Abstract
Context. The increasing number of newly detected exoplanets at short orbital periods raises questions about their formation and migration histories. Planet formation and migration depend heavily on the structure and dynamics of protoplanetary disks. A particular puzzle that requires explanation arises from one of the key results of the Kepler mission, namely the increase in the planetary occurrence rate with orbital period up to 10 days for F, G, K and M stars. Aims. We investigate the conditions for planet formation and migration near the dust sublimation front in protostellar disks around young Sun-like stars. We are especially interested in determining the positions where the drift of pebbles would be stopped, and where the migration of Earth-like planets and super-Earths would be halted. Methods. For this analysis we use iterative 2D radiation hydrostatic disk models which include irradiation by the star, and dust sublimation and deposition depending on the local temperature and vapor pressure. Results. Our results show the temperature and density structure of a gas and dust disk around a young Sun-like star. We perform a parameter study by varying the magnetized turbulence onset temperature, the accretion stress, the dust mass fraction, and the mass accretion rate. Our models feature a gas-only inner disk, a silicate sublimation front and dust rim starting at around 0.08 au, an ionization transition zone with a corresponding density jump, and a pressure maximum which acts as a pebble trap at around 0.12 au. Migration torque maps show Earth- and super-Earth-mass planets halt in our model disks at orbital periods ranging from 10 to 22 days. Conclusions. Such periods are in good agreement with both the inferred location of the innermost planets in multiplanetary systems, and the break in planet occurrence rates from the Kepler sample at 10 days. In particular, models with small grains depleted produce a trap located at a 10-day orbital period, while models with a higher abundance of small grains present a trap at around a 17-day orbital period. The snow line lies at 1.6 au, near where the occurrence rate of the giant planets peaks. We conclude that the dust sublimation zone is crucial for forming close-in planets, especially when considering tightly packed super-Earth systems.
Highlights
Our knowledge of the origins of planetary systems relies on our understanding of the disks of gas and dust orbiting young stars
One key result of the Kepler mission was the discovery of many planetary systems containing Earth-sized and super-Earth planets orbiting with periods between one day and one year (Lissauer et al 2011; Batalha et al 2013; Fabrycky et al 2014)
The results derived from the radiation hydrostatic solution for our reference model are shown in Figs. 1 and 2
Summary
Our knowledge of the origins of planetary systems relies on our understanding of the disks of gas and dust orbiting young stars. One key result of the Kepler mission was the discovery of many planetary systems containing Earth-sized and super-Earth planets orbiting with periods between one day and one year (Lissauer et al 2011; Batalha et al 2013; Fabrycky et al 2014). Further analysis of the results showed a clear rise in the occurrence rate of super-Earths (rocky planets of several Earth masses) with orbital periods longer than 10 days. Even more recently, Mulders et al (2018) have found, when including observational constraints on multiplanetary systems, that on average the innermost planet orbits with a 12-day period
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