Interstellar dust charging in dense molecular clouds: cosmic ray effects

The local cosmic-ray (CR) spectra are calculated for typical characteristic regions of a cold dense molecular cloud, to investigate two so far neglected mechanisms of dust charging: collection of suprathermal CR electrons and protons by grains, and photoelectric emission from grains due to the UV radiation generated by CRs. The two mechanisms add to the conventional charging by ambient plasma, produced in the cloud by CRs. We show that the CR-induced photoemission can dramatically modify the charge distribution function for submicron grains. We demonstrate the importance of the obtained results for dust coagulation: While the charging by ambient plasma alone leads to a strong Coulomb repulsion between grains and inhibits their further coagulation, the combination with the photoemission provides optimum conditions for the growth of large dust aggregates in a certain region of the cloud, corresponding to the densities $n(mathrm{H_2})$ between $sim10^4$ cm$^{-3}$ and $sim10^6$ cm$^{-3}$. The charging effect of CR is of generic nature, and therefore is expected to operate not only in dense molecular clouds but also in the upper layers and the outer parts of protoplanetary discs.

Cosmic-ray propagation at small scale: a support for protostellar disc formation

As long as magnetic fields remain frozen into the gas, the magnetic braking prevents the formation of protostellar discs. This condition is subordinate to the ionisation fraction characterising the inmost parts of a collapsing cloud. The ionisation level is established by the number and the energy of the cosmic rays able to reach these regions. Adopting the method developed in our previous studies, we computed how cosmic rays are attenuated as a function of column density and magnetic field strength. We applied our formalism to low- and high-mass star formation models obtained by numerical simulations of gravitational collapse that include rotation and turbulence. In general, we found that the decoupling between gas and magnetic fields, condition allowing the collapse to go ahead, occurs only when the cosmic-ray attenuation is taken into account with respect to a calculation in which the cosmic-ray ionisation rate is kept constant. We also found that the extent of the decoupling zone also depends on the dust grain size distribution and is larger if large grains (of radius about 0.1 microns) are formed by compression and coagulation during cloud collapse. The decoupling region disappears for the high-mass case due to magnetic field diffusion that is caused by turbulence and that is not included in the low-mass models. We infer that a simultaneous study of the cosmic-ray propagation during the clouds collapse may lead to values of the gas resistivity in the innermost few hundred AU around a forming protostar that is higher than generally assumed.

The role of cosmic rays on magnetic field diffusion and the formation of protostellar discs

The formation of protostellar discs is severely hampered by magnetic braking, as long as magnetic fields remain frozen in the gas. The latter condition depends on the levels of ionisation that characterise the innermost regions of a collapsing cloud. The chemistry of dense cloud cores and, in particular, the ionisation fraction is largely controlled by cosmic rays. The aim of this paper is to evaluate whether the attenuation of the flux of cosmic rays expected in the regions around a forming protostar is sufficient to decouple the field from the gas, thereby influencing the formation of centrifugally supported disc. We adopted the method developed in a former study to compute the attenuation of the cosmic-ray flux as a function of the column density and the field strength in clouds threaded by poloidal and toroidal magnetic fields. We applied this formalism to models of low- and high-mass star formation extracted from numerical simulations of gravitational collapse that include rotation and turbulence. For each model we determine the size of the magnetic decoupling zone, where collapse or rotation motion becomes unaffected by the local magnetic field. In general, we find that decoupling only occurs when the attenuation of cosmic rays is taken into account with respect to a calculation in which the cosmic-ray ionisation rate is kept constant. The extent of the decoupling zone also depends on the dust grain size distribution and is larger if large grains (of radius $sim 10^{-5}$ cm) are formed by compression and coagulation during cloud collapse. We conclude that a realistic treatment of cosmic-ray propagation and attenuation during cloud collapse may lead to a value of the resistivity of the gas in the innermost few hundred AU around a forming protostar that is higher than generally assumed.

Cosmic rays as regulators of molecular cloud properties

Cosmic rays are the main agents in controlling the chemical evolution and setting the ambipolar diffusion time of a molecular cloud. We summarise the processes causing the energy degradation of cosmic rays due to their interaction with molecular hydrogen, focusing on the magnetic effects that influence their propagation. Making use of magnetic field configurations generated by numerical simulations, we show that the increase of the field line density in the collapse region results in a reduction of the cosmic-ray ionisation rate. As a consequence the ionisation fraction decreases, facilitating the decoupling between the gas and the magnetic field.

Cosmic-ray ionisation in collapsing clouds

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.

Cosmic-ray propagation in molecular clouds

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.

Effects of magnetic fields on the cosmic-ray ionization of molecular cloud cores

Low-energy cosmic rays are the dominant source of ionization for molecular cloud cores. The ionization fraction, in turn, controls the coupling of the magnetic field to the gas and hence the dynamical evolution of the cores. The purpose of this work is to compute the attenuation of the cosmic-ray flux rate in a cloud core taking into account magnetic focusing, magnetic mirroring, and all relevant energy loss processes. We adopt a standard cloud model characterized by a mass-to-flux ratio supercritical by a factor of about 2 to describe the density and magnetic field distribution of a low-mass starless core, and we follow the propagation of cosmic rays through the core along flux tubes enclosing different amount of mass. We then extend our analysis to cores with different mass-to-flux ratios. We find that mirroring always dominates over focusing, implying a reduction of the cosmic-ray ionization rate by a factor of about 2-3 over most of a solar-mass core with respect to the value in the intercloud medium outside the core. For flux tubes enclosing larger masses the reduction factor is smaller, since the field becomes increasingly uniform at larger radii and lower densities. We also find that the cosmic-ray ionization rate is further reduced in clouds with stronger magnetic field, e.g. by a factor of about 4 for a marginally critical cloud. The magnetic field threading molecular cloud cores affects the penetration of low-energy cosmic rays and reduces the ionization rate by a factor 3-4 depending on the position inside the core and the magnetization of the core.