper explores the connection between quasi-periodicity and modulation in pulsating stars, using mathematical models of almost periodic functions to analyze complex stellar light curves observed by space telescopes.

Contribution

It introduces a mathematical framework based on band-limited almost periodic functions to describe and analyze non-repetitive modulation cycles in pulsating stars.

Findings

Analytical description of complex stellar light curves

Numerical simulations supporting the models

Systematic approach to star modulation analysis

Abstract

The observations of the photometric space telescopes CoRoT and Kepler show numerous Blazhko RR Lyrae stars which have non-repetitive modulation cycles. The phenomenon can be explained by multi-periodic, stochastic or chaotic processes. From a mathematical point of view, almost periodic functions describe all of them. We assumed band-limited almost periodic functions either for the light curves of the main pulsation or for the modulation functions. The resulting light curves can generally be described analytically and it can also be examined by numerical simulations. This presentation is a part of our systematic study on the modulation of pulsating stars (Benko et al. 2009, 2011, 2012).