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RE: Extrasolar Planet Migration
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Title: Q in Other Solar Systems
Authors: Aristotle Socrates, Boaz Katz, Subo Dong

A significant fraction of the hot Jupiters with final circularised orbital periods of less than 5 days are thought to form through the channel of high-eccentricity migration. Tidal dissipation at successive periastron passages removes orbital energy of the planet, which has the potential for changes in semi-major axis of a factor of ten to a thousand. In the equilibrium tide approximation we show that, in order for high-eccentricity migration to take place, the relative level of tidal dissipation in Jupiter analogues must be at least 10 times higher than the upper-limit attributed to the Jupiter-Io interaction. While this is not a severe problem for high-e migration, it contradicts the results of several previous calculations. We show that these calculations of high-e migration inadvertently over-estimated the strength of tidal dissipation by three to four orders of magnitude. These discrepancies were obscured by the use of various parameters, such as lag time \tau, tidal quality factor Q and viscous time t_V. We provide the values of these parameters required for the Jupiter-Io interaction, tidal circularisation and high-e migration. Implications for tidal theory as well as models of the inflated radii of hot Jupiters are discussed. Though the tidal Q is not, in general, well-defined, we derive a formula for it during high-eccentricity migration where Q is approximately constant throughout evolution.

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Title: Migration rates of planets due to scattering of planetesimals
Authors: Chris Ormel (UC Berkeley), Shigeru Ida (Tokyo Tech), Hidekazu Tanaka (Hokkaido University)

Planets migrate due to the recoil they experience from scattering solid (planetesimal) bodies. To first order, the torques exerted by the interior and exterior disks cancel, analogous to the cancellation of the torques from the gravitational interaction with the gas (type I migration). Assuming the dispersion-dominated regime and power-laws characterized by indices {\alpha} and {\beta} for the surface density and eccentricity profiles, we calculate the net torque on the planet. We consider both distant encounters and close (orbit-crossing) encounters. We find that the close and distant encounter torques have opposite signs with respect to their {\alpha} and {\beta} dependences; and that the torque is especially sensitive to the eccentricity gradient ({\beta}). Compared to type-I migration due to excitation of density waves, the planetesimal-driven migration rate is generally lower due to the lower surface density of solids in gas-rich disk, although this may be partially or fully offset when their eccentricity and inclination are small. Allowing for the feedback of the planet on the planetesimal disk through viscous stirring, we find that under certain conditions a self-regulated migration scenario emerges, in which the planet migrates at a steady pace that approaches the rate corresponding to the one-sided torque. If the local planetesimal disk mass to planet mass ratio is low, however, migration stalls. We quantify the boundaries separating the three migration regimes.

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Title: Deserts and pile-ups in the distribution of exoplanets due to photoevaporative disc clearing
Authors: R.D.Alexander, I.Pascucci

We present models of giant planet migration in evolving protoplanetary discs. We show that disc clearing by EUV photoevaporation can have a strong effect on the distribution of giant planet semi-major axes. During disc clearing planet migration is slowed or accelerated in the region where photoevaporation opens a gap in the disc, resulting in "deserts" where few giant planets are found and corresponding "pile-ups" at smaller and larger radii. However, the precise locations and sizes of these features are strong functions of the efficiency of planetary accretion, and therefore also strongly dependent on planet mass. We suggest that photoevaporative disc clearing may be responsible for the pile-up of ~Jupiter-mass planets at ~1AU seen in exoplanet surveys, and show that observations of the distribution of exoplanet semi-major axes can be used to test models of both planet migration and disc clearing.

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Title: Migration of Gas Giant Planets in Gravitationally Unstable Disks
Authors: Scott Michael, Richard H. Durisen, Aaron C. Boley

Characterisation of migration in gravitationally unstable disks is necessary to understand the fate of protoplanets formed by disk instability. As part of a larger study, we are using a 3D radiative hydrodynamics code to investigate how an embedded gas giant planet interacts with a gas disk that undergoes gravitational instabilities (GIs). This Letter presents results from simulations with a Jupiter-mass planet placed in orbit at 25 AU within a 0.14 solar mass disk. The disk spans 5 to 40 AU around a 1 solar mass star and is initially marginally unstable. In one simulation, the planet is inserted prior to the eruption of GIs; in another, it is inserted only after the disk has settled into a quasi-steady GI-active state, where heating by GIs roughly balances radiative cooling. When the planet is present from the beginning, its own wake stimulates growth of a particular global mode with which it strongly interacts, and the planet plunges inward six AU in about 10³ years. In both cases with embedded planets, there are times when the planet's radial motion is slow and varies in direction. At other times, when the planet appears to be interacting with strong spiral modes, migration both inward and outward can be relatively rapid, covering several AUs over hundreds of years. Migration in both cases appears to stall near the inner Lindblad resonance of a dominant low-order mode. Planet orbit eccentricities fluctuate rapidly between about 0.02 to 0.1 throughout the GI-active phases of the simulations.

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Hot Jupiters
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Title: Why are there so few hot Jupiters?
Authors: W.K.M. Rice, P.J. Armitage, D.F. Hogg

We use numerical simulations to model the migration of massive planets at small radii and compare the results with the known properties of 'hot Jupiters' (extrasolar planets with semi-major axes a < 0.1 AU). For planet masses Mp sin i > 0.5 MJup, the evidence for any 'pile-up' at small radii is weak (statistically insignificant), and although the mass function of hot Jupiters is deficient in high mass planets as compared to a reference sample located further out, the small sample size precludes definitive conclusions. We suggest that these properties are consistent with disc migration followed by entry into a magnetospheric cavity close to the star. Entry into the cavity results in a slowing of migration, accompanied by a growth in orbital eccentricity. For planet masses in excess of 1 Jupiter mass we find eccentricity growth timescales of a few x 10^5 years, suggesting that these planets may often be rapidly destroyed. Eccentricity growth appears to be faster for more massive planets which may explain changes in the planetary mass function at small radii and may also predict a pile-up of lower mass planets, the sample of which is still incomplete.

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Title: Building Giant-Planet Cores at a Planet Trap
Authors: Alessandro Morbidelli (OCA), Aurelien Crida, Frederic Masset, Richard P. Nelson

A well-known bottleneck for the core-accretion model of giant-planet formation is the loss of the cores into the star by Type-I migration, due to the tidal interactions with the gas disk. It has been shown that a steep surface-density gradient in the disk, such as the one expected at the boundary between an active and a dead zone, acts as a planet trap and prevents isolated cores from migrating down to the central star. We study the relevance of the planet trap concept for the accretion and evolution of systems of multiple planetary embryos/cores. We performed hydrodynamical simulations of the evolution of systems of multiple massive objects in the vicinity of a planet trap. The planetary embryos evolve in 3 dimensions, whereas the disk is modelled with a 2D grid. Synthetic forces are applied onto the embryos to mimic the damping effect that the disk has on their inclinations. Systems with two embryos tend to acquire stable, separated and non-migrating orbits, with the more massive embryo placed at the planet trap and the lighter one farther out in the disk. Systems of multiple embryos are intrinsically unstable. Consequently, a long phase of mutual scattering can lead to accreting collisions among embryos; some embryos are injected into the inner part of the disk, where they can be evacuated into the star by Type I migration. The system can resume a stable, non-migrating configuration only when the number of surviving embryos decreases to a small value (~2-4). This can explain the limited number of giant planets in our solar system. These results should apply in general to any case in which the Type-I migration of the inner embryo is prevented by some mechanism, and not solely to the planet trap scenario.

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Protoplanetary disc
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Title: Cavity opening by a giant planet in a protoplanetary disc and effects on planetary migration
Authors: A. Crida, A. Morbidelli

We study the effect of a Jovian planet on the gas distribution of a protoplanetary disc, using a new numerical scheme that allows us to take into consideration the global evolution of the disc, down to an arbitrarily small inner physical radius. We find that Jovian planets do not open cavities in the inner part of the disc (i.e. interior to their orbits) unless (a) the inner physical edge of the disc is close to the planet's location or (b) the planet is much more massive than the disc. In all other cases the planet simply opens a gap in the gas density distribution, whose global profile is essentially unchanged relative to the one that it would have if the planet were absent. We recognize, though, that the dust distribution can be significantly different from the gas distribution and that dust cavities might be opened in some situations, even if the gas is still present in the inner part of the disc.
Concerning the migration of the planet, we find that classical Type-II migration (with speed proportional to the viscosity of the disc) occurs only if the gap opened by the planet is deep and clean. If there is still a significant amount of gas in the gap, the migration of the planet is generally slower than the theoretical Type-II migration rate. In some situations, migration can be stopped or even reversed. We develop a simple model that reproduces satisfactorily the migration rate observed in the simulations, for a wide range of disc viscosities and planet masses and locations relative to the inner disc edge. Our results are relevant for extra-solar planetary systems, as they explain (a) why some hot Jupiters did not migrate all the way down to their parent stars and (b) why the outermost of a pair of resonant planets is typically the most massive one.

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Extrasolar Planet Migration
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A Decade of Extrasolar Planets around Normal Stars

Title: Planetary migration
Authors:
Philip J. Armitage, W. K. M. Rice

Gravitational torques between a planet and gas in the protoplanetary disk result in orbital migration of the planet, and are likely to play an important role in the formation and early evolution of planetary systems.
For masses comparable to those of observed giant extrasolar planets, the interaction with the disk is strong enough to form a gap, leading to coupled evolution of the planet and disk on a viscous time scale (Type II migration).
Both the existence of hot Jupiters, and the statistical distribution of observed orbital radii, are consistent with an important role for Type II migration in the history of currently observed systems. We discuss the possibility of improving constraints on migration by including information on the host stars' metallicity, and note that migration could also form a population of massive planets at large orbital radii that may be indirectly detected via their influence on debris disks.
For lower mass planets with masses of the order of that of the Earth, surface density perturbations created by the planet are small, and migration in a
laminar disk is driven by an intrinsic and apparently robust asymmetry between interior and exterior torques. Analytic and numerical calculations of this Type I migration are in reasonable accord, and predict rapid orbital decay during the final stages of the formation of giant planet cores.
The difficulty of reconciling Type I migration with giant planet formation may signal basic errors in our understanding of protoplanetary disks, core accretion, or both.
We discuss physical effects that might alter Type I behaviour, in particular the possibility that for sufficiently low masses turbulent fluctuations in the gas surface density dominate the torque, leading to random walk migration of very low mass bodies.

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Low mass planets: Type I migration

Low mass planets: For the lowest mass planets, the gravitational interaction between the planet and the gas disk is relatively weak. The planet excites a trailing spiral wave in the disk, and experiences a gravitational torque from the resulting perturbation to the disk surface density. In a real disk, this loss of angular momentum would cause the planet's orbit to decay, a process known as Type I orbital migration. This doesn't happen in the movie because the orbit is artificially kept fixed (and anyway the time scale of the simulation is too short for significant migration). The surface density profile of the disk (shown as function of radius in the inset graph) is not significantly modified by the presence of the planet at this stage.



Gap formation: Type II migration

Gap opening: As the planet mass grows, the strength of the resonant interaction with the gas disk increases. The exchange of angular momentum repels gas away from near the planet's orbit, creating an annular gap where the disk surface density is lower than it would be in the absence of the planet. At first, as shown in the middle frame above, the gap is only partially evacuated of gas. The details of how the remaining gas in the co orbital region interacts with the planet in this regime remain unclear.


Suppression of accretion at high planet masses

Type II migration: Once the planet's mass is high enough (above a Jupiter mass for the particular parameters of this simulation), its gravitational interaction with the disk succeeds in forming a deep, clean gap. Some gas continues to overflow the gap edges and is captured within the Hill sphere of the planet, adding to the planet mass. The rate of mass growth due to accretion across gaps decreases as the planet grows, at least if the orbital eccentricity remains small. The overall exchange of angular momentum between the planet and disk is now governed by the viscous evolution of the disk, and the planet is expected to migrate in the same sense as the disk gas (usually inward at small radii) while maintaining its position within a gap.

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