The existence of a radius valley in the Kepler size distribution stands as one of the most important observational constraints to understand the origin and composition of exoplanets with radii between those of Earth and Neptune. In this work we provide insights into the existence of the radius valley, first from a pure formation point of view and then from a combined formation-evolution model. We run global planet formation simulations including the evolution of dust by coagulation, drift, and fragmentation, and the evolution of the gaseous disc by viscous accretion and photoevaporation. A planet grows from a moon-mass embryo by either silicate or icy pebble accretion, depending on its position with respect to the water ice line. We include gas accretion, type I–II migration, and photoevaporation driven mass-loss after formation. We perform an extensive parameter study evaluating a wide range of disc properties and initial locations of the embryo. We find that due to the change in dust properties at the water ice line, rocky cores form typically with ∼3 M⊕ and have a maximum mass of ∼5 M⊕, while icy cores peak at ∼10 M⊕, with masses lower than 5 M⊕ being scarce. When neglecting the gaseous envelope, the formed rocky and icy cores account naturally for the two peaks of the Kepler size distribution. The presence of massive envelopes yields planets more massive than ∼10 M⊕ with radii above 4 R⊕. While the first peak of the Kepler size distribution is undoubtedly populated by bare rocky cores, as shown extensively in the past, the second peak can host half-rock–half-water planets with thin or non-existent H-He atmospheres, as suggested by a few previous studies. Some additional mechanisms inhibiting gas accretion or promoting envelope mass-loss should operate at short orbital periods to explain the presence of ∼10–40 M⊕ planets falling in the second peak of the size distribution.
Context. Recent high-resolution observations of protoplanetary disks have revealed ring-like structures that can be associated to pressure maxima. Pressure maxima are known to be dust collectors and planet migration traps. The great majority of planet formation studies are based either on the pebble accretion model or on the planetesimal accretion model. However, recent studies proposed hybrid accretion of pebbles and planetesimals as a possible formation mechanism for Jupiter. Aims. We aim to study the full process of planet formation consisting of dust evolution, planetesimal formation, and planet growth at a pressure maximum in a protoplanetary disk. Methods. We compute, through numerical simulations, the gas and dust evolution in a protoplanetary disk, including dust growth, fragmentation, radial drift, and particle accumulation at a pressure maximum. The pressure maximum appears due to an assumed viscosity transition at the water ice line. We also consider the formation of planetesimals by streaming instability and the formation of a moon-size embryo that grows into a giant planet by the hybrid accretion of pebbles and planetesimals, all within the pressure maximum. Results. We find that the pressure maximum is an efficient collector of dust drifting inwards. The condition of planetesimal formation by streaming instability is fulfilled due to the large amount of dust accumulated at the pressure bump. Subsequently, a massive core is quickly formed (in ~104 yr) by the accretion of pebbles. After the pebble isolation mass is reached, the growth of the core slowly continues by the accretion of planetesimals. The energy released by planetesimal accretion delays the onset of runaway gas accretion, allowing a gas giant to form after ~1 Myr of disk evolution. The pressure maximum also acts as a migration trap. Conclusions. Pressure maxima generated by a viscosity transition at the water ice line are preferential locations for dust traps, planetesimal formation by streaming instability, and planet migration traps. All these conditions allow the fast formation of a giant planet by the hybrid accretion of pebbles and planetesimals.
As planets grow the exchange of angular momentum with the gaseous component of the protoplanetary disc produces a net torque resulting in a variation of the semimajor axis of the planet. For low-mass planets not able to open a gap in the gaseous disc this regime is known as type I migration. Pioneer works studied this mechanism in isothermal discs finding fast inward type I migration rates that were unable to reproduce the observed properties of extrasolar planets. In the last years, several improvements have been made in order to extend the study of type I migration rates to non-isothermal discs. Moreover, it was recently shown that if the planet's luminosity due to solid accretion is taken into account, inward migration could be slowed down and even reversed. In this work, we study the planet formation process incorporating, and comparing, updated type I migration rates for non-isothermal discs and the role of planet's luminosity over such rates. We find that the latter can have important effects on planetary evolution, producing a significant outward migration for the growing planets.
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