Publications

• Protoplanetary Disk Size under Nonideal Magnetohydrodynamics: A General Formalism with Inclined Magnetic Field
  Lee Y.-N., Barshan R., Marchand P., Hennebelle P., 2024, ApJ, 961, 28
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  Many mechanisms have been proposed to alleviate the magnetic catastrophe, which prevents the Keplerian disk from forming inside a collapsing magnetized core. Such propositions include inclined field and nonideal magnetohydrodynamics effects, and have been supported with numerical experiments. Models have been formulated for typical disk sizes when a field threads the rotating disk, parallel to the rotation axis, while observations at the core scales do not seem to show evident correlation between the directions of angular momentum and the magnetic field. In the present study, we propose a new model that considers both vertical and horizontal fields and discuss their effects on the protoplanetary disk size.


• Fast methods for tracking grain coagulation and ionization. III. Protostellar collapse with non-ideal MHD
  Marchand P., Lebreuilly U., Mac Low M.-M., Guillet V. , 2023, A&A, 670, 61
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  Dust grains influence many aspects of star formation, including planet formation, opacities for radiative transfer, chemistry, and the magnetic field via Ohmic, Hall, and ambipolar diffusion. The size distribution of the dust grains is the primary characteristic influencing all these aspects. Grain size increases by coagulation throughout the star formation process. We describe here numerical simulations of protostellar collapse using methods described in earlier papers of this series. We compute the evolution of the grain size distribution from coagulation and the non-ideal magnetohydrodynamics effects self-consistently and at low numerical cost. We find that the coagulation efficiency is mostly affected by the time spent in high-density regions. Starting from sub-micron radii, grain sizes reach more than 100 {\mu}m in an inner protoplanetary disk that is only 1000 years old. We also show that the growth of grains significantly affects the resistivities, and indirectly the dynamics and angular momentum of the disk.


• Protostellar collapse simulations in spherical geometry with dust coagulation and fragmentation
  Lebreuilly U., Valluci-Goy V., Guillet V., Lombart M., Marchand P. , 2023, MNRAS, 518, 3326
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  We model the coagulation and fragmentation of dust grains during the protostellar collapse with our newly developed shark code. It solves the gas-dust hydrodynamics in a spherical geometry and the coagulation/fragmentation equation. It also computes the ionization state of the cloud and the Ohmic, ambipolar and Hall resistivities. We find that the dust size distribution evolves significantly during the collapse, large grain formation being controlled by the turbulent differential velocity. When turbulence is included, only ambipolar diffusion remains efficient at removing the small grains from the distribution, brownian motion is only efficient as a standalone process. The macroscopic gas-dust drift is negligible for grain growth and only dynamically significant near the first Larson core. At high density, we find that the coagulated distribution is unaffected by the initial choice of dust distribution. Strong magnetic fields are found to enhance the small grains depletion, causing an important increase of the ambipolar diffusion. This hints that the magnetic field strength could be regulated by the small grain population during the protostellar collapse. Fragmentation could be effective for bare silicates, but its modeling relies on the choice of ill-constrained parameters. It is also found to be negligible for icy grains. When fragmentation occurs, it strongly affects the magnetic resistivities profiles. Dust coagulation is a critical process that needs to be fully taken into account during the protostellar collapse. The onset and feedback of fragmentation remains uncertain and its modeling should be further investigated.


• Fast methods for tracking grain coagulation and ionization. II. Extension to thermal ionization
  Marchand P., Guillet V., Lebreuilly U., Mac Low M.-M. , 2022, A&A, 666, 27
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  Thermal ionization is a critical process at temperatures T > 10 3 K, particularly during star formation. An increase in ionization leads to a decrease in nonideal magnetohydrodynamics (MHD) resistivities, which has a significant impact on protoplanetary disks and protostar formation. We developed an extension of the fast computational ionization method presented in our recent paper to include thermal ionization. The model can be used to inexpensively calculate the density of ions and electrons and the electric charge of each size of grains for an arbitrary size distribution. This tool should be particularly useful for the self-consistent calculation of nonideal MHD resistivities in multidimensional simulations, especially of protostellar collapse and protoplanetary disks.


• Universal protoplanetary disk size under complete non-ideal magnetohydrodynamics: The interplay between ion-neutral friction, Hall effect, and the Ohmic dissipation
  Lee Y.-N., Marchand P., Liu Y.-H., Hennebelle P., 2021, ApJ, 922, 36
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  The role of non-ideal magnetohydrodynamics has been proven critical during the formation of the protoplanetary disk, particularly in regulating its size. We provide a simple model to predict the disk size under the interplay among the ambipolar diffusion, the Hall effect, and the Ohmic dissipation. The model predicts a small disk size of around 20 AU, that depends only sub-linearly on disk parameters, for a wide range of initial conditions of sub-Solar mass and moderate magnetization. It is able to explain phenomena manifested in existing numerical simulations, including the bimodal disk behavior under parallel and anti-parallel alignment between the rotation and magnetic field. In the parallel configuration, the disk size decreases and eventually disappears. In the anti-parallel configuration, and the disk has an outer partition (or pseudo-disk) that is flat, shrinking , and short-lived, as well as a inner partition that grows slowly with mass and is long-lived. Even with significant initial magnetization, the vertical field in the disk can only dominate at the early stage when the mass is low, and the toroidal field eventually dominates in all disks.


• Fast methods for tracking grain coagulation and ionization. I. Analytic derivation
  Marchand P., Guillet V., Lebreuilly U., Mac Low M.-M. , 2021, A&A, 649, 50
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  Dust grains play a major role in many astrophysical contexts. They affect the chemical, magnetic, dynamical, and optical properties of their environment, from galaxies down to the interstellar medium, star-forming regions, and protoplanetary disks. Their coagulation leads to shifts in their size distribution and ultimately to the formation of planets. However, although the coagulation process is rea- sonably uncomplicated to numerically implement by itself, it is difficult to couple it with multidimensional hydrodynamics numerical simulations because of its high computational cost. We propose here a simple method for tracking the coagulation of grains at far lower cost. Given an initial grain size distribution, the state of the distribution at time t is solely determined by the value of a single variable integrated along the trajectory, independently of the specific path taken by the grains. Although this method cannot account for processes other than coagulation, it is mathematically exact, fast, inexpensive, and can be used to evaluate the effect of grain coagulation in most astrophysical contexts. It is applicable to all coagulation kernels in which local physical conditions and grain properties can be separated. We also describe another method for calculating the average electric charge of grains and the density of ions and electrons in environments that are shielded from radiation fields, given the density and temperature of the gas, the cosmic-ray ionization rate, and the average mass of the ions. The equations we provide are fast to integrate numerically and can be used in multidimensional numerical simulations to self-consistently calculate on the fly the local resistivities that are required to model nonideal magnetohydrodynamics.


• Dust coagulation feedback on magnetohydrodynamic resistivities in protostellar collapse
  Guillet V., Hennebelle P., Pineau des Forêts G., Marcowith A., Commerçon, B., Marchand P. , 2020, A&A, 643, 17
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  Context. The degree of coupling between the gas and the magnetic field during the collapse of a core and the subsequent formation of a disk depends on the assumed dust size distribution. Aims. We study the impact of grain-grain coagulation on the evolution of magnetohydrodynamic (MHD) resistivities during the collapse of a prestellar core. Methods. We use a 1-D model to follow the evolution of the dust size distribution, out-of-equilibrium ionization state and gas chemistry during the collapse of a prestellar core. To compute the grain-grain collisional rate, we consider models for both random and systematic, size-dependent, velocities. We include grain growth through grain-grain coagulation and ice accretion, but ignore grain fragmentation. Results. Starting with a MRN (Mathis et al. 1977) size distribution, we find that coagulation in grain-grain collisions generated by hydrodynamical turbulence is not efficient at removing the smallest grains, and as a consequence does not affect much the evolution of the Hall and ambipolar diffusion MHD resistivities which still severly drop during the collapse like in models without coagulation. The inclusion of systematic velocities, possibly induced by the presence of ambipolar diffusion, increases the coagulation rate between small and large grains, removing small grains earlier in the collapse and therefore limiting the drop in the Hall and ambipolar diffusion resistivities. At intermediate densities (nH ∼ 108 cm−3 ), the Hall and ambipolar diffusion resistivities are found to be higher by 1 to 2 orders of magnitude in models with coagulation than in models where coagulation is ignored, and also higher than in a toy model without coagulation where all grains smaller than 0.1 µm would have been removed in the parent cloud before the collapse. Conclusions. When grain drift velocities induced by ambipolar diffusion are included, dust coagulation happening during the collapse of a prestellar core starting from an initial MRN dust size distribution appears to be efficient enough to increase the MHD resistivities to the values necessary to strongly modify the magnetically-regulated formation of planet-forming disk. A consistent treatement of the competition between fragmentation and coagulation is however necessary before reaching firm conclusions.


• Protostellar collapse: regulation of the angular momentum and onset of an ionic precursor
  Marchand P., Tomida K., Tanaka K.E.I., Commerçon B., Chabrier G. , 2020, ApJ, 900, 180
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  Through the magnetic braking and the launching of protostellar outflows, magnetic fields play a major role in the regulation of angular momentum in star formation, which directly impacts the formation and evolution of protoplanetary disks and binary systems. The aim of this paper is to quantify those phenomena in the presence of non-ideal magnetohydrodynamics effects, namely the Ohmic and ambipola r diffusion. We perform three-dimensional simulations of protostellar collapses varying the mass of the prestellar dense core, the thermal support (the α ratio) and the dust grain size-distribu tion. The mass mostly influences the magnetic braking in the pseudo-disk, while the thermal support impacts the accretion rate and hence the properties of the disk. Removing the grains smaller than 0. 1 μ m in the Mathis, Rumpl, Nordsieck (MRN) distribution enhances the ambipolar diffusion coefficient. Similarly to previous studies, we find that this change in the distribution reduces the magnet ic braking with an impact on the disk. The outflow is also significantly weakened. In either case, the magnetic braking largely dominates the outflow as a process to remove the angular momentum from t he disk. Finally, we report a large ionic precursor to the outflow with velocities of several km s −1 , which may be observable.


• Impact of the Hall effect in star formation : improving the angular momentum conservation
  Marchand P., Tomida K., Commerçon B., Chabrier G. , 2019, A&A, 631, 66
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  We present here a minor modification of our numerical implementation of the Hall effect for the 2D Riemann solver used in Constrained Transport schemes, as described in Marchand et al. (2018). In the previous work, the tests showed that the angular momentum was not conserved during protostellar collapse simulations, with significant impact. By removing the whistler waves speed from the characteristic speeds of non-magnetic variables in the 1D Riemann solver, we are able to improve the angular momentum conservation in our test-case by one order of magnitude, while keeping the second-order numerical convergence of the scheme. We also reproduce the simulations of Tsukamoto et al. (2015) with consistent resistivities, the three non-ideal MHD effects and initial rotation, and agree with their results. In this case, the violation of angular momentum conservation is negligible in regard to the total angular momentum and the angular momentum of the disk.


• Impact of the Hall effect in star formation and the issue of angular momentum conservation
  Marchand P., Commerçon B., Chabrier G. , 2018, A&A, 619, 36
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  We 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.


• Magnetically Self-regulated Formation of Early Protoplanetary Disks
  Hennebelle P., Commerçon B., Chabrier G., Marchand P. , 2016, ApJL, 830, 8
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  The formation of protoplanetary disks during the collapse of molecular dense cores is significantly influenced by angular momentum transport, notably by the magnetic torque. In turn, the evolution of the magnetic field is determined by dynamical processes and non-ideal MHD effects such as ambipolar diffusion. Considering simple relations between various timescales characteristic of the magnetized collapse, we derive an expression for the early disk radius, r? 18 {au} {({? }{AD}/0.1{{s}})}2/9{({B}z/0.1{{G}})}-4/9{(M/0.1{M}? )}1/3, where M is the total disk plus protostar mass, {? }{AD} is the ambipolar diffusion coefficient, and B z is the magnetic field in the inner part of the core. This is significantly smaller than the disks that would form if angular momentum was conserved. The analytical predictions are confronted against a large sample of 3D, non-ideal MHD collapse calculations covering variations of a factor 100 in core mass, a factor 10 in the level of turbulence, a factor 5 in rotation, and magnetic mass-to-flux over critical mass-to-flux ratios 2 and 5. The disk radius estimates are found to agree with the numerical simulations within less than a factor 2. A striking prediction of our analysis is the weak dependence of circumstellar disk radii upon the various relevant quantities, suggesting weak variations among class-0 disk sizes. In some cases, we note the onset of large spiral arms beyond this radius.


• A chemical solver to compute molecule and grain abundances and non-ideal MHD resistivities in prestellar core collapse calculations
  Marchand P., Masson J., Hennebelle P., Chabrier G., Commerçon B., Vaytet N., 2016, A&A, 592, 18
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  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.


• PhD Thesis (in English) : Study of the physical processes involved in star formation by turbulent gravitational collapse
  2017, Supervisors : Chabrier G. and Commerçon B.
  To access the file, click on "TH2017MARCHANDPIERRE.pdf" on the top right
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  The regulation of angular momentum is widely studied in star formation: how to characterize the gas rotation during the gravitational collapse that forms the star ? This question is related to several phenomena, such as planet formation or the creation of a binary system. From the pre-stellar cloud to the final star, the system loses most of its angular momentum, and several mechanisms have been proposed to explain this phenomena. We focus on non-ideal magnetohydrodynamics (MHD), which describes the behaviour of a magnetised fluid. Several studies suggest that including it into the theoretical and numerical models leads to results coherent with observations, which are, with the numerical simulations, the only ways to test the theoretical models in astrophysics. First, we develop a code computing the chemical equilibrium of elements composing the gas of the future star. This way, we retrieve the values of the resistivities determining the strength of several MHD processes. We also study the influence of several parameters on these values, the grain population or the cosmic-rays ionisation rate for instance. We then focus on the Hall effect, one of the three processes of non-ideal MHD and still scarcely studied in this context. We implement it into the eulerian code {\ttfamily RAMSES}, and perform numerical simulations to quantify its impact on a gravitational collapse. As predicted by theory, the Hall effect has a great influence on the size of the protoplanetary disk, in which planets form, and creates envelopes of gas rotating in the opposite direction from the rest of the system.