Context.
Planets form in protoplanetary discs. Their masses, distribution, and orbits sensitively depend on the structure of the protoplanetary discs. However, what sets the initial structure of the ...discs in terms of mass, radius and accretion rate is still unknown.
Aims.
It is therefore of great importance to understand exactly how protoplanetary discs form and what determines their physical properties. We aim to quantify the role of the initial dense core magnetisation, rotation, turbulence, and misalignment between rotation and magnetic field axis as well as the role of the accretion scheme onto the central object.
Methods.
We performed non-ideal magnetohydrodynamics numerical simulations using the adaptive mesh refinement code Ramses of a collapsing, one solar mass molecular core to study the disc formation and early, up to 100 kyr, evolution. We paid particular attention to the impact of numerical resolution and accretion scheme.
Results.
We found that the mass of the central object is almost independent of the numerical parameters such as the resolution and the accretion scheme onto the sink particle. The disc mass and to a lower extent its size, however heavily depend on the accretion scheme, which we found is itself resolution dependent. This implies that the accretion onto the star and through the disc are largely decoupled. For a relatively large domain of initial conditions (except at low magnetisation), we found that the properties of the disc do not change too significantly. In particular both the level of initial rotation and turbulence do not influence the disc properties provide the core is sufficiently magnetised. After a short relaxation phase, the disc settles in a stationary state. It then slowly grows in size but not in mass. The disc itself is weakly magnetised but its immediate surrounding on the contrary is highly magnetised.
Conclusions.
Our results show that the disc properties directly depend on the inner boundary condition, i.e. the accretion scheme onto the central object. This suggests that the disc mass is eventually controlled by a small-scale accretion process, possibly the star-disc interaction. Because of ambipolar diffusion and its significant resistivity, the disc diversity remains limited and except for low magnetisation, their properties are weakly sensitive to initial conditions such as rotation and turbulence.
In spite of decades of theoretical efforts, the physical origin of the stellar initial mass function (IMF) is still debated. Particularly crucial is the question of what sets the peak of the ...distribution. To investigate this issue, we perform high-resolution numerical simulations with radiative feedback exploring, in particular, the role of the stellar and accretion luminosities. We also perform simulations with a simple effective equation of state (EOS), and we investigate 1000 solar-mass clumps having, respectively, 0.1 and 0.4 pc of initial radii. We found that most runs, both with radiative transfer or an EOS, present similar mass spectra with a peak broadly located around 0.3-0.5 M and a power-law-like mass distribution at higher masses. However, when accretion luminosity is accounted for, the resulting mass spectrum of the most compact clump tends to be moderately top-heavy. The effect remains limited for the less compact one, which overall remains colder. Our results support the idea that rather than the radiative stellar feedback, this is the transition from the isothermal to the adiabatic regime, which occurs at a gas density of about 1010 cm−3, that is responsible for setting the peak of the IMF. This stems from (i) the fact that extremely compact clumps for which the accretion luminosity has a significant influence are very rare and (ii) the luminosity problem, which indicates that the effective accretion luminosity is likely weaker than expected.
Context. The temperature of the interstellar medium (ISM) is governed by several physical processes, including radiative cooling, external UV/cosmic-ray heating, and mechanical work due to ...compression and expansion. In regimes where the dynamical effect is important, the temperature deviates from that derived by simply balancing the heating and cooling functions. This renders the expression of the gas energy evolution with a simple equation of state (EOS) less straightforward. Aims. Given a cooling function, the behavior of the gas is subject to the combined effect of dynamical compression and radiative cooling. The goal of the present work is to derive the effective EOS of a collapsing gas within a full fluid solution. Methods. We solved the Navier-Stokes equations with a parametric cooling term in spherical coordinates, and looked for a self-similar collapse solution. Results. We present a solution that describes a cloud that is contracting while losing energy through radiation. This yields an effective EOS that can be generally applied to various ISM contexts, where the cooling function is available from first principles and is expressed as a power-law product of the density and temperature. Conclusions. Our findings suggest that a radiatively cooling gas under self-gravitating collapse can easily manifest an effective polytropic EOS, even isothermal in many scenarios. The present model provides theoretical justification for the simplifying isothermal assumptions of simulations at various scales, and can also provide a more realistic thermal recipe without additional computation costs.
The stellar initial mass function plays a critical role in the history of our universe. We propose a theory that is based solely on local processes, namely the dust opacity limit, the tidal forces, ...and the properties of the collapsing gas envelope. The idea is that the final mass of the central object is determined by the location of the nearest fragments, which accrete the gas located farther away, preventing it from falling onto the central object. To estimate the relevant statistics in the neighborhood of an accreting protostar, we perform high-resolution numerical simulations. We also use these simulations to further test the idea that fragmentation in the vicinity of an existing protostar is a determinant in setting the peak of the stellar spectrum. We develop an analytical model, which is based on a statistical counting of the turbulent density fluctuations, generated during the collapse, that have a mass at least equal to the mass of the first hydrostatic core, and sufficiently important to supersede tidal and pressure forces to be self-gravitating. The analytical mass function presents a peak located at roughly 10 times the mass of the first hydrostatic core, in good agreement with the numerical simulations. Since the physical processes involved are all local, occurring at scales of a few 100 au or below, and do not depend on the gas distribution at large scale and global properties such as the mean Jeans mass, the mass spectrum is expected to be relatively universal.
Observations suggest that star formation in filamentary molecular clouds occurs in a two-step process, with the formation of filaments preceding that of prestellar cores and stars. Here, we apply the ...gravoturbulent fragmentation theory of Hennebelle & Chabrier to a filamentary environment, taking into account magnetic support. We discuss the induced geometrical effect on the cores, with a transition from 3D geometry at small scales to 1D at large ones. The model predicts the fragmentation behavior of a filament for a given mass per unit length (MpL) and level of magnetization. This core mass function (CMF) for individual filaments is then convolved with the distribution of filaments to obtain the final system CMF. The model yields two major results. (i) The filamentary geometry naturally induces a hierarchical fragmentation process, first into groups of cores, separated by a length equal to a few filament Jeans lengths, i.e., a few times the filament width. These groups then fragment into individual cores. (ii) Non-magnetized filaments with high MpL are found to fragment excessively, at odds with observations. This is resolved by taking into account the magnetic field (treated simply as additional pressure support). The present theory suggests two complementary modes of star formation: although small (spherical or filamentary) structures will collapse directly into prestellar cores, according to the standard Hennebelle-Chabrier theory, the large (filamentary) ones, the dominant population according to observations, will follow the aforedescribed two-step process.
Context.
Understanding the origin of the initial mass function (IMF) of stars is a major problem for the star formation process and beyond.
Aim.
We investigate the dependence of the peak of the IMF ...on the physics of the so-called first Larson core, which corresponds to the point where the dust becomes opaque to its own radiation.
Methods.
We performed numerical simulations of collapsing clouds of 1000
M
⊙
for various gas equations of state (eos), paying great attention to the numerical resolution and convergence. The initial conditions of these numerical experiments are varied in the companion paper. We also develop analytical models that we compare to our numerical results.
Results.
When an isothermal eos is used, we show that the peak of the IMF shifts to lower masses with improved numerical resolution. When an adiabatic eos is employed, numerical convergence is obtained. The peak position varies with the eos, and using an analytical model to infer the mass of the first Larson core, we find that the peak position is about ten times its value. By analyzing the stability of nonlinear density fluctuations in the vicinity of a point mass and then summing over a reasonable density distribution, we find that tidal forces exert a strong stabilizing effect and likely lead to a preferential mass several times higher than that of the first Larson core.
Conclusions.
We propose that in a sufficiently massive and cold cloud, the peak of the IMF is determined by the thermodynamics of the high-density adiabatic gas as well as the stabilizing influence of tidal forces. The resulting characteristic mass is about ten times the mass of the first Larson core, which altogether leads to a few tenths of solar masses. Since these processes are not related to the large-scale physical conditions and to the environment, our results suggest a possible explanation for the apparent universality of the peak of the IMF.
Context.
Between the two research communities that study star formation and protoplanetary disk evolution, only a few efforts have been made to understand and bridge the gap between studies of a ...collapsing prestellar core and a developed disk. While it has generally been accepted for about a decade that the magnetic field and its nonideal effects play important roles during the stellar formation, simple models of pure hydrodynamics and angular momentum conservation are still widely employed in the studies of disk assemblage in the framework of the so-called alpha-disk model because these models are simple.
Aims.
We revisit the assemblage phase of the protoplanetary disk and employ current knowledge of the prestellar core collapse.
Methods.
We performed 3D magnetohydrodynamic (MHD) simulations with ambipolar diffusion and full radiative transfer to follow the formation of the protoplanetary disk within a collapsing prestellar core. The global evolution of the disk and its internal properties were analyzed to understand how the infalling envelope regulates the buildup and evolution of the disk. We followed the global evolution of the protoplanetary disk from the prestellar core collapse during 100 kyr with a reasonable resolution of AU. Two snapshots from this reference run were extracted and rerun with significantly increased resolution to resolve the interior of the disk.
Results.
The disk that formed under our simulation setup is more realistic and agrees with recent observations of disks around class 0 young stellar objects. The source function of the mass flux that arrives at the disk and the radial mass accretion rate within the disk are measured and compared to analytical self-similar models based on angular momentum conservation. The source function is very centrally peaked compared to classical hydrodynamical models, implying that most of the mass falling onto the star does not transit through the midplane of the disk. We also found that the disk midplane is almost dead to turbulence, whereas upper layers and the disk outer edge are highly turbulent, and this is where the accretion occurs. The snow line, located at about 5–10 AU during the infall phase, is significantly farther away from the center than in a passive disk. This result might be of numerical origin.
Conclusions.
We studied self-consistent protoplanetary disk formation from prestellar core collapse, taking nonideal MHD effects into account. We developed a zoomed rerun technique to quickly obtain a reasonable disk that is highly stratified, weakly magnetized inside, and strongly magnetized outside. During the class 0 phase of protoplanetary disk formation, the interaction between the disk and the infalling envelope is important and ought not be neglected. We measured the complex flow pattern and compared it to the classical models of pure hydrodynamical infall. Accretion onto the star is found to mostly depend on dynamics at large scales, that is, the collapsing envelope, and not on the details of the disk structure.
Context.
Stars constitute the building blocks of our Universe, and their formation is an astrophysical problem of great importance.
Aim.
We aim to understand the fragmentation of massive molecular ...star-forming clumps and the effect of initial conditions, namely the density and the level of turbulence, on the resulting distribution of stars. For this purpose, we conduct numerical experiments in which we systematically vary the initial density over four orders of magnitude and the turbulent velocity over a factor ten. In a companion paper, we investigate the dependence of this distribution on the gas thermodynamics.
Methods.
We performed a series of hydrodynamical numerical simulations using adaptive mesh refinement, with special attention to numerical convergence. We also adapted an existing analytical model to the case of collapsing clouds by employing a density probability distribution function (PDF) ∝
ρ
−1.5
instead of a lognormal distribution.
Results.
Simulations and analytical model both show two support regimes, a thermally dominated regime and a turbulence-dominated regime. For the first regime, we infer that d
N
∕d log
M
∝
M
0
, while for the second regime, we obtain d
N
∕d log
M
∝
M
−3∕4
. This is valid up to about ten times the mass of the first Larson core, as explained in the companion paper, leading to a peak of the mass spectrum at ~0.2
M
⊙
. From this point, the mass spectrum decreases with decreasing mass except for the most diffuse clouds, where disk fragmentation leads to the formation of objects down to the mass of the first Larson core, that is, to a few 10
−2
M
⊙
.
Conclusions.
Although the mass spectra we obtain for the most compact clouds qualitatively resemble the observed initial mass function, the distribution exponent is shallower than the expected Salpeter exponent of − 1.35. Nonetheless, we observe a possible transition toward a slightly steeper value that is broadly compatible with the Salpeter exponent for masses above a few solar masses. This change in behavior is associated with the change in density PDF, which switches from a power-law to a lognormal distribution. Our results suggest that while gravitationally induced fragmentation could play an important role for low masses, it is likely the turbulently induced fragmentation that leads to the Salpeter exponent.
Abstract
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.
Context. Stars are often observed to form in clusters and it is therefore important to understand how such a region of concentrated mass is assembled out of the diffuse medium. The properties of such ...a region eventually prescribe the important physical mechanisms and determine the characteristics of the stellar cluster. Aims. We study the formation of a gaseous protocluster inside a molecular cloud and associate its internal properties with those of the parent cloud by varying the level of the initial turbulence of the cloud with a view to better characterize the subsequent stellar cluster formation. Methods. We performed high resolution magnetohydrodynamic (MHD) simulations of gaseous protoclusters forming in molecular clouds collapsing under self-gravity. We determined ellipsoidal cluster regions via gas kinematics and sink particle distribution, permitting us to determine the mass, size, and aspect ratio of the cluster. We studied the cluster properties, such as kinetic and gravitational energy, and made links to the parent cloud. Results. The gaseous protocluster is formed out of global collapse of a molecular cloud and has non-negligible rotation owing to angular momentum conservation during the collapse of the object. Most of the star formation occurs in this region, which occupies only a small volume fraction of the whole cloud. This dense entity is a result of the interplay between turbulence and gravity. We identify such regions in simulations and compare the gas and sink particles to observed star-forming clumps and embedded clusters, respectively. The gaseous protocluster inferred from simulation results presents a mass-size relation that is compatible with observations. We stress that the stellar cluster radius, although clearly correlated with the gas cluster radius, depends sensitively on its definition. Energy analysis is performed to confirm that the gaseous protocluster is a product of gravoturbulent reprocessing and that the support of turbulent and rotational energy against self-gravity yields a state of global virial equilibrium, although collapse is occurring at a smaller scale and the cluster is actively forming stars. This object then serves as the antecedent of the stellar cluster, to which the energy properties are passed on. Conclusions. The gaseous protocluster properties are determined by the parent cloud out of which it forms, while the gas is indeed reprocessed and constitutes a star-forming environment that is different from that of the parent cloud.
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