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Register a new userMaking giant planet cores: convergent migration and growth of planetary embryos in non-isothermal discs
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Earth-mass bodies are expected to undergo Type I migration directed either inward or outward depending on the thermodynamical state of the protoplanetary disc. Zones of convergent migration exist where the Type I torque cancels out. We study the evolution of multiple protoplanets of a few Earth masses embedded in a non-isothermal protoplanetary disc. The protoplanets are located in the vicinity of a convergence zone located at the transition between two different opacity regimes. Inside the convergence zone, Type I migration is directed outward and outside the zone migration is directed inward. We used a grid-based hydrodynamical code that includes radiative effects. We performed simulations varying the initial number of embryos and tested the effect of including stochastic forces to mimic the effects resulting from turbulence. We also performed N-body runs calibrated on hydrodynamical calculations to follow the evolution on Myr timescales. For a small number of initial embryos (N = 5-7) and in the absence of stochastic forcing, the population of protoplanets migrates convergently toward the zero-torque radius and forms a stable resonant chain that protects embryos from close encounters. In systems with a larger initial number of embryos, or in which stochastic forces were included, these resonant configurations are disrupted. This in turn leads to the growth of larger cores via a phase of giant impacts, after which the system settles to a new stable resonant configuration. Giant planets cores with masses of 10 Earth masses formed in about half of the simulations with initial protoplanet masses of m_p = 3 Earth masses but in only 15% of simulations with m_p = 1 Earth mass. This suggests that if ~2-3 Earth mass protoplanets can form in less than ~1 Myr, convergent migration and giant collisions can grow giant planet cores at Type I migration convergence zones.
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Planetary systems are born in the disks of gas, dust and rocky fragments that surround newly formed stars. Solid content assembles into ever-larger rocky fragments that eventually become planetary embryos. These then continue their growth by accreting leftover material in the disc. Concurrently, tidal effects in the disc cause a radial drift in the embryo orbits, a process known as migration. Fast inward migration is predicted by theory for embryos smaller than three to five Earth masses. With only inward migration, these embryos can only rarely become giant planets located at Earths distance from the Sun and beyond, in contrast with observations. Here we report that asymmetries in the temperature rise associated with accreting infalling material produce a force (which gives rise to an effect that we call heating torque) that counteracts inward migration. This provides a channel for the formation of giant planets and also explains the strong planet-metallicity correlation found between the incidence of giant planets and the heavy-element abundance of the host stars.
Low-mass objects embedded in isothermal protoplanetary discs are known to suffer rapid inward Type I migration. In non-isothermal discs, recent work has shown that a decreasing radial profile of the disc entropy can lead to a strong positive corotation torque which can significantly slow down or reverse Type I migration in laminar viscous disc models. It is not clear however how this picture changes in turbulent disc models. The aim of this study is to examine the impact of turbulence on the torque experienced by a low-mass planet embedded in a non-isothermal protoplanetary disc. We particularly focus on the role of turbulence on the corotation torque whose amplitude depends on the efficiency of diffusion processes in the planets horseshoe region. We performed 2D numerical simulations using a grid-based hydrodynamical code in which turbulence is modelled as stochastic forcing. In order to provide estimations for the viscous and thermal diffusion coefficients as a function of the amplitude of turbulence, we first set up non-isothermal disc models for different values of the amplitude of the turbulent forcing. We then include a low-mass planet and determine the evolution of its running time-averaged torque. We show that in non-isothermal discs, the entropy-related corotation torque can indeed remain unsaturated in the presence of turbulence. For turbulence amplitudes that do not strongly affect the disc temperature profile, we find that the running time-averaged torque experienced by an embedded protoplanet is in fairly good agreement with laminar disc models with appropriate values for the thermal and viscous diffusion coefficients. In discs with turbulence driven by stochastic forcing, the corotation torque therefore behaves similarly as in laminar viscous discs and can be responsible for significantly slowing down or reversing Type I migration.
We carry out three-dimensional SPH simulations to study whether planets can survive in self-gravitating protoplanetary discs. The discs modelled here use a cooling prescription that mimics a real disc which is only gravitationally unstable in the outer regions. We do this by modelling the cooling using a simplified method such that the cooling time in the outer parts of the disc is shorter than in the inner regions, as expected in real discs. We find that both giant (> M_Sat) and low mass (< M_Nep) planets initially migrate inwards very rapidly, but are able to slow down in the inner gravitationally stable regions of the disc without needing to open up a gap. This is in contrast to previous studies where the cooling was modelled in a more simplified manner where regardless of mass, the planets were unable to slow down their inward migration. This shows the important effect the thermodynamics has on planet migration. In a broader context, these results show that planets that form in the early stages of the discs evolution, when they are still quite massive and self-gravitating, can survive.
We study the effects of diffusion on the non-linear corotation torque, or horseshoe drag, in the two-dimensional limit, focusing on low-mass planets for which the width of the horseshoe region is much smaller than the scale height of the disc. In the absence of diffusion, the non-linear corotation torque saturates, leaving only the Lindblad torque. Diffusion of heat and momentum can act to sustain the corotation torque. In the limit of very strong diffusion, the linear corotation torque is recovered. For the case of thermal diffusion, this limit corresponds to having a locally isothermal equation of state. We present some simple models that are able to capture the dependence of the torque on diffusive processes to within 20% of the numerical simulations.
Chondrules are millimeter-sized spherules that dominate primitive meteorites (chondrites) originating from the asteroid belt. The incorporation of chondrules into asteroidal bodies must be an important step in planet formation, but the mechanism is not understood. We show that the main growth of asteroids can result from gas-drag-assisted accretion of chondrules. The largest planetesimals of a population with a characteristic radius of 100 km undergo run-away accretion of chondrules within ~3 Myr, forming planetary embryos up to Mars sizes along with smaller asteroids whose size distribution matches that of main belt asteroids. The aerodynamical accretion leads to size-sorting of chondrules consistent with chondrites. Accretion of mm-sized chondrules and ice particles drives the growth of planetesimals beyond the ice line as well, but the growth time increases above the disk life time outside of 25 AU. The contribution of direct planetesimal accretion to the growth of both asteroids and Kuiper belt objects is minor. In contrast, planetesimal accretion and chondrule accretion play more equal roles for the formation of Moon-sized embryos in the terrestrial planet formation region. These embryos are isolated from each other and accrete planetesimals only at a low rate. However, the continued accretion of chondrules destabilizes the oligarchic configuration and leads to the formation of Mars-sized embryos and terrestrial planets by a combination of direct chondrule accretion and giant impacts.
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