Radiation Magnetohydrodynamics In Global Simulations Of Protoplanetary Disks

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 radiative module is three times faster than the MHD step for the disk setup we consider. We obtain weak scaling efficiencies of 70% up to 1024 cores. We present the first global 3D radiation MHD simulations of a stratified protoplanetary disk. The disk model parameters are chosen to approximate those of the system AS 209 in the star-forming region Ophiuchus. Starting the simulation from a disk in radiative and hydrostatic equilibrium, the magnetorotational instability quickly causes MHD turbulence and heating in the disk. For the disk parameters we use, turbulent dissipation heats the disk midplane and raises the temperature by about 15% compared to passive disk models. A roughly flat vertical temperature profile establishes in the disk optically thick region close to the midplane. We reproduce the vertical temperature profile with a viscous disk models for which the stress tensor vertical profile is flat in the bulk of the disk and vanishes in the disk corona. The present paper demonstrates for the first time that global radiation MHD simulations of turbulent protoplanetary disks are feasible with current computational facilities. This opens up the windows to a wide range of studies of the dynamics of protoplanetary disks inner parts, for which there are significant observational constraints.Comment: Accepted to A&

The dynamical state of the First Hydrostatic Core Candidate Cha-MMS1

Observations of First Hydrostatic Core candidates, a theoretically predicted evolutionary link between the prestellar and protostellar phases, are vital for probing the earliest phases of star formation. We aim to determine the dynamical state of the First Hydrostatic Core candidate Cha-MMS1. We observed Cha-MMS1 in various transitions with the APEX and Mopra telescopes. The molecular emission was modeled with a radiative transfer code to derive constraints on the envelope kinematics. We derive an internal luminosity of 0.08 - 0.18 Lsol. An average velocity gradient of 3.1(0.1) km/s/pc over 0.08 pc is found perpendicular to the filament in which Cha-MMS1 is embedded. The gradient is flatter in the outer parts and at the innermost 2000 - 4000 AU. These features suggest solid-body rotation beyond 4000 AU and slower, differential rotation beyond 8000 AU. The origin of the flatter gradient in the innermost parts is unclear. The classical infall signature is detected in HCO+ 3-2 and CS 2-1. The radiative transfer modeling indicates a uniform infall velocity in the outer parts of the envelope. An infall velocity field scaling with r^(-0.5) is consistent with the data for r < 9000 AU. The infall velocities are 0.1 - 0.2 km/s at r > 3300 AU and 0.04 - 0.6 km/s at r < 3300 AU. Both the internal luminosity of Cha-MMS1 and the infall velocity field in its envelope are consistent with predictions of MHD simulations for the first core phase. There is no evidence for a fast, large-scale outflow stemming from Cha-MMS1 but excess emission from the high-density tracers CS 5-4, CO 6-5, and CO 7-6 suggests the presence of higher-velocity material at the inner core. Its internal luminosity excludes Cha-MMS1 being a prestellar core. The kinematical properties of its envelope are consistent with Cha-MMS1 being a first core candidate or a very young Class 0 protostar.(abridged).Comment: Accepted for publication in A&A. 27 pages, 22 figures, 13 tables. A version with high-resolution figures is available on request to the first autho

Nascent bipolar outflows associated with the first hydrostatic core candidates Barnard 1b-N and 1b-S

In the theory of star formation, the first hydrostatic core (FHSC) phase is a critical step in which a condensed object emerges from a prestellar core. This step lasts about one thousand years, a very short time compared with the lifetime of prestellar cores, and therefore is hard to detect unambiguously. We present IRAM Plateau de Bure observations of the Barnard 1b dense molecular core, combining detections of H2CO and CH3OH spectral lines and dust continuum at 2.3" resolution (~ 500 AU). The two compact cores B1b-N and B1b-S are detected in the dust continuum at 2mm, with fluxes that agree with their spectral energy distribution. Molecular outflows associated with both cores are detected. They are inclined relative to the direction of the magnetic field, in agreement with predictions of collapse in turbulent and magnetized gas with a ratio of mass to magnetic flux somewhat higher than the critical value, \mu ~ 2 - 7. The outflow associated with B1b-S presents sharp spatial structures, with ejection velocities of up to ~ 7 kms from the mean velocity. Its dynamical age is estimated to be ~2000 yrs. The B1b-N outflow is smaller and slower, with a short dynamical age of ~1000 yrs. The B1b-N outflow mass, mass-loss rate, and mechanical luminosity agree well with theoretical predictions of FHSC. These observations confirm the early evolutionary stage of B1b-N and the slightly more evolved stage of B1b-S.Comment: 6 pages, 3 figure

Impact of the Hall effect in star formation and the issue of angular momentum conservation

This is the author accepted manuscript. The final version is available from EDP Sciences via the DOI in this recordWe present an implementation of the Hall term in the non-ideal magnetohydrodynamics equations into the adaptive-mesh-refinement code RAMSES to study its impact on star formation. Recent works show that the Hall effect heavily influences the regulation of the angular momentum in collapsing dense cores, strengthening or weakening the magnetic braking. Our method consists of a modification of the two-dimensional constrained transport scheme. Our scheme shows convergence of second-order in space and the frequency of the propagation of whistler waves is accurate. We confirm previous results, namely that during the collapse, the Hall effect generates a rotation of the fluid with a direction in the mid-plane that depends on the sign of the Hall resistivity, while counter-rotating envelopes develop on each side of the mid-plane. However, we find that the predictability of our numerical results is severely limited. The angular momentum is not conserved in any of our dense core-collapse simulations with the Hall effect: a large amount of angular momentum is generated within the first Larson core, a few hundred years after its formation, without compensation by the surrounding gas. This issue is not mentioned in previous studies and may be correlated to the formation of the accretion shock on the Larson core. We expect that this numerical effect could be a serious issue in star formation simulations.We acknowledge financial support from “Programme National de PhysiqueStellaire” (PNPS) of CNRS/INSU, CEA, and CNES, France, and from an International Research Fellowship of the Japan Society for the Promotion of Science

Multigroup radiation hydrodynamics with flux-limited diffusion and adaptive mesh refinement

International audienceContext. Radiative transfer plays a crucial role in the star formation process. Because of the high computational cost, radiation-hydrodynamics simulations performed up to now have mainly been carried out in the grey approximation. In recent years, multifrequency radiation-hydrodynamics models have started to be developed in an attempt to better account for the large variations in opacities as a function of frequency.Aims. We wish to develop an efficient multigroup algorithm for the adaptive mesh refinement code RAMSES which is suited to heavy proto-stellar collapse calculations.Methods. Because of the prohibitive timestep constraints of an explicit radiative transfer method, we constructed a time-implicit solver based on a stabilized bi-conjugate gradient algorithm, and implemented it in RAMSES under the flux-limited diffusion approximation.Results. We present a series of tests that demonstrate the high performance of our scheme in dealing with frequency-dependent radiation-hydrodynamic flows. We also present a preliminary simulation of a 3D proto-stellar collapse using 20 frequency groups. Differences between grey and multigroup results are briefly discussed, and the large amount of information this new method brings us is also illustrated.Conclusions. We have implemented a multigroup flux-limited diffusion algorithm in the RAMSES code. The method performed well against standard radiation-hydrodynamics tests, and was also shown to be ripe for exploitation in the computational star formation context

Simulations of protostellar collapse using multigroup radiation hydrodynamics. I. The first collapse

Radiative transfer plays a major role in the process of star formation. Many simulations of gravitational collapse of a cold gas cloud followed by the formation of a protostellar core use a grey treatment of radiative transfer coupled to the hydrodynamics. However, dust opacities which dominate extinction show large variations as a function of frequency. In this paper, we used frequency-dependent radiative transfer to investigate the influence of the opacity variations on the properties of Larson's first core. We used a multigroup M1 moment model in a 1D radiation hydrodynamics code to simulate the spherically symmetric collapse of a 1 solar mass cloud core. Monochromatic dust opacities for five different temperature ranges were used to compute Planck and Rosseland means inside each frequency group. The results are very consistent with previous studies and only small differences were observed between the grey and multigroup simulations. For a same central density, the multigroup simulations tend to produce first cores with a slightly higher radius and central temperature. We also performed simulations of the collapse of a 10 and 0.1 solar mass cloud, which showed the properties of the first core to be independent of the initial cloud mass, with again no major differences between grey and multigroup models. For Larson's first collapse, where temperatures remain below 2000 K, the vast majority of the radiation energy lies in the IR regime and the system is optically thick. In this regime, the grey approximation does a good job reproducing the correct opacities, as long as there are no large opacity variations on scales much smaller than the width of the Planck function. The multigroup method is however expected to yield more important differences in the later stages of the collapse when high energy (UV and X-ray) radiation is present and matter and radiation are strongly decoupled.Comment: 9 pages, 5 figures, accepted for publication in A&

The role of cosmic rays on magnetic field diffusion and the formation of protostellar discs

International audienceContext. The formation of protostellar discs is severely hampered by magnetic braking, as long as magnetic fields remain frozen in the gas. The latter condition depends on the levels of ionisation that characterise the innermost regions of a collapsing cloud.Aims. The chemistry of dense cloud cores and, in particular, the ionisation fraction is largely controlled by cosmic rays. The aim of this paper is to evaluate whether the attenuation of the flux of cosmic rays expected in the regions around a forming protostar is sufficient to decouple the field from the gas, thereby influencing the formation of centrifugally supported disc.Methods. We adopted the method developed in a former study to compute the attenuation of the cosmic-ray flux as a function of the column density and the field strength in clouds threaded by poloidal and toroidal magnetic fields. We applied this formalism to models of low- and high-mass star formation extracted from numerical simulations of gravitational collapse that include rotation and turbulence.Results. For each model we determine the size of the magnetic decoupling zone, where collapse or rotation motion becomes unaffected by the local magnetic field. In general, we find that decoupling only occurs when the attenuation of cosmic rays is taken into account with respect to a calculation in which the cosmic-ray ionisation rate is kept constant. The extent of the decoupling zone also depends on the dust grain size distribution and is larger if large grains (of radius ~10-5 cm) are formed by compression and coagulation during cloud collapse. The decoupling region disappears for the high-mass case. This is due to magnetic field diffusion caused by turbulence that is not included in the low-mass models.Conclusions. We conclude that a realistic treatment of cosmic-ray propagation and attenuation during cloud collapse may lead to a value of the resistivity of the gas in the innermost few hundred AU around a forming protostar that is higher than generally assumed. Forthcoming self-consistent calculations should investigate whether this effect is strong enough to effectively decouple the gas from the field and to compute the amount of angular momentum lost by infalling fluid particles when they enter the decoupling zone

Protostellar birth with ambipolar and ohmic diffusion

This is the final version of the article. Available from EDP Sciences via the DOI in this record.The transport of angular momentum is capital during the formation of low-mass stars; too little removal and rotation ensures stellar densities are never reached, too much and the absence of rotation means no protoplanetary disks can form. Magnetic diffusion is seen as a pathway to resolving this long-standing problem. We investigate the impact of including resistive MHD in simulations of the gravitational collapse of a 1 solar mass gas sphere, from molecular cloud densities to the formation of the protostellar seed; the second Larson core. We used the AMR code RAMSES to perform two 3D simulations of collapsing magnetised gas spheres, including self-gravity, radiative transfer, and a non-ideal gas equation of state to describe H2 dissociation which leads to the second collapse. The first run was carried out under the ideal MHD approximation, while ambipolar and ohmic diffusion was incorporated in the second calculation. In the ideal MHD simulation, the magnetic field dominates the energy budget everywhere inside and around the first core, fueling interchange instabilities and driving a low-velocity outflow. High magnetic braking removes essentially all angular momentum from the second core. On the other hand, ambipolar and ohmic diffusion create a barrier which prevents amplification of the magnetic field beyond 0.1 G in the first Larson core which is now fully thermally supported. A significant amount of rotation is preserved and a small Keplerian-like disk forms around the second core. When studying the radiative efficiency of the first and second core accretion shocks, we found that it can vary by several orders of magnitude over the 3D surface of the cores. Magnetic diffusion is a pre-requisite to star-formation; it enables the formation of protoplanetary disks in which planets will eventually form, and also plays a determinant role in the formation of the protostar itself.We are indebted to the anonymous referee for his/her insightful comments that have vastly improved the solidity of our study, with no stones left unturned. We also thank Troels Haugbølle for very useful discussions during the writing of this paper. NV gratefully acknowledges support from the European Commission through the Horizon 2020 Marie Skłodowska-Curie Actions Individual Fellowship 2014 programme (Grant Agreement no. 659706). The research leading to these results has also received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement no. 247060). We acknowledge financial support from "Programme National de Physique Stellaire" (PNPS) of CNRS/INSU, CEA and CNES, France. This work was granted access to the HPC resources of CINES (Occigen) under the allocation 2016-047247 made by GENCI. We also made use of the astrophysics HPC facility at the University of Copenhagen, which is supported by a research grant (VKR023406) from Villum Fonden. In addition, we thank the Service d’Astrophysique, IRFU, CEA Saclay, and the Laboratoire Astrophysique Instrumentation Modélisation, France, for granting us access to the supercomputer IRFUCOAST where the groundwork with many test calculations were performed. All the figures were created using the OSIRIS8 visualization package for RAMSES, except Fig. 4 which was rendered with the PARAVIEW9 software

Chemical solver to compute molecule and grain abundances and non-ideal MHD resistivities in prestellar core collapse calculations

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.We develop a detailed chemical network relevant to the conditions characteristic of prestellar core collapse. We solve the system of time-dependent differential equations to calculate the equilibrium abundances of molecules and dust grains, with a size distribution given by size-bins for these latter. These abundances are used to compute the different non-ideal magneto-hydrodynamics resistivities (ambipolar, Ohmic and Hall), needed to carry out simulations of protostellar collapse. For the first time in this context, we take into account the evaporation of the grains, the thermal ionisation of Potassium, Sodium and Hydrogen at high temperature, and the thermionic emission of grains in the chemical network, and we explore the impact of various cosmic ray ionisation rates. All these processes significantly affect the non-ideal magneto-hydrodynamics resistivities, which will modify the dynamics of the collapse. Ambipolar diffusion and Hall effect dominate at low densities, up to n_H = 10^12 cm^-3, after which Ohmic diffusion takes over. We find that the time-scale needed to reach chemical equilibrium is always shorter than the typical dynamical (free fall) one. This allows us to build a large, multi-dimensional multi-species equilibrium abundance table over a large temperature, density and ionisation rate ranges. This table, which we make accessible to the community, is used during first and second prestellar core collapse calculations to compute the non-ideal magneto-hydrodynamics resistivities, yielding a consistent dynamical-chemical description of this process