Planet Occurrence within 0.25 AU of Solar-type Stars from Kepler (1103.2541v1)

Abstract: We report the distribution of planets as a function of planet radius (R_p), orbital period (P), and stellar effective temperature (Teff) for P < 50 day orbits around GK stars. These results are based on the 1,235 planets (formally "planet candidates") from the Kepler mission that include a nearly complete set of detected planets as small as 2 Earth radii (Re). For each of the 156,000 target stars we assess the detectability of planets as a function of R_p and P. We also correct for the geometric probability of transit, R*/a. We consider first stars within the "solar subset" having Teff = 4100-6100 K, logg = 4.0-4.9, and Kepler magnitude Kp < 15 mag. We include only those stars having noise low enough to permit detection of planets down to 2 Re. We count planets in small domains of R_p and P and divide by the included target stars to calculate planet occurrence in each domain. Occurrence of planets varies by more than three orders of magnitude and increases substantially down to the smallest radius (2 Re) and out to the longest orbital period (50 days, ~0.25 AU) in our study. For P < 50 days, the radius distribution is given by a power law, df/dlogR= k R^\alpha. This rapid increase in planet occurrence with decreasing planet size agrees with core-accretion, but disagrees with population synthesis models. We fit occurrence as a function of P to a power law model with an exponential cutoff below a critical period P_0. For smaller planets, P_0 has larger values, suggesting that the "parking distance" for migrating planets moves outward with decreasing planet size. We also measured planet occurrence over Teff = 3600-7100 K, spanning M0 to F2 dwarfs. The occurrence of 2-4 Re planets in the Kepler field increases with decreasing Teff, making these small planets seven times more abundant around cool stars than the hottest stars in our sample. [abridged]

• The paper’s main contribution is a precise quantification of planet occurrence rates by correcting for detection biases in Kepler data.
• Its analysis shows that planets between 2 and 4 Earth radii occur at about 0.13 per star, with smaller planets being even more common.
• The findings challenge existing planet formation theories and support the core-accretion model by emphasizing the prevalence of close-in, small exoplanets.

Planet Occurrence within 0.25 AU of Solar-type Stars from Kepler

The paper "Planet Occurrence within 0.25 AU of Solar-type Stars from Kepler," conducted by Howard et al., presents an analysis of the distribution of exoplanets as a function of their radius, orbital period, and host star's effective temperature based on the Kepler mission data. This research principally focuses on planets orbiting solar-type stars within 0.25 Astronomical Units (AU) and is informed by data from the 1,235 planet candidates identified in the Kepler mission, which targets a subset of bright main-sequence GK stars.

Methodology and Corrections for Bias

The paper describes a framework to estimate planet occurrence by examining the detectability of planets based on the noise characteristics of individual stars, effectively accounting for the detection bias inherent in the survey. The researchers corrected for the geometric probability of transit and detection completeness, thus quantifying planet occurrence more precisely. However, a key methodological adjustment is necessary due to photometric noise constraints; only systems with significant signal-to-noise ratios (SNR) are considered, providing confidence in transit detections and consequently in extracted exoplanet statistics.

Numerical Results

The occurrence of planets within 50-day orbital periods is quantified by the paper, revealing a strong inverse relationship between planet size and occurrence rate. Notably, for planets between 2 and 4 Earth radii, the occurrence is measured at approximately 0.130 planets per star. A substantial increase in occurrence is observed for smaller radii and longer orbital periods, contradicting earlier theoretical projections of a "planet desert" for super-Earth and Neptune-sized planets in close orbits.

Theoretical and Practical Implications

The findings posed by Howard et al. have significant ramifications for planet formation theories, especially those centered around core accretion processes. Notably, the rapid rise in occurrence with decreasing planet size supports the core-accretion model; however, it challenges previous population synthesis models that predicted a scarcity of close-in super-Earths and Neptunes. These discrepancies suggest a need for revised models that accurately simulate the physical environments and migratory pathways of these planets.

Furthermore, the analysis reveals that smaller planets (R < 4 Earth radii) are more frequently found around cooler host stars, hinting at a possible metallicity or stellar mass effect that correlates with planet formation efficiency.

Future Prospects

The results encourage further studies into the correlation of planet occurrence with host star metallicity, temperature, and luminosity to deepen our understanding of planetary formation. Future research can leverage Kepler's extended observations to extend these findings to planets with radii approaching Earth's size. Expanding this research could also refine theoretical models regarding planet density and composition, influencing our interpretations of planet formation dynamics.

In conclusion, this paper provides an intricate and data-driven exploration of exoplanet distributions, setting a new benchmark in the understanding of short-period planets around solar-type stars. It calls for enhanced theoretical models and sustained observational campaigns to validate and expand upon these findings.