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Register a new userWhich planets trigger longer-lived vortices: low-mass or high-mass?
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Recent ALMA observations have found many protoplanetary discs with rings that can be explained by gap-opening planets less massive than Jupiter. Meanwhile, recent studies have suggested that protoplanetary discs should have low levels of turbulence. Past computational work on low-viscosity discs has hinted that these two developments might not be self-consistent because even low-mass planets can be accompanied by vortices instead of conventional double rings. We investigate this potential discrepancy by conducting hydrodynamic simulations of growing planetary cores in discs with various aspect ratios ($H/r=0.04$, 0.06, 0.08) and viscosities ($1.5 times 10^{-5} lesssim alpha lesssim 3 times 10^{-4}$), having these cores accrete their gas mass directly from the disc. With $alpha < 10^{-4}$, we find that sub-Saturn-mass planets in discs with $H/r le 0.06$ are more likely to be accompanied by dust asymmetries compared to Jupiter-mass planets because they can trigger several generations of vortices in succession. We also find that vortices with $H/r = 0.08$ survive $>6000$ planet orbits regardless of the planet mass or disc mass because they are less affected by the planets spiral waves. We connect our results to observations and find that the outward migration of vortices with $H/r ge 0.08$ may be able to explain the cavity in Oph IRS 48 or the two clumps in MWC 758. Lastly, we show that the lack of observed asymmetries in the disc population in Taurus is unexpected given the long asymmetry lifetimes in our low viscosity simulations ($alpha sim 2 times 10^{-5}$), a discrepancy we suggest is due to these discs having higher viscosities.
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We study torques on migrating low-mass planets in locally isothermal discs. Previous work on low-mass planets generally kept the planet on a fixed orbit, after which the torque on the planet was measured. In addition to these static torques, when the planet is allowed to migrate it experiences dynamical torques, which are proportional to the migration rate and whose sign depends on the background vortensity gradient. We show that in discs a few times more massive than the Minimum Mass Solar Nebula, these dynamical torques can have a profound impact on planet migration. Inward migration can be slowed down significantly, and if static torques lead to outward migration, dynamical torques can take over, taking the planet beyond zero-torque lines set by saturation of the corotation torque in a runaway fashion. This means the region in non-isothermal discs where outward migration is possible can be larger than what would be concluded from static torques alone.
Embedded planets disturb the density structure of the ambient disk and gravitational back-reaction will induce possibly a change in the planets orbital elements. The accurate determination of the forces acting on the planet requires careful numerical analysis. Recently, the validity of the often used fast orbital advection algorithm (FARGO) has been put into question, and special numerical resolution and stability requirements have been suggested. In this paper we study the process of planet-disk interaction for small mass planets of a few Earth masses, and reanalyze the numerical requirements to obtain converged and stable results. One focus lies on the applicability of the FARGO-algorithm. Additionally, we study the difference of two and three-dimensional simulations, compare global with local setups, as well as isothermal and adiabatic conditions. We study the influence of the planet on the disk through two- and three-dimensional hydrodynamical simulations. To strengthen our conclusions we perform a detailed numerical comparison where several upwind and Riemann-solver based codes are used with and without the FARGO-algorithm. With respect to the wake structure and the torque density acting on the planet we demonstrate that the FARGO-algorithm yields correct results, and that at a fraction of the regular cpu-time. We find that the resolution requirements for achieving convergent results in unshocked regions are rather modest and depend on the pressure scale height of the disk. By comparing the torque densities of 2D and 3D simulations we show that a suitable vertical averaging procedure for the force gives an excellent agreement between the two. We show that isothermal and adiabatic runs can differ considerably, even for adiabatic indices very close to unity.
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.
Disc-driven planet migration is integral to the formation of planetary systems. In standard, gas-dominated protoplanetary discs, low-mass planets or planetary cores undergo rapid inwards migration and are lost to the central star. However, several recent studies indicate that the solid component in protoplanetary discs can have a significant dynamical effect on disc-planet interaction, especially when the solid-to-gas mass ratio approaches unity or larger and the dust-on-gas drag forces become significant. As there are several ways to raise the solid abundance in protoplanetary discs, for example through disc winds and dust-trapping in pressure bumps, it is important to understand how planets migrate through a dusty environment. To this end, we study planet migration in dust-rich discs via a systematic set of high-resolution, two-dimensional numerical simulations. We show that the inwards migration of low-mass planets can be slowed down by dusty dynamical corotation torques. We also identify a new regime of stochastic migration applicable to discs with dust-to-gas mass ratios $gtrsim 0.3$ and particle Stokes numbers $gtrsim 0.03$. In these cases, disc-planet interaction leads to the continuous development of small-scale, intense dust vortices that scatter the planet, which can potentially halt or even reverse the inwards planet migration. We briefly discuss the observational implications of our results and highlight directions for future work.
Stimulated by the discovery of a number of close-in low-density planets, we generalise the Jeans escape parameter taking hydrodynamic and Roche lobe effects into account. We furthermore define $Lambda$ as the value of the Jeans escape parameter calculated at the observed planetary radius and mass for the planets equilibrium temperature and considering atomic hydrogen, independently of the atmospheric temperature profile. We consider 5 and 10 $M_{oplus}$ planets with an equilibrium temperature of 500 and 1000 K, orbiting early G-, K-, and M-type stars. Assuming a clear atmosphere and by comparing escape rates obtained from the energy-limited formula, which only accounts for the heating induced by the absorption of the high-energy stellar radiation, and from a hydrodynamic atmosphere code, which also accounts for the bolometric heating, we find that planets whose $Lambda$ is smaller than 15-35 lie in the boil-off regime, where the escape is driven by the atmospheric thermal energy and low planetary gravity. We find that the atmosphere of hot (i.e. $T_{rm eq}gtrapprox$ 1000 K) low-mass ($M_{rm pl}lessapprox$ 5 $M_{oplus}$) planets with $Lambda$ < 15-35 shrinks to smaller radii so that their $Lambda$ evolves to values higher than 15-35, hence out of the boil-off regime, in less than $approx$500 Myr. Because of their small Roche lobe radius, we find the same result also for hot (i.e. $T_{rm eq}gtrapprox$ 1000 K) higher mass ($M_{rm pl}lessapprox$ 10 $M_{oplus}$) planets with $Lambda$ < 15-35, when they orbit M-dwarfs. For old, hydrogen-dominated planets in this range of parameters, $Lambda$ should therefore be $geq$15-35, which provides a strong constraint on the planetary minimum mass and maximum radius and can be used to predict the presence of aerosols and/or constrain planetary masses, for example.
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