Analytic model for photometric variation due to starspots on a differentially rotating star

TL;DR

This paper introduces an analytic model to interpret stellar lightcurve variations caused by starspots on differentially rotating stars, aiding the analysis of Kepler data and future space missions.

Contribution

The paper develops a new analytical framework linking starspot properties and differential rotation to observed lightcurve harmonics, including limb darkening effects.

Findings

Model accurately predicts harmonic coefficients for starspot-induced lightcurves

Mock observations demonstrate potential to recover starspot and rotation parameters

Framework applicable to various rotating astronomical objects

Abstract

We present an analytic model of the lightcurve variation for stars with non-evolving starspots on a differentially rotating surface. The Fourier coefficients of the harmonics of the rotation period are expressed in terms of the latitude of the spot, $\ell_{s}$, and the observer's line-of-sight direction, $\ell_{o}$, including the limb darkening effect. We generate different realizations of multi-spots according to the model, and perform mock observations of the resulting lightcurve modulations. We discuss to what extent one can recover the properties of the spots and the parameters for the differential rotation law from the periodogram analysis. Although our analytical model neglects the evolution of spots on the stellar surface (dynamical motion, creation and annihilation), it provides a basic framework to interpret the photometric variation of stars, in particular from the existing Kepler data and the future space-born mission. It is also applicable to photometric modulations induced by rotation of various astronomical objects.