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Cosmic rays (CR) 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. 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. To check whether the CR ionisation rate (CRir) can fall below the critical value required to maintain good coupling, we first study the propagation of CRs 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 CRs using realistic magnetic field configurations generated by numerical simulations of a rotating collapsing core. 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 CR 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 CRir below 10^-18 s-1 in the central 300-400 AU, where density is higher than about 10^9 cm-3. This very low value of the CRir is attained in the cases of intermediate and low magnetisation (mass-to-flux ratio lambda=5 and 17, respectively) and for toroidal fields larger than about 40% of the total field. 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 CRir in a molecular cloud as a function of the density and the magnetic configuration.
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Galactic cosmic rays are a ubiquitous source of ionisation of the interstellar gas, competing with UV and X-ray photons as well as natural radioactivity in determining the fractional abundance of electrons, ions and charged dust grains in molecular clouds and circumstellar discs. We model the propagation of different components of Galactic cosmic rays versus the column density of the gas. Our study is focussed on the propagation at high densities, above a few g cm$^{-2}$, especially relevant for the inner regions of collapsing clouds and circumstellar discs. The propagation of primary and secondary CR particles (protons and heavier nuclei, electrons, positrons, and photons) is computed in the continuous slowing down approximation, diffusion approximation, or catastrophic approximation, by adopting a matching procedure for the different transport regimes. A choice of the proper regime depends on the nature of the dominant loss process, modelled as continuous or catastrophic. The CR ionisation rate is determined by CR protons and their secondary electrons below $approx 130$ g cm$^{-2}$ and by electron/positron pairs created by photon decay above $approx600$ g cm$^{-2}$. We show that a proper description of the particle transport is essential to compute the ionisation rate in the latter case, since the electron/positron differential fluxes depend sensitively on the fluxes of both protons and photons. Our results show that the CR ionisation rate in high-density environments, like, e.g., the inner parts of collapsing molecular clouds or the mid-plane of circumstellar discs, is larger than previously assumed. It does not decline exponentially with increasing column density, but follows a more complex behaviour due to the interplay of different processes governing the generation and propagation of secondary particles.
We discuss the mechanism of cluster formation in hierarchically collapsing molecular clouds. Recent evidence, both observational and numerical, suggests that molecular clouds (MCs) may be undergoing global, hierarchical gravitational collapse. The hierarchical regime consists of small-scale collapses within larger-scale ones. The latter implies that the star formation rate increases systematically during the early stages of evolution, and occurs via filamentary flows onto hubs of higher density, mass, and velocity dispersion, and culminates a few Myr after than the small-scale collapses have started to form stars. In turn, the small-scale collapses occur in clumps embedded in the filaments, and are themselves falling into the larger potential well of the still-ongoing large-scale collapse. The stars formed in the early, small-scale collapses share the infall motion of their parent clumps towards the larger potential trough, so that the filaments feed both gaseous and stellar material to the hubs. This leads to the presence of older stars in a region where new protostars are still forming, to a scale-free or fractal structure of the clusters, in which each unit is composed of smaller-scale ones, and to the eventual merging of the subunits, explaining the observed structural features of open clusters.
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Marco Padovani Laboratoire den Radioastronomie Millimetrique
, Ecole Normale Superieure et Observatoiren de Paris
2013
Cosmic-rays constitute the main ionising and heating agent in dense, starless, molecular cloud cores. We reexamine the physical quantities necessary to determine the cosmic-ray ionisation rate (especially the cosmic ray spectrum at E < 1 GeV and the ionisation cross sections), and calculate the ionisation rate as a function of the column density of molecular hydrogen. Available data support the existence of a low-energy component (below about 100 MeV) of cosmic-ray electrons or protons responsible for the ionisation of diffuse and dense clouds. We also compute the attenuation of the cosmic-ray flux rate in a cloud core taking into account magnetic focusing and magnetic mirroring, following the propagation of cosmic rays along flux tubes enclosing different amount of mass and mass-to-flux ratios. We find that mirroring always dominates over focusing, implying a reduction of the cosmic-ray ionisation rate by a factor of 3-4 depending on the position inside the core and the magnetisation of the core.
We discuss the mechanism of cluster formation in a numerical simulation of a molecular cloud (MC) undergoing global hierarchical collapse (GHC). The global nature of the collapse implies that the SFR increases over time. The hierarchical nature of the collapse consists of small-scale collapses within larger-scale ones. The large-scale collapses culminate a few Myr later than the small-scale ones and consist of filamentary flows that accrete onto massive central clumps. The small-scale collapses form clumps that are embedded in the filaments and falling onto the large-scale collapse centers. The stars formed in the early, small-scale collapses share the infall motion of their parent clumps. Thus, the filaments feed both gaseous and stellar material to the massive central clump. This leads to the presence of a few older stars in a region where new protostars are forming, and also to a self-similar structure, in which each unit is composed of smaller-scale sub-units that approach each other and may merge. Because the older stars formed in the filaments share the infall motion of the gas onto the central clump, they tend to have larger velocities and to be distributed over larger areas than the younger stars formed in the central clump. Finally, interpreting the IMF at face-value as a probability distribution implies that massive stars only form once the {it local} SFR is large enough to sample the IMF up to high masses. In combination with the increase of the SFR, this implies that massive stars tend to appear late in the evolution of the MC, and only in the central massive clumps. We discuss the correspondence of these features with observed properties of young stellar clusters, finding very good qualitative agreement, thus providing support to the scenario of global, hierarchical collapse of MCs, while explaining the origin of the observed cluster structure.
Formation of stars is now believed to be tightly linked to the dynamical evolution of interstellar filaments in which they form. In this paper we analyze the density structure and kinematics of a small network of infrared dark filaments, SDC13, observed in both dust continuum and molecular line emission with the IRAM 30m telescope. These observations reveal the presence of 18 compact sources amongst which the two most massive, MM1 and MM2, are located at the intersection point of the parsec-long filaments. The dense gas velocity and velocity dispersion observed along these filaments show smooth, strongly correlated, gradients. We discuss the origin of the SDC13 velocity field in the context of filament longitudinal collapse. We show that the collapse timescale of the SDC13 filaments (from 1 Myr to 4 Myr depending on the model parameters) is consistent with the presence of Class I sources in them, and argue that, on top of bringing more material to the centre of the system, collapse could generate additional kinematic support against local fragmentation, helping the formation of starless super-Jeans cores.
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