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Register a new userPlanetary Migration in Protoplanetary Disks
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Authors
Richard P. Nelson
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The known exoplanet population displays a great diversity of orbital architectures, and explaining the origin of this is a major challenge for planet formation theories. The gravitational interaction between young planets and their protoplanetary disks provides one way in which planetary orbits can be shaped during the formation epoch. Disk-planet interactions are strongly influenced by the structure and physical processes that drive the evolution of the protoplanetary disk. In this review we focus on how disk-planet interactions drive the migration of planets when different assumptions are made about the physics of angular momentum transport, and how it drives accretion flows in protoplanetary disk models. In particular, we consider migration in discs where: (i) accretion flows arise because turbulence diffusively transports angular momentum; (ii) laminar accretion flows are confined to thin, ionised layers near disk surfaces and are driven by the launching of magneto-centrifugal winds, with the midplane being completely inert; (iii) laminar accretion flows pervade the full column density of the disc, and are driven by a combination of large scale horizontal and vertical magnetic fields.
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We consider the radial migration of vortices in two-dimensional isothermal gaseous disks. We find that a vortex core, orbiting at the local gas velocity, induces velocity perturbations that propagate away from the vortex as density waves. The resulting spiral wave pattern is reminiscent of an embedded planet. There are two main causes for asymmetries in these wakes: geometrical effects tend to favor the outer wave, while a radial vortensity gradient leads to an asymmetric vortex core, which favors the wave at the side that has the lowest density. In the case of asymmetric waves, which we always find except for a disk of constant pressure, there is a net exchange of angular momentum between the vortex and the surrounding disk, which leads to orbital migration of the vortex. Numerical hydrodynamical simulations show that this migration can be very rapid, on a time scale of a few thousand orbits, for vortices with a size comparable to the scale height of the disk. We discuss the possible effects of vortex migration on planet formation scenarios.
The increasing number of newly detected exoplanets at short orbital periods raises questions about their formation and migration histories. 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. We investigate the conditions for planet formation and migration near the dust sublimation front in protostellar disks around young Sun-like stars. 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. 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. 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.
Studies of planet migration derived from disc planet interactions began before the discovery of exoplanets. The potential importance of migration for determining orbital architectures being realised, the field received greater attention soon after the initial discoveries of exoplanets. Early studies based on very simple disc models indicated very fast migration times for low mass planets that raised questions about its relevance. However, more recent studies, made possible with improving resources, that considered improved physics and disc models revealed processes that could halt or reverse this migration. That in turn led to a focus on special regions in the disc where migration could be halted. In this way the migration of low mass planets could be reconciled with formation theories. In the case of giant planets which have a nonlinear interaction with the disc, the migration should be slower and coupled to the evolution of the disc. The latter needs to be considered more fully to make future progress in all cases. Here we are primarily concerned with processes where migration is connected with the presence of the protopolanetary disk. Migration may also be induced by disc-free gravitational interactions amongst planets or with binary companions. This is only briefly discussed here.
The detection of a wide range of substructures such as rings, cavities and spirals has become a common outcome of high spatial resolution imaging of protoplanetary disks, both in the near-infrared scattered light and in the thermal millimetre continuum emission. The most frequent interpretation of their origin is the presence of planetary-mass companions perturbing the gas and dust distribution in the disk (perturbers), but so far the only bona-fide detection has been the two giant planets around PDS 70. Here, we collect a sample of 15 protoplanetary disks showing substructures in SPHERE scattered light images and present a homogeneous derivation of planet detection limits in these systems. We also estimate the mass of these perturbers through a Hill radius prescription and a comparison to ALMA data. Assuming that one single planet carves each substructure in scattered light, we find that more massive perturbers are needed to create gaps within cavities than rings, and that we might be close to a detection in the cavities of RX J1604, RX J1615, Sz Cha, HD 135344B and HD 34282. We reach typical mass limits in these cavities of 3-10 Mjup. For planets in the gaps between rings, we find that the detection limits of SPHERE are about an order of magnitude away in mass, and that the gaps of PDS 66 and HD 97048 seem to be the most promising structures for planet searches. The proposed presence of massive planets causing spiral features in HD 135344B and HD 36112 are also within SPHEREs reach assuming hot-start models.These results suggest that current detection limits are able to detect hot-start planets in cavities, under the assumption that they are formed by a single perturber located at the centre of the cavity. More realistic planet mass constraints would help to clarify whether this is actually the case, which might point to perturbers not being the only way of creating substructures.
Volatiles are compounds with low sublimation temperatures, and they make up most of the condensible mass in typical planet-forming environments. They consist of relatively small, often hydrogenated, molecules based on the abundant elements carbon, nitrogen and oxygen. Volatiles are central to the process of planet formation, forming the backbone of a rich chemistry that sets the initial conditions for the formation of planetary atmospheres, and act as a solid mass reservoir catalyzing the formation of planets and planetesimals. This growth has been driven by rapid advances in observations and models of protoplanetary disks, and by a deepening understanding of the cosmochemistry of the solar system. Indeed, it is only in the past few years that representative samples of molecules have been discovered in great abundance throughout protoplanetary disks - enough to begin building a complete budget for the most abundant elements after hydrogen and helium. The spatial distributions of key volatiles are being mapped, snow lines are directly seen and quantified, and distinct chemical regions within protoplanetary disks are being identified, characterized and modeled. Theoretical processes invoked to explain the solar system record are now being observationally constrained in protoplanetary disks, including transport of icy bodies and concentration of bulk condensibles. The balance between chemical reset - processing of inner disk material strong enough to destroy its memory of past chemistry, and inheritance - the chemically gentle accretion of pristine material from the interstellar medium in the outer disk, ultimately determines the final composition of pre-planetary matter. This chapter focuses on making the first steps toward understanding whether the planet formation processes that led to our solar system are universal.
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