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Register a new userOrbital migration of low-mass planets in evolutionary radiative models: Avoiding catastrophic infall
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Outward migration of low-mass planets has recently been shown to be a possibility in non-barotropic disks. We examine the consequences of this result in evolutionary models of protoplanetary disks. Planet migration occurs towards equilibrium radii with zero torque. These radii themselves migrate inwards because of viscous accretion and photoevaporation. We show that as the surface density and temperature fall, the planet orbital migration and disk depletion timescales eventually become comparable, with the precise timing depending on the mass of the planet. When this occurs, the planet decouples from the equilibrium radius. At this time, however, the gas surface density is already too low to drive substantial further migration. A higher mass planet, of 10 Earth masses, can open a gap during the late evolution of the disk, and stops migrating. Low mass planets, with 1 or 0.1 Earth masses, released beyond 1 AU in our models, avoid migrating into the star. Our results provide support for the reduced migration rates adopted in recent planet population synthesis models.
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Type-II migration of giant planets has a speed proportional to the discs viscosity for values of the alpha viscosity parameter larger than 1.e-4 . At lower viscosities previous studies, based on 2D simulations have shown that migration can be very chaotic and often characterized by phases of fast migration. The reason is that in low-viscosity discs vortices appear due to the Rossby-wave instability at the edges of the gap opened by the planet. Migration is then determined by vortex-planet interactions. Our aim is to study migration in low viscosity 3D discs. We performed numerical simulations using 2D (including self-gravity) and 3D codes. After selecting disc masses for which self-gravity is not important, 3D simulations without self-gravity can be safely used. In our nominal simulation only numerical viscosity is present. We then performed simulations with prescribed viscosity to assess the threshold below which the new migration processes appear. We show that for alpha viscosity <= 1.e-5 two migration modes are possible which differ from classical Type-II migration, in the sense that they are not proportional to the discs viscosity. The first occurs when the gap opened by the planet is not very deep. This occurs in 3D simulations and/or when a big vortex forms at the outer edge of the planetary gap, diffusing material into the gap. We call this type of migration vortex-driven migration. This migration is very slow and cannot continue indefinitely, because eventually the vortex dissolves. The second migration mode occurs when the gap is deep so that the planets eccentricity grows to a value ~0.2 due to inefficient eccentricity damping by corotation resonances. This second, faster migration mode appears to be typical of 2D models in discs with slower damping of temperatures perturbations.
Future instruments like NIRCam and MIRI on JWST or METIS at the ELT will be able to image exoplanets that are too faint for current direct imaging instruments. Evolutionary models predicting the planetary intrinsic luminosity as a function of time have traditionally concentrated on gas-dominated giant planets. We extend these cooling curves to Saturnian and Neptunian planets. We simulate the cooling of isolated core-dominated and gas giant planets with masses of 5 Earthmasses to 2 Jupitermasses. The luminosity includes the contribution from the cooling and contraction of the core and of the H/He envelope, as well as radiogenic decay. For the atmosphere we use grey, AMES-Cond, petitCODE, and HELIOS models. We consider solar and non-solar metallicities as well as cloud-free and cloudy atmospheres. The most important initial conditions, namely the core-to-envelope ratio and the initial luminosity are taken from planet formation simulations based on the core accretion paradigm. We first compare our cooling curves for Uranus, Neptune, Jupiter, Saturn, GJ 436b, and a 5 Earthmass-planet with a 1% H/He envelope with other evolutionary models. We then present the temporal evolution of planets with masses between 5 Earthmasses and 2 Jupitermasses in terms of their luminosity, effective temperature, radius, and entropy. We discuss the impact of different post formation entropies. For the different atmosphere types and initial conditions magnitudes in various filter bands between 0.9 and 30 micrometer wavelength are provided. Using black body fluxes and non-grey spectra, we estimate the detectability of such planets with JWST. It is found that a 20 (100) Earthmass-planet can be detected with JWST in the background limit up to an age of about 10 (100) Myr with NIRCam and MIRI, respectively.
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 semi-major 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 planets 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 planets 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.
We present the results of hydrodynamical simulations of the orbital evolution of planets undergoing runaway gas accretion in radiative discs. We consider accreting disc models with constant mass flux through the disc, and where radiative cooling balances the effect of viscous heating and stellar irradiation. We assume that 20-30 $M_oplus$ giant planet cores are formed in the region where viscous heating dominates and migrate outward under the action of a strong corotation torque. In the case where gas accretion is neglected, we find evidence for strong dynamical torques in accreting discs with accretion rates ${dot M}gtrsim 7times 10^{-8} ;M_odot/yr$. Their main effect is to increase outward migration rates by a factor of $sim 2$ typically. In the presence of gas accretion, however, runaway outward migration is observed with the planet passing through the zero-torque radius and the transition between the viscous heating and stellar heating dominated regimes. The ability for an accreting planet to enter a fast migration regime is found to depend strongly on the planet growth rate, but can occur for values of the mass flux through the disc of ${dot M}gtrsim 5times 10^{-8} ;M_odot/yr$. We find that an episode of runaway outward migration can cause an accreting planet formed in the 5-10 AU region to temporarily orbit at star-planet separations as large as $sim$60-70 AU. However, increase in the amplitude of the Lindblad torque associated with planet growth plus change in the streamline topology near the planet systematically cause the direction of migration to be reversed. Our results indicate that a planet can reach large orbital distances under the combined effect of dynamical torques and gas accretion, but an alternative mechanism is required to explain the presence of massive planets on wide orbits.
In order to study the origin of the architectures of low mass planetary systems, we perform numerical surveys of the evolution of pairs of coplanar planets in the mass range $(1-4) rmn{M}_{oplus}.$ These evolve for up to $2times10^7 rmn{yr}$ under a range of orbital migration torques and circularization rates assumed to arise through interaction with a protoplanetary disc. Near the inner disc boundary, significant variations of viscosity, interaction with density waves or with the stellar magnetic field could occur and halt migration, but allow ircularization to continue. This was modelled by modifying the migration and circularization rates. Runs terminated without an extended period of circularization in the absence of migration torques gave rise to either a collision, or a system close to a resonance. These were mostly first order with a few $%$ terminating in second order resonances. Both planetary eccentricities were small $< 0.1$ and all resonant angles liberated. This type of survey produced only a limited range of period ratios and cannot reproduce Kepler observations. When circularization alone operates in the final stages, divergent migration occurs causing period ratios to increase. Depending on its strength the whole period ratio range between $1$ and $2$ can be obtained. A few systems close to second order commensurabilities also occur. In contrast to when arising through convergent migration, resonant trapping does not occur and resonant angles circulate. Thus the behaviour of the resonant angles may indicate the form of migration that led to near resonance.
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