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Spin–orbit resonance, transit duration variation and possible secular perturbations in KOI-13

Authors

  • Gy. M. Szabó,

    Corresponding author
    1. Konkoly Observatory of the Hungarian Academy of Sciences, PO Box 67, H-1525 Budapest, Hungary
    2. Department of Experimental Physics and Astronomical Observatory, University of Szeged, H-6720 Szeged, Hungary
      E-mail: szgy@konkoly.hu
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  • A. Pál,

    1. Konkoly Observatory of the Hungarian Academy of Sciences, PO Box 67, H-1525 Budapest, Hungary
    2. Department of Astronomy, Eötvös University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
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  • A. Derekas,

    1. Konkoly Observatory of the Hungarian Academy of Sciences, PO Box 67, H-1525 Budapest, Hungary
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  • A. E. Simon,

    1. Konkoly Observatory of the Hungarian Academy of Sciences, PO Box 67, H-1525 Budapest, Hungary
    2. Department of Experimental Physics and Astronomical Observatory, University of Szeged, H-6720 Szeged, Hungary
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  • T. Szalai,

    1. Department of Optics and Quantum Electronics, University of Szeged, Dóm tér 9, H-6720 Szeged, Hungary
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  • L. L. Kiss

    1. Konkoly Observatory of the Hungarian Academy of Sciences, PO Box 67, H-1525 Budapest, Hungary
    2. Sydney Institute for Astronomy, School of Physics A28, University of Sydney, NSW 2006, Australia
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E-mail: szgy@konkoly.hu

ABSTRACT

KOI-13 is the first known transiting system exhibiting light-curve distortions due to gravity darkening of the rapidly rotating host star. In this Letter, we analyse publicly available Kepler Q2–Q3 short-cadence observations, revealing a continuous light variation with a period of Prot= 25.43 ± 0.05 h and a half-amplitude of 21 ppm, which is linked to stellar rotation. This period is in exact 5:3 resonance with the orbit of KOI-13.01, which is the first detection of a spin–orbit resonance in a host of a substellar companion. The stellar rotation leads to stellar oblateness, which is expected to cause secular variations in the orbital elements. We indeed detect the gradual increment of the transit duration with a rate of (1.14 ± 0.30) × 10−6 d cycle−1. The confidence of this trend is 3.85σ, and the two-sided false alarm probability is 0.012 per cent. We suggest that the reason for this variation is the expected change of the impact parameter, with a rate of d b/d t=−0.016 ± 0.004  yr−1. Assuming b≈ 0.25, KOI-13.01 may become a non-transiting object in 75–100 years. The observed rate is compatible with the expected secular perturbations due to the stellar oblateness yielded by the fast rotation.

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