Radiation Hydrodynamics Simulations of Photoevaporation of Protoplanetary Disks: Metallicity Dependence

Radiation Hydrodynamics Simulations of Photoevaporation of Protoplanetary Disks: Metallicity Dependence

Authors:
Nakatani et al

Abstract:

Protoplanetary disks are thought to have lifetimes of 3−6 million years in the solar neighborhood, but recent observations suggest that the disk lifetimes are shorter in a low metallicity environment. We perform a suite of radiation hydrodynamics simulations of photoevaporation of protoplanetary disks to study the disk structure and its long-term evolution of ∼10000 years, and the metallicity dependence of mass-loss rate. Our simulations follow hydrodynamics, extreme and far ultraviolet radiative transfer, and non-equilibrium chemistry in a self-consistent manner. Dust grain temperatures are also calculated consistently by solving the radiative transfer of the stellar irradiation and grain (re-)emission. We vary the disk gas metallicity over a wide range of 10−4Z⊙≤Z≤10 Z⊙. For our fiducial model with a 0.5 M⊙ central star with solar metallicity, the time-averaged photoevaporation rate is M˙ph=1.38×10−8M⊙yr−1. The photoevaporation rate is lower with higher metallicity in the range of 10−0.5Z⊙≲Z≲10 Z⊙, because dust shielding effectively prevents far-ultra violet (FUV) photons from penetrating into and heating the dense regions of the disk. The photoevaporation rate sharply declines at even lower metallicities in 10−1Z⊙≲Z≲10−0.5Z⊙, because FUV photoelectric heating is not efficient any more to raise the gas temperature and to drive outflows. At 10−4Z⊙≤Z≲10−1Z⊙, HI photoionization heating acts as a dominant gas heating process and drives photoevaporative flows with roughly a constant rate. The typical disk lifetime is shorter at Z=0.3 Z⊙ than at Z=Z⊙, being consistent with recent observations of the extreme outer galaxy.

RADIATION HYDRODYNAMICS MODELS OF THE INNER RIM IN PROTOPLANETARY DISKS

RADIATION HYDRODYNAMICS MODELS OF THE INNER RIM IN PROTOPLANETARY DISKS

Authors:

Flock et al

Abstract:

Many stars host planets orbiting within a few astronomical units (AU). The occurrence rate and distributions of masses and orbits vary greatly with the host star's mass. These close planets' origins are a mystery that motivates investigating protoplanetary disks' central regions. A key factor governing the conditions near the star is the silicate sublimation front, which largely determines where the starlight is absorbed, and which is often called the inner rim. We present the first radiation hydrodynamical modeling of the sublimation front in the disks around the young intermediate-mass stars called Herbig Ae stars. The models are axisymmetric and include starlight heating; silicate grains sublimating and condensing to equilibrium at the local, time-dependent temperature and density; and accretion stresses parameterizing the results of MHD magnetorotational turbulence models. The results compare well with radiation hydrostatic solutions and prove to be dynamically stable. Passing the model disks into Monte Carlo radiative transfer calculations, we show that the models satisfy observational constraints on the inner rim's location. A small optically thin halo of hot dust naturally arises between the inner rim and the star. The inner rim has a substantial radial extent, corresponding to several disk scale heights. While the front's overall position varies with the stellar luminosity, its radial extent depends on the mass accretion rate. A pressure maximum develops near the location of thermal ionization at temperatures of about 1000 K. The pressure maximum is capable of halting solid pebbles' radial drift and concentrating them in a zone where temperatures are sufficiently high for annealing to form crystalline silicates.

Examining the Accuracy of Astrophysical Disk Simulations With a Generalized Hydrodynamical Test Problem

Examining the Accuracy of Astrophysical Disk Simulations With a Generalized Hydrodynamical Test Problem

Authors:

Raskin et al

Abstract:

We discuss a generalization of the classic Keplerian disk test problem allowing for both pressure and rotational support, as a method of testing astrophysical codes incorporating both gravitation and hydrodynamics. We argue for the inclusion of pressure in rotating disk simulations on the grounds that realistic, astrophysical disks exhibit non-negligible pressure support. We then apply this test problem to examine the performance of various smoothed particle hydrodynamics (SPH) methods incorporating a number of improvements proposed over the years to help SPH better address problems noted in modeling the classical gravitation only Keplerian disk. We also apply this test to a newly developed extension of SPH based on reproducing kernels called CRKSPH. Counterintuitively, we find that pressure support worsens the performance of traditional SPH on this problem, causing unphysical collapse away from the steady-state disk solution even more rapidly than the purely gravitational problem, whereas CRKSPH greatly reduces this error.

LONG-TERM AND LARGE-SCALE HYDRODYNAMICAL SIMULATIONS OF MIGRATING PLANETS

LONG-TERM AND LARGE-SCALE HYDRODYNAMICAL SIMULATIONS OF MIGRATING PLANETS

Authors:

Benítez-Llambay et al

Abstract:

We present a new method that allows for long-term and large-scale hydrodynamical simulations of migrating planets over a grid-based Eulerian code. This technique, which consists of a remapping of the disk by tracking the planetary migration, enables runs of migrating planets over a time comparable to the age of protoplanetary disks. This method also has the potential to address efficiency problems related to the migration of multi-planet systems in gaseous disks and to improve the current results of the migration of massive planets by including global viscous evolution as well as detailed studies of the co-orbital region during migration. We perform different tests using the public code FARGO3D to validate this method and compare its results with those obtained using a classical fixed grid.

Particle dynamics in discs with turbulence generated by the vertical shear instability

Particle dynamics in discs with turbulence generated by the vertical shear instability

Authors:

Stoll et al

Abstract:

Among the candidates for generating turbulence in accretion discs in situations with low intrinsic ionization the vertical shear instability (VSI) has become an interesting candidate, as it relies purely on a vertical gradient in the angular velocity. Existing simulations have shown that α-values a few times 10−4 can be generated. The particle growth in the early planet formation phase is determined by the dynamics of dust particles. Here, we address in particular the efficiency of VSI-turbulence in concentrating particles in order to generate overdensities and low collision velocities. We perform 3D numerical hydrodynamical simulations of accretion discs around young stars that include radiative transport and irradiation from the central star. The motion of particles within a size range of a fraction of mm up to several m is followed using standard drag formula. We confirm that under realistic conditions the VSI is able to generate turbulence in full 3D protoplanetary discs. The irradiated disc shows turbulence within 10 to 60au. The mean radial motion of the gas is such that it is directed inward near the midplane and outward in the surface layers. We find that large particles drift inward with the expected speed, while small particles can experience phases of outward drift. Additionally, the particles show bunching behaviour with overdensities reaching 5 times the average value, which is strongest for dimensionless stopping times around unity. Particles in a VSI-turbulent discs are concentrated in large scale turbulent eddies and show low relative speeds that allow for growing collisions. The reached overdensities will also allow for the onset streaming instabilities further enhancing particle growth. The outward drift for small particles at higher disk elevations allows for the transport of processed high temperature material in the Solar System to larger distances.

A self-similar solution for thermal disk winds

A self-similar solution for thermal disc winds

Authors:

Clarke et al

Abstract:

We derive a self-similar description for the 2D streamline topology and flow structure of an axi-symmetric, thermally driven wind originating from a disc in which the density is a power law function of radius. Our scale-free solution is strictly only valid in the absence of gravity or centrifugal support; comparison with 2D hydrodynamic simulations of winds from Keplerian discs however demonstrates that the scale-free solution is a good approximation also in the outer regions of such discs, and can provide a reasonable description even for launch radii well within the gravitational radius of the flow. Although other authors have considered the flow properties along streamlines whose geometry has been specified in advance, this is the first isothermal calculation in which the flow geometry and variation of flow variables along streamlines is determined self-consistently. It is found that the flow trajectory is very sensitive to the power-law index of radial density variation in the disc: the steeper the density gradient, the stronger is the curvature of streamlines close to the flow base that is required in order to maintain momentum balance perpendicular to the flow. Steeper disc density profiles are also associated with more rapid acceleration, and a faster fall-off of density, with height above the disc plane. The derivation of a set of simple governing equations for the flow structure of thermal winds from the outer regions of power law discs offers the possibility of deriving flow observables without having to resort to hydrodynamical simulation.

Drag-driven instability of a dust layer in a magnetized protoplanetary disk

Drag-driven instability of a dust layer in a magnetized protoplanetary disc

Authors:

Shadmehri et al

Abstract:

We study drag-driven instability in a protoplanetary disc consisting of a layer of single-sized dust particles which are coupled to the magnetized gas aerodynamically and the particle-to-gas feedback is included. We find a dispersion relation for axisymmetric linear disturbances and growth rate of the unstable modes are calculated numerically. While the secular gravitational instability in the absence of particle-to-gas feedback predicts the dust layer is unstable, magnetic fields significantly amplifies the instability if the Toomre parameter for the gas component is fixed. We also show that even a weak magnetic field is able to amplify the instability more or less irrespective of the dust-gas coupling.

Radiation hydrodynamical models of the inner rim in protoplanetary disks

Radiation hydrodynamical models of the inner rim in protoplanetary disks

Authors:

Flock et al

Abstract:

Many stars host planets orbiting within a few astronomical units (AU). The occurrence rate and distributions of masses and orbits vary greatly with the host stars mass. These close planets origins are a mystery that motivates investigating protoplanetary disks central regions. A key factor governing the conditions near the star is the silicate sublimation front, which largely determines where the starlight is absorbed, and which is often called the inner rim. We present the first radiation hydrodynamical modeling of the sublimation front in the disks around the young intermediate-mass stars called Herbig Ae stars. The models are axisymmetric, and include starlight heating, silicate grains sublimating and condensing to equilibrium at the local, time-dependent temperature and density, and accretion stresses parametrizing the results of MHD magneto-rotational turbulence models. The results compare well with radiation hydrostatic solutions, and prove to be dynamically stable. Passing the model disks into Monte Carlo radiative transfer calculations, we show that the models satisfy observational constraints on the inner rims location. A small optically-thin halo of hot dust naturally arises between the inner rim and the star. The inner rim has a substantial radial extent, corresponding to several disk scale heights. While the fronts overall position varies with the stellar luminosity, its radial extent depends on the mass accretion rate. A pressure maximum develops near the location of thermal ionization at temperatures about 1000 K. The pressure maximum is capable of halting solid pebbles radial drift and concentrating them in a zone where temperatures are sufficiently high for annealing to form crystalline silicates.

The Effect of Electron Heating on Protoplanetary Disk Magnetorotational Turbulence

The Effect of Electron Heating on Magnetorotational Turbulence in Protoplanetary Disks: Self-regulation and Reduced Turbulence Strength

Authors:

Mori et al

Abstract:

The magnetorotational instability (MRI) drives vigorous turbulence in a region of protoplanetary disks where the ionization fraction is sufficiently high. It has recently been shown that the electric field induced by the MRI can heat up electrons and thereby affect the ionization balance in the gas. In particular, in a disk where abundant dust grains are present, the electron heating causes a reduction of the electron abundance, thereby preventing further growth of the MRI. By using the nonlinear Ohm's law that takes into account electron heating, we investigate where in protoplanetary disks this negative feedback between the MRI and ionization chemistry becomes important. We find that the "e-heating zone," the region where the electron heating limits the saturation of the MRI, extends out to 80 AU in the minimum-mass solar nebula with abundant submicron-sized grains. This region is considerably larger than the conventional dead zone whose radial extent is ∼20 AU in the same disk model. Our simple estimate based on the scaling between the Maxwell stress and current density shows that that the MRI turbulence in the e-heating zone should have a significantly low saturation level, with the viscosity parameter α being from 10−5 to 10−3 at the midplane. This implies that the MRI should be "virtually dead" deep inside the e-heating zone. We also find that (sub)micron-sized grains in the e-heating zone are so negatively charged that their collisional growth is unlikely to occur.

Cooling Requirements for the Vertical Shear Instability in Protoplanetary Disks

Cooling Requirements for the Vertical Shear Instability in Protoplanetary Disks

Authors:

Lin et al

Abstract:

It is difficult to understand how cold circumstellar disks accrete onto their central stars. A hydrodynamic mechanism, the vertical shear instability (VSI), offers a means to drive angular momentum transport in cold accretion disks such as protoplanetary disks (PPDs). The VSI is driven by a weak vertical gradient in the disk's orbital motion. In order to grow, the VSI must overcome vertical buoyancy, a strongly stabilizing influence in cold disks, where heating is dominated by external irradiation. Rapid cooling, via radiative losses, reduces the effective buoyancy and allows the VSI to operate. In this paper, we quantify the cooling timescale, tc, needed for growth of the VSI. We perform a linear analysis of the VSI with cooling in vertically global and radially local disk models. For irradiated disks, we find that the VSI is most vigorous for rapid cooling with tc<Ω−1Kh|q|/(γ−1) in terms of the Keplerian orbital frequency, ΩK, the disk's aspect ratio, h≪1, the radial power-law temperature gradient, q, and the adiabatic index, γ. For longer cooling times, the VSI is much less effective because growth slows and shifts to smaller length scales, which are more prone to viscous or turbulent decay. We apply our results to PPD models where tc is determined by the opacity of dust grains. We find that the VSI is most effective at intermediate radii, from ∼5AU to ∼50AU with a characteristic growth time of ∼30 local orbital periods. Growth is suppressed by long cooling times both in the opaque inner disk and the optically thin outer disk. A reduction in the dust opacity by a factor of 10 increases cooling times enough to quench the VSI at all disk radii. Thus the formation of solid protoplanets, a sink for dust grains, can impede the VSI.

The Hydrodynamic Flow Around an Exoplanet in a Protoplanetary Disk

The 3D Flow Field Around an Embedded Planet

Authors:

Fung et al

Abstract:

Understanding the 3D flow topology around a planet embedded in its natal disk is crucial to the study of planet formation. 3D modifications to the well-studied 2D flow topology have the potential to resolve longstanding problems in both planet migration and accretion. We present a detailed analysis of the 3D isothermal flow field around a 5 Earth-mass planet on a fixed circular orbit, simulated using our high-resolution multi-GPU hydrodynamics code PEnGUIn. We show that, overall, the horseshoe region has a columnar structure extending vertically much beyond the Hill sphere of the planet. This columnar structure is only broken for some of the widest horseshoe streamlines, along which high altitude fluid descends and converges rapidly toward the planet, enters its Bondi sphere, performs one horseshoe turn, and exits radially in the midplane. A portion of this flow gathers enough speed to exit the horseshoe region altogether. We call this newly identified feature the "transient" horseshoe flow. As the flow continues close to the disk midplane, it splits into the up-down symmetric parts, and rolls up into a pair of counter-rotating, horizontal vortex lines shed downstream into the wake of the planet. This flow, unique to 3D, affects both planet migration and accretion. It prevents the planet from sustaining a hydrostatic atmosphere due to its intrusion into the Bondi sphere, and it also leads to a significant corotation torque on the planet, unanticipated by 2D analysis. In the reported simulation, starting with a Σ∼r−3/2 radial surface density profile, this torque is positive and largely cancels with the negative differential Lindblad torque, resulting in an almost 2 orders of magnitude reduction in the inferred rate of planet migration. Finally, we report that 3D effects can be suppressed by a sufficiently large disk viscosity, leading to results similar to those in 2D.

Simulating Exoplanet Protoatmospheres

Hydrodynamics of Embedded Planets' First Atmospheres. I. A Centrifugal Growth Barrier for 2D Flows

Authors:

Ormel et al

Abstract:

In the core accretion paradigm of planet formation, gas giants only form a massive atmosphere after their progenitors exceeded a threshold mass: the critical core mass. Most (exo)planets, being smaller and rock/ice-dominated, never crossed this line. Nevertheless, they were massive enough to attract substantial amounts of gas from the disc, while their atmospheres remained in pressure-equilibrium with the disc. Our goal is to characterise the hydrodynamical properties of the atmospheres of such embedded planets and their implication for their (long-term) evolution. In this paper -- the first in series -- we start to investigate the properties of an isothermal and inviscid flow past a small, embedded planet by conducting local, 2D hydrodynamical simulations. Using the PLUTO code we confirm that the flow is steady and bound. This steady outcome is most apparent for the log-polar grid (with the grid spacing proportional to the distance from the planet). For low-mass planets, Cartesian grids are somewhat less efficient as they have difficulty to follow the circular, large speeds in the deep atmosphere. Relating the amount of rotation to the gas fraction of the atmosphere, we find that more massive atmospheres rotate faster -- a finding consistent with Kelvin's circulation theorem. Rotation therefore limits the amount of gas that planets can acquire from the nebula. Dependent on the Toomre-Q parameter of the circumstellar disc, the planet's atmosphere will reach Keplerian rotation before self-gravity starts to become important.

The Kozai-Lidov Mechanism in Hydrodynamical Disks

The Kozai-Lidov Mechanism in Hydrodynamical Disks

Authors:

Martin et al

Abstract:

We use three dimensional hydrodynamical simulations to show that a highly misaligned accretion disk around one component of a binary system can exhibit global Kozai-Lidov cycles, where the inclination and eccentricity of the disk are interchanged periodically. This has important implications for accreting systems on all scales, for example, the formation of planets and satellites in circumstellar and circumplanetary disks, outbursts in X-ray binary systems and accretion on to supermassive black holes.

Modeling Convection in Exoatmospheres

THEORY AND SIMULATIONS OF ROTATING CONVECTION

Authors:

Barker et al

Abstract:

We study thermal convection in a rotating fluid in order to better understand the properties of convection zones in rotating stars and planets. We first derive a mixing-length theory for rapidly rotating convection, arriving at the results of Stevenson via simple physical arguments. The theory predicts the properties of convection as a function of the imposed heat flux and rotation rate, independent of microscopic diffusivities. In particular, it predicts the mean temperature gradient, the rms velocity and temperature fluctuations, and the size of the eddies that dominate heat transport. We test all of these predictions with high resolution three-dimensional hydrodynamical simulations of Boussinesq convection in a Cartesian box. The results agree remarkably well with the theory across more than two orders of magnitude in rotation rate. For example, the temperature gradient is predicted to scale as the rotation rate to the four-fifths power at fixed flux, and the simulations yield 0.75 ± 0.06. We conclude that the mixing-length theory is a solid foundation for understanding the properties of convection zones in rotating stars and planets.