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spotrod: a semi-analytic model for transits of spotted stars

The Hubble Space Telescope (HST) and the Kepler space mission observed a large number of planetary transits showing anomalies due to starspot eclipses, with more such observations expected in the near future by the K2 mission and the Transiting Exoplanet Survey Satellite (TESS). To facilitate analysis of this phenomenon, we present spotrod, a model for planetary transits of stars with an arbitrary limb darkening law and a number of homogeneous, circular spots on their surface. A free, open source implementation written in C, ready to use in Python, is available for download. We analyze Kepler observations of the planetary host star HAT-P-11, and study the size and contrast of more than two hundred starspots. We find that the flux ratio of spots ranges at least from 0.6 to 0.9, corresponding to an effective temperature approximately 100 to 450 K lower than the stellar surface, although it is possible that some spots are darker than 0.5. The largest detected spots have a radius less than approximately 0.2 stellar radii.