We report on the orbital architectures of Kepler systems having multiple planet candidates identified in the analysis of data from the first six quarters of Kepler data and reported by Batalha et al. (2013). These data show 899 transiting planet candidates in 365 multiple-planet systems and provide a powerful means to study the statistical properties of planetary systems. Using a generic massradius relationship, we find that only two pairs of planets in these candidate systems (out of 761 pairs total) appear to be on Hill-unstable orbits, indicating ∼ 96% of the candidate planetary systems are correctly interpreted as true systems. We find that planet pairs show little statistical preference to be near mean-motion resonances. We identify an asymmetry in the distribution of period ratios near firstorder resonances (e.g., 2:1, 3:2), with an excess of planet pairs lying wide of resonance and relatively few lying narrow of resonance. Finally, based upon the transit duration ratios of adjacent planets in each system, we find that the interior planet tends to have a smaller transit impact parameter than the exterior planet does. This finding suggests that the mode of the mutual inclinations of planetary orbital planes is in the range 1.0• -2.2• , for the packed systems of small planets probed by these observations.

About one-third of the ∼1200 transiting planet candidates detected in the first four months of Kepler data are members of multiple candidate systems. There are 115 target stars with two candidate transiting planets, 45 with three, 8 with four, and one each with five and six. We characterize the dynamical properties of these candidate multi-planet systems. The distribution of observed period ratios shows that the vast majority of candidate pairs are neither in nor near low-order mean motion resonances. Nonetheless, there are small but statistically significant excesses of candidate pairs both in resonance and spaced slightly too far apart to be in resonance, particularly near the 2:1 resonance. We find that virtually all candidate systems are stable, as tested by numerical integrations that assume a nominal mass-radius relationship. Several considerations strongly suggest that the vast majority of these multi-candidate systems are true planetary systems. Using the observed multiplicity frequencies, we find that a single population of planetary systems that matches the higher multiplicities underpredicts the number of singly-transiting systems. We provide constraints on the true multiplicity and mutual inclination distribution of the multi-candidate systems, revealing a population of systems with multiple super-Earth-size and Neptune-size planets with low to moderate mutual inclinations.

We report the distribution of planets as a function of planet radius, orbital period, and stellar effective temperature for orbital periods less than 50 days around Solar-type (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 R ⊕ . For each of the 156,000 target stars we assess the detectability of planets as a function of planet radius, R p , and orbital period, P , using a measure of the detection efficiency for each star. We also correct for the geometric probability of transit, R ⋆ /a. We consider first Kepler target stars within the "solar subset" having T eff = 4100-6100 K, log g = 4.0-4.9, and Kepler magnitude Kp < 15 mag, i.e. bright, main sequence GK stars. We include only those stars having photometric noise low enough to permit detection of planets down to 2 R ⊕ . 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. The resulting occurrence of planets varies by more than three orders of magnitude in the radius-orbital period plane and increases substantially down to the smallest radius (2 R ⊕ ) and out to the longest orbital period (50 days, ∼0.25 AU) in our study. For P < 50 days, the distribution of planet radii is given by a power law, df /d log R = k R R α with k R = 2.9 +0.5 −0.4 , α = −1.92 ± 0.11, and R = R p /R ⊕ . This rapid increase in planet occurrence with decreasing planet size agrees with the prediction of core-accretion formation, but disagrees with population synthesis models that predict a desert at super-Earth and Neptune sizes for close-in orbits. Planets with orbital periods shorter than 2 days are extremely rare; for R p > 2 R ⊕ we measure an occurrence of less than 0.001 planets per star. For all planets with orbital periods less than 50 days, we measure occurrence of 0.130 ± 0.008, 0.023 ± 0.003, and 0.013 ± 0.002 planets per star for planets with radii 2-4, 4-8, and 8-32 R ⊕ , in agreement with Doppler surveys. 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 a broader stellar T eff range of 3600-7100 K, spanning M0 to F2 dwarfs. Over this range, the occurrence of 2-4 R ⊕ planets in the Kepler field linearly increases with decreasing T eff , making these small planets seven times more abundant around cool stars (3600-4100 K) than the hottest stars in our sample (6600-7100 K).