Circumplanetary disks (CPDs) regulate the late accretion to the giant planet and serve as the birthplace for satellites. Understanding their characteristics via simulations also helps to prepare for ...their observations. Here we study disks around 1, 3, 5, and 10 MJup planets with 3D global radiative hydrodynamic simulations with sub-planet peak resolution and various planetary temperatures. We found that as the 1 MJup planet radiates away its formation heat, the circumplanetary envelope transitions to a disk between and 4000 K. In the case of 3-10 MJup planets, a disk always forms. The temperature profile of the CPDs is very steep, the inner 1/6th is higher than the silicate condensation temperature, and the entire disk is higher than the water freezing point, making satellite formation impossible in this early stage (<1 Myr). Satellites might form much later and first in the outer parts of the disk, migrating inwards later on. Our disk masses are 1, 7, and 20 for the 1, 3, 5, and 10 MJup gas giants, respectively, and we provide an empirical formula to estimate the subdisk masses based on the planet- and circumstellar disk (CSD) mass. Our finding is that the cooler the planet, the lower the temperature of the subdisk, and the higher the vertical influx velocities. The planetary gap is also both deeper and wider. We also show that the gaps in 2D and 3D are different. The subdisk eccentricity increases with and violently interacts with the CSD, making satellite-formation less likely when .
Abstract
We carried out 3D dust + gas radiative hydrodynamic simulations of forming planets. We investigated a parameter grid of a Neptune-mass, a Saturn-mass, a Jupiter-mass, and a five-Jupiter-mass ...planet at 5.2, 30, and 50 au distance from their star. We found that the meridional circulation (Szulágyi et al. 2014; Fung & Chiang 2016) drives a strong vertical flow for the dust as well, hence the dust is not settled in the midplane, even for millimeter-sized grains. The meridional circulation will deliver dust and gas vertically onto the circumplanetary region, efficiently bridging over the gap. The Hill-sphere accretion rates for the dust are ∼10
−8
–10
−10
M
Jup
yr
−1
, increasing with planet mass. For the gas component, the gain is 10
−6
–10
−8
M
Jup
yr
−1
. The difference between the dust and gas-accretion rates is smaller with decreasing planetary mass. In the vicinity of the planet, the millimeter-sized grains can get trapped easier than the gas, which means the circumplanetary disk might be enriched with solids in comparison to the circumstellar disk. We calculated the local dust-to-gas ratio (DTG) everywhere in the circumstellar disk and identified the altitude above the midplane where the DTG is 1, 0.1, 0.01, and 0.001. The larger the planetary mass, the more the millimeter-sized dust is delivered and a larger fraction of the dust disk is lifted by the planet. The stirring of millimeter-sized dust is negligible for Neptune-mass planets or below, but significant above Saturn-mass planets.
Circumplanetary discs can be found around forming giant planets, regardless of whether core accretion or gravitational instability built the planet. We carried out state-of-the-art hydrodynamical ...simulations of the circumplanetary discs for both formation scenarios, using as similar initial conditions as possible to unveil possible intrinsic differences in the circumplanetary disc mass and temperature between the two formation mechanisms. We found that the circumplanetary discs' mass linearly scales with the circumstellar disc mass. Therefore, in an equally massive protoplanetary disc, the circumplanetary discs formed in the disc instability model can be only a factor of 8 more massive than their core-accretion counterparts. On the other hand, the bulk circumplanetary disc temperature differs by more than an order of magnitude between the two cases. The subdiscs around planets formed by gravitational instability have a characteristic temperature below 100 K, while the core-accretion circumplanetary discs are hot, with temperatures even greater than 1000 K when embedded in massive, optically thick protoplanetary discs. We explain how this difference can be understood as the natural result of the different formation mechanisms. We argue that the different temperatures should persist up to the point when a full-fledged gas giant forms via disc instability; hence, our result provides a convenient criterion for observations to distinguish between the two main formation scenarios by measuring the bulk temperature in the planet vicinity.
ABSTRACT
Due to recent high-resolution ALMA observations, there is an accumulating evidence for presence of giant planets with masses from ${\sim } 0.01 \, {\rm {M}}_{\rm {J}}$ to a few $\, {\rm ...{M}}_{\rm {J}}$ with separations up to 100 au in the annular structures observed in young protoplanetary discs. We point out that these observations set unique ‘live’ constraints on the process of gas accretion on to sub-Jovian planets that were not previously available. Accordingly, we use a population synthesis approach in a new way: we build time-resolved models and compare the properties of the synthetic planets with the ALMA data at the same age. Applying the widely used gas accretion formulae leads to a deficit of sub-Jovian planets and an overabundance of a few Jupiter mass planets compared to observations. We find that gas accretion rate on to planets needs to be suppressed by about an order of magnitude to match the observed planet mass function. This slower gas giant growth predicts that the planet mass should correlate positively with the age of the protoplanetary disc, albeit with a large scatter. This effect is not clearly present in the ALMA data but may be confirmed in the near future with more observations.
We present three-dimensional simulations with nested meshes of the dynamics of the gas around a Jupiter mass planet with the jupiter and fargoca codes. We implemented a radiative transfer module into ...the jupiter code to account for realistic heating and cooling of the gas. We focus on the circumplanetary gas flow, determining its characteristics at very high resolution (80 per cent of Jupiter's diameter). In our nominal simulation where the temperature evolves freely by the radiative module and reaches 13000 K at the planet, a circumplanetary envelope was formed filling the entire Roche lobe. Because of our equation of state is simplified and probably overestimates the temperature, we also performed simulations with limited maximal temperatures in the planet region (1000, 1500, and 2000 K). In these fixed temperature cases circumplanetary discs (CPDs) were formed. This suggests that the capability to form a CPD is not simply linked to the mass of the planet and its ability to open a gap. Instead, the gas temperature at the planet's location, which depends on its accretion history, plays also fundamental role. The CPDs in the simulations are hot and cooling very slowly, they have very steep temperature and density profiles, and are strongly sub-Keplerian. Moreover, the CPDs are fed by a strong vertical influx, which shocks on the CPD surfaces creating a hot and luminous shock-front. In contrast, the pressure supported circumplanetary envelope is characterized by internal convection and almost stalled rotation.
ABSTRACT
We investigated the formation and evolution of satellite systems in a cold, extended circumplanetary disc (CPD) around a 10MJupiter gas giant, which was formed by gravitational instability ...at 50 au from its star. The disc parameters were from a 3D global smoothed particle hydrodynamics simulation. We used a population synthesis approach, where we placed satellite embryos in this disc, and let them accrete mass, migrate, collide until the gaseous disc is dissipated. In each run, we changed the initial dust-to-gas ratio, dispersion- and refilling time-scales within reasonable limits, as well as the number of embryos and their starting locations. We found that most satellites have mass similar to the Galilean ones, but very few can reach a maximum of 3MEarth due to the massive CPD. Large moons are often form as far as 0.5Rdisc. The migration rate of satellites are fast, hence during the disc lifetime, an average of 10MEarth worth of moons will be engulfed by the planet, increasing greatly its metallicity. We also investigated the effect of the planet’s semimajor axis on the resulting satellite systems by rescaling our model. This test revealed that for the discs closer to the star, the formed moons are lighter, and a larger amount of satellites are lost into the planet due to the even faster migration. Finally, we checked the probability of detecting satellites like our population, which resulted in a low number of ≤ 3 per cent even with upcoming powerful telescopes like E-ELT.
ABSTRACT
The moons of giant planets are believed to form in situ in circumplanetary discs (CPDs). Here, we present an N-body population synthesis framework for satellite formation around a ...Jupiter-like planet, in which the dust-to-gas ratio, the accretion rate of solids from the protoplanetary disc, the number, and the initial positions of protosatellites were randomly chosen from realistic distributions. The disc properties were from 3D radiative simulations sampled in 1D and 2D grids and evolved semi-analytically with time. The N-body satellitesimals accreted mass from the solid component of the disc, interacted gravitationally with each other, experienced close-encounters, both scattering and colliding. With this improved modeling, we found that only about $15{{\ \rm per\ cent}}$ of the resulting population is more massive than the Galilean one, causing migration rates to be low and resonant captures to be uncommon. In 10 per cent of the cases, moons are engulfed by the planet, and 1 per cent of the satellite-systems lose at least 1 Earth-mass into the planet, contributing only in a minor part to the giant planet’s envelope’s heavy element content. We examined the differences in outcome between the 1D and 2D disc models and used machine learning techniques (Randomized Dependence Coefficient together with t-SNE) to compare our population with the Galilean system. Detecting our population around known transiting Jupiter-like planets via transits and TTVs would be challenging, but $14{{\ \rm per\ cent}}$ of the moons could be spotted with an instrumental transit sensitivity of 10−5.
For the very first time we present 3D simulations of planets embedded in stellar irradiated discs. It is well known that thermal effects could reverse the direction of planetary migration from ...inwards to outwards, potentially saving planets in the inner, optically thick parts of the protoplanetary disc. When considering stellar irradiation in addition to viscous friction as a source of heating, the outer disc changes from a shadowed to a flared structure. Using a suited analytical formula it has been shown that in the flared part of the disc the migration is inwards; planets can migrate outwards only in shadowed regions of the disc, because the radial gradient of entropy is stronger there. In order to confirm this result numerically, we have computed the total torque acting on planets held on fixed orbits embedded in stellar irradiated 3D discs using the hydrodynamical code fargoca. We find qualitatively good agreement between the total torque obtained with numerical simulations and the one predicted by the analytical formula. For large masses (>20 M⊕) we find quantitative agreement, and we obtain outwards migration regions for planets up to 60 M⊕ in the early stages of accretional discs. We find nevertheless that the agreement with the analytic formula is quite fortuitous because the formula underestimates the size of the horseshoe region; this error is compensated by imperfect estimates of other terms, most likely the cooling rate and the saturation.
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