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Ugo Lebreuilly

Publications and source records attributed to Ugo Lebreuilly.

At least 19 recordsLinked to original sources

Magnetohydrodynamics of charged interstellar dust. Multifluid models and study of the linear modes

Interstellar grains play key roles in star and planet formation, including the coupling of the gas to the magnetic field during the protostellar collapse. These roles depend on the local grain size distribution, which requires a multifluid treatment of charged dust. We aim to understand the fundamental physics of the dynamics of a dust distribution in interaction with the gas and the magnetic field. In particular, the purpose is to characterize the (de)coupling conditions of these different components. We provide a multifluid model of charged dust which accounts for the inertia of the grains. A chemical network is used to simulate the charge equilibrium in collapsing protostellar cores. We compute the Alfven modes and the magnetosonic modes to understand the coupling regimes between the gas, the dust fluids, and the magnetic field. We also analyze and compare to the predictions of existing models, that are the neutral dust multifluid and the standard non-ideal magnetohydrodynamics. The charged multifluid model agrees with non-ideal magnetohydrodynamics on the larger scales of a collapsing dense core and the forming disk, while we successfully extend to new regimes where the inertia of dust grains matters. We found that high charge-to-mass dust grains carry the propagation of magnetohydrodynamical waves in protostellar envelopes. We provide analytical expressions of the speed of these waves depending on the dust distribution. The magnetocompressive perturbations lead to local dust-to-gas ratio variations at au scales. A theoretical understanding of the dynamics of a charged dust distribution is provided in the linear regime. The closed set of magnetohydrodynamics equations can be implemented in numerical codes to explore nonlinear effects during the protostellar collapse such as turbulence, angular momentum transport and magnetic dust clumping.

astro-ph.GA

On the 3D time evolution of the dust size distribution in protostellar envelopes

Dust plays a fundamental role during protostellar collapse, disk and planet formation. Recent observations suggest that efficient dust growth may begin early, in the protostellar envelopes, potentially even before the formation of the disk. Three-dimensional models of protostellar evolution, addressing multi-size dust growth, gas and dust dynamics and magnetohydrodynamics, are required to characterize the dust evolution in the embedded stages of star formation. We aim to establish a new framework for dust evolution models, following in 3D the dust size distribution both in time and space, in MHD models describing the formation and evolution of star-disk systems, at low numerical cost. We present our work coupling the COALA dust evolution module into the code RAMSES, performing the first 3D MHD simulation of protostellar collapse including simultaneously polydisperse dust growth modeled by the Smoluchowski equation as well as dust dynamics in the terminal velocity approximation. Ice-coated micron-sized grains can rapidly grow in the envelope and survive by not entering the fragmentation regime. The evolution of the dust size distribution is highly anisotropic due to the turbulent nature of the collapse and the development of favorable locations such as outflow cavity walls, which enhance locally the dust-to-gas ratio. We analyzed the first 3D non-ideal MHD simulations that self-consistently account for the dust dynamics and growth during the protostellar stage. Very early in the lifetime of a young embedded protostar, micron-sized grains can grow, and locally the dust size distribution deviates significantly from the MRN initial shape. This new numerical method opens the perspective to treat simultaneously gas/dust dynamics and dust growth in 3D simulations at a low numerical cost for several astrophysical environments.

astro-ph.SR

A new multifluid method for dusty astrophysical flows. Application to turbulent protostellar collapses

Stars and planets form in collapsing clouds of gas and dust. The presence of dust grains and their local distribution play a significant role throughout the protostellar sequence, from the thermodynamics and the chemistry of molecular clouds to the opacity of collapsing protostellar cores and the coupling between the gas and the magnetic field and down to planet formation in young and evolved disks. We aim to simulate the dynamics of the dust, considering the whole range of grain sizes, from few nanometers to millimeters. We implemented a neutral pressureless multifluid that samples the dust size distribution in the RAMSES code. This multifluid is dynamically coupled to the gas via a drag source term and self-gravity, relying on the Eulerian approach. We designed a Riemann solver for the gas and dust mixture that prevents unphysical dust-to-gas ratio variations for well-coupled grains. We illustrated the capacities of the code by performing simulations of a protostellar collapse down to the formation of a first hydrostatic core, both for small and large dust grains. Grains over 100 microns significantly decouple from the gas. The spatial maps and the probability density functions indicate that dust enrichment within the first hydrostatic core and in some locations of the envelope increases as a function of the grain size and the level of initial turbulence. Thanks to the novel Riemann solver, we recovered the terminal velocity regime, even at low resolution. Moreover, we successfully extended it to regimes where the grain inertia matters. The multifluid module performs the coupling between the dust and the gas self-consistently all through the dynamical scales. The dust enrichment in the first hydrostatic core and the envelope have been revised here, assuming the initial turbulence and grain sizes. This enables us to probe new potential conditions for planet formation.

astro-ph.IM

The Rosetta Stone Project. II. The correlation between star formation efficiency and L/M indicator for the evolutionary stages of star-forming clumps in post-processed radiative magnetohydrodynamics simulations

Context. The evolution of massive star-forming clumps that are progenitors of high-mass young stellar objects are often classified based on a variety of observational indicators ranging from near-infrared to radio wavelengths. Among them, the ratio of the bolometric luminosity to the mass of their envelope, $L/M$, has been observationally diagnosed as a good indicator for the evolutionary classification of parsec-scale star-forming clumps in the Galaxy. Aims. We developed the Rosetta Stone project$\unicode{x2013}$an end-to-end framework designed to enable an accurate comparison between simulations and observations for investigating the formation and evolution of massive clumps. In this study, we calibrate the $L/M$ indicator in relation to the star formation efficiency (SFE) and the clump age, as derived from our suite of simulations. Methods. We performed multi-wavelength radiative transfer post-processing of radiative magnetohydrodynamics (RMHD) simulations of the collapse of star-forming clumps fragmenting into protostars. We generated synthetic observations to obtain far-infrared emission from $70$ to $500\,μ$m, as was done in the Hi-GAL survey, and at $24\,μ$m in the MIPSGAL survey, which were then used to build the spectral energy distributions (SEDs) and estimate the $L/M$ parameter. An additional $1.3\,$mm wavelength in ALMA Band 6 was also produced for the comparison with observational data. We applied observational techniques$\unicode{x2013}$commonly employed by observers$\unicode{x2013}$to the synthetic data in order to derive the corresponding physical parameters. Results. We find a correlation between $L/M$ and the SFE, with a power-law form $L/M\propto {\rm SFE}^{1.20^{+0.02}_{-0.02}}$. This correlation is independent of the mass of the clumps and the choice of initial conditions of the simulations in which they formed. (Abridged)

astro-ph.GA

The Rosetta Stone Project. I. A suite of radiative magnetohydrodynamics simulations of high-mass star-forming clumps

Context. Star formation and, in particular, high-mass star formation are key astrophysical processes that are far from being fully understood. Unfortunately, progress in these fields is slow because observations are hard to interpret as they cannot be directly compared to numerical simulations. Synthetic observations are therefore necessary to better constrain the models. Aims. With the Rosetta Stone project, we aim to develop an end-to-end pipeline to compare star formation simulations with observations as accurately as possible in order to study the evolution from clumps scales to stars. Methods. Using the adaptive mesh-refinement code RAMSES, we computed a first grid of model of star-forming clumps to develop our pipeline and explore the impact of the clump initial conditions on their evolution. The main purpose of this set of simulations is to be converted into synthetic observations to enable a direct comparison with real star-forming clumps observed with Herschel and ALMA. Results. The Rosetta Stone simulations presented here provide a catalog available for full post-processing and subsequent comparison with observations (RS1). Among all the parameters explored here, the strength of the magnetic field has the strongest influence on the clump evolution (fragmentation, star formation, global collapse) at both large and small scales. Numerical parameters such as the resolution per Jeans length or the threshold for accretion onto sink particles affects the formation of low-mass sinks. Finally, the widely used L/M ratio is found to be a good indicator of the clump evolutionary state regardless of its initial condition, but this could change when more feedback processes (jets, HII regions) are included. Conclusions. We now have a new suite of simulations of star-forming clumps that is available for full post-processing and subsequent comparison with the observations,

astro-ph.SR

The Rosetta Stone project. III. ALMA synthetic observations of fragmentation in high-mass star-forming clumps

The physical mechanisms that regulate the collapse of high-mass parsec-scale clumps and allow them to form clusters of new stars represent a crucial aspect of star formation. To investigate these mechanisms, we developed the Rosetta Stone project: an end-to-end (simulations-observations) framework that is based on the systematic production of realistic synthetic observations of clump fragmentation and their comparison with real data. In this work, we compare ALMA 1.3mm continuum dust emission observations from the SQUALO survey with a new set of 24 radiative magnetohydrodynamical simulations of high-mass clump fragmentation, post-processed using the CASA software to mimic the observing strategy of SQUALO. The simulations were initialized combining typical values of clump mass (500,1000 solar masses) and radius (~0.4pc) with two levels of turbulence (Mach number of 7,10) and three levels of magnetization (mass-to-flux ratio of ~3,10,100). Following the clump evolution over time with two random seeds projected along three orthogonal directions, we produced a collection of 732 synthetic fields. The synthetic observations of clump fragmentation at ~7000AU revealed between 2 and 14 fragments per field. Among the initial conditions of the simulations, magnetic fields have the largest impact on the fragment multiplicity at these scales. In advanced stages of clump evolution, a lower number of fragments is preferentially associated with magnetized clumps. Fragments identified at ~7000AU correspond to individual or multiple sink particles in ~75% of the cases, suggesting that not all fragments are actively forming stars. Both sinks and fragments accrete mass throughout the whole clump evolution, favoring a scenario in which fragments are not isolated from the environment. Our study demonstrates the importance of synthetic observations in interpreting results from interferometric observations.

astro-ph.SR

Birth of magnetized low-mass protostars and circumstellar disks

Although protostars and disks are often studied separately owing to numerical and observational challenges, breakthroughs in recent years have highlighted the need to study both objects in concert. The role of magnetic fields in this regard must be investigated. We aim to describe the birth of the protostar and that of its disk, as well as their early joint evolution following the second collapse. We wish to study the structure of the nascent star-disk system, while focusing on the innermost sub-AU region. We carry out high resolution 3D RMHD simulations, describing the collapse of dense cloud cores to stellar densities. The calculations reach $\approx 2.3$ yr after protostellar birth. Our simulations are also compared to their hydro counterpart to better isolate the role of magnetic fields. When accounting for ambipolar diffusion, the efficiency of magnetic braking is drastically reduced and the nascent protostar reaches breakup velocity, thus forming a rotationally supported disk. The diffusion of the magnetic field also allows for the implantation of a $\sim \mathrm{kG}$ field in the protostar, which is thereafter maintained. The magnetic field is mainly toroidal in the star-disk system, although a notable vertical component threads it. We also show that the nascent disk is prone to the MRI, although our resolution is inadequate to capture the mechanism. We note a sensitivity of the disk's properties with regards to the angular momentum inherited prior to the second collapse, as well as the magnetic field strength. These calculations carry multiple implications on several issues in stellar formation theory, and offer perspectives for future modeling of the system. Should the fossil field hypothesis to explain the origins of magnetic fields in young stellar objects hold, we show that a $\sim \mathrm{kG}$ field strength may be implanted and maintained in the protostar at birth.

astro-ph.SR

The evolution of the $M_{\mathrm{d}}-M_{\star}$ and $\dot M-M_{\star}$ correlations traces protoplanetary disc dispersal

(Abridged) Observational surveys of entire star-forming regions have provided evidence of power-law correlations between the disc properties and the stellar mass, especially the disc mass (${M_d \propto M_*}^{λ_m}$) and the accretion rate ($\dot M \propto {M_*}^{λ_{acc}}$). Whether the secular disc evolution affects said correlations is still debated: while the purely viscous scenario has been probed, other mechanisms could impact differently. We study the evolution of the slopes $λ_m$ and $λ_{acc}$ in the wind-driven and hybrid case and compare it to the viscous prediction, using a combination of analytical calculations and numerical simulations (performed with the 1D population synthesis code Diskpop, that we also present and release). Assuming $M_d(0) \propto {M_*}^{λ_{m, 0}}$ and $\dot M(0) \propto {M_*}^{λ_{acc, 0}}$ as initial conditions, we find that viscous and hybrid accretion preserve the shape of the correlations and evolve their slope; on the other hand, MHD winds change the shape of the correlations, bending them according to the scaling of the accretion timescale with the stellar mass. We also show how a spread in the initial conditions conceals this behaviour. We then analyse the impact of disc dispersal, and find that the currently available sample sizes ($\sim 30$ discs at 5 Myr) introduce stochastic oscillations in the slopes evolution, which dominate over the physical signatures. Increasing the sample size could mitigate this issue: $\sim 140$ discs at 5 Myr, corresponding to the complete Upper Sco sample, would give small enough error bars to use the evolution of the slopes as a proxy for the driving mechanism of disc evolution. Finally, we discuss how the observational claim of steepening slopes necessarily leads to an initially steeper $M_d - M_*$ correlation with respect to $\dot M - M_*$.

astro-ph.EP

Dust evolution during the protostellar collapse: influence on the coupling between the neutral gas and the magnetic field

The coupling between the magnetic field and the gas during the collapsing phase of star-forming cores is strongly affected by the dust size distribution, which is expected to evolve. We aim to investigate the influence of key parameters on the evolution of the dust distribution as well as on the magnetic resistivities during the protostellar collapse. We perform collapsing single zone simulations with shark. The code computes the evolution of the dust distribution, accounting for different grain growth and destruction processes. It also computes the magnetic resistivities. We find that the dust distribution significantly evolves during the protostellar collapse, shaping the magnetic resistivities. The peak size of the distribution, the population of small grains and consequently the magnetic resistivities are controlled by both coagulation and fragmentation rates. Under standard assumptions, the small grains coagulate very early as they collide by ambipolar drift, yielding magnetic resistivities orders of magnitude away from the non-evolving dust case. In particular, the ambipolar resistivity η_AD is very high prior to nH=10^10 cm^-3, and as a consequence magnetic braking should be ineffective. In this case, large size protoplanetary disks should result, which is inconsistent with recent observations. To alleviate this tension, we identify mechanisms to reduce the ambipolar resistivity during the protostellar collapse. The most promising are namely: electrostatic repulsion and grain-grain erosion. The evolution of the magnetic resistivities during the protostellar collapse and consequently the shape of the magnetic field in the early life of the protoplanetary disk strongly depends on the possibility to repopulate the small grains or to prevent their early coagulation. Therefore, it is crucial to better constrain the collision outcomes and the dust grain elastic properties.

astro-ph.SR

Accuracy of ALMA estimates of young disk radii and masses. Predicted observations from numerical simulations

Protoplanetary disks, which are the natural consequence of the gravitational collapse of the dense molecular cloud cores, host the formation of the known planetary systems in our universe. Substantial efforts have been dedicated to investigating the properties of these disks in the more mature Class II stage, either via numerical simulations of disk evolution from a limited range of initial conditions or observations of their dust continuum and line emission from specific molecular tracers. The results coming from these two standpoints have been used to draw comparisons. However, few studies have investigated the main limitations at work when measuring the embedded Class 0/I disk properties from observations, especially in a statistical fashion. In this study, we provide a first attempt to compare the accuracy of some critical disk parameters in Class 0/I systems, as derived on real ALMA observational data, with the corresponding physical parameters that can be directly defined by theoreticians and modellers in numerical simulations. The approach we follow here is to provide full post-processing of the numerical simulations and apply it to the synthetic observations the same techniques used by observers to derive the physical parameters. We performed 3D Monte Carlo radiative transfer and mock interferometric observations of the disk populations formed in a magnetohydrodynamic (MHD) simulation model of disk formation through the collapse of massive clumps with the tools \textsc{Radmc-3d} and \textsc{Casa}, respectively, to obtain their synthetic observations. With these observations, we re-employed the techniques commonly used in disk modelling from their continuum emissions to infer the properties that would most likely be obtained with real interferometers. We then demonstrated how these properties may vary with respect to the gas kinematics analyses and dust continuum modelling.

astro-ph.EP

Dynamics of dust grains in turbulent molecular clouds. Conditions for decoupling and limits of different numerical implementations

Dust grain dynamics in molecular clouds is regulated by its interplay with supersonic turbulent gas motions. The conditions under which dust grains decouple from the dynamics of gas remain poorly constrained. We first aim to investigate the critical dust grain size for dynamical decoupling, using both analytical predictions and numerical experiments. Second, we aim to set the range of validity of two fundamentally different numerical implementations for the evolution of dust and gas mixtures in turbulent molecular clouds. We carried out a suite of numerical experiments using two different schemes. First, we used a monofluid formalism in the terminal velocity approximation (TVA) on a Eulerian grid. Second, we used a two-fluid scheme, in which the dust dynamics is handled with Lagrangian super-particles, and the gas dynamics on a Eulerian grid. The monofluid results are in good agreement with the theoretical critical size for decoupling. We report dust dynamics decoupling for Stokes number St>0.1, that is, dust grains of $s>4~μ$m in size. We find that the TVA is well suited for grain sizes of 10 $μ$m in molecular clouds, in particular in the densest regions. However, the maximum dust enrichment measured in the low-density material where St>1 is questionable. In the Lagrangian dust experiments, we show that the results are affected by the numerics for all dust grain sizes. At St<<1, the dust dynamics is largely affected by artificial trapping in the high-density regions, leading to spurious variations of the dust concentration. At St>1, the maximum dust enrichment is regulated by the grid resolution used for the gas dynamics. The results of previous similar numerical work should therefore be revisited with respect to the limitations we highlight in this study. Dust enrichment of submicron dust grains is unlikely to occur in the densest parts of molecular clouds.

astro-ph.GA

Fast methods for tracking grain coagulation and ionization. III. Protostellar collapse with non-ideal MHD

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 μm 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.

astro-ph.SR

Protostellar collapse simulations in spherical geometry with dust coagulation and fragmentation

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.

astro-ph.GA

How magnetic field and stellar radiative feedback influences the collapse and the stellar mass spectrum of a massive star forming clump

In spite of decades of theoretical efforts, the physical origin of the stellar initial mass function (IMF) is still debated. We aim at understanding the influence of various physical processes such as radiative stellar feedback, magnetic field and non-ideal magneto-hydrodynamics on the IMF. We present a series of numerical simulations of collapsing 1000 M$_\odot$ clumps taking into account radiative feedback and magnetic field with spatial resolution down to 1 AU. Both ideal and non-ideal MHD runs are performed and various radiative feedback efficiencies are considered. We also develop analytical models that we confront to the numerical results. The sum of the luminosities produced by the stars in the calculations is computed and it compares well with the bolometric luminosities reported in observations of massive star forming clumps. The temperatures, velocities and densities are also found to be in good agreement with recent observations. The stellar mass spectrum inferred for the simulations is, generally speaking, not strictly universal and in particular varies with magnetic intensity. It is also influenced by the choice of the radiative feedback efficiency. In all simulations, a sharp drop in the stellar distribution is found at about $M_{min} \simeq$ 0.1 M$_\odot$, which is likely a consequence of the adiabatic behaviour induced by dust opacities at high densities. As a consequence, when the combination of magnetic and thermal support is not too large, the mass distribution presents a peak located at 0.3-0.5 M$_\odot$. When magnetic and thermal support are large, the mass distribution is better described by a plateau, i.e. $d N / d \log M \propto M^{-Γ}$, $Γ\simeq 0$. Abridged

astro-ph.GA

Chemical Diversity in Protoplanetary Disks and Its Impact on the Formation History of Giant Planets

Giant planets can interact with multiple and chemically diverse environments in protoplanetary discs while they form and migrate to their final orbits. The way this interaction affects the accretion of gas and solids shapes the chemical composition of the planets and of their atmospheres. Here we investigate the effects of different chemical structures of the host protoplanetary disc on the planetary composition. We consider both scenarios of molecular (inheritance from the pre-stellar cloud) and atomic (complete chemical reset) initial abundances in the disc. We focus on four elemental tracers of different volatility: C, O, N, and S. We explore the entire extension of possible formation regions suggested by observations by coupling the disc chemical scenarios with N-body simulations of forming and migrating giant planets. The planet formation process produces giant planets with chemical compositions significantly deviating from that of the host disc. We find that the C/N, N/O, and S/N ratios follow monotonic trends with the extent of migration. The C/O ratio shows a more complex behaviour, dependent on the planet accretion history and on the chemical structure of the formation environment. The comparison between S/N* and C/N* (where * indicates normalisation to the stellar value), constrains the relative contribution of gas and solids to the total metallicity. Giant planets whose metallicity is dominated by the contribution of the gas are characterised by N/O* > C/O* > C/N* and allow for constraining the disc chemical scenario. When the planetary metallicity is instead dominated by the contribution of the solids we find that C/N* > C/O* > N/O*.

astro-ph.EP

Fast methods to track grain coagulation and ionization. II. Extension to thermal ionization

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.

astro-ph.SR

Protoplanetary disk birth in massive star forming clumps: the essential role of the magnetic field

Protoplanetary disks form through angular momentum conservation in collapsing dense cores. In this work, we perform the first simulations with a maximal resolution down to the astronomical unit (au) of protoplanetary disk formation, through the collapse of 1000 solar mass clumps, treating self-consistently both non-ideal magnetohydrodynamics with ambipolar diffusion as well as radiative transfer in the flux-limited diffusion approximation including stellar feedback. Using the adaptive mesh-refinement code RAMSES, we investigate the influence of the magnetic field on the disks properties with three models. We show that, without magnetic fields, a population dominated by large disks is formed, which is not consistent with Class 0 disk properties as estimated from observations. The inclusion of magnetic field leads, through magnetic braking, to a very different evolution. When it is included, small < 50 au disks represent about half the population. In addition, about ~ 70% of the stars have no disk in this case which suggests that our resolution is still insufficient to preserve the smaller disks. With ambipolar diffusion, the proportion of small disks is also prominent and we report a flat mass distribution around 0.01-0.1 solar mass and a typical disk-to-star mass ratios of ~0.01-0.1. This work shows that the magnetic field and its evolution plays a prominent role in setting the initial properties of disk populations.

astro-ph.SR

Fast methods for tracking grain coagulation and ionization. I. Analytic derivation

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 reasonably 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.

astro-ph.GA