Diffusive Versus Free-Streaming Cosmic Ray Transport in Molecular Clouds

Understanding the cosmic ray (CR) ionization rate is crucial in order to simulate the dynamics of, and interpret the chemical species observed in molecular clouds. Calculating the CR ionization rate requires both accurate knowledge of the spectrum of MeV to GeV protons at the edge of the cloud as well as a model for the propagation of CRs into molecular clouds. Some models for the propagation of CRs in molecular clouds assume the CRs to stream freely along magnetic field lines, while in others they propagate diffusively due to resonant scattering off of magnetic disturbances excited by MHD turbulence present in the medium. We discuss the conditions under which CR diffusion can operate in a molecular cloud, calculate the local CR spectrum and ionization rate in both a free-streaming and diffusive propagation model, and highlight the different results from the two models. We also apply these two models to the propagation through the ISM to obtain the spectrum seen by Voyager 1, and show that such a spectrum favors a diffusive propagation model.Comment: Submitted to Ap

Cosmic-ray ionisation in circumstellar discs

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.Comment: 19 pages, 11 figures, accepted by A&

Production of atomic hydrogen by cosmic rays in dark clouds

The presence of small amounts of atomic hydrogen, detected as absorption dips in the 21 cm line spectrum, is a well-known characteristic of dark clouds. The abundance of hydrogen atoms measured in the densest regions of molecular clouds can be only explained by the dissociation of H$_2$ due to cosmic rays. We want to assess the role of Galactic cosmic rays in the formation of atomic hydrogen, by using recent developments in the characterisation of the low-energy spectra of cosmic rays and advances in the modelling of their propagation in molecular clouds. We model the attenuation of the interstellar cosmic rays entering a cloud and compute the dissociation rate of molecular hydrogen due to collisions with cosmic-ray protons and electrons as well as fast hydrogen atoms. We compare our results with the available observations. The cosmic-ray dissociation rate is entirely determined by secondary electrons produced in primary ionisation collisions. These secondary particles constitute the only source of atomic hydrogen at column densities above $\sim10^{21}$ cm$^{-2}$. We also find that the dissociation rate decreases with column density, while the ratio between the dissociation and ionisation rates varies between about 0.6 and 0.7. From comparison with observations we conclude that a relatively flat spectrum of interstellar cosmic-ray protons, as the one suggested by the most recent Voyager 1 data, can only provide a lower bound for the observed atomic hydrogen fraction. An enhanced spectrum of low-energy protons is needed to explain most of the observations. Our findings show that a careful description of molecular hydrogen dissociation by cosmic rays can explain the abundance of atomic hydrogen in dark clouds. An accurate characterisation of this process at high densities is crucial for understanding the chemical evolution of star-forming regions.Comment: 7 pages, 7 figures, accepted by Astronomy and Astrophysic

Structural correlations in diffusiophoretic colloidal mixtures with nonreciprocal interactions

Nonreciprocal effective interaction forces can occur between mesoscopic particles in colloidal suspensions that are driven out of equilibrium. These forces violate Newton's third law actio  =  reactio on coarse-grained length and time scales. Here we explore the statistical mechanics of Brownian particles with nonreciprocal effective interactions. Our model system is a binary fluid mixture of spherically symmetric, diffusiophoretic mesoscopic particles, and we focus on the time-averaged particle pair- and triplet-correlation functions. Based on the many-body Smoluchowski equation we develop a microscopic statistical theory for the particle correlations and test it by computer simulations. For model systems in two and three spatial dimensions, we show that nonreciprocity induces distinct nonequilibrium pair correlations. Our predictions can be tested in experiments with chemotactic colloidal suspensions

Impact of magneto-rotational instability on grain growth in protoplanetary disks: I. Relevant turbulence properties

Turbulence in the protoplanetary disks induces collisions between dust grains, and thus facilitates grain growth. We investigate the two fundamental assumptions of the turbulence in obtaining grain collisional velocities -- the kinetic energy spectrum and the turbulence autocorrelation time -- in the context of the turbulence generated by the magneto-rotational instability (MRI). We carry out numerical simulations of the MRI as well as driven turbulence, for a range of physical and numerical parameters. We find that the convergence of the turbulence $\alpha$-parameter does not necessarily imply the convergence of the energy spectrum. The MRI turbulence is largely solenoidal, for which we observe a persistent kinetic energy spectrum of $k^{-4/3}$. The same is obtained for solenoidal driven turbulence with and without magnetic field, over more than 1 dex near the dissipation scale. This power-law slope appears to be converged in terms of numerical resolution, and to be due to the bottleneck effect. The kinetic energy in the MRI turbulence peaks at the fastest growing mode of the MRI. In contrast, the magnetic energy peaks at the dissipation scale. The magnetic energy spectrum in the MRI turbulence does not show a clear power-law range, and is almost constant over approximately 1 dex near the dissipation scale. The turbulence autocorrelation time is nearly constant at large scales, limited by the shearing timescale, and shows a power-law drop close to $k^{-1}$ at small scales, with a slope steeper than that of the eddy crossing time. The deviation from the standard picture of the Kolmogorov turbulence with the injection scale at the disk scale height can potentially have a significant impact on the grain collisional velocities.Comment: Accepted by Ap

Magnetic Mirroring and Focusing of Cosmic Rays

We study the combined impact of magnetic mirroring and focusing on the ionization by cosmic rays (CRs) in dense molecular clouds and circumstellar disks. We show that for effective column densities of up to $\sim10^{25}$ cm$^{-2}$ (where ionization is the main mechanism of energy losses by CRs) the two effects practically cancel each other out, provided the magnetic field strength has a single peak along field lines. In this case the ionization rate at a given location is controlled solely by attenuation of interstellar CRs due to energy losses. The situation is very different in the presence of magnetic pockets -- local minima of the field strength, where the CR density and thus ionization can be reduced drastically. We obtain simple analytical expressions allowing accurate calculation of the ionization rate in these regions.Comment: Accepted to Ap

Coagulation-Fragmentation Equilibrium for Charged Dust: Abundance of Submicron Grains Increases Dramatically in Protoplanetary Disks

Dust coagulation in protoplanetary disks is not straightforward and is subject to several slow-down mechanisms, such as bouncing, fragmentation and radial drift to the star. Furthermore, dust grains in UV-shielded disk regions are negatively charged due to collisions with the surrounding electrons and ions, which leads to their electrostatic repulsion. For typical disk conditions, the relative velocities between micron-size grains are small and their collisions are strongly affected by the repulsion. On the other hand, collisions between pebble-size grains can be too energetic, leading to grain fragmentation. The aim of the present paper is to study a combined effect of the electrostatic and fragmentation barriers on dust evolution. We numerically solve the Smoluchowski coagulation-fragmentation equation for grains whose charging occurs under conditions typical for the inner disk regions, where thermal ionization operates. We find that dust fragmentation efficiently resupplies the population of small grains under the electrostatic barrier. As a result, the equilibrium abundance of sub-micron grains is enhanced by several orders of magnitude compared to the case of neutral dust. For some conditions with fragmentation velocities $\sim 1$ m s$^{-1}$, macroscopic grains are completely destroyed.Comment: accepted for publication in Ap

Dust grains cannot grow to millimeter sizes in protostellar envelopes

A big question in the field of star and planet formation is the time at which substantial dust grain growth occurs. The observed properties of dust emission across different wavelength ranges have been used as an indication that millimeter-sized grains are already present in the envelopes of young protostars. However, this interpretation is in tension with results from coagulation simulations, which are not able to produce such large grains in these conditions. In this work, we show analytically that the production of millimeter-sized grains in protostellar envelopes is impossible under the standard assumptions about the coagulation process. We discuss several possibilities that may serve to explain the observed dust emission in the absence of in-situ grain growth to millimeter sizes.Comment: Accepted to Ap