Non-ideal MHD, Stability, and Dissipation in Protoplanetary Disks

4 Aug 2014, 11:30 → 8 Aug 2014, 13:30 Europe/Copenhagen

Auditorium A (Niels Bohr Institute)

Monday, 4 August

Registration

12:30 Welcoming Lunch

Opening Remarks

Convener: Dr Martin Pessah (Niels Bohr International Academy)

slides nbia-ppdisk-2014-welcome.pdf

Monday Afternoon

Convener: Prof. Mordecai-Mark Mac Low (American Museum of Natural History)

1 The Formation and Evolution of Protoplanetary Disks: The Critical Effects of Non-Ideal Magnetohydrodynamics

This review starts with the description of the formation and early evolution of protoplanetary disks. Recent advance in the modeling with resistive magneto-hydrodynamics codes with various numerical techniques has enabled our understanding on the driving of outflows/jets and the formation of circumstellar disks in a self-consistent manner. This provides improved descriptions of the initial condition for the evolution of the disks where planet formation possibly takes place. Magnetic de-coupling due to high density enables massive disks to form and these disks are subject to gravitational instability. The gravitationally unstable region is surrounded by the injection points of the magneto-hydrodynamical outflows during the formation phase of circumstellar disks. In this phase the strong gravitational torque due to self-gravitational spiral arms drives efficient mass accretion onto the central star. Once most of the mass in the disk accreted onto the central star, the self-gravity of the disk becomes unimportant and the mass accretion rate decreases significantly. This later phase corresponds to the classical concept of the protoplanetary disk where the mass accretion may be driven by magneto-rotational instability (MRI). The effect of non-ideal magneto-hydrodynamical effects remain important because of the low ionization degree in protoplanetary disks. Complicated Ohm’s law is expected in the regions where dust grains are the main charge carrier. This review outlines some of the complexities, such as non-linear Ohm’s law and ionization due to energized electrons. Future work is discussed with the emphasis on the importance of the description of vertical magnetic flux leakage from the disk in global simulation of MRI, since this is ultimately required in the solution of “the magnetic flux problem” of star formation.

Speaker: Prof. Shu-ichiro Inutsuka (Nagoya University)

Slides Inutsuka.pdf

2 Mass transport regimes in the solar protoplanetary disk - evidence from meteoritic components

Chondrite meteorites are fragments of asteroids that did not undergo melting and differentiation and, thus, provide a record of the earliest stages of the solar protoplanetary disk. Ordinary and enstatite chondrites are derived from parent asteroids that originated in the accretion region of terrestrial planets whereas the parent asteroids of the water-rich carbonaceous chondrites most likely accreted in the giant planet region. The dominant constituent of chondrites are millimeter-sized chondrules formed by transient heating events in the protoplanetary disk. Although it has long been accepted that chondrules formed 1 to 2 Myr after condensation of the solar system first solids, calcium-aluminium-rich inclusions (CAIs), recent high-resolution uranium-corrected Pb-Pb dates indicate that chondrule formation started contemporaneously with CAIs and lasted ~3 Myr. Moreover, chondrules from individual chondrites show variability in 54Cr/52Cr ratios, which track genetic relationships between early-formed solids and their respective reservoirs. Collectively, these observations indicate that chondrules from individual chondrite groups originated in different regions of the protoplanetary disk and were subsequently transported to the accretion regions of their respective parent bodies. In this talk, we report new uranium-corrected Pb-Pb ages as well as 54Cr/52Cr ratios for chondrules from enstatite, ordinary and various classes of carbonaceous chondrites. Our results indicate that chondrule populations from individual chondrite groups show a comparable age range of ~3 Myr. Chondrules from enstatite and ordinary chondrites show 54Cr/52Cr ratios restricted to inner solar system compositions. In contrast, carbonaceous chondrite chondrules record greater 54Cr/52Cr variability, with both inner and outer solar system signatures. These data require different outward mass transport regimes but limited inward transport of outer solar system material in the formation region of terrestrial planets during the main accretion phase of chondrite parent asteroids. We explore the role of protostellar jets and disk winds as potential mass transport mechanisms to account for the observed meteoritic data.

Speaker: Prof. Martin Bizzarro (Centre for Star and Planet Formation)

Slides NBIA_mb.ppt.pdf

15:15 Coffee Break

3 Protostellar accretion disks and their outflows

Magnetocentrifugal jets and magnetically-driven turbulence have been recognized as the leading candidates for transporting the excess angular momentum of protostellar disks, thereby enabling mass accretion onto the central object. It is also clear that magnetic diffusivity plays a central role in the overall disk accretion and outflow processes. However, the impact of magnetic dissipation on the structure and observational signatures of these objects remains poorly understood. In my talk, I will examine the launching of outflows from the surfaces of weakly-ionised protostellar disks, and present models that calculate the vertical and radial structure of the disk and the emerging wind. These models allow us to study the properties of the disk and wind as a function of location, and the radial extent of the wind-launching region. Finally, I will discuss the implications and future applications of these studies, including the analysis of the observational signatures of the protostellar system.

Speaker: Dr Raquel Salmeron (The Australian National University)

Slides Talk_submitted.pdf

4 Disk winds driven by MRI --some aspects and applications--

Magnetorotational instability is supposed to play a role in not only transporting the angular momentum in protoplanetary disks but also driving disk disk winds. However, detailed properties of the disk winds are not well understood. In this talk, starting from the result of our ideal MHD simulations for MRI-driven vertical outflows in a local shearing box, we discuss how the mass loss rate and time dependency of the outflow are modified when we include (i) dead zones with resistive MHD simulations in the local shearing box and (ii) large-scale flows with global simulations in spherical coordinates. We would also like to introduce the mass accretion and the transport of large-scale magnetic fields observed in the global simulations, in connection with the disk winds.

Speaker: Dr Takeru Suzuki (Department of Physics, Nagoya University)

Slides http://www.ta.phys.nagoya-u.ac.jp/stakeru/research/glbdsk/ SuzukiTakeru.pdf

5 Global simulations of protoplanetary discs with Ohmic resistivity and ambipolar diffusion

As the nurseries of planetary systems, protoplanetary discs are of key interest to planet formation theory. Their dynamics and structure depend critically on the influence of magnetic fields. Being comparatively cold and dense, the physical state of the disc plasma is dominated by external ionizing X-ray and cosmic-ray radiation, leading to a layered vertical structure -- with turbulent, magnetised surface layers and a magnetically-decoupled midplane. This 'dead-zone' picture is further complicated by ambipolar diffusion, which is expected to dominate in the tenuous hot corona of the disc and within the low-density gaps opened by protoplanetary cores. With ambipolar diffusion included, it is expected that parts of the disk will be stabilized and a magnetically-driven wind will be launched. This has so far only been studied in simplified local models that neglect the global structure of the protoplanetary disc. The recognition of the importance of additional non-ideal effects such as ambipolar diffusion or Hall effect has led to serious questioning of the paradigm of magneto-rotational turbulence and has renewed interest in the role played by disk winds and purely hydrodynamic instabilities. The former are best studied in a global disc model. We present results from the first global simulations that include the effect of ambipolar diffusion and show the launching of a magneto-centrifugal wind.

Speaker: Dr Oliver Gressel (NBIA)

Slides ogressel_ppd_ad.pdf

6 Discussion I

Tuesday, 5 August

Tuesday Morning

Convener: Prof. Richard Nelson (Queen Mary University of London)

7 Magnetic drift in protoplanetary and circumplanetary discs

Flux-freezing breaks down under the low levels of ionisation in molecular cloud cores and protoplanetary discs. The dominant processes are ambipolar diffusion and hall drift, which enable slippage of magnetic flux through the predominantly neutral gas. The nature of the field line drift through the bulk neutral component of the gas is as important as its magnitude. Under ambipolar diffusion, magnetic field lines in the direction of the local magnetic stress; the drift is accompanied by dissipation associated with collisions between charged and neutral species. The Hall effect introduces a drift perpendicular to the local magnetic stresses that is unaccompanied by dissipation. Hall drift dominates ambipolar diffusion over a wide range of radii in protoplanetary disks and likely plays a significant role during gravitational collapse of cloud cores. I shall outline the physics underlying magnetic drift in a partially ionised medium and then discuss applications to gravitational collapse, magnetorotational instability and jet acceleration in protoplanetary and circumplanetary discs.

Speaker: Prof. Mark Wardle (Macquarie University)

Slides Wardle_-_Magnetic_drift.pdf

8 Global Multifluid Simulations of the Magnetorotational Instability in Protoplanetary Disks

The mechanisms which drive circumstellar disk evolution are still poorly understood. In this context the MRI is likely to play an important role in the evolution of protoplanetary disks. I will discuss the results of O'Keeffe & Downes (2014) who perform global multifluid simulations of protoplanetary disks which study the magnetorotational instability (MRI). The inclusion of non-ideal effects have a significant effect on the ability to create turbulence in the disk. These simulations examine the role of non-ideal effects (ambipolar diffusion, the Hall effect and parallel resistivity) on the non-linear evolution of the MRI in weakly ionised protoplanetary disks in the region where the Hall effect is believed to dominate. The efficiency of angular momentum transport, parameterised by the alpha-parameter, is found to be significantly increased. The results strongly suggest that the Hall effect is responsible for enhancement of the MRI, with the appropriate orientation, where a net field is present. This result confirms the findings of Sano & Stone (2002a,b) and Salmeron & Wardle (2003). I will also present preliminary results from more recent simulations which focus on the effect of the inclusion of a charged dust species and the time evolution of the distribution of charged species.

Speaker: Donna Rodgers Lee (Dublin Institute for Advanced Studies)

Slides copenhagen_2014.pdf

9 Magnetic Self-Organization in Hall-Dominated Magnetorotational Turbulence

The magnetorotational instability (MRI) is the most promising mechanism by which angular momentum is efficiently transported outwards in astrophysical disks. However, its application to protoplanetary disks remains problematic. These disks are so poorly ionized that they may not support magnetorotational turbulence in regions referred to as "dead zones". While purported dead zones have captured the attention of disk theorists for nearly 20 years, there is generally no consensus regarding whether they are, in fact, dead. The problem is complicated by two non-ideal MHD processes -- ambipolar diffusion and the Hall effect -- the latter having been largely ignored in numerical studies of the MRI until recently. In this talk, I will present several surprising results on how these effects are likely to modify the magnetic and turbulent behavior of protoplanetary disks. With a focus on models of unstratified disks dominated by a vertical magnetic flux, I will show that the Hall-MRI can saturate by producing large-scale, long-lived, axisymmetric structures in the magnetic field that cause a steep reduction in turbulent transport and instigate dust-corralling zonal flows. Ambipolar diffusion provides a field-strength-dependent diffusivity, which causes these zonal flows to "breathe" at a predictable frequency. A subsequent talk by Geoffroy Lesur will focus on stratified disks, in which a net azimuthal magnetic flux is produced and dominates the dynamics. Our results call into question contemporary models of layered accretion.

Speaker: Dr Matthew Kunz (Princeton University)

Slides KunzCopenhagen2014.pdf

10:30 Coffee Break

10 Thanatology in protoplanetary discs

The existence of magnetically driven turbulence in protoplanetary discs has been a central question since the discovery of the magnetorotational instability (MRI). Early models considered Ohmic diffusion only and led to a scenario of layered accretion, in which a magnetically ``dead'' zone in the disc midplane is embedded within magnetically ``active'' surface layers at distances of about 1--10 au from the central protostellar object. Recent work has suggested that a combination of Ohmic dissipation and ambipolar diffusion can render both the midplane and surface layers of the disc inactive and that torques due to magnetically driven outflows are required to explain the observed accretion rates. In this talk, I will present recent results revisiting this problem including all three non-ideal MHD effects: Ohmic diffusion, Ambipolar diffusion and the Hall effect. I will show in particular that the Hall effect can ``revive'' dead zones by providing a large scale magnetic torque in the disc midplane, potentially leading to significant accretion rates. Implications for the global evolution of protoplanetary discs will be discussed.

Speaker: Dr Geoffroy Lesur (CNRS/IPAG)

Slides Copenhague-GLesur.pdf

11 Gas Dynamics in Protoplanetary Disks including Ohmic, Hall and Ambipolar Diffusion

I will present recent local stratified shearing-box simulations on the gas dynamics of protoplanetary disks (PPDs) that self-consistently take into account all three non-ideal MHD effects. I argue that PPDs are most likely threaded by external poloidal magnetic flux, and will address 1). launching of magnetocentrifugal wind in the inner disk, 2). dependence of the gas dynamics on the external magnetic flux due to the Hall effect, and 3). layered accretion toward the outer disk. Limitations of the shearing-box approach and prospects to perform global simulations will also be discussed.

Speaker: Dr Xuening Bai (Harvard-Smithsonian Center for Astrophysics)

Slides Bai.pdf

12 Discussion II

12:30 Lunch Break

Tuesday Afternoon

Convener: Prof. Jeremy Goodman (Princeton University)

13 Exploring the Saturation of the MRI via Weakly Nonlinear Analysis

Understanding the mechanism by which the magnetorotational instability (MRI) saturates is key to understanding the process by which it drives anisotropic MHD turbulence and transports angular momentum. Previous work has laid down the framework necessary to perform a weakly nonlinear analysis of the MRI near onset (that is, when the background magnetic field is just weak enough for the MRI to be unstable to its most unstable mode). Such analyses have been essential in understanding the turbulent transport of heat by convection in the Rayleigh-Benard problem, and we seek to extend those successes to the transport of angular momentum by the MRI. We derive the equation for perturbation growth in the weakly non-linear case, correcting an error in the literature, and then solve the equation using the general-purpose spectral code Dedalus. One major advantage to analytic studies such as these is that we can capture the behavior despite the scale separations caused by large ratios of molecular viscosities and resistivities (magnetic Prandtl numbers). We will present our initial results on the saturation properties of the MRI for a variety of dimensionless parameters.

Speaker: Ms Susan Clark (Columbia University)

Slides Clark_weakly_nonlinear_MRI.pdf

14 Magnetorotational instability saturation and transition to anisotropic turbulence

The magnetorotational instability (MRI) plays a key role in transfer of angular momentum outward in accretion disks. We study the growth of secondary parasite instabilities which trigger the saturation of the MRI. We examine the late linear stage of the MRI and transition to turbulence. We seek to gain a qualitative and quantitive understanding of the nature of the turbulence resulting from the MRI: its anisotropy and time-dependent evolution in a self-sustaining process. We carried out a set of magnetohydrodynamic local shearing box simulations in 2D and 3D to investigate the nonlinear saturation the magnetorotational instability due secondary instabilities. Both in the compressible and incompressible regimes the exact MRI solution was the first to mode appear, in agreement with linear theory. The exact MRI modes are rapidly broken down in less than one orbit by the fast growing Kelvin-Helmholtz parasite instability. We find that the chains of alternating vortices grow and cause the MRI flow to become disrupted, leading to saturation. We isolated the effects of the instability and identified signatures in 3D and 2D axisymmetric flows. We compared the evolution of the parasite Kelvin-Helmholtz mode with theory and found confirmation of its growth rate with theory. We studied the 3d time evolution in Fourier space and quantified the anisotropy of turbulence driven by the magnetorotational instability.

Speaker: Dr Gareth Murphy (Niels Bohr International Academy, NBI)

Slides MRI_Saturation_And_Transition_To_Turbulence.pdf

15:00 Coffee Break

15 Locality and not locality in magnetized accretion flows

Theories of magnetically mediated accretion flows have focused on shearing radial magnetic field by orbital motions. We show that this generates dynamically important Poynting flux which transports energy radially. This means that disks are better thought of as layered slabs powered by their inner, accreting edge, rather than concentric annuli with vertical energy transport. We also demonstrate that using shearing boxes to estimate magnetic energy densities, stresses and accretion rates is flawed because shearing boxes set their own, unlimited, external energy supply. More, shearing boxes do not allow for meridional flows: shearing boxes are by construction not flared. Further, we show how even global simulations with large radial extents must carefully treat their radial boundary conditions.

Speaker: Dr Alexander Hubbard (American Museum of Natural History)

Slides Locality-not-locality.pdf

16 Discussion III

Conference Dinner: Louisiana Museum of Modern Art

http://www.louisiana.dk/

We have organised a coach that will take us from NBI to the Museum Restaurant. We expect to be back in Copenhagen around 9pm.

Wednesday, 6 August

Wednesday Morning

Convener: Prof. James Stone (Princeton University)

17 Magnetic Coupling in Protoplanetary Disks

I will review the main ionizing processes at work in protostellar and circumplanetary disks, the chemical reactions controlling the recombination, and the resulting distributions of ionization state and conductivity. A small volume near the central star or planet reaches temperatures above 1000 K, hot enough for collisional ionization of the alkali elements. At high mass flow rates and also around the more massive stars, the gas can even be hot enough for thermal ionization of hydrogen. In the disk's colder outer regions, the ionization is non-thermal and comes from interstellar cosmic rays, stellar energetic protons, X-rays, and UV photons, and the radionuclides found in the dust embedded within the disk gas. The cosmic rays and stellar protons produce showers of energetic particles that ionize the disk at low rates to column depths of about 100 g/cm^2. The X-rays and UV photons ionize at higher rates but penetrate only to about 10 g/cm^2 and less than 0.1 g/cm^2, respectively. The radionuclides yield residual ionization deep inside the disk, beyond the reach of the other effects. The free charges created by these ionizing processes are destroyed by recombination reactions which occur on dust particles in the disk's dense interior, where the grains outnumber the free electrons and ions. Recombination occurs in the gas phase in the atmosphere, where free electrons are so abundant that the grains' charge saturates at the Coulomb limit. Balancing the ionization with the recombination yields the charged particle population and thus the conductivity. The thermally-ionized zone is well-coupled to magnetic fields, with the Ohmic resistivity the largest non-ideal term. The colder regions show a layered pattern. The weakly-ionized interior is subject to Ohmic diffusion, in which collisions decouple all main charge carriers from the magnetic fields, and to Hall drift, in which some of the charged species remain tied to the fields. The atmosphere is better-ionized, but nevertheless poorly-coupled to magnetic fields because the low densities mean low ion-neutral collision rates and thus strong ambipolar diffusion. The ambipolar term is also important far from the star, on the disk's low-density outer fringe.

Speaker: Neal Turner (JPL/Caltech)

Slides NBIACopenhagen20140804web.pdf

18 Magnetic turbulence in inner radii of protoplanetary disks

In protoplanetary disks, magnetic turbulence driven by MRI is generally suppressed by non-ideal MHD effects due to low ionization fractions. However, thermal ionization may revive ideal MHD in inner radii. To see the effects of thermal ionization, it is crucial to obtain temperatures correctly. For that purpose, we utilize radiation MHD shearing box simulations employing realistic EOS and opacities. In this paper, we present preliminary results of the simulations to discuss magnetic turbulence in inner radii of protoplanetary disks, including possibilities for thermal ionization instability to drive FU Ori outbursts.

Speaker: Dr Shigenobu Hirose (JAMSTEC)

Slides slide.pdf

10:15 Coffee Break

19 Temperature Fluctuations and Current Sheets in Protoplanetary Disks

The magnetorotational instability (MRI) drives magnetized turbulence in sufficiently ionized regions of protoplanetary disks, leading to mass accretion. The dissipation of the potential energy associated with this accretion is a component of the balance which determines the thermal structure of the disk. This is expected to be most significant in the inner regions, at the midplane inside the inner edge of the dead zone. To model the resulting thermal structure of the disk, it is critical to recognize that magnetized turbulence dissipates its energy intermittently in current sheet structures. I will discuss our recent study of this intermittent energy dissipation using high resolution numerical models including a constant resistivity and radiative thermal diffusion in an optically thick regime. Our models predict that these turbulent current sheets drive order unity temperature variations even where the MRI is damped strongly by Ohmic resistivity (McNally et al. 2014). I will also discuss the impacts of variable resistivity, including the possibility of the development of `short-circuit’ modified current sheets (Hubbard et al. 2012, McNally et al. 2013). The temperature fluctuations that can be driven by magnetic dissipation have the possibility of being responsible for the remelting of CAIs, melting of chondrules, and thermal processing of other solid components of the disk.

Speaker: Colin McNally (NBIA, NBI)

Slides nbiappd2014.pdf

20 Nonlinear Ohm's law: electric heating of plasmas and its effect on MHD in protoplanetary disks

Non-ideal MHD effects play crucial roles in magnetohydrodynamics (MHD) of protoplanetary disks. It is conventionally assumed that electric fields in the neutral gas rest frame are so weak that they have no effect on the kinetics of ions and electrons. However, a simple order-of-magnitude estimate shows that comoving electric fields associated with MRI-driven turbulence can be strong enough to heat up electrons in some part of protoplanetary disks. We study how the electric heating of electrons affects the ionization state of the disks using a simple chemical reaction model. We find that the heating of electrons results in a reduction of the ionization degree and hence to an enhancement of the magnetic resistivity. This occurs simply because heated electrons collide with grains more frequently than cool electrons. This fact suggests that MRI-driven turbulence may be self-stabilizing, i.e., electric fields accociated with MRI turbulence may kill MRI. We also find that the electric current can become a decreasing function of the electric field strength at such high-field regimes. This "negative differential resistivity" (NDR) is found to destabilize the displacement current, meaning that Ampere's law breaks down even if the fluid motion is nonrelativistic.

Speaker: Dr Satoshi Okuzumi (Tokyo Institute of Technology)

Slides copenhagen1408.pdf

21 Discussion IV

12:30 Lunch Break

Wednesday Afternoon

Convener: Philip Armitage (University of Colorado)

22 Linear stability of accretion disks under the influence of stratification and thermal relaxation

Keplerian disks have proven to be extremely stable to perturbations, when magnetic fields are not in operation. But disks around young stars are complicated entities - they share a lot of properties with planetary atmospheres and one can learn a lot from the stability of rotating stars. Disks around young stars have a radial temperature gradient driven by stellar irradiation, which leads to a thermal wind, e.g. vertical shear. In addition the temperature gradient leads to a height dependent radial stratification that can be radially buoyant. Without thermal relaxation these disks are linearly stable, but with the right amount of cooling and heating for instance by the radiative transport of heat, one can drive a Goldreich-Schubert-Fricke Instability (see for instance Nelson et al 2013) and a Convective Overstability (Klahr and Hubbard 2014; Lyra 2014). In this talk I discuss some recent results from linear stability analysis and numerical experiments.

Speaker: Dr Hubert Klahr (MPIA)

Slides KlahrKopenhagen2014.pdf

23 Nonlinear evolution of the vertical shear instability in accretion discs

Accretion discs with radial temperature gradients have angular velocity profiles that vary both with radius and height. The presence of vertical shear can lead to a hydrodynamic instability (the vertical shear instability - VSI) that is essentially a manifestation of the Goldreich-Schubert-Fricke instability in the disc context. In this talk I will present the results from a recent study in which the nonlinear saturated state of this instability has been examined. The issues that I will discuss include the formation and life times of vortices, the magnitudes of the resulting transport coefficients, the relation between the VSI, the subcritical baroclinic instability and the convective overstability, and prospects for the instability operating in realistic models of protoplanetary discs that include stellar irradiation and internal heat transport.

Speaker: Prof. Richard Nelson (Queen Mary University of London)

Slides Copenhagen-VSI-upload.pdf

15:00 Coffee Break

24 On Vertically Global, Horizontally Local Models for Astrophysical Disks

The shearing box has been extensively used for studying local processes in accretion disks. This framework is appropriate for studying barotropic disks, for which the pressure is only a function of the density and the angular frequency is independent of height. I will introduce a more general framework by showing that, given a global disk model, it is possible to develop consistent models that are local in horizontal planes and global in height with shearing-periodic boundary conditions. These models can be non-axisymmetric for globally barotropic disks but should be axisymmetric for globally baroclinic disks. I will illustrate the potential of this new framework with two prominent applications, namely the vertical shear instability and the magnetorotational instability. I will discuss the prospects of using this new framework to study a wide variety of astrophysical phenomena.

Speaker: Dr Martin Pessah (Niels Bohr International Academy)

Slides mpessah-nbia-ppdisk-2014.pdf

25 Discussion V

Beer in the Park

Thursday, 7 August

Thursday Morning

Convener: Prof. Mark Wardle (MacquarieUniversity)

26 Signatures of accretion and MRI in protostellar disks

Accretion rates are usually diagnosed via boundary-layer emission. However, this does not directly reveal the stresses that transport angular momentum. If MRI is responsible, then it may be confined to active layers off the disk midplane at some radii. On the other hand, recent years have seen a growing body of observations of molecular emission lines from high altitudes in the disk, usually ascribed to radiative heating by stellar UV and X-rays. I will show that turbulent heating of active layers may also have observable consequences for the molecular lines, especially rovibrational CO transitions in the mid infrared from a few AU.

Speaker: Prof. Jeremy Goodman (Princeton University)

Slides pdht.pdf

27 Observational Signatures of MRI-driven Turbulence in Protoplanetary Disks: Connecting Numerical Simulations with ALMA

Protoplanetary disks play a key role in star and planet formation processes.  Turbulence in these disks, which arises from the magnetorotational instability (MRI), not only causes accretion of mass onto the central star, but also sets the conditions for processes such as dust settling, planetesimal formation, and planet migration.  However, the exact nature of this turbulence is still not very well constrained in these systems. In this talk, I will describe new work, utilizing both state-of-the-art numerical simulations and high resolution radio observations, to directly link numerical predictions for the turbulent velocity structure of protoplanetary disks to observations by the Atacama Large Millimeter Array (ALMA). ALMA’s unprecedented resolution will allow us to generate a three-dimensional view of disk turbulence by measuring the turbulent broadening component of molecular lines at different disk heights and radii. A direct comparison between the observed turbulence values and those obtained from simulations will strongly constrain our theoretical understanding of these disks and the conditions under which planetary systems develop.

Speaker: Dr Jacob Simon (Sagan Fellow, Southwest Research Institute, JILA/University of Colorado)

Slides Non-ideal_MHD,_Stability,_and_Dissipation_in_Protoplanetary_Disks_-_Talk.pdf

10:00 Coffee Break

28 The Effects of Far-UV Irradiation on the Thermal Structure of Disks

It is generally expected that most low-mass young stars have a (time-variable) far-UV excess which is correlated with ongoing accretion. Although far-UV photons cannot ionise hydrogen, they are important for dissociating hydrogen, ionising carbon, as well as other processes (e.g., photoelectric heating of dust, pumping of molecular hydrogen). In this talk, I will present the results of radiation hydrodynamics models of protoplanetary disks that include far-UV irradiation plus chemistry. More importantly, I will focus on how far-UV photons alter the disk both thermally and structurally.

Speaker: Dr Jon Ramsey (Universität Heidelberg, Zentrum für Astronomie, Insitut für Theoretische Astrophysik)

Slides talk.pdf

29 Structures and Dynamics in the Outer Regions of Turbulent Protoplanetary Disks.

In this talk we present current results from our research using global 3D non-ideal MHD stratified disk simulations. We focus on axisymmetric and non-axisymmetric structures, evocate by the magneto-rotational instability in the outer regions of a protoplanetary disk. We performed non-ideal global 3D MHD stratified simulation of the dead-zone outer edge using the FARGO MHD code PLUTO. The stellar and disk parameters are taken from the current best-fit models for the systems HH30, CB26, and Butterfly-Star. The 2D temperature and density profiles are calculated consistently from a given surface density profile and Monte-Carlo radiative transfer. The 2D Ohmic resistivity profile is calculated using the dust chemistry model. The model with strong Ohmic dissipation develops a large zonal-flow structure at the outer edge of the dead-zone. This structure manifests itself as a gap followed by a ring structure in the surface density. We confirm that this structure could be observed with current ALMA configurations. Our models show a new possibility to generate density gaps in the outer regions of protoplanetary disks other than a planet.

Speaker: Dr Mario Flock (DSM/IRFU/SAP CEA)

Slides Flock.pdf

30 Discussion VI

12:30 Lunch Break

Thursday Afternoon

Convener: Dr Hubert Klahr (MPIA)

31 Implications of dead zones for planet formation

Simple dynamical models for planet formation start from initial conditions in which planetesimals form across a broad range of radii in a smooth gas disk. Such conditions are hard to reconcile with current thinking, which emphasizes the primacy of aerodynamic drift, dead zones, and planetesimal formation via the streaming instability. I will discuss the possibility that most planet formation is seeded at particle traps, situated at radii where the physical conditions in the disk change abruptly. Such a model has some theoretical appeal, and I will discuss whether it could be consistent with Solar System and extrasolar planet observations.

Speaker: Philip Armitage (University of Colorado)

Slides armitage_talk.pdf

32 Meteoritic and planetary data constrain models of disk evolution, support magnetorotational instability models with non-uniform alpha

The magnetorotational instability (MRI) is predicted to occur in the more ionizaed regions of protoplanetary disks (PPDs), but it is recognized that the MRI cannot act in magnetically “dead”, less ionized zones (Jin et al. 1996; Gammie 1996; Sano et al. 2002, etc.). As the actions of Ohmic dissipation, ambipolar diffusion and Hall effects have become better understood, doubts have been raised about the ability of the MRI to drive angular momentum transport in PPDs. Attention is turning to disk winds and non-turbulent mechanisms. In this abstract I argue that models of disk transport must consider two pieces of information from meteoritics and planetary science: the efficient outward transport of refractory materials from the inner solar system, confirmed by the Stardust mission; and the structure of the Minimum Mass Solar Nebula as revised by Desch (2007). These constraints support models of a PPD in which the MRI is active in its outer regions but must be frustrated by a large dead zone in the inner regions. Models of PPD evolution are always better constrained by data from meteoritics and planetary science than by astronomical observations. After decades of ambiguous modeling efforts, the discovery of refractory inclusions like Inti in the Stardust sample at once confirmed that materials were efficiently transported from a few AU to the comet-forming region. The masses and location of the planets is still our best guide to the structure of the protoplanetary disk. Using the new starting positions of the planets from the Nice model (Gomes et al. 2005), Desch (2007) showed that the outer solar system (5-30 AU) surface density had to vary as r-2.2. A disk with such a steep surface density profile must be marked by net outward transport. But models of disks with uniform “alpha” viscosity (Shakura & Sunyaev 1973) typically predict disks with shallower profiles like r-1 (Hartmann et al. 1998). What is the cause of this steep profile? Desch (2007) invoked external photoevaporation of the disk, but Mitchell & Stewart (2010) showed that while this effect steepens the profile to r-1.85, it alone is not the cause of an r-2.2 profile. We have constructed disk evolution models including external photoevaporation by nearby massive stars, but also including non-uniform alpha. For the external photoevaporation we follow Adams et al. (2004) and assume G0=300, an ultraviolet flux like those seen by disks forming in massive clusters. We compute the ionization chemistry due to X-ray ionization from the central star (with Lxr=10^30 erg/s), simple grains-free chemistry, and then use the computed ion fraction to calculate a viscosity using the formulation of Bai & Stone (2011, 2013), assuming saturation of the magnetohydrodynamic turbulence so that α = 1 /2β. The disk surface density is evolved using the standard formulas of Lynden-Bell & Pringle (1974). We find that throughout most of the evolution a dead zone exists inside a few AU, but the average alpha is still somewhat high, α ~ 10-3. In the active layers > a few AU, α ~ 10-2 or more. Because alpha is high in the outer layers, they evolve rapidly, transporting mass from the region < a few AU to the outer photoevaporated disk edge at ~ 50 AU. Consistent with this outward transport, the surface density profile Σ(r) in the relevant 5-30 AU region is steep, with slope between r-2 and r-3 throughout the evolution. Without non-uniform alpha we would have reproduced the slope of Mitchell & Stewart (2010), r-1.85. We conclude that non-uniform alpha is required to reproduce the structure of our disk inferred by Desch (2007), and to explain the efficient outward transport of inner solar system materials.

Speaker: Dr Steve Desch (Arizona State University)

Slides Desch-0807.pdf

15:00 Coffee Break

33 Hyper-global zoom-in simulations of protostellar disc formation

We use the adaptive mesh refinement computer code RAMSES to model, for the first time, the formation of protoplanetary disks in realistic star formation environments, with resolution scaling over a billion, covering a range from outer scales of about 50 pc to inner scales of less than 0.01 AU. The models are done in three steps, with the first step having a dynamic resolution of ~65,000, following individual star formation in a GMC model. In the 2nd step, the neighborhoods of several stars with a final system mass of 1-2 solar masses are followed during the accretion process, with a smallest mesh size of 2.5 AU, sufficient to follow the development of the large scale structure of their accretion from the environment to the disks. Finally, a selection of these disks are studied over shorter time intervals, of the order 100-1000 yr, with cell sizes ranging down to 0.01 AU, sufficient to resolve the vertical structure of a significant radius fraction of the disks. The purpose of this procedure is to characterize the typical properties of accretion disks around solar mass protostars, with as few free parameters as possible, and to gather a statistical sample of such conditions, to quantify the extent of statistical variation of properties. This is a vast improvement over models where initial and boundary conditions have to be chosen arbitrarily. Here, the initial and boundary conditions follow instead from the statistical properties of the interstellar medium, which are reasonably well established, as per for example the Larson relations on large scales.

Speaker: Troels Haugbølle (NBI & StarPlan)

Slides TroelsHaugboelle-NBIAdisks-2014.pdf

34 The demise of the SAD model

The Standard Accretion Disk (SAD) model, based on the assumption that angular momentum transport in accretion disk is mainly in the radial direction, has been the at the center of much of the work on accretion disks since the days of Lynden-Bell & Pringle (1974) and Shakura & Sunyaev (1976). Remarkably, over essentially the same period of time, a completely different – and most likely much more fruitful – concept, where angular momentum transport (along with mass and energy transport) is mainly in the vertical direction, has lived an apparently nearly independent life (Blandford & Rees 1974, Blandford 1976, Blandford & Payne 1982, Lovelace et al 1986, Konigl 1989, Konigl & Pudritz 2000, …). I will discuss these concepts, and show that in the light of both observations and recent very high resolution simulations of star formation, which start out from conditions calibrated on well observed ISM properties and cover a scale range of nearly 1:10^9, the SAD model is no longer sustainable.

Speaker: Prof. Åke Nordlund (Niels Bohr Institute & StarPlan)

Slides NordlundNBIAdisks_43.pdf

35 Discussion VII

Friday, 8 August

Friday Morning

Convener: Prof. Shu-ichiro Inutsuka (Nagoya University)

36 Magnetohydrodynamics of planet-disk interaction

The interaction of a planet with a viscous hydrodynamic disk has been well studied in the literature. However, protoplanetary disks are not viscous hydrodynamical flows. Rather, they are inviscid (in the dead zone), or they are turbulent (where the magnetic field couples to the gas). We present some recent studies of the interaction of low-mass planets with both inviscid hydrodynamical disks, and turbulent MHD disks. We find that even a low mass planet can open gaps in both cases due to nonlinear wave steepening, in contradiction to the "thermal criterion" for gap opening. Comparison with previous results from net toroidal flux/zero flux MHD simulations indicates that the magnetic field geometry plays an important role in the gap opening process. We also report on the discovery of a new source of torque in planet-disk interactions associated with buoyancy waves excited when the equation of state is not modeled using the isothermal approximation. Finally, we report on efforts to include non-ideal MHD processes such as ambipolar diffusion and the Hall effect on the MHD of planet-disk interaction.

Speaker: Prof. James Stone (Princeton University)

Slides PPD-gas-planet.pdf

37 Dust particle dynamics in MRI turbulent disks with ambipolar diffusion

Turbulence in protoplanetary disks affects various stages of planet formation. First, it prevents particles' settling to the disk midplane, making planetesimal formation more difficult. Second, it causes stochastic planet migration and prevents gap opening by planets. By carrying out global MHD simulations with dust particles, we have studied settling and radial drift of dust particles in MRI turbulent disks with either ideal MHD or non-ideal MHD with ambipolar diffusion (AD). After a giant planet has formed in the disk, the planet opens a gap in the turbulent disk. In disks dominated by AD, the edge of the planet-induced gap is unstable to vortex formation. Such a vortex can efficiently trap dust particles, which is consistent with recent ALMA transitional disk observations.

Speaker: Dr Zhaohuan Zhu (Princeton University)

Slides copenhagan.pdf

10:00 Coffee Break

38 Interaction of the Streaming Instability and the Large-scale Gas Dynamics

The streaming instability is a promising mechanism to overcome the barriers in direct dust growth and lead to the formation of planetesimals. Most previous studies of the streaming instability, however, were focused on a local region of a protoplanetary disk with a limited simulation domain such that only one filamentary concentration of solids has been observed. The characteristic separation between filaments is therefore not known. To address this, we conduct the largest-scale simulations of the streaming instability to date such that the effect of vertical gas stratification become prominent. We observe more frequent merging and splitting of filaments in simulation boxes of high vertical extent. We find multiple filamentary concentrations of solids, which measures the characteristic separation of planetesimal forming events driven by the streaming instability and thus the initial feeding zone of planetesimals. Given the findings that the streaming instability interacts with the gas over at least one gas scale height, it remains unclear if it is also significantly affected by the dynamics of a magnetized protoplanetary disk. We will discuss our work in progress on capturing even further dynamical range for this kind of numerical simulations.

Speaker: Dr Chao-Chin Yang (Lund University)

Slides copenhagen_ccyang.pdf

39 How gas turbulence influences planet formation

Dust sedimentation is controlled by the strength of the gas turbulence. The degree of sedimentation is one of the most important factors in setting the conditions for planetesimal formation and pebble accretion. I will present a self-consistent theory framework for planet formation, from dust to fully-fledged planets, and highlight phases in the growth where progress requires an increased understanding of the strength of gas turbulence in protoplanetary discs.

Speaker: Dr Anders Johansen (Lund University)

Slides talk_anders_johansen.pdf

40 Workshop Wrap-Up

Speaker: Philip Armitage (University of Colorado)

Slides armitage_wrapup.pdf

12:15 Closing Remarks

12:30 Lunch