Modeling starspots on low mass star GJ 1243 observed by TESS Kamil Bicz, Robert Falewicz, Małgorzata Pietras Astronomical Institute, University of Wrocław, Kopernika 11, 51-622 Wrocław, Poland Email: bicz@astro.uni.wroc.pl Abstract Quasi-periodic modulations of the stellar light curve may result from dark spots crossing the visible stellar disc. Since the release of the ﬁrst TESS sector the possibility of examining such quasi-periodic modulations by assumed dark spots has increased. Thanks to this observations we tried to detect starspot coverage of low mass stars with visible variability of their luminosity. Using the light curves from TESS satellite and the new, BASSMAN package to ﬁt spot models of different complexities, will constructed starspots distribution on individual stars. These models will then be tested to reveal a connection between the starspots and the stellar ﬂares, in order to provide insight into the overall stellar magnetic ﬁeld. Here we present results of modeling of starspots on GJ 1243 with our new tool and compare the results with the previous reconstructions of the spatial distribution. Introduction GJ 1243 (also known as TIC273589987) is fully convective M4.0V dwarf at a distance 11.95 pc, with mass 0.24 M⊙, radius 0.27 R⊙, effective temperature 3261 K (MAST catalog1) and rotation period equal P = 0.592596 ± 0.00021 day [1]. GJ 1243 also has estimated differential rotation parameter of equal 0.012 ± 0.002 rad/day [1] (for the Sun α⊙= 0.2 rad/day). This star was observed only during two, lasting ∼27 days periods, namely TESS sectors 14 and 15. We selected 33433 individual bright- ness measurements (with 2-minute cadence) acquired over approximately 47 days of observations. Due to very low differential rotation shear and very slow changes of the minimal ﬂux phase mainly in sector 15 (Fig. 1) we estimated spottedness of each sector separately without taking differential rotation into account. Small changes in phase of minimal ﬂux of GJ 1243 are more likely caused by evolution of one of the spots than the differential rotation. There are no signiﬁcant changes in phase of maximal ﬂux value. In our analysis we assumed inclination i = 32◦estimated by analysis of spectral observations of this star at wavelengths from 3600 ˚A to 10000 ˚A and Kepler long cadence data [11]. We estimated the amplitude of GJ 1243 normalized ﬂux as 1.00741 by phasing the light curve from sector 14 and 15 and taking the maximal value of averaged phased data. 1690 1700 1710 1720 1730 TBJD [days] 0.0 0.2 0.4 0.6 0.8 1.0 Phase 1.00 1.01 1.02 1.03 1.04 1.05 1.06 Normalized flux Figure 1: Mapping of relative ﬂux (pixel shade, from dark to light) as a function of rotation phase and time for all TESS data of ﬂux vs. time and phase. Red dots with ﬁtted third degree polynomial represent minimal signal in phases and green dots with ﬁtted linear function represent maximal signal in phase. Methods To model starspots on analysed star we used software BASSMAN (Best rAndom StarSpots Model calculAtioN) written in Python 3, by K. Bicz and designed to model starspots on stellar surface using its observational light curve. BASSMAN recreates light curve of spotted star by ﬁtting spot(s) model to data maximising the log probability of star with spots model and is sampling matched model using Markov chain Monte Carlo by ﬁtting contrasts, sizes, stellar longitudes and latitudes of spot(s). The program uses numerous ready-made software packages to model the spots on the star: starry [4], PyMC3 [7], exoplanet [3], theano [12]. We compare our results with analytical solution for average temperature of the spots on a star with effective temperature Teﬀusing [6]: Tspot = 0.751Teﬀ−3.58 · 10−5T 2 eﬀ+ 808 (1) and to estimate percentage of stellar surface covered by spots we use [5, 10]: Aspot Astar = 100% · ∆F F " 1 − Tspot Teﬀ 4#−1 (2) where (∆F/F) is normalized amplitude of light variations, Tspot is mean temperature of spots esti- mated from equation 1 and T