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

Abstract: 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, a target harboring two previously confirmed Saturn-size planets (Kepler-9b and Kepler-9c) 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-9d) in a multiple system, rather than a false positive. The radius is determined to be 1.64 (+0.19/-0.14) R(Earth), and current spectroscopic observations are as yet insufficient to establish its mass.

Overview of the Light Curve Analysis for Kepler-9 and the Validation of Kepler-9d

The paper delves into a sophisticated approach to analyzing the transit light curves of potential exoplanetary candidates like those observed by the Kepler Mission. It specifically addresses the challenge of distinguishing real planetary signals from false positives caused by astrophysical phenomena, known as "blends". The study focuses primarily on Kepler-9, a system with two confirmed gas giants, Kepler-9b and Kepler-9c, identified through their transit signatures and transit timing variations (TTVs), alongside a third candidate signal, now validated as the super-Earth-size planet Kepler-9d.

False Positive Scenarios and Methodology

The authors developed a comprehensive procedure involving detailed modeling of Kepler photometric data to investigate the likelihood of false positives. These can arise from scenarios such as:

• Background Eclipsing Binaries (BEBs): Where the light curves may be contaminated by another pair of stars not gravitationally bound to the host star system.
• Hierarchical Triple Systems: Consisting of a binary star system gravitationally bound to the primary star.
• Background star-planet pairs: Situations where the apparent transit signal is caused by a star-planet system unrelated to the target star but within the same line of sight.

The method utilized in this research, known as \, involves simulating these blend situations by varying parameters (e.g., masses and distances of stars in a potential binary) and comparing these models to the observed photometric data to see which, if any, could pass unnoticed and mimic a planetary signal.

Key Findings and Validation of Kepler-9d

1. Kepler-9b and Kepler-9c Validation: The study employs its method to rule out blends for these two signals independently of the TTVs, confirming their planetary nature through light curve modeling alone.

2. Kepler-9d Validation: For KOI-377.03, the potential super-Earth signal, the authors performed extensive tests to exclude a wide array of false positive scenarios. After eliminating the majority of blends using a combination of \, high-resolution imaging, and centroid shifts due to transits, the planetary origin of the signal was verified with a high confidence level.

3. Implications for Super-Earth Frequency: Based on the frequencies of certain blend scenarios remaining possible, and compared against estimated occurrence rates of super-Earths from radial velocity surveys and Kepler data, the study argues that the planet hypothesis is overwhelmingly more probable.

4. Impact on Exoplanetary Studies: This research emphasizes the utility of the Kepler light curves themselves in excluding false positive signals, advocating a robust pathway for validating candidates that might not be amenable to follow-up spectroscopic confirmation due to their faintness or the low mass of their signals.

Future Prospects and Conclusions

The paper suggests that future developments in the field may benefit from this approach, especially for validating Earth-sized exoplanets in the habitable zone. It also underscores the increasing importance of integrating statistical methodologies with direct observational techniques to achieve credible planetary validation. This is paramount for effectively leveraging the extensive datasets provided by missions like Kepler, which has opened new frontiers in exoplanet research.

Through this comprehensive analysis, the paper contributes significantly to the methodologies used for exoplanet validation, particularly in complex systems with multiple planetary candidates, demonstrating practical applications to promote better understanding and exploration of distant worlds. Kepler-9d emerges as a reliable component of this multi-planet system, showcasing the potential for discovering and confirming small, fascinating exoplanets using detailed photometric analysis accompanied by statistical validation techniques.