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Register a new userGap formation in a self-gravitating disk and the associated migration of the embedded giant planet
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We present the results of our recent study on the interactions between a giant planet and a self-gravitating gas disk. We investigate how the disks self-gravity affects the gap formation process and the migration of the giant planet. Two series of 1-D and 2-D hydrodynamic simulations are performed. We select several surface densities and focus on the gravitationally stable region. To obtain more reliable gravity torques exerted on the planet, a refined treatment of disks gravity is adopted in the vicinity of the planet. Our results indicate that the net effect of the disks self-gravity on the gap formation process depends on the surface density of the disk. We notice that there are two critical values, Sigma_I and Sigma_II. When the surface density of the disk is lower than the first one, Sigma_0 < Sigma_I, the effect of self-gravity suppresses the formation of a gap. When Sigma_0 > Sigma_I, the self-gravity of the gas tends to benefit the gap formation process and enlarge the width/depth of the gap. According to our 1-D and 2-D simulations, we estimate the first critical surface density Sigma_I approx 0.8MMSN. This effect increases until the surface density reaches the second critical value Sigma_II. When Sigma_0 > Sigma_II, the gravitational turbulence in the disk becomes dominant and the gap formation process is suppressed again. Our 2-D simulations show that this critical surface density is around 3.5MMSN. We also study the associated orbital evolution of a giant planet. Under the effect of the disks self-gravity, the migration rate of the giant planet increases when the disk is dominated by gravitational turbulence. We show that the migration timescale associates with the effective viscosity and can be up to 10^4 yr.
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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.
A massive planet in a protoplanetary disc will open a gap in the disc material which acts as a transition between Type I and Type II planetary migration. Type II migration is slower than Type I migration, however it is still desirable to slow down Type II migration to allow gas giant planets with semi-major axis in the range 5 to 10AU to exist, similarly to our Solar system. We investigate a method of slowing down and reversing Type II migration by heating the outer gap edge due to incident radiation from the central star. Using an approximate vertically averaged heating method we find that Type II migration can be slowed or in extreme cases reversed if we assume near maximum allowed irradiation from the central star. Therefore, we believe this is a very interesting phenomenon that should be investigated in greater detail using three dimensional hydrodynamic and radiative transfer simulations.
Debris disks are exoplanetary systems containing planets, minor bodies (such as asteroids and comets) and debris dust. Unseen planets are presumed to perturb the minor bodies into crossing orbits, generating small dust grains that are detected via remote sensing. Debris disks have been discovered around main sequence stars of a variety of ages (from 10 Myr to several Gyr) and stellar spectral types (from early A-type to M-type stars). As a result, they serve as excellent laboratories for understanding whether the architecture and the evolution of our Solar System is common or rare. This white paper addresses two outstanding questions in debris disk science: (1) Are debris disk minor bodies similar to asteroids and comets in our Solar System? (2) Do planets separate circumstellar material into distinct reservoirs and/or mix material during planet migration? We anticipate that SOFIA/HIRMES, JWST, and WFIRST/CGI will greatly improve our understanding of debris disk composition, enabling the astronomical community to answer these questions. However, we note that despite their observational power, these facilities will not provide large numbers of detections or detailed characterization of cold ices and silicates in the Trans Neptunian zone. Origins Space Telescope is needed to revolutionize our understanding of the bulk composition and mixing in exoplanetary systems.
We investigate the tidal interaction between a low-mass planet and a self-gravitating protoplanetary disk, by means of two-dimensional hydrodynamic simulations. We first show that considering a planet freely migrating in a disk without self-gravity leads to a significant overestimate of the migration rate. The overestimate can reach a factor of two for a disk having three times the surface density of the minimum mass solar nebula. Unbiased drift rates may be obtained only by considering a planet and a disk orbiting within the same gravitational potential. In a second part, the disk self-gravity is taken into account. We confirm that the disk gravity enhances the differential Lindblad torque with respect to the situation where neither the planet nor the disk feels the disk gravity. This enhancement only depends on the Toomre parameter at the planet location. It is typically one order of magnitude smaller than the spurious one induced by assuming a planet migrating in a disk without self-gravity. We confirm that the torque enhancement due to the disk gravity can be entirely accounted for by a shift of Lindblad resonances, and can be reproduced by the use of an anisotropic pressure tensor. We do not find any significant impact of the disk gravity on the corotation torque.
We investigate a repulsion mechanism between two low-mass planets migrating in a protoplanetary disk, for which the relative migration switches from convergent to divergent. This mechanism invokes density waves emitted by one planet transferring angular momentum to the coorbital region of the other and then directly to it through the horseshoe drag. We formulate simple analytical estimates, which indicate when the repulsion mechanism is effective. One condition for a planet to be repelled is that it forms a partial gap in the disk and another is that this should contain enough material to support angular momentum exchange with it. Using two-dimensional hydrodynamical simulations we obtain divergent migration of two super-Earths embedded in a protoplanetary disk because of repulsion between them and verify these conditions. To investigate the importance of resonant interaction we study the migration of planet pairs near first-order commensurabilities. It appears that proximity to resonance is significant but not essential. In this context we find repulsion still occurs when the gravitational interaction between the planets is removed sugesting the importance of angular momentum transfer through waves excited by another planet. This may occur through the scattering of coorbital material (the horseshoe drag), or material orbiting close by. Our results indicate that if conditions favor the repulsion between two planets described above, we expect to observe planet pairs with their period ratios greater, often only slightly greater, than resonant values or possibly rarity of commensurability.
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