Accretion Stress Research Articles

Hydrodynamic turbulence in disks with embedded planets

The vertical shear instability (VSI) is a source of hydrodynamic turbulence that can drive vigorous vertical mixing and moderate levels of accretion in protoplanetary disks, and it could be observable in the near future. With high-resolution three-dimensional numerical hydrodynamics simulations, we modeled the behavior of the VSI in protoplanetary disks with and without embedded planets. We then measured its accretion and mixing capabilities by comparing the full Reynolds stress, which includes the contribution of nonaxisymmetric features, such as spiral arms and vortices, to the Reynolds stress due to the azimuthally averaged velocity field, which can be attributed to good approximation to the VSI. We verified that the VSI can contribute to the accretion stress and showed that, depending on disk conditions, an embedded planet can coexist with or suppress VSI turbulent stress. Specifically, the presence of spiral shocks launched by a planet or planet-generated vortices can interfere with the VSI near the planet’s vicinity, with the instability recovering at large enough distances from the planet or vortex. Our results suggest that observations of VSI signatures are unlikely in disks that contain massive, nonaxisymmetric features.

A comparative study on natural gas hydrate accumulation models at active and passive continental margins

The comparative study on natural gas hydrate accumulation models between active and passive continental margins as well as their controlling factors is of great significance to the guidance of natural gas hydrate exploration. Based on the data and research results of international typical active continental margin hydrate accumulation areas such as the Cascadia margin of the Northeast Pacific, the Nankai trough, etc. and passive continental margin areas like the Blake Ridge, the models of the gas hydrate accumulation system are summarized and numerically simulated, and a preliminary comparison of active and passive continental margin reservoir accumulation models was also carried out. The following results were obtained. (1) The active continental margin provides a driving force and channel for vertical gas migration, which induces deep free gas and in-situ biogas to migrate along the fault. The migration channels are mainly faults, fractures and slumps produced by subduction–accretion. (2) Coarse-grained turbidity sediments such as silt and sandy silt have good porosity and permeability. Moreover, the sediment thickness on the accretionary wedge is large, which provides a good storage space for hydrate accumulation. (3) Numerical simulations of the Blake Ridge, and Niger Delta hydrate accumulation show that the passive continental margin lacks the lateral stress caused by the subduction zone compared with the active continental margin. However, due to the plastic materials in the thick sedimentary layer, high-pressure fluids and volcanic activities outside the continental margin, vertical accretion and tensile stress are generated and the accumulation rate of diffusion-type hydrates mainly depends on the methane supply rate. (4) Organic matter content, gas production rate, geothermal gradient and sedimentation rate at the passive continental margin have different effects on the spatial distribution of hydrate content. Mud volcanoes or diapir structures provide an ideal place for the formation and occurrence of hydrates.

Particle Dynamics in 3D Self-gravitating Disks. II. Strong Gas Accretion and Thin Dust Disks

Abstract Observations suggest that protoplanetary disks have moderate accretion rates onto the central young star, especially at early stages (e.g., HL Tau), indicating moderate disk turbulence. However, recent ALMA observations suggest that dust is highly settled, implying weak turbulence. Motivated by such tension, we carry out 3D stratified local simulations of self-gravitating disks, focusing on the settling of dust particles in actively accreting disks. We find that gravitationally unstable disks can have moderately high accretion rates while maintaining a relatively thin dust disk for two reasons. First, accretion stress from the self-gravitating spirals (self-gravity stress) can be stronger than the stress from turbulence (Reynolds stress) by a factor of 5–20. Second, the strong gravity from the gas to the dust decreases the dust scale height by another factor of ∼2. Furthermore, the turbulence is slightly anisotropic, producing a larger Reynolds stress than the vertical dust diffusion coefficient. Thus, gravitoturbulent disks have unusually high vertical Schmidt numbers (Sc z ) if we scale the total accretion stress with the vertical diffusion coefficient (e.g., Sc z ∼ 10–100). The reduction of the dust scale height by the gas gravity should also operate in gravitationally stable disks (Q > 1). Gravitational forces between particles become more relevant for the concentration of intermediate dust sizes, forming dense clouds of dust. After comparing with HL Tau observations, our results suggest that self-gravity and gravity among different disk components could be crucial for solving the conflict between the protoplanetary disk accretion and dust settling, at least at the early stages.

FGF21-protection against fructose-induced lipid accretion and oxidative stress is influenced by maternal nutrition in male progeny

Abstract Fructose intake from added sugars correlates with the epidemic rise in metabolic syndrome. Nevertheless, consumption of beverages sweetened with fructose is allowed in gestation. We have studied how adult male progeny from control (C/F), fructose- (F/F) and glucose-fed (G/F) mothers respond to liquid fructose (10% wt/vol), and compared them to the control group (C/C). Interestingly, plasma levels of fibroblast growth factor 21 (FGF21) were augmented in fructose-fed males, mainly in F/F group. FGF21 has proven to be a protective agent against steatosis and oxidative stress. Accordingly, FGF21 protected against fructose-induced lipid accumulation in livers of C/F and F/F males, but not in G/F. However, fructose-induced lipid oxidation was found in the adipose tissue of F/F males due to an impaired response of their antioxidant system. Maternal carbohydrate intake does influence the adult male offspring’s response to liquid fructose presumably by affecting the FGF21 function.

Planet formation and migration near the silicate sublimation front in protoplanetary disks

Context. The increasing number of newly detected exoplanets at short orbital periods raises questions about their formation and migration histories. Planet formation and migration depend heavily on the structure and dynamics of protoplanetary disks. A particular puzzle that requires explanation arises from one of the key results of the Kepler mission, namely the increase in the planetary occurrence rate with orbital period up to 10 days for F, G, K and M stars. Aims. We investigate the conditions for planet formation and migration near the dust sublimation front in protostellar disks around young Sun-like stars. We are especially interested in determining the positions where the drift of pebbles would be stopped, and where the migration of Earth-like planets and super-Earths would be halted. Methods. For this analysis we use iterative 2D radiation hydrostatic disk models which include irradiation by the star, and dust sublimation and deposition depending on the local temperature and vapor pressure. Results. Our results show the temperature and density structure of a gas and dust disk around a young Sun-like star. We perform a parameter study by varying the magnetized turbulence onset temperature, the accretion stress, the dust mass fraction, and the mass accretion rate. Our models feature a gas-only inner disk, a silicate sublimation front and dust rim starting at around 0.08 au, an ionization transition zone with a corresponding density jump, and a pressure maximum which acts as a pebble trap at around 0.12 au. Migration torque maps show Earth- and super-Earth-mass planets halt in our model disks at orbital periods ranging from 10 to 22 days. Conclusions. Such periods are in good agreement with both the inferred location of the innermost planets in multiplanetary systems, and the break in planet occurrence rates from the Kepler sample at 10 days. In particular, models with small grains depleted produce a trap located at a 10-day orbital period, while models with a higher abundance of small grains present a trap at around a 17-day orbital period. The snow line lies at 1.6 au, near where the occurrence rate of the giant planets peaks. We conclude that the dust sublimation zone is crucial for forming close-in planets, especially when considering tightly packed super-Earth systems.

Photophoresis in the circumjovian disk and its impact on the orbital configuration of the Galilean satellites

Jupiter has four large regular satellites called the Galilean satellites: Io, Europa, Ganymede, and Callisto. The inner three of the Galilean satellites orbit in a 4:2:1 mean motion resonance; therefore their orbital configuration may originate from the stopping of the migration of Io near the bump in the surface density distribution and following resonant trapping of Europa and Ganymede. The formation mechanism of the bump near the orbit of the innermost satellite, Io, is not yet understood, however. Here, we show that photophoresis in the circumjovian disk could be the cause of the bump using analytic calculations of steady-state accretion disks. We propose that photophoresis in the circumjovian disk could stop the inward migration of dust particles near the orbit of Io. The resulting dust-depleted inner region would have a higher ionization fraction, and thus admit increased magnetorotational-instability-driven accretion stress in comparison to the outer region. The increase of the accretion stress at the photophoretic dust barrier would form a bump in the surface density distribution, halting the migration of Io.

Radiation Hydrodynamical Turbulence in Protoplanetary Disks: Numerical Models and Observational Constraints

Abstract Planets are born in protostellar disks, which are now observed with enough resolution to address questions about internal gas flows. Magnetic forces are possibly drivers of the flows, but ionization state estimates suggest that much of the gas mass decouples from magnetic fields. Thus, hydrodynamical instabilities could play a major role. We investigate disk dynamics under conditions typical for a T Tauri system, using global 3D radiation-hydrodynamics simulations with embedded particles and a resolution of 70 cells per scale height. Stellar irradiation heating is included with realistic dust opacities. The disk starts in joint radiative balance and hydrostatic equilibrium. The vertical shear instability (VSI) develops into turbulence that persists up to at least 1600 inner orbits (143 outer orbits). Turbulent speeds are a few percent of the local sound speed at the midplane, increasing to 20%, or 100 m s−1, in the corona. These are consistent with recent upper limits on turbulent speeds from optically thin and thick molecular line observations of TW Hya and HD 163296. The predominantly vertical motions induced by the VSI efficiently lift particles upward. Grains 0.1 and 1 mm in size achieve scale heights greater than expected in isotropic turbulence. We conclude that while kinematic constraints from molecular line emission do not directly discriminate between magnetic and nonmagnetic disk models, the small dust scale heights measured in HL Tau and HD 163296 favor turbulent magnetic models, which reach lower ratios of the vertical kinetic energy density to the accretion stress.

Electron Heating and Saturation of Self-regulating Magnetorotational Instability in Protoplanetary Disks

Abstract Magnetorotational instability (MRI) has the potential to generatevigorous turbulence in protoplanetary disks, although its turbulence strength and accretion stress remain debatable because of the uncertainty of MRI with a low ionization fraction. We focus on the heating of electrons by strong electric fields, which amplifies nonideal magnetohydrodynamic effects. The heated electrons frequently collide with and stick to dust grains, which in turn decreases the ionization fraction and is expected to weaken the turbulent motion driven by MRI. In order to quantitatively investigate the nonlinear evolution of MRI, including the electron heating, we perform magnetohydrodynamical simulation with the unstratified shearing box. We introduce a simple analytic resistivity model depending on the current density by mimicking the resistivity given by the calculation of ionization. Our simulation confirms that the electron heating suppresses magnetic turbulence when the electron heating occurs with low current density. We find a clear correlation between magnetic stress and current density, which means that the magnetic stress is proportional to the squared current density. When the turbulent motion is completely suppressed, laminar accretion flow is caused by an ordered magnetic field. We give an analytical description of the laminar stateusing a solution of linear perturbation equations with resistivity. We also propose a formula that successfully predicts the accretion stress in the presence of the electron heating.

Rossby wave instability does not require sharp resistivity gradients

Rossby wave instability (RWI) at dead zone boundaries may play an important role in planet formation. Viscous hydrodynamics results suggest RWI is excited only when the viscosity changes over a radial distance less than two density scale heights. However in the disks around Solar-mass T Tauri stars, it is not viscosity but magnetic forces that provide the accretion stress beyond about 10 AU, where surface densities are low enough so stellar X-rays and interstellar cosmic rays can penetrate. Here we aim to explore the conditions for RWI in the smooth transition with increasing distance, from resistive and magnetically-dead to conducting and magnetically-active. We perform 3D unstratified MHD simulations with the Pencil Code, using static resistivity profiles. As a result, we find that in MHD, contrary to viscous models, the RWI is triggered even with a gradual change in resistivity extending from 10 to 40 AU (i.e., spanning 15 scale heights for aspect ratio 0.1). This is because magneto-rotational turbulence sets in abruptly when the resistivity reaches a threshold level. At higher resistivities the longest unstable wavelength is quenched, resulting in a sharp decline of the Maxwell stress towards the star. The sharp gradient in the magnetic forces leads to a localized density bump, that is in turn Rossby wave unstable. We conclude that even weak gradients in the resistivity can lead to sharp transitions in the Maxwell stress. The upshot is that the RWI is more easily activated in the outer disk than previously thought. Rossby vortices at the outer dead zone boundary thus could underlie the dust asymmetries seen in the outer reaches of transition disks.

LARGE-SCALE AZIMUTHAL STRUCTURES OF TURBULENCE IN ACCRETION DISKS: DYNAMO TRIGGERED VARIABILITY OF ACCRETION

We investigate the significance of large scale azimuthal, magnetic and velocity modes for the MRI turbulence in accretion disks. We perform 3D global ideal MHD simulations of global stratified proto-planetary disk models. Our domains span azimuthal angles of \pi/4, \pi/2, \pi and 2\pi. We observe up to 100% stronger magnetic fields and stronger turbulence for the restricted azimuthal domain models \pi/2 and \pi/4 compared to the full 2\pi model. We show that for those models, the Maxwell Stress is larger due to strong axisymmetric magnetic fields, generated by the \alpha \Omega dynamo. Large radial extended axisymmetric toroidal fields trigger temporal magnification of accretion stress. All models display a positive dynamo-\alpha in the northern hemisphere (upper disk). The parity is distinct in each model and changes on timescales of 40 local orbits. In model 2\pi, the toroidal field is mostly antisymmetric in respect to the midplane. The eddies of the MRI turbulence are highly anisotropic. The major wavelengths of the turbulent velocity and magnetic fields are between one and two disk scale heights. At the midplane, we find magnetic tilt angles around 8-9 degree increasing up to 12-13 degree in the corona. We conclude that an azimuthal extent of \pi is sufficient to reproduce most turbulent properties in 3D global stratified simulations of magnetised accretion disks.

Turbulence in global simulations of magnetized thin accretion discs

We use a global magnetohydrodynamic simulation of a geometrically thin accretion disk to investigate the locality and detailed structure of turbulence driven by the magnetorotational instability (MRI). The model disk has an aspect ratio $H / R \simeq 0.07$, and is computed using a higher-order Godunov MHD scheme with accurate fluxes. We focus the analysis on late times after the system has lost direct memory of its initial magnetic flux state. The disk enters a saturated turbulent state in which the fastest growing modes of the MRI are well-resolved, with a relatively high efficiency of angular momentum transport $< < \alpha > > \approx 2.5 \times 10^{-2}$. The accretion stress peaks at the disk midplane, above and below which exists a moderately magnetized corona with patches of superthermal field. By analyzing the spatial and temporal correlations of the turbulent fields, we find that the spatial structure of the magnetic and kinetic energy is moderately well-localized (with correlation lengths along the major axis of $2.5H$ and $1.5H$ respectively), and generally consistent with that expected from homogenous incompressible turbulence. The density field, conversely, exhibits both a longer correlation length and a long correlation time, results which we ascribe to the importance of spiral density waves within the flow. Consistent with prior results, we show that the mean local stress displays a well-defined correlation with the local vertical flux, and that this relation is apparently causal (in the sense of the flux stimulating the stress) during portions of a global dynamo cycle. We argue that the observed flux-stress relation supports dynamo models in which the structure of coronal magnetic fields plays a central role in determining the dynamics of thin-disk accretion.

TURBULENCE AND STEADY FLOWS IN THREE-DIMENSIONAL GLOBAL STRATIFIED MAGNETOHYDRODYNAMIC SIMULATIONS OF ACCRETION DISKS

We present full 2 Pi global 3-D stratified MHD simulations of accretion disks. We interpret our results in the context of proto-planetary disks. We investigate the turbulence driven by the magneto-rotational instability (MRI) using the PLUTO Godunov code in spherical coordinates with the accurate and robust HLLD Riemann solver. We follow the turbulence for more than 1500 orbits at the innermost radius of the domain to measure the overall strength of turbulent motions and the detailed accretion flow pattern. We find that regions within two scale heights of the midplane have a turbulent Mach number of about 0.1 and a magnetic pressure two to three orders of magnitude less than the gas pressure, while outside three scale heights the magnetic pressure equals or exceeds the gas pressure and the turbulence is transonic, leading to large density fluctuations. The strongest large-scale density disturbances are spiral density waves, and the strongest of these waves has m=5. No clear meridional circulation appears in the calculations because fluctuating radial pressure gradients lead to changes in the orbital frequency, comparable in importance to the stress gradients that drive the meridional flows in viscous models. The net mass flow rate is well-reproduced by a viscous model using the mean stress distribution taken from the MHD calculation. The strength of the mean turbulent magnetic field is inversely proportional to the radius, so the fields are approximately force-free on the largest scales. Consequently the accretion stress falls off as the inverse square of the radius.

Trapping solids at the inner edge of the dead zone: 3-D global MHD simulations

The poorly-ionized interior of the protoplanetary disk is the location where dust coagulation processes may be most efficient. However even here, planetesimal formation may be limited by the loss of solid material through radial drift, and by collisional fragmentation of the particles. Our aim is to investigate the possibility that solid particles are trapped at local pressure maxima in the dynamically evolving disk. We perform the first 3-D global non-ideal MHD calculations of the disk treating the turbulence driven by the magneto-rotational instability. The domain contains an inner MRI-active region near the young star and an outer midplane dead zone, with the transition between the two modeled by a sharp increase in the magnetic diffusivity. The azimuthal magnetic fields generated in the active zone oscillate over time, changing sign about every 150 years. We thus observe the radial structure of the `butterfly pattern' seen previously in local shearing-box simulations. The mean magnetic field diffuses from the active zone into the dead zone, where the Reynolds stress nevertheless dominates. The greater total accretion stress in the active zone leads to a net reduction in the surface density, so that after 800 years an approximate steady state is reached in which a local radial maximum in the midplane pressure lies near the transition radius. We also observe the formation of density ridges within the active zone. The dead zone in our models possesses a mean magnetic field, significant Reynolds stresses and a steady local pressure maximum at the inner edge, where the outward migration of planetary embryos and the efficient trapping of solid material are possible.

On the Vertical Structure of Radiation-dominated Accretion Disks

The vertical structure of black hole accretion disks in which radiation dominates the total pressure is investigated using a three-dimensional radiation-MHD calculation. The domain is a small patch of disk centered 100 Schwarzschild radii from a black hole of 108 M☉, and the stratified shearing-box approximation is used. Magnetorotational instability converts gravitational energy to turbulent magnetic and kinetic energy. The gas is heated by magnetic dissipation and by radiation damping of the turbulence, and cooled by diffusion and advection of radiation through the vertical boundaries. The resulting structure differs in several fundamental ways from the standard Shakura-Sunyaev picture. The disk consists of three layers. At the midplane, the density is large, and the magnetic pressure and total accretion stress are less than the gas pressure. In lower density surface layers that are optically thick, the magnetic pressure and stress are greater than the gas pressure but less than the radiation pressure. Horizontal density variations in the surface layers exceed an order of magnitude. Magnetic fields in the regions of greatest stress are buoyant, and dissipate as they rise, so the heating rate declines more slowly with height than the stress. Much of the dissipation occurs at low column depth, and the interior is cooler and less radiation-dominated than in the Shakura-Sunyaev model with the same surface mass density and flux. The mean structure is convectively stable.

General Relativistic Magnetohydrodynamic Simulations of Black Hole Accretion Disks: Results and Observational Implications

A selection of results from the general relativistic MHD accretion simulations described in the previous talk are presented. We find that the magnetic field strength increases sharply with decreasing radius and is also enhanced near rapidly-spinning black holes. The greater magnetic field strength associated with rapid black hole rotation leads to a large outward electromagnetic angular momentum flux that substantially reduces both the mean accretion rate and the net accreted angular momentum per unit rest-mass. This electromagnetic stress strongly violates the traditional guess that the accretion stress vanishes at and inside the marginally stable orbit. Possible observational consequences include a constraint on the maximum spin of black holes, enhancement to the radiative efficiency, and concentration of fluorescent Fe Kα to the innermost part of the accretion disk.

Local Three‐dimensional Simulations of Magnetorotational Instability in Radiation‐dominated Accretion Disks

We examine the small-scale dynamics of black hole accretion disks in which radiation pressure exceeds gas pressure. Local patches of disk are modeled by numerically integrating the equations of radiation MHD in the flux-limited diffusion approximation. The shearing-box approximation is used, and the vertical component of gravity is neglected. Magnetorotational instability (MRI) leads to turbulence in which accretion stresses are due primarily to magnetic torques. When radiation is locked to gas over the length and timescales of fluctuations in the turbulence, the accretion stress, density contrast, and dissipation differ little from those in the corresponding calculations, with radiation replaced by extra gas pressure. However, when radiation diffuses each orbit a distance that is comparable to the rms vertical wavelength of the MRI, radiation pressure is less effective in resisting squeezing. Large density fluctuations occur, and radiation damping of compressive motions converts P dV work into photon energy. The accretion stress in calculations having a net vertical magnetic field is found to be independent of opacity over the range explored and approximately proportional to the square of the net field. In calculations with zero net magnetic flux, the accretion stress depends on the portion of the total pressure that is effective in resisting compression. The stress is lower when radiation diffuses rapidly with respect to the gas. We show that radiation-supported Shakura-Sunyaev disks accreting via internal magnetic stresses are likely to have radiation marginally coupled to turbulent gas motions in their interiors.