arXiv subjects

Gennaro D'Angelo

Publications and source records attributed to Gennaro D'Angelo.

33 records · Page 2Linked to original sources

arXiv2013

Three-Dimensional Radiation-Hydrodynamics Calculations of the Envelopes of Young Planets Embedded in Protoplanetary Disks

We perform global three-dimensional (3D) radiation-hydrodynamics calculations of the envelopes surrounding young planetary cores of 5, 10, and 15 Earth masses, located in a protoplanetary disk at 5 and 10 AU from a solar-mass star. We apply a nested-grid technique to resolve the thermodynamics of the disk at the orbital-radius length scale and that of the envelope at the core-radius length scale. The gas is modeled as a solar mixture of molecular and atomic hydrogen, helium, and their ions. The equation of state accounts for both gas and radiation, and gas energy includes contributions from rotational and vibrational states of molecular hydrogen and from ionization of atomic species. Dust opacities are computed from first principles, applying the full Mie theory. One-dimensional (1D) calculations of planet formation are used to supplement the 3D calculations by providing energy deposition rates in the envelope due to solids accretion. We compare 1D and 3D envelopes and find that masses and gas accretion rates agree within factors of 2, and so do envelope temperatures. The trajectories of passive tracers are used to define the size of 3D envelopes, resulting in radii much smaller than the Hill radius and smaller than the Bondi radius. The moments of inertia and angular momentum of the envelopes are determined and the rotation rates are derived from the rigid-body approximation, resulting in slow bulk rotation. We find that the polar flattening is < ~0.05. The dynamics of the accretion flow is examined by tracking the motion of tracers that move into the envelope. The anisotropy of this flow is characterized in terms of both its origin and impact site at the envelope surface. Gas merges with the envelope preferentially at mid- to high latitudes.

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arXiv2013

Deuterium Burning in Massive Giant Planets and Low-Mass Brown Dwarfs formed by Core-Nucleated Accretion

Formation of bodies near the deuterium-burning limit is considered by detailed numerical simulations according to the core-nucleated giant planet accretion scenario. The objects, with heavy-element cores in the range 5-30 Mearth, are assumed to accrete gas up to final masses of 10-15 Jupiter masses (Mjup). After the formation process, which lasts 1-5 Myr and which ends with a 'cold-start', low-entropy configuration, the bodies evolve at constant mass up to an age of several Gyr. Deuterium burning via proton capture is included in the calculation, and we determined the mass, M50, above which more than 50% of the initial deuterium is burned. This often-quoted borderline between giant planets and brown dwarfs is found to depend only slightly on parameters, such as core mass, stellar mass, formation location, solid surface density in the protoplanetary disk, disk viscosity, and dust opacity. The values for M50 fall in the range 11.6-13.6 Mjup, in agreement with previous determinations that do not take the formation process into account. For a given opacity law during the formation process, objects with higher core masses form more quickly. The result is higher entropy in the envelope at the completion of accretion, yielding lower values of M50. For masses above M50, during the deuterium-burning phase, objects expand and increase in luminosity by 1 to 3 orders of magnitude. Evolutionary tracks in the luminosity-versus-time diagram are compared with the observed position of the companion to Beta Pictoris.

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arXiv2012

Outward Migration of Jupiter and Saturn in Evolved Gaseous Disks

The outward migration of a pair of resonant-orbit planets, driven by tidal interactions with a gas-dominated disk, is studied in the context of evolved solar nebula models. The planets' masses, M1 and M2, correspond to those of Jupiter and Saturn. Hydrodynamical calculations in two and three dimensions are used to quantify the migration rates and analyze the conditions under which the outward migration mechanism may operate. The planets are taken to be fully formed after 1e6 and before 3e6 years. The orbital evolution of the planets in an evolving disk is then calculated until the disk's gas is completely dissipated. Orbital locking in the 3:2 mean motion resonance may lead to outward migration under appropriate conditions of disk viscosity and temperature. However, resonance locking does not necessarily result in outward migration. This is the case, for example, if convergent migration leads to locking in the 2:1 mean motion resonance, as post-formation disk conditions seem to suggest. Accretion of gas on the planets may deactivate the outward migration mechanism by raising the mass ratio M2/M1 and/or by reducing the accretion rate toward the star, hence depleting the inner disk. For migrating planets locked in the 3:2 mean motion resonance, there are stalling radii that depend on disk viscosity and on stellar irradiation, when it determines the disk's thermal balance. Planets locked in the 3:2 orbital resonance that start moving outward from within 1-2 AU may reach beyond 5 AU only under favorable conditions. However, within the explored space of disk parameters, only a small fraction - less than a few per cent - of the models predict that the interior planet reaches beyond 4 AU.

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arXiv2010

Three-dimensional Disk-Planet Torques in a Locally Isothermal Disk

We determine an expression for the Type I planet migration torque involving a locally isothermal disk, with moderate turbulent viscosity (~0.0005 < alpha < ~0.05), based on three-dimensional nonlinear hydrodynamical simulations. The radial gradients (in a dimensionless logarithmic form) of density and temperature are assumed to be constant near the planet. We find that the torque is roughly equally sensitive to the surface density and temperature radial gradients. Both gradients contribute to inward migration when they are negative. Our results indicate that two-dimensional calculations with a smoothed planet potential, used to account for the effects of the third dimension, do not accurately determine the effects of density and temperature gradients on the three-dimensional torque. The results suggest that substantially slowing or stopping planet migration by means of changes in disk opacity or shadowing is difficult and appears unlikely for a disk that is locally isothermal. The scalings of the torque and torque density with planet mass and gas sound speed follow the expectations of linear theory. We also determine an improved formula for the torque density distribution that can be used in one-dimensional long-term evolution studies of planets embedded in locally isothermal disks. This formula can be also applied in the presence of mildly varying radial gradients and of planets that open gaps. We illustrate its use in the case of migrating super-Earths and determine some conditions sufficient for survival.

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arXiv2010

Giant Planet Formation

Gas giant planets play a fundamental role in shaping the orbital architecture of planetary systems and in affecting the delivery of volatile materials to terrestrial planets in the habitable zones. Current theories of gas giant planet formation rely on either of two mechanisms: the core accretion model and the disk instability model. In this chapter, we describe the essential principles upon which these models are built and discuss the successes and limitations of each model in explaining observational data of giant planets orbiting the Sun and other stars.

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arXiv2009

Formation of Jupiter and Conditions for Accretion of the Galilean Satellites

We present an overview of the formation of Jupiter and its associated circumplanetary disk. Jupiter forms via a combination of planetesimal accretion and gravitational accumulation of gas from the surrounding solar nebula. The formation of the circumjovian gaseous disk, or subnebula, straddles the transitional stage between runaway gas accretion and Jupiter's eventual isolation from the solar disk. This isolation, which effectively signals the termination of Jupiter's accretion, takes place as Jupiter opens a deep gas gap in the solar nebula, or the solar nebula gas dissipates. We describe the conditions for accretion of the Galilean satellites, including the timescales for their formation, and mechanisms for their survival, all within the context of key constraints for satellite formation models. The environment in which the regular satellites form is tied to the timescale for circumplanetary disk dispersal, which depends on the nature and persistence of turbulence. In the case that subnebula turbulence decays as gas inflow wanes, we present a novel mechanism for satellite survival involving gap opening by the largest satellites. On the other hand, assuming that sustained turbulence drives subnebula evolution on a short timescale compared to the satellite formation timescale, we review a model that emphasizes collisional processes to explain satellite observations. We briefly discuss the mechanisms by which solids may be delivered to the circumplanetary disk. However, we expect that planetesimal delivery mechanisms likely provide the bulk of material for satellite accretion.

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arXiv2008

Models of Jupiter's Growth Incorporating Thermal and Hydrodynamic Constraints

[Abridged] We model the growth of Jupiter via core nucleated accretion, applying constraints from hydrodynamical processes that result from the disk-planet interaction. We compute the planet's internal structure using a Henyey-type stellar evolution code. The planet's interactions with the protoplanetary disk are calculated using 3-D hydrodynamic simulations. Previous models of Jupiter's growth have taken the radius of the planet to be approximately one Hill sphere radius, Rhill. However, 3-D hydrodynamic simulations show that only gas within 0.25Rhill remains bound to the planet, with the more distant gas eventually participating in the shear flow of the protoplanetary disk. Therefore in our new simulations, the planet's outer boundary is placed at the location where gas has the thermal energy to reach the portion of the flow not bound to the planet. We find that the smaller radius increases the time required for planetary growth by ~5%. Thermal pressure limits the rate at which a planet less than a few dozen times as massive as Earth can accumulate gas from the protoplanetary disk, whereas hydrodynamics regulates the growth rate for more massive planets. Within a moderately viscous disk, the accretion rate peaks when the planet's mass is about equal to the mass of Saturn. In a less viscous disk hydrodynamical limits to accretion are smaller, and the accretion rate peaks at lower mass. To account for disk dissipation, we perform some of our simulations of Jupiter's growth within a disk whose surface gas density decreases on a timescale of 3Myr. According to our simulations, proto-Jupiter's distended and thermally-supported envelope was too small to capture the planet's current retinue of irregular satellites as advocated by Pollack et al. (1979).

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arXiv2008

Evolution of Migrating Planets Undergoing Gas Accretion

We analyze the orbital and mass evolution of planets that undergo run-away gas accretion by means of 2D and 3D hydrodynamic simulations. The disk torque distribution per unit disk mass as a function of radius provides an important diagnostic for the nature of the disk-planet interactions. We first consider torque distributions for nonmigrating planets of fixed mass and show that there is general agreement with the expectations of resonance theory. We then present results of simulations for mass-gaining, migrating planets. For planets with an initial mass of 5 Earth masses, which are embedded in disks with standard parameters and which undergo run-away gas accretion to one Jupiter mass (Mjup), the torque distributions per unit disk mass are largely unaffected by migration and accretion for a given planet mass. The migration rates for these planets are in agreement with the predictions of the standard theory for planet migration (Type I and Type II migration). The planet mass growth occurs through gas capture within the planet's Bondi radius at lower planet masses, the Hill radius at intermediate planet masses, and through reduced accretion at higher planet masses due to gap formation. During run-away mass growth, a planet migrates inwards by only about 20% in radius before achieving a mass of ~1 Mjup. For the above models, we find no evidence of fast migration driven by coorbital torques, known as Type III migration. We do find evidence of Type III migration for a fixed mass planet of Saturn's mass that is immersed in a cold and massive disk. In this case the planet migration is assumed to begin before gap formation completes. The migration is understood through a model in which the torque is due to an asymmetry in density between trapped gas on the leading side of the planet and ambient gas on the trailing side of the planet.

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arXiv2006

Evolution of Giant Planets in Eccentric Disks

We investigate the interaction between a giant planet and a viscous circumstellar disk by means of high-resolution, two-dimensional hydrodynamical simulations. We consider planet masses that range from 1 to 3 Jupiter masses (Mjup) and initial orbital eccentricities that range from 0 to 0.4. We find that a planet can cause eccentricity growth in a disk region adjacent to the planet's orbit, even if the planet's orbit is circular. Disk-planet interactions lead to growth in a planet's orbital eccentricity. The orbital eccentricities of a 2 Mjup and a 3 Mjup planet increase from 0 to 0.11 within about 3000 orbits. Over a similar time period, the orbital eccentricity of a 1 Mjup planet grows from 0 to 0.02. For a case of a 1 Mjup planet with an initial eccentricity of 0.01, the orbital eccentricity grows to 0.09 over 4000 orbits. Radial migration is directed inwards, but slows considerably as a planet's orbit becomes eccentric. If a planet's orbital eccentricity becomes sufficiently large, e > ~0.2, migration can reverse and so be directed outwards. The accretion rate towards a planet depends on both the disk and the planet orbital eccentricity and is pulsed over the orbital period. Planet mass growth rates increase with planet orbital eccentricity. For e~0.2 the mass growth rate of a planet increases by approximately 30% above the value for e=0. For e > ~0.1, most of the accretion within the planet's Roche lobe occurs when the planet is near the apocenter. Similar accretion modulation occurs for flow at the inner disk boundary which represents accretion toward the star.

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arXiv2005

Gas Flow Across Gaps in Protoplanetary Disks

We analyze the gas accretion flow through a planet-produced gap in a protoplanetary disk. We adopt the alpha disk model and ignore effects of planetary migration. We develop a semi-analytic, one-dimensional model that accounts for the effects of the planet as a mass sink and also carry out two-dimensional hydrodynamical simulations of a planet embedded in a disk. The predictions of the mass flow rate through the gap based on the semi-analytic model generally agree with the hydrodynamical simulations at the 25% level. Through these models, we are able to explore steady state disk structures and over large spatial ranges. The presence of an accreting Jupiter-mass planet significantly lowers the density of the disk within a region of several times the planet's orbital radius. The mass flow rate across the gap (and onto the central star) is typically 10% to 25% of the mass accretion rate outside the orbit of the planet, for planet-to-star mass ratios that range from 5e-5 to 1e-3.

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arXiv2004

The dependence of protoplanet migration rates on coorbital torques

We investigate the migration rates of high-mass protoplanets embedded in accretion discs via two and three-dimensional hydrodynamical simulations. The simulations follow the planet's radial motion and employ a nested-grid code that allows for high resolution close to the planet. We concentrate on the possible role of the coorbital torques in affecting migration rates. We analyse two cases: (a) a Jupiter-mass planet in a low-mass disc and (b) a Saturn-mass planet in a high-mass disc. Planet migration in case (b) is much more susceptible to coorbital torques than in case (a). We find that the coorbital torques in both cases do not depend sensitively on whether the planet is allowed to migrate through the disc or is held on a fixed orbit. We also examine the dependence of the planet's migration rate on the numerical resolution near the planet. For case (a), numerical convergence is relatively easy to obtain, even when including torques arising from deep within the planet's Hill sphere. The migration rate in this case is numerically on order of the Type II migration rate and much smaller than the Type I rate, if the disc has 0.01 solar-masses inside 26 AU. Torques from within the Hill sphere provide a substantial opposing contribution to the migration rate. In case (b), the gas mass within the Hill sphere is larger than the planet's mass and convergence is more difficult to obtain. If the torques within the Hill sphere are ignored, convergence is more easily achieved but the migration rate is artificially large. At our highest resolution, the migration rate for case (b) is much less than the Type I rate, but somewhat larger than the Type II rate.

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arXiv2004

On the Observability of Giant Protoplanets in Circumstellar Disks

We investigate the possibility to detect giant planets that are still embedded in young circumstellar disks. Based on models with different stellar, planetary, and disk masses, and different radial positions of the planet we analyze the resulting submillimeter appearance of these systems. We find that the influence of the planet on the spectral energy distribution could not be distinguished from that of other disk parameters. However, dust reemission images of the disks show that the hot region in the proximity of a young planet, along with the gap, could indeed be detected and mapped with the Atacama Large Millimeter Array in the case of nearby circumstellar disks (d<100pc) in approximate face-on orientation.

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arXiv2003

Thermo-Hydrodynamics of Circumstellar Disks with High-mass Planets

With a series of numerical simulations, we analyze the thermo-hydrodynamical evolution of circumstellar disks containing Jupiter-size protoplanets. In the framework of the two-dimensional approximation, we consider an energy equation that includes viscous heating and radiative effects in a simplified, yet consistent form. Multiple nested grids are used in order to study both global and local features around the planet. By means of different viscosity prescriptions, we investigate various temperature regimes. A planetary mass range from 0.1 to 1 Mj is examined. Computations show that gap formation is a general property which affects density, pressure, temperature, optical thickness, and radiated flux distributions. However, it remains a prominent feature only when the kinematic viscosity is on the order of 10^(15) cm^2/s or lower. Around accreting planets, a circumplanetary disk forms that has a surface density profile decaying exponentially with the distance and whose mass is 5-6 orders of magnitudes smaller than Jupiter's mass. Circumplanetary disk temperature profiles decline roughly as the inverse of the distance from the planet. Temperatures range from some 10 to ~1000 K. Planetary accretion and migration rates depend on the viscosity regime, with discrepancies within an order of magnitude. Estimates of growth and migration time scales inferred by these models are on the same orders of magnitude as those previously obtained with locally isothermal simulations.

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arXiv2003

Orbital Migration and Mass Accretion of Protoplanets in 3D Global Computations with Nested Grids

We investigate the evolution of protoplanets with different masses embedded in an accretion disk, via global fully three-dimensional hydrodynamical simulations. We consider a range of planetary masses extending from one and a half Earth's masses up to one Jupiter's mass, and we take into account physically realistic gravitational potentials of forming planets. In order to calculate accurately the gravitational torques exerted by disk material and to investigate the accretion process onto the planet, the flow dynamics has to be thoroughly resolved on long as well as short length scales. We achieve this strict resolution requirement by applying a nested-grid refinement technique which allows to greatly enhance the local resolution. Our results from altogether 51 simulations show that for large planetary masses, approximately above a tenth of the Jupiter's mass, migration rates are relatively constant, as expected in type II migration regime and in good agreement with previous two-dimensional calculations. In a range between seven and fifteen Earth's masses, we find a dependency of the migration speed on the planetary mass that yields time scales considerably longer than those predicted by linear analytical theories. This property may be important in determining the overall orbital evolution of protoplanets. The growth time scale is minimum around twenty Earth-masses, but it rapidly increases for both smaller and larger mass values. Significant differences between two- and three-dimensional calculations are found in particular for objects with masses smaller than ten Earth-masses. We also derive an analytical approximation for the numerically computed mass growth rates.

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arXiv2001

Nested-grid calculations of disk-planet interaction

We study the evolution of embedded protoplanets in a protostellar disk using very high resolution nested-grid computations. This method allows us to perform global simulations of planets orbiting in disks and, at the same time, to resolve in detail the dynamics of the flow inside the Roche lobe of the planet. The primary interest of this work lies in the analysis of the gravitational torque balance acting on the planet. For this purpose we study planets of different masses, ranging from one Earth-mass up to one Jupiter-mass, assuming typical parameters of the protostellar disk. The high resolution of the method allows a precise determination of the mass flow onto the planet and the resulting torques. The obtained migration time scales are in the range from few times 10^4 years, for intermediate mass planets, to 10^6 years, for very low and high mass planets. Typical growth time scales depend strongly on the planetary mass, ranging from a few hundred years, in the case of Earth-type planets, to several ten thousand years, in the case of Jupiter-type planets.

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