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Planetesimal formation models often invoke the gravitational collapse of pebble clouds to overcome various barriers to grain growth and propose processes to concentrate particles sufficiently to trigger this collapse. On the other hand, the geochemical approach for planet formation constrains the conditions for planetesimal formation and evolution by providing temperatures that should be reached to explain the final composition of planetesimals, the building blocks of planets. To elucidate the thermal evolution during gravitational collapse, we used numerical simulations of a self-gravitating cloud of particles and gas coupled with gas drag. Our goal is to determine how the gravitational energy relaxed during the contraction is distributed among the different energy components of the system, and how this constrains a thermal and dynamical planetesimal's history. We identify the conditions necessary to achieve a temperature increase of several hundred kelvins, and as much as 1600 K. Our results emphasise the key role of the gas during the collapse., Comment: 12 pages, 12 figures, accepted for publication in A&A

Context: Protoplanetary discs are known to form around nascent stars from their parent molecular cloud as a result of angular momentum conservation. As they progressively evolve and dissipate, they also form planets. While a lot of modeling efforts have been dedicated to their formation, the question of their secular evolution, from the so-called class 0 embedded phase to the class II phase where discs are believed to be isolated, remains poorly understood. Aims: We aim to explore the evolution between the embedded stages and the class II stage. We focus on the magnetic field evolution and the long-term interaction between the disc and the envelope. Methods: We use the GPU-accelerated code \textsc{Idefix} to perform a 3D, barotropic, non-ideal magnetohydrodynamic (MHD) secular core collapse simulation that covers the system evolution from the collapse of the pre-stellar core until 100 kyr after the first hydrostatic core formation and the disc settling while ensuring sufficient vertical and azimuthal resolutions (down to $10^{-2}$ au) to properly resolve the disc internal dynamics and non-axisymmetric perturbations. Results: The disc evolution leads to a power-law gas surface density in Keplerian rotation that extends up to a few 10 au. The magnetic flux trapped in the disc during the initial collapse decreases from 100 mG at disc formation down to 1 mG by the end of the simulation. After the formation of the first hydrostatic core, the system evolves in three phases. A first phase with a small ($\sim 10$ au), unstable, strongly accreting ($\sim10^{-5}$ $\mathrm{M_\odot \, yr^{-1}}$) disc that loses magnetic flux over the first 15 kyr, a second phase where the magnetic flux is advected with a smooth, expanding disc fed by the angular momentum of the infalling material..., Comment: 17 pages, 14 figures, accepted for publication in Astronomy & Astrophysics

Context: FUors outbursts are a crucial stage of accretion in young stars. However a complete mechanism at the origin of the outburst still remains missing. Aims: We aim at constraining the instability mechanism in FU Orionis star itself, by directly probing the size and the evolution in time of the outburst region with near-infrared interferometry, and to confront it to physical models of this region. Methods: FU Orionis has been a regular target of near-infrared interferometry. In this paper, we analyze more than 20 years of interferometric observations to perform a temporal monitoring of the region of the outburst, and compare it to the spatial structure deduced from 1D MHD simulations. Results: We measure from the interferometric observations that the size variation of the outburst region is compatible with a constant or slightly decreasing size over time in the H and K band. The temporal variation and the mean sizes are consistently reproduced by our 1D MHD simulations. We find that the most compatible scenario is a model of an outburst occurring in a magnetically layered disk, where a Magneto-Rotational Instability (MRI) is triggered by a Gravitational Instability (GI) at the outer edge of a dead-zone. The scenario of a pure Thermal Instability (TI) fails to reproduce our interferometric sizes since it can only be sustained in a very compact zone of the disk <0.1 AU. The scenario of MRI-GI could be compatible with an external perturbation enhancing the GI, such as tidal interactions with a stellar companion, or a planet at the outer edge of the dead-zone. Conclusions: The layered disk model driven by MRI turbulence is favored to interpret the spatial structure and temporal evolution of FU Orionis outburst region. Understanding this phase gives a crucial link between the early phase of disk evolution and the process of planet formation in the first inner AUs., Comment: Accepted for publication in A&A

In dwarf nov{\ae} and low-mass X-ray binaries, the tidal potential excites spiral waves in the accretion disc. Spiral wave driven accretion may be important in quiescent discs, where the angular momentum transport mechanism has yet to be identified. Previous studies were limited to unrealistically high temperatures for numerical studies or to specific regimes for analytical studies. We perform the first numerical simulation of spiral wave driven accretion in the cold temperature regime appropriate to quiescent discs, which have Mach numbers > 100. We use the new GPU-accelerated finite volume code Idefix to produce global hydrodynamics 2D simulations of the accretion discs of dwarf nov{\ae} systems with a fine-enough spatial resolution to capture the short scale-height of cold, quiescent discs with Mach numbers ranging from 80 to 370. Running the simulations on timescales of tens of binary orbits shows transient angular momentum transport that decays as the disc relaxes from its initial conditions. We find the angular momentum parameter {\alpha} drops to values << 0.01 , too weak to drive accretion in quiescence.

Exascale super-computers now becoming available rely on hybrid energy-efficient architectures that involve an accelerator such as Graphics Processing Units (GPU). Leveraging the computational power of these machines often means a significant rewrite of the numerical tools each time a new architecture becomes available. To address these issues, we present Idefix, a new code for astrophysical flows that relies on the Kokkos meta-programming library to guarantee performance portability on a wide variety of architectures while keeping the code as simple as possible for the user. Idefix is based on a Godunov finite-volume method that solves the non-relativistic HD and MHD equations on various grid geometries. Idefix includes a wide choice of solvers and several additional modules (constrained transport, orbital advection, non-ideal MHD) allowing users to address complex astrophysical problems. Idefix has been successfully tested on Intel and AMD CPUs (up to 131 072 CPU cores on Irene-Rome at TGCC) as well as NVidia and AMD GPUs (up to 1024 GPUs on Adastra at CINES). Idefix achieves more than 1e8 cell/s in MHD on a single NVidia V100 GPU and 3e11 cell/s on 256 Adastra nodes (1024 GPUs) with 95% parallelization efficiency (compared to a single node). For the same problem, Idefix is up to 6 times more energy efficient on GPUs compared to Intel Cascade Lake CPUs. Idefix is now a mature exascale-ready open-source code that can be used on a large variety of astrophysical and fluid dynamics applications., Comment: 18 pages, 18 figures, 3 tables, accepted for publication in Astronomy & Astrophysics

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, covering hydrodynamic and magnetohydrodynamic turbulence, gas-dust instabilities, dust clumping and disk winds. We show how these physical processes have been tested from observations and highlight standing questions that should be addressed in the future., Comment: 32 pages, 7 figures, to appear in Protostars and Planets VII, eds: Shu-ichiro Inutsuka, Yuri Aikawa, Takayuki Muto, Kengo Tomida, and Motohide Tamura

In their early stages, protoplanetary discs are sufficiently massive to undergo gravitational instability (GI). This instability is thought to be involved in mass accretion, planet formation via gas fragmentation, the generation of spiral density waves, and outbursts. A key and very recent area of research is the interaction between the GI and magnetic fields in young protoplanetary discs, in particular whether this instability is able to sustain a magnetic field via a dynamo. We conduct three-dimensional, stratified shearing-box simulations using two independent codes, PLUTO and Athena++, to characterise the GI dynamo in poorly ionised protostellar discs subject to ambipolar diffusion. We find that the dynamo operates across a large range of ambipolar Elssaser number Am (which characterises the strength of ambipolar diffusion) and is particularly strong in the regime Am=10-100, with typical magnetic to thermal energy ratios of order unity. The dynamo is only weakly dependent on resolution (at least for Am <100), box size, and cooling law. The magnetic field is produced by the combination of differential rotation and large-scale vertical roll motions associated with spiral density waves. Our results have direct implications for the dynamo process in young protoplanetary discs and possibly some regions of AGN discs., Comment: accepted in MNRAS

Astrophysical disks are likely embedded in an ambient vertical magnetic field. This ambient field is known to drive magneto-rotational turbulence in the disk bulk but is also responsible for the launching of magnetized outflows at the origin of astrophysical jets. The vertical structure and long-term (secular) evolution of such a system lack quantitative predictions. It is nevertheless this secular evolution that is proposed to explain time variability in many accreting systems such as X-ray binaries. We compute and analyze global 3D ideal-MHD simulations of an accretion disk threaded by a large-scale magnetic field. We evaluate the role of the turbulent terms in the equilibrium of the system. We then compute the transport of mass, angular momentum, and magnetic fields in the disk to characterize its secular evolution. We perform a parameter survey to characterize the influence of disk properties on secular transport. We find that weakly magnetized disks drive jets that carry away a small fraction of the disk angular momentum. The mass-weighted accretion speed remains subsonic although, there is always an upper turbulent atmospheric region where transonic accretion takes place. We show that a strongly magnetized version of the magneto-rotational instability drives this turbulence. The disk structure is drastically different from the conventional hydrostatic picture. The magnetic field is always dragged inwards in the disk, at a velocity that increases with the disk magnetization. Beyond a threshold on the latter, the disk undergoes a profound radial readjustment. It leads to the formation of an inner accretion-ejection region with a supersonic mass-weighted accretion speed and where the magnetic field distribution becomes steady, near equipartition with the thermal pressure. This inner structure shares many properties with the Jet Emitting Disk model described by Ferreira (1997)., Comment: Paper accepted on A&A, November 30, 2020

We analyze a sample of 12 HST-selected edge-on protoplanetary disks for which the vertical extent of the emission layers can be constrained directly. We present ALMA high angular resolution continuum images (0.1arcsec) of these disks at two wavelengths, 0.89mm and 2.06mm (respectively ALMA bands 7 and 4), supplemented with archival band 6 data (1.33mm) where available. For most sources, the millimeter continuum emission is more compact than the scattered light, both in the vertical and radial directions. Six sources are resolved along their minor axis in at least one millimeter band, providing direct information on the vertical distribution of the millimeter grains. For the second largest disk of the sample, the significant difference in vertical extent between band 7 and band 4 suggests efficient size-selective vertical settling of large grains. Furthermore, the only Class I object in our sample shows evidence of flaring in the millimeter. Along the major axis, all disks are well resolved. Four of them are larger in band 7 than in band 4 in the radial direction, and three have a similar radial extent in all bands. For all disks, we also derive the millimeter brightness temperature and spectral index maps. We find that the disks are likely optically thick and that the dust emission reveals low brightness temperatures in most cases (<10K). The integrated spectral indices are similar to those of disks at lower inclination. The comparison of a generic radiative transfer disk model with our data shows that at least 3 disks are consistent with a small millimeter dust scale height, of a few au (measured at r=100au). This is in contrast with the more classical value of h_g\sim10au derived from scattered light images and from gas line measurements. These results confirm, by direct observations, that large (millimeter) grains are subject to significant vertical settling in protoplanetary disks., Comment: Accepted for publication in Astronomy and Astrophysics Updates: Few typos in the text + Table A.1

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., Comment: 115 pages, 46 figures, accepted for publication in the lecture notes series of the Journal of Plasma Physics (Cambridge University Press)

Large-scale vertical magnetic fields are believed to play a key role in the evolution of protoplanetary discs. Associated with non-ideal effects, such as ambipolar diffusion, they are known to launch a wind that could drive accretion in the outer part of the disc ($R> 1$ AU). They also potentially lead to self-organisation of the disc into large-scale axisymmetric structures, similar to the rings recently imaged by sub-millimetre or near-infrared instruments (ALMA and SPHERE). The aim of this paper is to investigate the mechanism behind the formation of these gaseous rings, but also to understand the dust dynamics and its emission in discs threaded by a large-scale magnetic field. To this end, we performed global magneto-hydrodynamics (MHD) axisymmetric simulations with ambipolar diffusion using a modified version of the PLUTO code. We explored different magnetisations with the midplane $\beta$ parameter ranging from $10^5$ to $10^3$ and included dust grains -- treated in the fluid approximation -- ranging from $100 \mu$m to 1 cm in size. We first show that the gaseous rings (associated with zonal flows) are tightly linked to the existence of MHD winds. Secondly, we find that millimetre-size dust is highly sedimented, with a typical scale height of 1 AU at $R=100$ AU for $\beta=10^4$, compatible with recent ALMA observations. We also show that these grains concentrate into pressure maxima associated with zonal flows, leading to the formation of dusty rings. Using the radiative transfer code MCFOST, we computed the dust emission and make predictions on the ring-gap contrast and the spectral index that one might observe with interferometers like ALMA., Comment: 17 pages, accepted in A&A

Gravitational instability (GI) controls the dynamics of young massive protoplanetary discs. Apart from facilitating gas accretion on to the central protostar, it must also impact on the process of planet formation: directly through fragmentation, and indirectly through the turbulent concentration of small solids. To understand the latter process, it is essential to determine the dust dynamics in such a turbulent flow. For that purpose, we conduct a series of 3D shearing box simulations of coupled gas and dust, including the gas's self-gravity and scanning a range of Stokes numbers, from 0.001 to ~0.2. First, we show that the vertical settling of dust in the midplane is significantly impeded by gravitoturbulence, with the dust scale-height roughly 0.6 times the gas scale height for centimetre grains. This is a result of the strong vertical diffusion issuing from (a) small-scale inertial-wave turbulence feeding off the GI spiral waves and (b) the larger-scale vertical circulations that naturally accompany the spirals. Second, we show that at R=50 AU concentration events involving sub-metre particles and yielding order 1 dust to gas ratios are rare and last for less than an orbit. Moreover, dust concentration is less efficient in 3D than in 2D simulations. We conclude that GI is not especially prone to the turbulent accumulation of dust grains. Finally, the large dust scale-height measured in simulations could be, in the future, compared with that of edge-on discs seen by ALMA, thus aiding detection and characterisation of GI in real systems., Comment: Accepted in MNRAS, 13 pages

Semi-analytical models of disk outflows have successfully described magnetically-driven, self-confined super-Alfv\'enic jets from near Keplerian accretion disks. These Jet Emitting Disks are possible for high levels of disk magnetization $\mu$ defined as $\mu=2/\beta$ where beta is the usual plasma parameter. In near-equipartition JEDs, accretion is supersonic and jets carry away most of the disk angular momentum. However, these solutions prove difficult to compare with cutting edge numerical simulations, for the reason that numerical simulations show wind-like outflows but in the domain of small magnetization. In this work, we present for the first time self-similar isothermal solutions for accretion-ejection structures at small magnetization levels. We elucidate the role of MRI-like structures in the acceleration processes that drive this new class of solutions. The disk magnetization $\mu$ is the main control parameter: massive outflows driven by the pressure of the toroidal magnetic field are obtained up to $\mu \sim 10^{-2}$, while more tenuous centrifugally-driven outflows are obtained at larger $\mu$ values. The generalized parameter space and the astrophysical consequences are discussed. We believe that these new solutions could be a stepping stone in understanding the way astrophysical disks drive either winds or jets. Defining jets as self-confined outflows and winds as uncollimated outflows, we propose a simple analytical criterion based on the initial energy content of the outflow, to discriminate jets from winds. We show that jet solution are achieved at all magnetization level, while winds could be obtained only in weakly magnetized disks that feature heating., Comment: Accepted 23/09/2019

Rings and gaps have been observed in a wide range of protoplanetary discs, from young systems like HLTau to older discs like TW Hydra. Recent disc simulations have shown that magnetohydrodynamic (MHD) turbulence (in the ideal or non-ideal regime) can lead to the formation of rings and be an alternative to the embedded planets scenario. In this paper, we investigate how these ring form in this context and seek a generic formation process, taking into account the various dissipative regimes and magnetizations probed by the past simulations. We identify the existence of a linear and secular instability, driven by MHD winds, and giving birth to rings of gas having a width larger than the disc scale height. We show that the linear theory is able to make reliable predictions regarding the growth rates, ring/gap contrast and spacing, by comparing these predictions to a series of 2D (axisymmetric) and 3D MHD numerical simulations. In addition, we demonstrate that these rings can act as dust traps provided that the disc is sufficiently magnetised, with plasma beta lower than $10^4$. Given its robustness, the process identified in this paper could have important implications, not only for protoplanetary discs but also for a wide range of accreting systems threaded by large-scale magnetic fields., Comment: 17 pages, accepted in A&A

Context. Disks around pre-main-sequence stars evolve over time by turbulent viscous spreading. The main contender to explain the strength of the turbulence is the Magneto-Rotational-Instability (MRI) model, whose efficiency depends on the disk ionization fraction. Aims. We aim at computing self-consistently the chemistry including PAH charge chemistry, the grain charging and an estimate of an effective value of the turbulence alpha parameter in order to find observational signatures of disk turbulence. Methods. We introduced PAH and grain charging physics and their interplay with other gas-phase reactions in the physico-chemical code ProDiMo. Non-ideal magnetohydrodynamics effects such as Ohmic and ambipolar diffusion are parametrized to derive an effective value for the turbulent parameter alpha_eff . We explored the effects of turbulence heating and line broadening on CO isotopologue sub-millimeter lines. Results. The spatial distribution of alpha_eff depends on various unconstrained disk parameters such as the magnetic parameter beta_mag or the cosmic ray density distribution inside the protoplanetary disks. The inner disk midplane shows the presence of the so-called dead-zone where the turbulence is quasi-inexistent. The disk is heated mostly by thermal accommodation on dust grains in the dead-zone, by viscous heating outside the dead-zone up to a few hundred astronomical units, and by chemical heating in the outer disk. The CO rotational lines probe the warm molecular disk layers where the turbulence is at its maximum. However, the effect of turbulence on the CO line profiles is minimal and difficult to distinguish from the thermal broadening. Conclusions. Viscous heating of the gas in the disk midplane outside the dead-zone is efficient. The determination of alpha from CO rotational line observations alone is challenging., Comment: accepted to A&A. 29 pages

MHD turbulence plays a crucial role in the dust dynamics of protoplanetary discs. It affects planet formation, vertical settling and is one possible origin of the large scale axisymmetric structures, such as rings, recently imaged by ALMA and SPHERE. Among the variety of MHD processes, the magnetorotational instability (MRI) has raised particular interest since it provides a source of turbulence and potentially organizes the flow into radial structures. However, the weak ionization of discs prevents the MRI from being excited beyond 1 AU. The strong sedimentation of millimetre dust measured in T-Tauri discs is also in contradiction with predictions based on ideal MRI turbulence. In this paper, we study the effects of non-ideal MHD and winds on the dynamics and sedimentation of dust grains. We consider a weakly ionized plasma subject to ambipolar diffusion characterizing the disc outer regions (>1 AU). For that, we perform numerical MHD simulations in the stratified shearing box, using the PLUTO code. Our simulations show that the mm-cm dust is contained vertically in a very thin layer, with typical heightscale ~0.4 AU at 30 AU, compatible with recent ALMA observations. Horizontally, the grains are trapped within pressure maxima induced by ambipolar diffusion, leading to the formation of dust rings. For micrometer grains, dust and gas scaleheights are similar. In this regime, the settling cannot be explained by a simple 1D diffusion theory but results from a large scale 2D circulation induced by both MHD winds and zonal flows. Overall, our results show that non-ideal MHD effects and their related winds play a major role in shaping the radial and vertical distribution of dust in protoplanetary discs. Leading to substantial accretion efficiency, non-ideal effects also a promising avenue to reconcile the low turbulent activity measured in discs with their relatively high accretion rates., Comment: 22 pages, 21 figures, accepted in A&A

The eruptive cycles of dwarf novae (DN) are thought to be due to a thermal-viscous instability in the accretion disk surrounding the white dwarf (WD). This model has long been known to imply a stress to pressure ratio \alpha ~0.1 in outburst compared to \alpha ~ 0.01 in quiescence. Such an enhancement in $\alpha$ has recently been observed in simulations of turbulent transport driven by the magneto-rotational instability (MRI) when convection is present, without requiring a net magnetic flux. We independently recover this result by carrying out PLUTO MHD simulations of vertically stratified, radiative, shearing boxes with the thermodynamics and opacities appropriate to DN. The results are robust against the choice of vertical boundary conditions. The thermal equilibrium solutions found by the simulations trace the well-known S-curve in the density-temperature plane. We confirm that the high values of \alpha ~ 0.1 occur near the tip of the hot branch of the S-curve, where convection is active. However, we also present thermally-stable simulations at lower temperatures that have standard values of \alpha ~ 0.03 despite the presence of vigorous convection. We find no simple relationship between \alpha and the strength of the convection, as measured by the ratio of convective to radiative flux. The cold branch is only very weakly ionized so, in the second part of this work, we studied the impact of non-ideal MHD effects on transport. We include resistivity in the simulations and find that the MRI-driven transport is quenched (\alpha ~ 0) below the critical density at which the magnetic Reynolds number R_m \leq 10^4. This is problematic as X-ray emission observed in quiescent systems requires ongoing accretion onto the WD. We verify that these X-rays cannot self-sustain MRI-driven turbulence by photo-ionizing the disk and discuss possible solutions to the issue of accretion in quiescence., Comment: 14 pages, 13 figures, 1 table; accepted for publication in A&A

Understanding the diversity of planets requires to study the morphology and the physical conditions in the protoplanetary disks in which they form. We observed and spatially resolved the disk around the ~10 Myr old protoplanetary disk HD 100453 in polarized scattered light with SPHERE/VLT at optical and near-infrared wavelengths, reaching an angular resolution of ~0.02", and an inner working angle of ~0.09". We detect polarized scattered light up to ~0.42" (~48 au) and detect a cavity, a rim with azimuthal brightness variations at an inclination of 38 degrees, two shadows and two symmetric spiral arms. The spiral arms originate near the location of the shadows, close to the semi major axis. We detect a faint spiral-like feature in the SW that can be interpreted as the scattering surface of the bottom side of the disk, if the disk is tidally truncated by the M-dwarf companion currently seen at a projected distance of ~119 au. We construct a radiative transfer model that accounts for the main characteristics of the features with an inner and outer disk misaligned by ~72 degrees. The azimuthal brightness variations along the rim are well reproduced with the scattering phase function of the model. While spirals can be triggered by the tidal interaction with the companion, the close proximity of the spirals to the shadows suggests that the shadows could also play a role. The change in stellar illumination along the rim, induces an azimuthal variation of the scale height that can contribute to the brightness variations. Dark regions in polarized images of transition disks are now detected in a handful of disks and often interpreted as shadows due to a misaligned inner disk. The origin of such a misalignment in HD 100453, and of the spirals, is unclear, and might be due to a yet-undetected massive companion inside the cavity, and on an inclined orbit., Comment: A&A, accepted

In Keplerian accretion disks, turbulence and magnetic fields may be jointly excited through a subcritical dynamo process involving the magnetorotational instability (MRI). High-resolution simulations exhibit a tendency towards statistical self-organization of MRI dynamo turbulence into large-scale cyclic dynamics. Understanding the physical origin of these structures, and whether they can be sustained and transport angular momentum efficiently in astrophysical conditions, represents a significant theoretical challenge. The discovery of simple periodic nonlinear MRI dynamo solutions has recently proven useful in this respect, and has notably served to highlight the role of turbulent magnetic diffusion in the seeming decay of the dynamics at low magnetic Prandtl number Pm (magnetic diffusivity larger than viscosity), a common regime in accretion disks. The connection between these simple structures and the statistical organization reported in turbulent simulations remained elusive, though. Here, we report the numerical discovery in moderate aspect ratio Keplerian shearing boxes of new periodic, incompressible, three-dimensional nonlinear MRI dynamo solutions with a larger dynamical complexity reminiscent of such simulations. These "chimera" cycles are characterized by multiple MRI-unstable dynamical stages, but their basic physical principles of self-sustainment are nevertheless identical to those of simpler cycles found in azimuthally elongated boxes. In particular, we find that they are not sustained at low Pm either due to subcritical turbulent magnetic diffusion. These solutions offer a new perspective into the transition from laminar to turbulent instability-driven dynamos, and may prove useful to devise improved statistical models of turbulent accretion disk dynamos., Comment: 12 pages, 8 figures, submitted to A&A

Angular momentum transport in accretion discs is often believed to be due to magnetohydrodynamic turbulence mediated by the magnetorotational instability. Despite an abundant literature on the MRI, the parameters governing the saturation amplitude of the turbulence are poorly understood and the existence of an asymptotic behavior in the Ohmic diffusion regime is not clearly established. We investigate the properties of the turbulent state in the small magnetic Prandtl number limit. Since this is extremely computationally expensive, we also study the relevance and range of applicability of the most common subgrid scale models for this problem. Unstratified shearing boxes simulations are performed both in the compressible and incompressible limits, with a resolution up to 800 cells per disc scale height. The latter constitutes the largest resolution ever attained for a simulation of MRI turbulence. In the presence of a mean magnetic field threading the domain, angular momentum transport converges to a finite value in the small Pm limit. When the mean vertical field amplitude is such that {\beta}, the ratio between the thermal and magnetic pressure, equals 1000, we find {\alpha}~0.032 when Pm approaches zero. In the case of a mean toroidal field for which {\beta}=100, we find {\alpha}~0.018 in the same limit. Both implicit LES and Chollet-Lesieur closure model reproduces these results for the {\alpha} parameter and the power spectra. A reduction in computational cost of a factor at least 16 (and up to 256) is achieved when using such methods. MRI turbulence operates efficiently in the small Pm limit provided there is a mean magnetic field. Implicit LES offers a practical and efficient mean of investigation of this regime but should be used with care, particularly in the case of a vertical field. Chollet-Lesieur closure model is perfectly suited for simulations done with a spectral code., Comment: Accepted for publication in A&A

The magnetorotational (MRI) dynamo has long been considered one of the possible drivers of turbulent angular momentum transport in astrophysical accretion disks. However, various numerical results suggest that this dynamo may be difficult to excite in the astrophysically relevant regime of magnetic Prandtl number (Pm) significantly smaller than unity, for reasons currently not well understood. The aim of this article is to present the first results of an ongoing numerical investigation of the role of both linear and nonlinear dissipative effects in this problem. Combining a parametric exploration and an energy analysis of incompressible nonlinear MRI dynamo cycles representative of the transitional dynamics in large aspect ratio shearing boxes, we find that turbulent magnetic diffusion makes the excitation and sustainment of this dynamo at moderate magnetic Reynolds number (Rm) increasingly difficult for decreasing Pm. This results in an increase in the critical Rm of the dynamo for increasing kinematic Reynolds number (Re), in agreement with earlier numerical results. Given its very generic nature, we argue that turbulent magnetic diffusion could be an important determinant of MRI dynamo excitation in disks, and may also limit the efficiency of angular momentum transport by MRI turbulence in low Pm regimes., Comment: 7 pages, 6 figures

Planets appear to form in environments shaped by the gas flowing through protostellar disks to the central young stars. The flows in turn are governed by orbital angular momentum transfer. In this chapter we summarize current understanding of the transfer processes best able to account for the flows, including magneto-rotational turbulence, magnetically-launched winds, self-gravitational instability and vortices driven by hydrodynamical instabilities. For each in turn we outline the major achievements of the past few years and the outstanding questions. We underscore the requirements for operation, especially ionization for the magnetic processes and heating and cooling for the others. We describe the distribution and strength of the resulting flows and compare with the long-used phenomenological $\alpha$-picture, highlighting issues where the fuller physical picture yields substantially different answers. We also discuss the links between magnetized turbulence and magnetically-launched outflows, and between magnetized turbulence and hydrodynamical vortices. We end with a summary of the status of efforts to detect specific signatures of the flows., Comment: Refereed review chapter accepted for publication in Protostars and Planets VI, University of Arizona Press (2014), eds. H. Beuther, R. Klessen, C. Dullemond & Th. Henning. 24 pages, 7 figures. The talk presented at the Protostars and Planets VI conference is available at http://youtube.com/watch?v=tEgw0PXwkGE

Magnetorotational dynamo action in Keplerian shear flow is a three-dimensional, nonlinear magnetohydrodynamic process whose study is relevant to the understanding of accretion and magnetic field generation in astrophysics. Transition to this form of dynamo is subcritical and shares many characteristics of transition to turbulence in non-rotating hydrodynamic shear flows. This suggests that these different fluid systems become active through similar generic bifurcation mechanisms, which in both cases have eluded detailed understanding so far. In this paper, we investigate numerically the bifurcation mechanisms at work in the incompressible Keplerian magnetorotational dynamo problem in the shearing box framework. Using numerical techniques imported from dynamical systems research, we show that the onset of chaotic dynamo action at magnetic Prandtl numbers larger than unity is primarily associated with global homoclinic and heteroclinic bifurcations of nonlinear magnetorotational dynamo cycles. These global bifurcations are supplemented by local bifurcations of cycles marking the beginning of period-doubling cascades. This suggests that nonlinear magnetorotational dynamo cycles provide the pathway to turbulent injection of both kinetic and magnetic energy in incompressible magnetohydrodynamic Keplerian shear flow in the absence of an externally imposed magnetic field. Studying the nonlinear physics and bifurcations of these cycles in different regimes and configurations may subsequently help to better understand the conditions of excitation of magnetohydrodynamic turbulence and instability-driven dynamos in various astrophysical systems and laboratory experiments. The detailed characterization of global bifurcations provided for this three-dimensional subcritical fluid dynamics problem may also prove useful for the problem of transition to turbulence in hydrodynamic shear flows., Comment: 43 pages, 17 figures, accepted for publication in J. Fluid Mech

The nature of dynamo action in shear flows prone to magnetohydrodynamic instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to the three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and non-axisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understand the transitional and statistical properties of subcritical magnetorotational turbulence., Comment: 10 pages, 6 figures, accepted for publication in Physical Review E

We consider the radial migration of vortices in two-dimensional isothermal gaseous disks. We find that a vortex core, orbiting at the local gas velocity, induces velocity perturbations that propagate away from the vortex as density waves. The resulting spiral wave pattern is reminiscent of an embedded planet. There are two main causes for asymmetries in these wakes: geometrical effects tend to favor the outer wave, while a radial vortensity gradient leads to an asymmetric vortex core, which favors the wave at the side that has the lowest density. In the case of asymmetric waves, which we always find except for a disk of constant pressure, there is a net exchange of angular momentum between the vortex and the surrounding disk, which leads to orbital migration of the vortex. Numerical hydrodynamical simulations show that this migration can be very rapid, on a time scale of a few thousand orbits, for vortices with a size comparable to the scale height of the disk. We discuss the possible effects of vortex migration on planet formation scenarios., Comment: 13 pages, 13 figures, accepted for publication in ApJ

The Sun is a magnetic star whose cyclic activity is thought to be linked to internal dynamo mechanisms. A combination of numerical modelling with various levels of complexity is an efficient and accurate tool to investigate such intricate dynamical processes. We investigate the role of the magnetic buoyancy process in 2D Babcock-Leighton dynamo models, by modelling more accurately the surface source term for poloidal field. Methods. To do so, we reintroduce in mean-field models the results of full 3D MHD calculations of the non-linear evolution of a rising flux tube in a convective shell. More specifically, the Babcock-Leighton source term is modified to take into account the delay introduced by the rise time of the toroidal structures from the base of the convection zone to the solar surface. We find that the time delays introduced in the equations produce large temporal modulation of the cycle amplitude even when strong and thus rapidly rising flux tubes are considered. Aperiodic modulations of the solar cycle appear after a sequence of period doubling bifurcations typical of non-linear systems. The strong effects introduced even by small delays is found to be due to the dependence of the delays on the magnetic field strength at the base of the convection zone, the modulation being much less when time delays remain constant. We do not find any significant influence on the cycle period except when the delays are made artificially strong. A possible new origin of the solar cycle variability is here revealed. This modulated activity and the resulting butterfly diagram are then more compatible with observations than what the standard Babcock-Leighton model produces., Comment: 13 pages, 10 figures, accepted for publication in A&A

In the recent years, MRI-driven turbulent transport has been found to depend in a significant way on fluid viscosity $\nu$ and resistivity $\eta$ through the magnetic Prandtl number $Pm=\nu/\eta$. In particular, the transport decreases with decreasing $Pm$; if persistent at very large Reynolds numbers, this trend may lead to question the role of MRI-turbulence in YSO disks, whose Prandtl number is usually very small. In this context, the principle objective of the present investigation is to characterize in a refined way the role of dissipation. Another objective is to characterize the effect of linear (channel modes) and quasi-linear (parasitic modes) physics in the behavior of the transport. These objectives are addressed with the help of a number of incompressible numerical simulations. The horizontal extent of the box size has been increased in order to capture all relevant (fastest growing) linear and secondary parasitic unstable modes. The major results are the following: i- The increased accuracy in the computation of transport averages shows that the dependence of transport on physical dissipation exhibits two different regimes: for $Pm \lesssim 1$, the transport has a power-law dependence on the magnetic Reynolds number rather than on the Prandtl number; for $Pm > 1$, the data are consistent with a primary dependence on $Pm$ for large enough ($\sim 10^3$) Reynolds numbers. ii- The transport-dissipation correlation is not clearly or simply related to variations of the linear modes growth rates. iii- The existence of the transport-dissipation correlation depends neither on the number of linear modes captured in the simulations, nor on the effect of the parasitic modes on the saturation of the linear modes growth. iv- The transport is usually not dominated by axisymmetric (channel) modes, Comment: 11 pages, 9 figures. Accepted for publication in A&A

The mechanism of angular momentum transport in accretion discs has long been debated. Although the magnetorotational instability appears to be a promising process, poorly ionized regions of accretion discs may not undergo this instability. In this letter, we revisit the possibility of transporting angular momentum by turbulent thermal convection. Using high-resolution spectral methods, we show that strongly turbulent convection can drive outward angular momentum transport at a rate that is, under certain conditions, compatible with observations of discs. We find however that the angular momentum transport is always much weaker than the vertical heat transport. These results indicate that convection might be another way to explain global disc evolution, provided that a sufficiently unstable vertical temperature profile can be maintained., Comment: 6 pages, 5 figures, accepted in MNRAS

(abridged) Aims: We present new results exhibiting a subcritical baroclinic instability (SBI) in local shearing box models. We describe the 2D and 3D behaviour of this instability using numerical simulations and we present a simple analytical model describing the underlying physical process. Results: A subcritical baroclinic instability is observed in flows stable for the Solberg-Hoiland criterion using local simulations. This instability is found to be a nonlinear (or subcritical) instability, which cannot be described by ordinary linear approaches. It requires a radial entropy gradient weakly unstable for the Schwartzchild criterion and a strong thermal diffusivity (or equivalently a short cooling time). In compressible simulations, the instability produces density waves which transport angular momentum outward with typically alpha<3e-3, the exact value depending on the background temperature profile. Finally, the instability survives in 3D, vortex cores becoming turbulent due to parametric instabilities. Conclusions: The subcritical baroclinic instability is a robust phenomenon, which can be captured using local simulations. The instability survives in 3D thanks to a balance between the 2D SBI and 3D parametric instabilities. Finally, this instability can lead to a weak outward transport of angular momentum, due to the generation of density waves by the vortices., Comment: 12 pages, 17 figures, Accepted in A&A

(abriged) MRI turbulence is a leading mechanism for the generation of an efficient turbulent transport of angular momentum in an accretion disk through a turbulent viscosity effect. It is believed that the same process could also transport large-scale magnetic fields in disks, reshaping the magnetic structures in these objects. This process, known as turbulent resistivity, has been suggested and used in several accretion-ejection models and simulations to produce jets. Still, the efficiency of MRI-driven turbulence to transport large-scale magnetic fields is largely unknown. We investigate this problem both analytically and numerically. We introduce a linear calculation of the MRI in the presence of a spatially inhomogeneous mean magnetic field. We show that, in this configuration, MRI modes lead to an efficient magnetic field transport, on the order of the angular momentum transport. We next use fully non linear simulations of MRI turbulence to compute the turbulent resistivity in several magnetic configurations. We find that the turbulent resistivity is on the order of the turbulent viscosity in all our simulations, although somewhat lower. The turbulent resistivity tensor is found to be highly anisotropic with a diffusion coefficient 3 times greater in the radial direction than in the vertical direction. These results support the possibility of driving jets from turbulent disks; the resulting jets may not be steady., Comment: 11 pages, 8 figures, accepted for publication in Astronomy and Astrophysics

(Abriged) The existence of large-scale and long-lived 2D vortices in accretion discs has been debated for more than a decade. They appear spontaneously in several 2D disc simulations and they are known to accelerate planetesimal formation through a dust trapping process. However, the issue of the stability of these structures to the imposition of 3D disturbances is still not fully understood, and it casts doubts on their long term survival. Aim: We present new results on the 3D stability of elliptical vortices embedded in accretion discs, based on a linear analysis and several non-linear simulations. Methods: We derive the linearised equations governing the 3D perturbations in the core of an elliptical vortex, and we show that they can be reduced to a Floquet problem. We solve this problem numerically in the astrophysical regime and we present several analytical limits for which the mechanism responsible for the instability can be explained. Finally, we compare the results of the linear analysis to some high resolution simulations. Results: We show that most anticyclonic vortices are unstable due to a resonance between the turnover time and the local epicyclic oscillation period. In addition, we demonstrate that a strong vertical stratification does not create any additional stable domain of aspect ratio, but it significantly reduces growth rates for relatively weak (and therefore elongated) vortices. Conclusions: Elliptical vortices are always unstable, whatever the horizontal or vertical aspect-ratio is. The instability can however be weak and is often found at small scales, making it difficult to detect in low-order finite-difference simulations., Comment: 13 pages, 14 figures, accepted for publication by A&A. Animations available on author's website

(Abriged) The magnetorotational instability (MRI) is believed to be an efficient way to transport angular momentum in accretion discs. It has also been suggested as a way to amplify magnetic fields in discs, the instability acting as a nonlinear dynamo. Recent numerical work has shown that a large-scale magnetic field, which is predominantly azimuthal, can be sustained by motions driven by the MRI of this same field. Following this idea, we present an analytical calculation of the MRI in the presence of an azimuthal field with a non-trivial vertical structure. We find that the mean radial EMF associated to MRI modes tends to reduce the magnetic energy, acting like a turbulent resistivity by mixing the non-uniform azimuthal field. Meanwhile, the azimuthal EMF generates a radial field that, in combination with the Keplerian shear, tends to amplify the azimuthal field and can therefore assist in the dynamo process. This effect, however, is reversed for sufficiently strong azimuthal fields, naturally leading to a saturation of the dynamo and possibly to a cyclic behaviour of the magnetic field, as found in previous numerical works., Comment: 15 pages, 5 figures

(abridged) MHD turbulence is known to exist in shearing boxes with either zero or nonzero net magnetic flux. However, the way turbulence survives in the zero-net-flux case is not explained by linear theory and appears as a purely numerical result. Aims: We look for a nonlinear mechanism able to explain the persistence of MHD turbulence in shearing boxes with zero net magnetic flux, and potentially leading to large-scale dynamo action. Method: Spectral nonlinear simulations of the magnetorotational instability are shown to exhibit a large-scale axisymmetric magnetic field, maintained for a few orbits. The generation process of this field is investigated using the results of the simulations and an inhomogeneous linear approach. Results: The mechanism by which turbulence is sustained in zero-net-flux shearing boxes is shown to be related to the existence of a large-scale azimuthal field, surviving for several orbits. In particular, it is shown that MHD turbulence in shearing boxes can be seen as a dynamo process coupled to a magnetorotational-type instability., Comment: 11 pages, 11 figures, Accepted in A&A

We study the influence of the choice of transport coefficients (viscosity and resistivity) on MHD turbulence driven by the magnetorotational instability (MRI) in accretion disks. We follow the methodology described in paper I: we adopt an unstratified shearing box model and focus on the case where the net vertical magnetic flux threading the box vanishes. For the most part we use the finite difference code ZEUS, including explicit transport coefficients in the calculations. However, we also compare our results with those obtained using other algorithms (NIRVANA, the PENCIL code and a spectral code) to demonstrate both the convergence of our results and their independence of the numerical scheme. We find that small scale dissipation affects the saturated state of MHD turbulence. In agreement with recent similar numerical simulations done in the presence of a net vertical magnetic flux, we find that turbulent activity (measured by the rate of angular momentum transport) is an increasing function of the magnetic Prandtl number Pm for all values of the Reynolds number Re that we investigated. We also found that turbulence disappears when the Prandtl number falls below a critical value Pm_c that is apparently a decreasing function of Re. For the limited region of parameter space that can be probed with current computational resources, we always obtained Pm_c>1. We conclude that the magnitudes of the transport coefficients are important in determining the properties of MHD turbulence in numerical simulations in the shearing box with zero net flux, at least for Reynolds numbers and magnetic Prandtl numbers that are such that transport is not dominated by numerical effects and thus can be probed using current computational resources., Comment: 10 pages, 13 figures, accepted in A&A. Numerical results improved, minor changes in the text

The magneto-rotational instability is presently the most promising source of turbulent transport in accretion disks. However, some important issues still need to be addressed to quantify the role of MRI in disks; in particular no systematic investigation of the role of the physical dimensionless parameters of the problem on the dimensionless transport has been undertaken yet. First, we complete existing investigations on the field strength dependence by showing that the transport in high magnetic pressure disks close to marginal stability is highly time-dependent and surprisingly efficient. Second, we bring to light a significant dependence of the global transport on the magnetic Prandtl number, with $\alpha\propto Pm^\delta$ for the explored range: $0.12

Hydrodynamic unstratified keplerian flows are known to be linearly stable at all Reynolds numbers, but may nevertheless become turbulent through nonlinear mechanisms. However, in the last ten years, conflicting points of view have appeared on this issue. We have revisited the problem through numerical simulations in the shearing sheet limit. It turns out that the effect of the Coriolis force in stabilizing the flow depends on whether the flow is cyclonic (cooperating shear and rotation vorticities) or anticyclonic (competing shear and rotation vorticities); keplerian flows are anticyclonic. We have obtained the following results: i/ The Coriolis force does not quench turbulence in subcritical flows; ii/ The resolution demand, when moving away from the marginal stability boundary, is much more severe for anticyclonic flows than for cyclonic ones. Presently available computer resources do not allow numerical codes to reach the keplerian regime. iii/ The efficiency of turbulent transport is directly correlated to the Reynolds number of transition to turbulence $Rg$, in such a way that the Shakura-Sunyaev parameter $\alpha\sim 1/Rg$. iv/ Even the most optimistic extrapolations of our numerical data show that subcritical turbulent transport would be too inefficient in keplerian flows by several orders of magnitude for astrophysical purposes. v/ Our results suggest that the data obtained for keplerian-like flows in a Taylor-Couette settings are largely affected by secondary flows, such as Ekman circulation., Comment: 21 pages, 17 figures, accepted in Astronomy and Astrophysics