Modeling Kepler transit light curves as false positives: Rejection of blend scenarios for Kepler-9, and validation of Kepler-9 d, a super-earth-size planet in a multiple system

Light curves from the Kepler Mission contain valuable information on the nature of the phenomena producing the transit-like signals. To assist in exploring the possibility that they are due to an astrophysical false positive, we describe a procedure (BLENDER) to model the photometry in terms of a "blend" rather than a planet orbiting a star. A blend may consist of a background or foreground eclipsing binary (or star-planet pair) whose eclipses are attenuated by the light of the candidate and possibly other stars within the photometric aperture. We apply BLENDER to the case of Kepler-9 (KIC 3323887), a target harboring two previously confirmed Saturn-size planets (Kepler-9 b and Kepler-9 c) showing transit timing variations, and an additional shallower signal with a 1.59 day period suggesting the presence of a super-Earth-size planet. Using BLENDER together with constraints from other follow-up observations we are able to rule out all blends for the two deeper signals and provide independent validation of their planetary nature. For the shallower signal, we rule out a large fraction of the false positives that might mimic the transits. The false alarm rate for remaining blends depends in part (and inversely) on the unknown frequency of small-size planets. Based on several realistic estimates of this frequency, we conclude with very high confidence that this small signal is due to a super-Earth-size planet (Kepler-9 d) in a multiple system, rather than a false positive. The radius is determined to be 1.64+0.19-0.14 R., and current spectroscopic observations are as yet insufficient to establish its mass.