Starspots and Activity of the Flare Star GJ 1243
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The photometric variability of the uniqueMdwarf flare star GJ 1243 (KIC 9726699) is investigated using the most complete set of observationalmaterial obtained with the Kepler Space Telescope. The analysis is based on 49 487 individual brightness measurements obtained during an interval of 1460 days (nearly four years). The periodicity of the brightness variations with the period Pphot = 0.59261 ± 0.00060d is confirmed. The temperature inhomogeneities on the stellar surface reconstructed from the light curve are used to drive maps of these surface-temperature inhomogeneities (of the filling factor f). The resulting maps are used to determine the positions of active regions. Analysis of the surface-temperature maps for GJ 1243 led to the conclusion that the positions of spots on the stellar surface displayed appreciable evolution during the analyzed time interval. The maximum value for the lower limit on the differentialrotation parameter ΔΩ is 0.0022 rad/day. This more accurate estimate of ΔΩ is lower than the values presented earlier by Davenport et al.  (0.0058 and 0.0036 rad/day), due to the more accurate account of variations in the positions of the most active longitude in the current study. However, the differentialrotation estimate obtained in  using a method based on fitting the evolution of spots using twodimensional Gaussian functions essentially coincides with the new estimate presented here. The fractional area of the total spotted surface S of the star during the observing interval considered varied from 7 to 2%. The amplitude of the brightness variability of the star slowly decreased, varying in the range 1.6−0.5%. Overall, the position of GJ 1243 in spottedness–age, spottedness–rotation period, and spottedness–Rossby number diagrams agrees very well with the general character of the dependences displayed in earlier studies of M dwarfs.
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