Protoplanetary discs are made of gas and dust orbiting a young star. They are also the birth place of planetary systems, which motivates a large amount of observational and theoretical research.
In these lecture notes, I present a review of the magnetic mechanisms applied to the outer regions R>1 AU of these discs, which are the planet-formation regions. In contrast to usual astrophysical plasmas, the gas in these regions is noticeably cold (T<300 K) and dense, which implies a very low ionisation fraction close to the disc midplane. In these notes, I deliberately ignore the innermost R~0.1 AU region which is influenced by the star-disk interaction and various radiative effects.
I start by presenting a short overview of the observational evidence for the dynamics of these objects. I then introduce the methods and approximations used to model these plasmas, including non-ideal MHD, and the uncertainties associated with this approach. In this framework, I explain how the global dynamics of these discs is modelled, and I present a stability analysis of this plasma in the local approximation, introducing the non-ideal magneto-rotational instability. Following this mostly analytical part, I discuss numerical models which have been used to describe the saturation mechanisms of this instability, and the formation of large-scale structures by various saturation mechanisms. Finally, I show that local numerical models are insufficient since magnetised winds are also emitted from the surface of these objects. After a short introduction on winds physics, I present global models of protoplanetary discs, including both a large-scale wind and the non-ideal dynamics of the disc.
It has recently been established that the evolution of protoplanetary disks is primarily driven by magnetized disk winds, requiring large-scale magnetic flux threading the disks. The size of such disks is expected to shrink in time, as opposed to the conventional scenario of viscous expansion. We present the first global 2D non-ideal magnetohydrodynamic (MHD) simulations of protoplanetary disks that are truncated in the outer radius, aiming to understand the interaction of the disk with the interstellar environment, as well as global evolution of the disk and magnetic flux. We find that as the…
The gas temperature in protoplanetary disks (PPDs) is determined by a combination of irradiation heating and accretion heating, with the latter conventionally attributed to turbulent dissipation. However, recent studies have suggested that the inner disk (a few AU) is largely laminar, with accretion primarily driven by magnetized disk winds, as a result of nonideal magnetohydrodynamic (MHD) effects from weakly ionized gas, suggesting an alternative heating mechanism by Joule dissipation. We perform local stratified MHD simulations including all three nonideal MHD effects (ohmic, Hall, and ambi…
Recent observations suggest late accretion, which is generally nonaxisymmetric, onto protoplanetary disks. We investigated nonaxisymmetric late accretion considering the effects of magnetic fields. Our model assumes a cloudlet encounter event at a few hundred au scale, where a magnetized gas clump (cloudlet) encounters a protoplanetary disk. We studied how the cloudlet size and the magnetic field strength affect the rotational velocity profile in the disk after the cloudlet encounter. The results show that a magnetic field can either decelerate or accelerate the rotational motion of the cloudl…
Our aim is to study the thermal and dynamical evolution of protoplanetary disks in global simulations, including the physics of radiation transfer and magneto-hydrodynamic (MHD) turbulence caused by the magneto-rotational instability. We develop a radiative transfer method based on the flux-limited diffusion approximation that includes frequency dependent irradiation by the central star. This hybrid scheme is implemented in the PLUTO code. The focus of our implementation is on the performance of the radiative transfer method. Using an optimized Jacobi preconditioned BiCGSTAB solver, the radiat…
Beyond the $α$ model: scaling the wind-driven accretion rate in protoplanetary disks using systematic non-ideal magnetohydrodynamical simulations
Department of Earth and Planetary Sciences, Institute of Science Tokyo（东京科学地球与行星科学系）；Institute for Advanced Study and Department of Astronomy, Tsinghua University（清华大学高等研究院天文学系）
The magnetohydrodynamics (MHD) of protoplanetary disks are strongly subject to the non-ideal MHD effects arising from the low ionization fraction of the disk gas. A strong electric field induced by gas motions can heat ionized gas particles and can thereby affect the ionization balance in the disks. Our previous studies revealed that in dusty protoplanetary disks, the Ohmic conductivity decreases with increasing electric field strength until the electrical breakdown of the disk gas occurs. In this study, we extend our previous work to more general cases where both electric and magnetic fields …
Aims: We investigate the evolution of protoplanetary discs (PPDs hereafter) with magnetically driven disc winds and viscous heating. Methods: We consider an initially massive disc with ~0.1 Msun to track the evolution from the early stage of PPDs. We solve the time evolution of surface density and temperature by taking into account viscous heating and the loss of the mass and the angular momentum by the disc winds within the framework of a standard alpha model for accretion discs. Our model parameters, turbulent viscosity, disc wind mass loss, and disc wind torque, which are adopted from local…
The building of planetary systems is controlled by the gas and dust dynamics of protoplanetary disks. While the gas is simultaneously accreted onto the central star and dissipated away by winds, dust grains aggregate and collapse to form planetesimals and eventually planets. This dust and gas dynamics involves instabilities, turbulence and complex non-linear interactions which ultimately control the observational appearance and the secular evolution of these disks. This chapter is dedicated to the most recent developments in our understanding of the dynamics of gaseous and dusty disks, coverin…
By constructing a global model based on 3D local magnetohydrodynamical (MHD) simulations, we show that the disk wind driven by magnetorotational instability (MRI) plays a significant role in the dispersal of the gas component of proto-planetary disks. Because the mass loss time scale by the MRI-driven disk winds is proportional to the local Keplerian rotation period, a gas disk dynamically evaporates from the inner region with possibly creating a gradually expanding inner hole, while a sizable amount of the gas remains in the outer region. The disk wind is highly time-dependent with quasi-peri…
We characterize magnetically driven accretion at radii between 1 au and 100 au in protoplanetary discs, using a series of local non-ideal magnetohydrodynamic (MHD) simulations. The simulations assume a Minimum Mass Solar Nebula (MMSN) disc that is threaded by a net vertical magnetic field of specified strength. Confirming previous results, we find that the Hall effect has only a modest impact on accretion at 30 au, and essentially none at 100 au. At 1-10 au the Hall effect introduces a pronounced bi-modality in the accretion process, with vertical magnetic fields aligned to the disc rotation s…
We investigate a massive ($\varSigma \sim 10000 g cm^{-2}$ at 1 AU) protoplanetary disc model by means of 3D radiation magnetohydrodynamics simulations. The vertical structure of the disc is determined self-consistently by a balance between turbulent heating caused by the MRI and radiative cooling. Concerning the vertical structure, two different regions can be distinguished: A gas-pressure dominated, optically thick midplane region where most of the dissipation takes place, and a magnetically dominated, optically thin corona which is dominated by strong shocks. At the location of the photosph…
The dynamical evolution of protoplanetary disks is of key interest for building a comprehensive theory of planet formation and to explain the observational properties of these objects. Using the magnetohydrodynamics code Athena++, with an isothermal shearing box setup, we study the boundary between the active and dead zone, where the accretion rate changes and mass can accumulate. We quantify how the turbulence level is affected by the presence of a non uniform ohmic resistivity in the radial-x direction that leads to a region of inhibited turbulence (or dead zone). Comparing the turbulent act…
We perform a population synthesis of protoplanetary discs including infall with a total of $50\,000$ simulations using a 1D vertically integrated viscous evolution code, studying a large parameter space in final stellar mass. Initial conditions and infall locations are chosen based on the results from a radiation-hydrodynamic population synthesis of circumstellar discs. We also consider a different infall prescription based on a magnetohydrodynamic (MHD) collapse simulation in order to assess the influence of magnetic fields on disc formation. The duration of the infall phase is chosen to prod…
Using radiation magnetohydrodynamics simulations with realistic opacities and equation of state, and zero net magnetic flux, we have explored thermodynamics in the inner part of protoplanetary discs where magnetic turbulence is expected. The thermal equilibrium curve consists of the upper, lower, and middle branches. The upper (lower) branch corresponds to hot (cool) and optically very (moderately) thick discs, respectively, while the middle branch is characterized by convective energy transport near the midplane. Convection is also the major energy transport process near the low surface densi…
Protoplanetary discs are poorly ionised due to their low temperatures and high column densities, and are therefore subject to three "non-ideal" magnetohydrodynamic effects: Ohmic dissipation, ambipolar diffusion, and the Hall effect. The existence of magnetically driven turbulence in these discs has been a central question since the discovery of the magnetorotational instability. 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 ~1…
We investigate the formation and evolution of "primordial" dusty rings occurring in the inner regions of protoplanetary discs, with the help of long-term, coupled dust-gas, magnetohydrodynamic simulations. The simulations are global and start from the collapse phase of the parent cloud core, while the dead zone is calculated via an adaptive $α$ formulation by taking into account the local ionization balance. The evolution of the dusty component includes its growth and back reaction on to the gas. Previously, using simulations with only a gas component, we showed that dynamical rings form at th…
The gas dynamics of weakly ionized protoplanetary disks (PPDs) is largely governed by the coupling between gas and magnetic fields, described by three non-ideal magnetohydrodynamical (MHD) effects (Ohmic, Hall, ambipolar). Previous local simulations incorporating these processes have revealed that the inner regions of PPDs are largely laminar accompanied by wind-driven accretion. We conduct 2D axisymmetric, fully global MHD simulations of these regions ($\sim1-20$ AU), taking into account all non-ideal MHD effects, with tabulated diffusion coefficients and approximate treatment of external ion…
The mechanisms of angular momentum transport and level of turbulence in protoplanetary disks (PPDs) are crucial for understanding many aspects of planet formation. In the recent years, it has been realized that the magneto-rotational instability (MRI) tends to be suppressed in PPDs due to non-ideal MHD effects, and the disk is largely laminar with accretion driven by magnetized disk winds. In parallel, several hydrodynamical mechanisms have been identified that likely also generate vigorous turbulence and drive disk accretion. We study the interplay between MHD winds in PPDs with the vertical …
We study particle trapping at the edge of a gap opened by a planet in a protoplanetary disk. In particular, we explore the effects of turbulence driven by the magnetorotational instability on particle trapping, using global three-dimensional magnetohydrodynamic (MHD) simulations including Lagrangian dust particles. We study disks either in the ideal MHD limit or dominated by ambipolar diffusion (AD) that plays an essential role at the outer regions of a protoplanetary disk. With ideal MHD, strong turbulence (the equivalent viscosity parameter $α\sim 10^{-2}$) in disks prevents vortex formation…
We use local numerical simulations to investigate the strength and nature of magnetohydrodynamic (MHD) turbulence in the outer regions of protoplanetary disks, where ambipolar diffusion is the dominant non-ideal MHD effect. The simulations include vertical stratification and assume zero net vertical magnetic flux. We employ a super time-stepping technique to ameliorate the Courant restriction on the diffusive time step. We find that in idealized stratified simulations, with a spatially constant ambipolar Elsasser number Am, turbulence driven by the magnetorotational instability (MRI) behaves i…
The gas dynamics of protoplanetary disks (PPDs) is largely controlled by non-ideal magnetohydrodynamic (MHD) effects including Ohmic resistivity, the Hall effect and ambipolar diffusion. Among these the role of the Hall effect is the least explored and most poorly understood. We have included all three non-ideal MHD effects in a self-consistent manner to investigate the role of the Hall effect on PPD gas dynamics using local shearing-box simulations. In this first paper, we focus on the inner region of PPDs, where previous studies excluding the Hall effect have revealed that the inner disk up …
This paper shows that the eccentric debris rings seen around the stars Fomalhaut and HD 202628 are narrower than expected in the standard eccentric planet perturbation scenario (sometimes referred to as "pericenter glow"). The standard scenario posits an initially circular and narrow belt of planetesimals at semi-major axis $a$, whose eccentricity is increased to $e_f$ after the gas disc has dispersed by secular perturbations from an eccentric planet, resulting in a belt of width $2ae_f$. In a minor modification of this scenario, narrower belts can arise if the planetesimals are initially ecce…
Photoevaporation of protoplanetary discs by high energy radiation from the central young stellar object is currently the favourite model to explain the sudden dispersal of discs from the inside out. While several theoretical works have provided a detailed pictured of this process, the direct observational validation is still lacking. Emission lines produced in these slow moving protoplanetary disc winds may bear the imprint of the wind structure and thus provide a potential diagnostic of the underlying dispersal process. In this paper we primarily focus on the collisionally excited neutral oxy…
Circumstellar discs may become warped or broken into distinct planes if there is a stellar or planetary companion with an orbit that is misaligned with respect to the disc. There is mounting observational evidence for protoplanetary discs with misaligned inner discs and warps that may be caused by such interactions with a previously undetected companion, giving us a tantalising indication of possible planets forming there. Hydrodynamical and radiative transfer models indicate that the temperature varies azimuthally in warped discs due to the variable angle at which the disc surface faces the s…
The Protoplanetary Discussions conference --- held in Edinburgh, UK, from 7th --11th March 2016 --- included several open sessions led by participants. This paper reports on the discussions collectively concerned with the multiphysics modelling of protoplanetary discs, including the self-consistent calculation of gas and dust dynamics, radiative transfer and chemistry. After a short introduction to each of these disciplines in isolation, we identify a series of burning questions and grand challenges associated with their continuing development and integration. We then discuss potential pathway…
Protoplanetary discs should exhibit a weak vertical variation in their rotation profiles. Typically this `vertical shear' issues from a baroclinic effect driven by the central star's radiation field, but it might also arise during the launching of a magnetocentrifugal wind. As a consequence, protoplanetary discs are subject to a hydrodynamical instability, the `vertical shear instability' (VSI), whose breakdown into turbulence could transport a moderate amount of angular momentum and facilitate, or interfere with, the process of planet formation. Magnetic fields may suppress the VSI, however, …
Nearly all young stars are initially surrounded by `protoplanetary' discs of gas and dust, and in the case of single stars at least 30\% of these discs go on to form planets. The process of protoplanetary disc formation can result in initial misalignments, where the disc orbital plane is different to the stellar equator in single star systems, or to the binary orbital plane in systems with two stars. A quirk of the dynamics means that initially misaligned `circumbinary' discs -- those that surround two stars -- are predicted to evolve to one of two possible stable configurations, one where the…
We consider the mechanism of photophoretic transport in protoplanetary disks that are optically thick to radiation. Here, photophoresis is not caused by the central star but by temperature fluctuations that subject suspended solid particles, including chondrules, to non-isotropic thermal radiation within the disk. These short-lived temperature fluctuations can explain time-of-flight size sorting and general number density enhancements. The same mechanism will also lead to velocity fluctuations of dust aggregates beyond $100\,\mathrm{m\,s^{-1}}$ for mm-sized particles in protoplanetary disks. A…
In this paper, the effect of self-gravity on the protoplanetary discs is investigated. The mechanisms of angular momentum transport and energy dissipation are assumed to be the viscosity due to turbulence in the accretion disc. The energy equation is considered in situation that the released energy by viscosity dissipation is balanced with cooling processes. The viscosity is obtained by equality of dissipation and cooling functions, and is used for angular momentum equation. The cooling rate of the flow is calculated by a prescription, $d u/d t=-u/τ_{cool}$, that $u$ and $τ_{cool}$ are interna…
Protoplanetary discs are crucial to understanding how planets form and evolve, but these objects are subject to the vagaries of the birth environments of their host stars. In particular, photoionising radiation from massive stars has been shown to be an effective agent in disrupting protoplanetary discs. External photoevaporation leads to the inward evolution of the radii of discs, whereas the internal viscous evolution of the disc causes the radii to evolve outwards. We couple N-body simulations of star-forming regions with a post-processing analysis of disc evolution to determine how the rad…
One of the main problems in planet formation, hampering the growth of small dust to planetesimals, is the so-called radial-drift barrier. Pebbles of cm to dm sizes are thought to drift radially across protoplanetary discs faster than they can grow to larger sizes, and thus to be lost to the star. To overcome this barrier, drift has to be slowed down or stopped, or growth needs to be sped up. In this paper, we investigate the role of porosity on both drift and growth. We have developed a model for porosity evolution during grain growth and applied it to numerical simulations of protoplanetary d…
We consider continuum free-free radio emission from the upper atmosphere of protoplanetary discs as a probe of the ionized luminosity impinging upon the disc. Making use of previously computed hydrodynamic models of disc photoevaporation within the framework of EUV and X-ray irradiation, we use radiative transfer post-processing techniques to predict the expected free-free emission from protoplanetary discs. In general, the free-free luminosity scales roughly linearly with ionizing luminosity in both EUV and X-ray driven scenarios, where the emission dominates over the dust tail of the disc an…
Many theoretical studies have shown that external photoevaporation from massive stars can severely truncate, or destroy altogether, the gaseous protoplanetary discs around young stars. In tandem, several observational studies report a correlation between the mass of a protoplanetary disc and its distance to massive ionising stars in star-forming regions, and cite external photoevaporation by the massive stars as the origin of this correlation. We present N-body simulations of the dynamical evolution of star-forming regions and determine the mass-loss in protoplanetary discs from external photo…
We analyse N-body simulations of star-forming regions to investigate the effects of external far and extreme ultra-violet photoevaporation from massive stars on protoplanetary discs. By varying the initial conditions of simulated star-forming regions, such as the spatial distribution, net bulk motion (virial ratio), and density, we investigate which parameters most affect the rate at which discs are dispersed due to external photoevaporation. We find that disc dispersal due to external photoevaporation is faster in highly substructured star-forming regions than in smooth and centrally concentr…
Spatially resolving the immediate surroundings of young stars is a key challenge for the planet formation community. SPHERE on the VLT represents an important step forward by increasing the opportunities offered by optical or near-infrared imaging instruments to image protoplanetary discs. The Guaranteed Time Observation Disc team has concentrated much of its efforts on polarimetric differential imaging, a technique that enables the efficient removal of stellar light and thus facilitates the detection of light scattered by the disc within a few au from the central star. These images reveal int…
With hydrodynamical simulations we examine the evolution of a protoplanetary disc around $α$ Centauri B including the effect of the eccentric orbit binary companion $α$ Centauri A. The initially circular orbit disc undergoes two types of eccentricity growth. First, the eccentricity oscillates on the orbital period of the binary, $P_{\rm orb}$, due to the eccentricity of the binary orbit. Secondly, for a sufficiently small disc aspect ratio, the disc undergoes global forced eccentricity oscillations on a time-scale of around $20\,P_{\rm orb}$. These oscillations damp out through viscous dissipa…
We study the evolution and final dispersal of protoplanetary discs that evolve under the action of internal and external photoevaporation, and different degrees of viscous transport. We identify five distinct dispersal pathways, which are i) very long lived discs ($>20\,$Myr), ii) inside-out dispersal where internal photoevaporation dominates and opens inner holes, iii) outside-in dispersal where external photoevaporation dominates through disc truncation and two intermediate regimes characterised by lingering material in the inner disc with the outer disc dispersed predominantly by either int…
Planetary systems form in gas-dust protoplanetary discs via the growth of solid bodies. In this paper, we show that the most intriguing stage of such growth --- namely, the transformation of 1-10 m boulders into kilometre-sized planetesimals --- can be explained by a mechanism of gravitational instability. The present work focused on the origin of self-gravitating clumps in which planetesimal formation could take place. Our computer simulations demonstrated that such clumps of gas and boulders formed due to the development of a two-phase instability. This instability revealed a so-called 'mutu…
Computing the flow from externally FUV irradiated protoplanetary discs requires solving complicated and expensive photodissociation physics iteratively in conjunction with hydrodynamics. Previous studies have therefore been limited to 1D models of this process. In this paper we compare 2D-axisymmetric models of externally photoevaporating discs with their 1D analogues, finding that mass loss rates are consistent to within a factor four. The mass loss rates in 2D are higher, in part because half of the mass loss comes from the disc surface (which 1D models neglect). 1D mass loss rates used as t…
We aim to understand under which conditions a low mass planet can open a gap in viscous dusty protoplanetary discs. For this purpose, we extend the theory of dust radial drift to include the contribution from the tides of an embedded planet and from the gas viscous forces. From this formalism, we derive i) a grain size-dependent criterion for dust gap opening in discs, ii) an estimate of the location of the outer edge of the dust gap and iii) an estimate of the minimum Stokes number above which low-mass planets are able to carve gaps which appear only in the dust disc. These analytical estimat…
