We analyze the transit timing variations (TTV) obtained by the Kepler mission for 22 sub-Jovian planet pairs (19 published, 3 new) that lie close to mean motion resonances. We find that the TTV phases for most of these pairs lie close to zero, consistent with an eccentricity distribution that has a very low root-mean-squared value of e ∼ 0.01; but about a quarter of the pairs possess much higher eccentricities, up to e ∼ 0.1-0.4. For the low-eccentricity pairs, we are able to statistically remove the effect of eccentricity to obtain planet masses from TTV data. These masses, together with those measured by radial velocity, yield a best-fit mass-radius relation M ∼ 3 M⊕(R/R⊕). This corresponds to a constant surface escape velocity of ∼20 km/s. We separate the planets into two distinct groups: "mid-sized" (those greater than 3 R⊕) and "compact" (those smaller). All mid-sized planets are found to be less dense than water and therefore must contain extensive H/He envelopes that are comparable in mass to that of their cores. We argue that these planets have been significantly sculpted by photoevaporation. Surprisingly, mid-sized planets, a minority among Kepler candidates, are discovered exclusively around stars more massive than 0.8 M☉. The compact planets, on the other hand, are often denser than water. Combining our density measurements with those from radial velocity studies, we find that hotter compact planets tend to be denser, with the hottest ones reaching rock density. Moreover, hotter planets tend to be smaller in size. These results can be explained if the compact planets are made of rocky cores overlaid with a small amount of hydrogen, ≤ 1% in mass, with water contributing little to their masses or sizes. Photoevaporation has exposed bare rocky cores in cases of the hottest planets. Our conclusion that these planets are likely not water worlds contrasts with some previous studies. While mid-sized planets most likely accreted their hydrogen envelope from the proto-planetary disks, compact planets could have obtained theirs via either accretion or outgassing. The presence of the two distinct classes suggests that 3 R⊕ could be identified as the dividing line between "hot Neptunes" and "super-Earths."
planets and satellites: composition - planets and satellites: dynamical evolution and stability - planets and satellites: formation