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We have established precise planet radii, semimajor axes, incident stellar fluxes, and stellar masses for 909 planets in 355 multi-planet systems discovered by Kepler. In this sample, we find that planets within a single multi-planet system have correlated sizes: each planet is more likely to be the size of its neighbor than a size drawn at random from the distribution of observed planet sizes. In systems with three or more planets, the planets tend to have a regular spacing: the orbital period ratios of adjacent pairs of planets are correlated. Furthermore, the orbital period ratios are smaller in systems with smaller planets, suggesting that the patterns in planet sizes and spacing are linked through formation and/or subsequent orbital dynamics. Yet, we find that essentially no planets have orbital period ratios smaller than 1.2, regardless of planet size. Using empirical mass-radius relationships, we estimate the mutual Hill separations of planet pairs. We find that 93% of the planet pairs are at least 10 mutual Hill radii apart, and that a spacing of ∼20 mutual Hill radii is most common. We also find that when comparing planet sizes, the outer planet is larger in 65% ± 0.4% of cases, and the typical ratio of the outer to inner planet size is positively correlated with the temperature difference between the planets. This could be the result of photo-evaporation.

Strongly irradiated giant planets are observed to have radii larger than thermal evolution models predict. Although these inflated planets have been known for over 15 years, it is unclear whether their inflation is caused by the deposition of energy from the host star or the inhibited cooling of the planet. These processes can be distinguished if the planet becomes highly irradiated only when the host star evolves onto the red giant branch. We report the discovery of K2-97b, a 1.31 ±0.11 R J, 1.10 ±0.11 M J planet orbiting a 4.20 ±0.14 R o, 1.16 ±0.12 M o red giant star with an orbital period of 8.4 days. We precisely constrained stellar and planetary parameters by combining asteroseismology, spectroscopy, and granulation noise modeling along with transit and radial velocity measurements. The uncertainty in planet radius is dominated by systematic differences in transit depth, which we measure to be up to 30% between different light-curve reduction methods. Our calculations indicate the incident flux on this planet was 170+140-60 times the incident flux on Earth, while the star was on the main sequence. Previous studies suggest that this incident flux is insufficient to delay planetary cooling enough to explain the present planet radius. This system thus provides the first evidence that planets may be inflated directly by incident stellar radiation rather than by delayed loss of heat from formation. Further studies of planets around red giant branch stars will confirm or contradict this hypothesis and may reveal a new class of re-inflated planets.