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

Effect of strong wakes on waves in two-dimensional plasma crystals

We study effects of the particle-wake interactions on the dispersion and polarization of dust lattice wave modes in two-dimensional plasma crystals. Most notably, the wake-induced coupling between the modes causes the branches to "attract" each other, and their polarizations become elliptical. Upon the mode hybridization the major axes of the ellipses (remaining mutually orthogonal) rotate by $45^\circ$. To demonstrate importance of the obtained results for experiments, we plot spectral densities of the longitudinal and transverse waves revealing distinct fingerprints of the mixed polarization. Furthermore, we show that at strong coupling the hybrid mode is significantly shifted towards smaller wave numbers, away from the border of the first Brillouin zone (where the hybrid mode is localized for a weak coupling).Comment: 10 pages, 6 figure

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.Comment: accepted by 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&

Glass transition of charged particles in two-dimensional confinement

The glass transition of mesoscopic charged particles in two-dimensional confinement is studied by mode-coupling theory. We consider two types of effective interactions between the particles, corresponding to two different models for the distribution of surrounding ions that are integrated out in coarse-grained descriptions. In the first model, a planar monolayer of charged particles is immersed in an unbounded isotropic bath of ions, giving rise to an isotropically screened Debye-H\"uckel- (Yukawa-) type effective interaction. The second, experimentally more relevant system is a monolayer of negatively charged particles that levitate atop a flat horizontal electrode, as frequently encountered in laboratory experiments with complex (dusty) plasmas. A steady plasma current towards the electrode gives rise to an anisotropic effective interaction potential between the particles, with an algebraically long-ranged in-plane decay. In a comprehensive parameter scan that covers the typical range of experimentally accessible plasma conditions, we calculate and compare the mode-coupling predictions for the glass transition in both kinds of systems.Comment: 10 pages, 8 figure

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

Agglomeration of microparticles in complex plasmas

Agglomeration of highly charged microparticles was observed and studied in complex plasma experiments carried out in a capacitively coupled rf discharge. The agglomeration was caused by strong dust density waves triggered in a particle cloud by decreasing neutral gas pressure. Using a high-speed camera during this unstable regime, it was possible to resolve the motion of individual microparticles and to show that the relative velocities of some particles were sufficiently high to overcome the mutual Coulomb repulsion and hence to result in agglomeration. After stabilising the cloud again through the increase of the pressure, we were able to observe the aggregates directly with a long-distance microscope. We show that the agglomeration rate deduced from our experiments is in good agreement with theoretical estimates. In addition, we briefly discuss the mechanisms that can provide binding of highly charged microparticles in a plasma.Comment: submitted to Phys. Plasm

Dimension-free estimates on distances between subsets of volume ε\varepsilon inside a unit-volume body

Average distance between two points in a unit-volume body $K \subset \mathbb{R}^n$ tends to infinity as $n \to \infty$. However, for two small subsets of volume $\varepsilon > 0$ the situation is different. For unit-volume cubes and euclidean balls the largest distance is of order $\sqrt{-\ln \varepsilon}$, for simplexes and hyperoctahedrons $-$ of order $-\ln \varepsilon$, for $\ell_p$ balls with $p \in [1;2]$ $-$ of order $(-\ln \varepsilon)^{\frac{1}{p}}$. These estimates are not dependent on the dimensionality $n$. The goal of the paper is to study this phenomenon. Isoperimetric inequalities will play a key role in our approach

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