We investigate the conditions of ideal magnetohydrodynamic (MHD) turbulence responsible for the relative orientation between density gradients (∇ρ) and magnetic fields (B) in molecular clouds (MCs). ...For that purpose, we construct an expression for the time evolution of the angle (φ) between ∇ρ and B based on the transport equations of MHD turbulence. Using this expression, we find that the configuration where ∇ρ and B are mostly parallel, cosφ = ± 1, and where ∇ρ and B are mostly perpendicular, cosφ = 0, constitute equilibrium points, that is, the system tends to evolve towards either of these configurations and they are more represented than others. This would explain the predominant alignment or anti-alignment between column density (NH) structures and the projected magnetic field orientation (⟨B̂⊥⟩) reported in observations. Additionally, we find that departures from the cosφ = 0 configurations are related to convergent flows, quantified by the divergence of the velocity field (∇·v) in the presence of a relatively strong magnetic field. This would explain the observed change in relative orientation between NH structures and ⟨B̂⊥⟩ towards MCs, from mostly parallel at low NH to mostly perpendicular at the highest NH, as the result of the gravitational collapse and/or convergence of flows. Finally, we show that the density threshold that marks the observed change in relative orientation towards MCs, from NH and ⟨B̂⊥⟩ being mostly parallel at low NH to mostly perpendicular at the highest NH, is related to the magnetic field strength and constitutes a crucial piece of information for determining the role of the magnetic field in the dynamics of MCs.
Context. Theoretical studies of collapsing clouds have found that even a relatively weak magnetic field may prevent the formation of disks and their fragmentation. However, most previous studies have ...been limited to cases where the magnetic field and the rotation axis of the cloud are aligned. Aims. We study the transport of angular momentum, and its effects on disk formation, for non-aligned initial configurations and a range of magnetic intensities. Methods. We perform three-dimensional, adaptive mesh, numerical simulations of magnetically supercritical collapsing dense cores using the magneto-hydrodynamic code Ramses. We compute the contributions of all the relevant processes transporting angular momentum, in both the envelope and the region of the disk. We clearly define centrifugally supported disks and thoroughly study their properties. Results. At variance with earlier analyses, we show that the transport of angular momentum acts less efficiently in collapsing cores with non-aligned rotation and magnetic field. Analytically, this result can be understood by taking into account the bending of field lines occurring during the gravitational collapse. For the transport of angular momentum, we conclude that magnetic braking in the mean direction of the magnetic field tends to dominate over both the gravitational and outflow transport of angular momentum. We find that massive disks, containing at least 10% of the initial core mass, can form during the earliest stages of star formation even for mass-to-flux ratios as small as three to five times the critical value. At higher field intensities, the early formation of massive disks is prevented. Conclusions. Given the ubiquity of Class I disks, and because the early formation of massive disks can take place at moderate magnetic intensities, we speculate that for stronger fields, disks will form later, when most of the envelope will have been accreted. In addition, we speculate that some observed early massive disks may actually be outflow cavities, mistaken for disks by projection effects.
Context. In the context of star and planet formation, understanding the formation of disks is of fundamental importance. Aims. Previous studies found that the magnetic field has a very strong impact ...on the collapse of a prestellar cloud, by possibly suppressing the formation of a disk even for relatively modest values of the magnetic intensity. Since observations infer that cores have a substantial level of magnetization, this raises the question of how disks form. However, most studies have been restricted to the case in which the initial angle, α, between the magnetic field and the rotation axis equals 0°. Here we explore and analyse the influence of non aligned configurations on disk formation. Methods. We perform 3D ideal MHD, AMR numerical simulations for various values of μ, the ratio of the mass-to-flux to the critical mass-to-flux, and various values of α. Results. We find that disks form more easily as α increases from 0 to 90°. We propose that as the magnetized pseudo-disks become thicker with increasing α, the magnetic braking efficiency is lowered. We also find that even small values of α ($\simeq$10–20°) show significant differences with the aligned case. Conclusions. Within the framework of ideal MHD, and for our choice of initial conditions, centrifugally supported disks cannot form for values of μ smaller than $\simeq$3 when the magnetic field and the rotation axis are perpendicular, and smaller than about $\simeq$5–10 when they are perfectly aligned.
Context. It is believed that the majority of stars form in clusters. Therefore it is likely that the gas physical conditions that prevail in forming clusters largely determine the properties of stars ...that form, in particular, the initial mass function (IMF). Aims. We develop an analytical model to account for the formation of low-mass clusters and the formation of stars within clusters. Methods. The formation of clusters is determined by an accretion rate, the virial equilibrium, as well as energy and thermal balance. For this, both molecular and dust cooling are considered using published rates. The star distribution is computed within the cluster using the physical conditions inferred from this model and the Hennebelle & Chabrier theory. Results. Our model reproduces well the mass-size relation of low-mass clusters (up to a few ≃ 103M⊙ of stars corresponding to about five times more gas) and an IMF that is i) very close to the Chabrier IMF, ii) weakly dependent on the mass of the clusters, iii) relatively robust to (i.e. not too steeply dependent on) variations in physical quantities such as accretion rate, radiation, and cosmic ray abundances. Conclusions. The weak dependence of the mass distribution of stars on the cluster mass results from the compensation between varying clusters densities, velocity dispersions, and temperatures that are all inferred from first physical principles. This constitutes a possible explanation for the apparent universality of the IMF within the Galaxy, although variations with the local conditions may certainly be observed.
We develop a detailed chemical network relevant to calculate the conditions that are 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 nH = 1012 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.
Context. Cosmic rays play an important role in dense molecular cores, affecting their thermal and dynamical evolution and initiating the chemistry. Several studies have shown that the formation of ...protostellar discs in collapsing clouds is severely hampered by the braking torque exerted by the entrained magnetic field on the infalling gas, as long as the field remains frozen to the gas. Aims. In this paper we examine the possibility that the concentration and twisting of the field lines in the inner region of collapse can produce a significant reduction of the ionisation fraction. Methods. To check whether the cosmic-ray ionisation rate can fall below the critical value required to maintain good coupling, we first study the propagation of cosmic rays in a model of a static magnetised cloud varying the relative strength of the toroidal/poloidal components and the mass-to-flux ratio. We then follow the path of cosmic rays using realistic magnetic field configurations generated by numerical simulations of a rotating collapsing core with different initial conditions. Results. We find that an increment of the toroidal component of the magnetic field, or, in general, a more twisted configuration of the field lines, results in a decrease in the cosmic-ray flux. This is mainly due to the magnetic mirroring effect that is stronger where larger variations in the field direction are present. In particular, we find a decrease of the cosmic-ray ionisation rate below 10-18 s-1 in the central 300–400 AU, where density is higher than about 109 cm-3. This very low value of the ionisation rate is attained in the cases of intermediate and low magnetisation (mass-to-flux ratio λ = 5 and 17, respectively) and for toroidal fields larger than about 40% of the total field. Conclusions. Magnetic field effects can significantly reduce the ionisation fraction in collapsing clouds. We provide a handy fitting formula to compute approximately the attenuation of the cosmic-ray ionisation rate in a molecular cloud as a function of the density and the magnetic configuration.
Context. Even though turbulent motions are found everywhere in astrophysical systems, the origin of this turbulence is poorly understood. When cosmic structures form, they grow in mass via accretion ...from their surrounding environment. Aims. We propose that accretion is able to drive internal turbulent motions in a wide range of astrophysical objects and study this process in the case of galaxies, molecular clouds, and protoplanetary disks. Methods. We use a combination of numerical simulations and analytical arguments to predict the level of turbulence as a function of the accretion rate, the dissipation scale, and the density contrast, and compare our models with observational data. Results. We find that in Milky Way type galaxies the observed level of turbulence in the interstellar medium can be explained by accretion, provided that the galaxies gain mass at a rate comparable to the rate at which they form stars. This process is particularly relevant in the extended outer disks beyond the star-forming radius. For it to drive turbulence in dwarf galaxies, the accretion rate needs to exceed the star formation rate by a large factor, so we expect other sources to dominate. We also calculate the rate at which molecular clouds grow in mass when they build up from the atomic component of the galactic gas and find that their internal turbulence is likely to be driven by accretion as well. It is the very process of cloud formation that excites turbulent motions on small scales by establishing the turbulent cascade. In the case of T Tauri disks, we show that accretion can drive subsonic turbulence if the rate at which gas falls onto the disk is comparable to the rate at which disk material accretes onto the central star. This also explains the observed relation of accretion rate and stellar mass, $\dot{M}$ $\propto$ $M_\star^{1.8}$. The efficiency required to convert infall motion into turbulence is a few percent in all three cases. Conclusions. We conclude that accretion-driven turbulence is a universal concept with far-reaching implications for a wide range of astrophysical objects.
Angular momentum transport and the formation of rotationally supported structures are major issues in our understanding of protostellar core formation. Whereas purely hydrodynamical simulations lead ...to large Keplerian disks, ideal magnetohydrodynamics (MHD) models yield the opposite result, with essentially no disk formation. We focus more particularly on the effect of ambipolar diffusion on the properties of the first Larson core and its surrounding structure, exploring various initial magnetisations and magnetic field versus rotation axis orientations of a 1 M collapsing prestellar dense core. We used the non-ideal magnetohydrodynamics version of the adaptive mesh refinement code RAMSES to carry out these calculations. In all cases, these disks remain significantly smaller than disks found in pure hydrodynamical simulations. Ambipolar diffusion thus bears a crucial impact on the regulation of magnetic flux and angular momentum transport during the collapse of a prestellar core and the formation of the resulting protostellar core-disk system, enabling the formation and growth of rotationally supported structures.
Context.
Understanding the initial properties of star forming material and how they affect the star formation process is a key question. The infalling gas must redistribute most of its initial ...angular momentum inherited from prestellar cores before reaching the central stellar embryo. Disk formation has been naturally considered as a possible solution to this “angular momentum problem”. However, how the initial angular momentum of protostellar cores is distributed and evolves during the main accretion phase and the beginning of disk formation has largely remained unconstrained up to now.
Aims.
In the framework of the IRAM CALYPSO survey, we obtained observations of the dense gas kinematics that we used to quantify the amount and distribution of specific angular momentum at all scales in collapsing-rotating Class 0 protostellar envelopes.
Methods.
We used the high dynamic range C
18
O (2−1) and N
2
H
+
(1−0) datasets to produce centroid velocity maps and probe the rotational motions in the sample of 12 envelopes from scales ~50 to ~5000 au.
Results.
We identify differential rotation motions at scales ≲1600 au in 11 out of the 12 protostellar envelopes of our sample by measuring the velocity gradient along the equatorial axis, which we fit with a power-law model v ∝
r
α
. This suggests that coherent motions dominate the kinematics in the inner protostellar envelopes. The radial distributions of specific angular momentum in the CALYPSO sample suggest the following two distinct regimes within protostellar envelopes: the specific angular momentum decreases as
j
∝
r
1.6±0.2
down to ~1600 au and then tends to become relatively constant around ~6 × 10
−4
km s
−1
pc down to ~50 au.
Conclusions.
The values of specific angular momentum measured in the inner Class 0 envelopes suggest that material directly involved in the star formation process (<1600 au) has a specific angular momentum on the same order of magnitude as what is inferred in small T-Tauri disks. Thus, disk formation appears to be a direct consequence of angular momentum conservation during the collapse. Our analysis reveals a dispersion of the directions of velocity gradients at envelope scales >1600 au, suggesting that these gradients may not be directly related to rotational motions of the envelopes. We conclude that the specific angular momentum observed at these scales could find its origin in other mechanisms, such as core-forming motions (infall, turbulence), or trace an imprint of the initial conditions for the formation of protostellar cores.
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