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

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.

arXiv comment31 pages, 15 figures, accepted for publication in PASJ

References in corpus (31)

• Rotation Periods of 34,030 Kepler Main-Sequence Stars: The Full Autocorrelation Sample
• Weakened magnetic braking as the origin of anomalously rapid rotation in old field stars
• The Rossiter-McLaughlin effect and analytic radial velocity curves for transiting extrasolar planetary systems
• Fundamental Properties of Kepler Planet-Candidate Host Stars using Asteroseismology
• Standing on the shoulders of Dwarfs: the $Kepler$ asteroseismic LEGACY sample I - oscillation mode parameters
• The Dependence of Differential Rotation on Temperature and Rotation
• Starspots, spin-orbit misalignment, and active latitudes in the HAT-P-11 exoplanetary system
• Inferring probabilistic stellar rotation periods using Gaussian processes
• Starspots and spin-orbit alignment in the WASP-4 exoplanetary system
• On differential rotation and overshooting in solar-like stars
• The asteroseismic potential of Kepler: first results for solar-type stars
• Photometric Amplitude Distribution of Stellar Rotation of Kepler KOIs-Indication for Spin-Orbit Alignment of Cool Stars and High Obliquity for Hot Stars
• Colors of a Second Earth: Estimating the fractional areas of ocean, land, and vegetation of Earth-like exoplanets
• Determination of Three-dimensional Spin-orbit Angle with Joint Analysis of Asteroseismology, Transit Lightcurve, and the Rossiter-McLaughlin Effect: Cases of HAT-P-7 and Kepler-25
• Asteroseismic detection of latitudinal differential rotation in 13 Sun-like stars
• Measurements of Stellar Inclinations for Kepler Planet Candidates
• A Preponderance of Perpendicular Planets
• Complex magnetic topology and strong differential rotation on the low-mass T Tauri star V2247 Oph
• The Information Content in Analytic Spot Models of Broadband Precision Lightcurves
• Colors of a Second Earth II: Effects of Clouds on Photometric Characterization of Earth-like Exoplanets
• Small-Scale and Global Dynamos and the Area and Flux Distributions of Active Regions, Sunspot Groups, and Sunspots: A Multi-Database Study
• Imaging starspot evolution on Kepler target KIC 5110407 using light curve inversion
• An Isolated White Dwarf with a 70 second Spin Period
• A Relationship Between Stellar Age and Spot Coverage
• Hot Stars With Kepler Planets Have High Obliquities
• The misaligned orbit of the Earth-sized planet Kepler-408b
• exocartographer: A Bayesian Framework for Mapping Exoplanets in Reflected Light
• Characterizing the feedback of magnetic field on the differential rotation of solar-like stars
• Analytic Reflected Lightcurves for Exoplanets
• On the size distribution of spots within sunspot groups
• Obliquity of an Earth-like planet from frequency modulation of its direct imaged lightcurve: mock analysis from general circulation model simulation