Super-Earths are exoplanets larger than the Earth and smaller than the Neptune. While they do not exist in our solar system, they are the most common planets discovered around other stars. From their size and mass, we infer super-Earths to have typical gas envelope mass fraction of ~1%. This is rather massive compared to the Earth (0.0001% by mass atmosphere) but it is tiny compared to Jupiters. Super-Earths are observed to have masses that range 2 to 15 Earth masses. If one throws a 5 Earth mass rock in a gaseous nebula, the rock will accrete as much mass in gas as its core in 10 Myr and undergo the so-called runaway gas accretion to become a Jupiter. If one throws instead a 10 Earth mass rock in a gaseous nebula, the runaway gas accretion will be triggered within 1 Myr. Protoplanetary disks typically live for 1 to 10 Myrs so how can we explain the typical envelope mass fraction of super-Earths ~1% that we see today?
We present two possible solutions in Lee, Chiang, & Ormel 2014. We discuss the physics of gas accretion onto super-Earth sized cores and derive analytic scaling relationships describing the time evolution of the envelope mass fraction as a function of the core mass and metallicity in Lee & Chiang 2015. We conclude in Lee & Chiang 2016 that super-Earths can successfully avoid runaway gas accretion and build ~1% envelope mass fraction if they form in an environment that is short-lived and gas-depleted, like the inner cavity of transitional disks. So little gas is present at the time of core assembly that cores hardly migrate by disk torques: formation of super-Earths can be in situ.
Top: Time evolution of envelope mass fraction atop 7 Earth mass rocky core emplaced at 0.1 AU. Different colours correspond to different levels of gas depletion (here, measured with respect to minimum mass extrasolar nebula from Chiang & Laughlin 2013). A 7 Earth mass core can end up with <10% envelope mass fraction in gas-poor, short-lived nebulae.
Super-Earths and smaller planets around FGKM dwarfs are evenly distributed in log orbital period down to ∼10 days, but dwindle in number at shorter periods. Both the break at ∼10 days and the slope of the occurrence rate down to ∼1 day can be attributed to the truncation of protoplanetary disks by their host star magnetospheres at corotation. In Lee & Chiang (2017), we demonstrate this by deriving planet occurrence rate profiles from empirical distributions of pre-main-sequence stellar rotation periods. Observed profiles are better reproduced when planets are distributed randomly in disks—as might be expected if planets formed in situ—rather than piled up near disk edges, as would be the case if they migrated in by disk torques. Planets can be brought from disk edges to ultra-short (less than 1 day) periods by asynchronous equilibrium tides raised on their stars.
Top: in situ planet formation in disks truncated at corotation by host star magnetospheres, in combination with tidal migration, can reproduce the observed occurrence rates of sub-Neptunes. Black and blue points represent observations of planets orbiting FGK dwarfs by Fressin et al. (2013) and Sanchis-Ojeda et al. (2014), respectively, and red points represent observations of planets orbiting early M dwarfs by Dressing & Charbonneau (2015).
A small fraction of planets larger than the Neptune (but smaller than the Jupiter) have masses as low as 2 Earth masses. To explain their large radii and small masses, these "super-puffs" must have ~20% of their mass in their gaseous envelope. If one throws a 2 Earth mass rock in a gaseous nebula, the rock will accrete only ~3% gas by mass within ~1 Myr, even in gas-rich environment. How can we explain these puffy, low mass planets? We demonstrate in Lee & Chiang (2016) that super-puffs have to form outside ~ 1 AU in a dust-free environment then migrate in.
Top: time evolution of envelope mass fraction atop a 2 Earth mass rocky core. Cores need to be placed outside 1 AU and the accreted gas must be dust-free to build >10% envelope by mass within the disk gas dispersal time (gray bar). The blue bar represents the inferred envelope mass fraction of an observed super-puff Kepler-51b.