Mario Flock

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

We present full 2π global three-dimensional stratified magnetohydrodynamic (MHD) simulations of accretion disks. We interpret our results in the context of protoplanetary disks. We investigate the turbulence driven by the magnetorotational 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 in those 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.

COMPARING NUMERICAL METHODS FOR ISOTHERMAL MAGNETIZED SUPERSONIC TURBULENCE

Many astrophysical applications involve magnetized turbulent flows with shock waves. Ab initio star formation simulations require a robust representation of supersonic turbulence in molecular clouds on a wide range of scales imposing stringent demands on the quality of numerical algorithms. We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine popular astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. These applications employ a variety of numerical approaches, including both split and unsplit, finite difference and finite volume, divergence preserving and divergence cleaning, a variety of Riemann solvers, and a range of spatial reconstruction and time integration techniques. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss the convergence of various characteristics for the turbulence decay test and the impact of various components of numerical schemes on the accuracy of solutions. The nine codes gave qualitatively the same results, implying that they are all performing reasonably well and are useful for scientific applications. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the magnetic field using the constrained transport method and using little to no explicit artificial viscosity. Codes that fall short in one or more of these areas are still useful, but they must compensate for higher numerical dissipation with higher numerical resolution. This paper is the largest, most comprehensive MHD code comparison on an application-like test problem to date. We hope this work will help developers improve their numerical algorithms while helping users to make informed choices about choosing optimal applications for their specific astrophysical problems.

THREE-DIMENSIONAL MAGNETOHYDRODYNAMIC SIMULATIONS OF PLANET MIGRATION IN TURBULENT STRATIFIED DISKS

We performed 3D MHD simulations of planet migration in stratified disks using the Godunov code PLUTO, where the disk is turbulent due to the magnetorotational instability. We study the migration for planets with different planet-star mass ratios q = Mp/Ms. In agreement with previous studies, for the low-mass planet cases (q = 5 × 10 and 10), migration is dominated by random fluctuations in the torque. For a Jupiter-mass planet (q = Mp/Ms = 10 −3 for Ms = 1M⊙), we find a reduction of the magnetic stress inside the orbit of the planet and around the gap region. After an initial stage where the torque on the planet is positive, it reverses and we recover migration rates similar to those found in disks where the turbulent viscosity is modelled by an α viscosity. For the intermediate-mass planets (q = 5 × 10, 10 and 2 × 10) we find a new and so far unexpected behavior. In some cases they experience sustained and systematic outwards migration for the entire duration of the simulation. For this case, the horseshoe region is resolved and torques coming from the corotation region can remain unsaturated due to the stresses in the disk. These stresses are generated directly by the magnetic field. The magnitude of the horseshoe drag can overcome the negative Lindblad contribution when the local surface density profile is flat or increasing outwards, which we see in certain locations in our simulations due to the presence of a zonal flow. The intermediate-mass planet is migrating radially outwards in locations where there is a positive gradient of a pressure bump (zonal flow). Subject headings: accretion disks MHD planets:formation turbulence

Gaps, rings, and non-axisymmetric structures in protoplanetary disks: Emission from large grains

Dust grains with sizes around (sub)mm are expected to couple only weakly to the gas motion in regions beyond 10 au of circumstellar disks. In this work, we investigate the influence of the spatial distribution of such grains on the (sub)mm appearance of magnetized protoplanetary disks. We perform non-ideal global 3D magneto-hydrodynamic stratified disk simulations including particles of different sizes (50 micron to 1 cm), using a Lagrangian particle solver. We calculate the spatial dust temperature distribution, including the dynamically coupled submicron-sized dust grains, and derive ideal continuum re-emission maps of the disk through radiative transfer simulations. Finally, we investigate the feasibility to observe specific structures in the thermal re-emission maps with the Atacama Large Millimeter/submillimeter Array (ALMA). The pressure bump close to the outer edge of the dead-zone leads to particle trapping in ring structures. More specifically, vortices in the disk concentrate the dust and create an inhomogeneous distribution of the solid material in the azimuthal direction. The large-scale disk perturbations are preserved in the (sub)mm re-emission maps. The observable structures are very similar to those expected to result from planet-disk interaction. The larger dust particles increase the brightness contrast between gap and ring structures. We find that rings, gaps and the dust accumulation in the vortex could be traced with ALMA down to a scale of a few astronomical units in circumstellar disks located in nearby star-forming regions. Finally, we present a brief comparison of these structures with those recently found with ALMA in the young circumstellar disks of HL Tau and Oph IRS 48.

TURBULENCE IN WEAKLY IONIZED PROTOPLANETARY DISKS

We investigate the characteristic properties of self-sustained magneto-rotational instability (MRI) turbulence in low-ionized protoplanetary disks. We study the transition regime between active and dead zones, performing three-dimensional global non-ideal MHD simulations of stratified disks covering a range of magnetic Reynolds numbers between 2700 Rm 6600. We found converged and saturated MRI turbulence for Rm 5000 with a strength of αSS ~ 0.01. Below Rm 5000, the MRI starts to decay at the midplane at first because the Elsasser number drops below 1. We find a transition regime between 3300Rm 5000 where the MRI turbulence is still sustained but damped. At around Rm 3000, the MRI turbulence decays but could be reestablished due to the accumulation of the toroidal magnetic field or the radial transport of the magnetic field from the active region. Below Rm < 3000, the MRI cannot be sustained and is decaying. Here, hydrodynamical motions, like density waves, dominate. We observe anti-cyclonic vortices in the transition between the dead zone and the active zone.

High-order Godunov schemes for global 3D MHD simulations of accretion disks - I. Testing the linear growth of the magneto-rotational instability

We assess the suitability of various numerical MHD algorithms for astrophysical accretion disk simulations with the PLUTO code. The well-studied linear growth of the magneto-rotational instability is used as the benchmark test for a comparison between the implementations within PLUTO and against the ZeusMP code. The results demonstrate the importance of using an upwind reconstruction of the electro-motive force (EMF) in the context of a constrained transport scheme, which is consistent with plane-parallel, grid-aligned flows. In contrast, constructing the EMF from the simple average of the Godunov fluxes leads to a numerical instability and the unphysical growth of the magnetic energy. We compare the results from 3D global calculations using different MHD methods against the analytical solution for the linear growth of the MRI, and discuss the effect of numerical dissipation. The comparison identifies a robust and accurate code configuration that is vital for realistic modeling of accretion disk processes.

THE VLA VIEW OF THE HL TAU DISK: DISK MASS, GRAIN EVOLUTION, AND EARLY PLANET FORMATION

The first long-baseline ALMA campaign resolved the disk around the young star HL Tau into a number of axisymmetric bright and dark rings. Despite the very young age of HL Tau these structures have been interpreted as signatures for the presence of (proto)planets. The ALMA images triggered numerous theoretical studies based on disk-planet interactions, magnetically driven disk structures, and grain evolution. Of special interest are the inner parts of disks, where terrestrial planets are expected to form. However, the emission from these regions in HL Tau turned out to be optically thick at all ALMA wavelengths, preventing the derivation of surface density profiles and grain size distributions. Here, we present the most sensitive images of HL Tau obtained to date with the Karl G. Jansky Very Large Array at 7.0 mm wavelength with a spatial resolution comparable to the ALMA images. At this long wavelength the dust emission from HL Tau is optically thin, allowing a comprehensive study of the inner disk. We obtain a total disk dust mass of 0.001 - 0.003 Msun, depending on the assumed opacity and disk temperature. Our optically thin data also indicate fast grain growth, fragmentation, and formation of dense clumps in the inner densest parts of the disk. Our results suggest that the HL Tau disk may be actually in a very early stage of planetary formation, with planets not already formed in the gaps but in the process of future formation in the bright rings.

Can dead zones create structures like a transition disk

Context. Regions of low ionisation where the activity of the magneto-rotational instability is suppressed, the so-called dead zones, have been suggested to explain gaps and asymmetries of transition disks. Dead zones are therefore a potential cause for the observational signatures of transition disks without requiring the presence of embedded planets. Aims. We investigate the gas and dust evolution simultaneously assuming simplified prescriptions for a dead zone and a magnetohydrodynamic (MHD) wind acting on the disk. We explore whether the resulting gas and dust distribution can create signatures similar to those observed in transition disks. Methods. We imposed a dead zone and/or an MHD wind in the radial evolution of gas and dust in protoplanetary disks. For the dust evolution, we included the transport, growth, and fragmentation of dust particles. To compare with observations, we produced synthetic images in scattered optical light and in thermal emission at mm wavelengths. Results. In all models with a dead zone, a bump in the gas surface density is produced that is able to efficiently trap large particles (≳ 1 mm) at the outer edge of the dead zone. The gas bump reaches an amplitude of a factor of ~5, which can be enhanced by the presence of an MHD wind that removes mass from the inner disk. While our 1D simulations suggest that such a structure can be present only for ~1 Myr, the structure may be maintained for a longer time when more realistic 2D/3D simulations are performed. In the synthetic images, gap-like low-emission regions are seen at scattered light and in thermal emission at mm wavelengths, as previously predicted in the case of planet-disk interaction. Conclusions. Main signatures of transition disks can be reproduced by assuming a dead zone in the disk, such as gap-like structure in scattered light and millimetre continuum emission, and a lower gas surface density within the dead zone. Previous studies showed that the Rossby wave instability can also develop at the edge of such dead zones, forming vortices and also creating asymmetries.

3D Radiation Nonideal Magnetohydrodynamical Simulations of the Inner Rim in Protoplanetary Disks

Many planets orbit within an AU of their stars, raising questions about their origins. Particularly puzzling are the planets found near the silicate sublimation front. We investigate conditions near the front in the protostellar disk around a young intermediate-mass star, using the first global 3-D radiation non-ideal MHD simulations in this context. We treat the starlight heating; the silicate grains sublimation and deposition at the local, time-varying temperature and density; temperature-dependent Ohmic dissipation; and various initial magnetic fields. The results show magnetorotational turbulence around the sublimation front at 0.5 AU. The disk interior to 0.8 AU is turbulent, with velocities exceeding 10% of the sound speed. Beyond 0.8 AU is the dead zone, cooler than 1000 K and with turbulence orders of magnitude weaker. A local pressure maximum just inside the dead zone concentrates solid particles, favoring their growth. Over many orbits, a vortex develops at the dead zones inner edge, increasing the disks thickness locally by around 10%. We synthetically observe the results using Monte Carlo transfer calculations, finding the sublimation front is near-infrared bright. The models with net vertical magnetic fields develop extended, magnetically-supported atmospheres that reprocess extra starlight, raising the near-infrared flux 20%.The vortex throws a nonaxisymmetric shadow on the outer disk. At wavelengths > 2 micron, the flux varies several percent on monthly timescales. The variations are more regular when the vortex is present. The vortex is directly visible as an arc at ultraviolet through near-infrared wavelengths, given sub-AU spatial resolution.

RADIATION HYDRODYNAMICS MODELS OF THE INNER RIM IN PROTOPLANETARY DISKS

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.