Anisotropic diffusion of galactic cosmic ray protons and their steady-state azimuthal distribution

Galactic transport models for cosmic rays involve the diffusive motion of these particles in the interstellar medium. Due to the large-scale structured galactic magnetic field this diffusion is anisotropic with respect to the local field direction. We included this transport effect along with continuous loss processes in a quantitative model of galactic propagation for cosmic ray protons which is based on stochastic differential equations. We calculated energy spectra at different positions along the Sun's galactic orbit and compared them to the isotropic diffusion case. The results show that a larger amplitude of variation as well as different spectral shapes are obtained in the introduced anisotropic diffusion scenario and emphasize the need for accurate galactic magnetic field models.Comment: 7 pages, 5 figures, accepted for publication in A&

Toward more realistic analytic models of the heliotail: Incorporating magnetic flattening via distortion flows

Both physical arguments and simulations of the global heliosphere indicate that the tailward heliopause is flattened considerably in the direction perpendicular to both the incoming flow and the large-scale interstellar magnetic field. Despite this fact, all of the existing global analytical models of the outer heliosheath's magnetic field assume a circular cross section of the heliotail. To eliminate this inconsistency, we introduce a mathematical procedure by which any analytically or numerically given magnetic field can be deformed in such a way that the cross sections along the heliotail axis attain freely prescribed, spatially dependent values for their total area and aspect ratio. The distorting transformation of this method honors both the solenoidality condition and the stationary induction equation with respect to an accompanying flow field, provided that both constraints were already satisfied for the original magnetic and flow fields prior to the transformation. In order to obtain realistic values for the above parameters, we present the first quantitative analysis of the heliotail's overall distortion as seen in state-of-the-art three-dimensional hybrid MHD-kinetic simulations.Comment: 15 pages, 8 figures. Published in The Astrophysical Journa

Parameter estimation of superdiffusive motion of energetic particles upstream of heliospheric shocks

In-situ spacecraft observations recently suggested that the transport of energetic particles accelerated at heliospheric shocks can be anomalous, i.e. the mean square displacement can grow non-linearly in time. In particular, a new analysis technique has permitted the study of particle transport properties from energetic particle time profiles upstream of interplanetary shocks. Indeed, the time/spatial power laws of the differential intensity upstream of several shocks are indicative of superdiffusion. A complete determination of the key parameters of superdiffusive transport comprises the power-law index, the superdiffusion coefficient, the related transition scale at which the energetic particle profiles turn to decay as power laws, and the energy spectral index of the shock accelerated particles. Assuming large-scale spatial homogeneity of the background plasma, the power-law behaviour can been derived from both a (microscopic) propagator formalism and a (macroscopic) fractional transport equation. We compare the two approaches and find a relation between the diffusion coefficients used in the two formalisms. Based on the assumption of superdiffusive transport, we quantitatively derive these parameters by studying energetic particle profiles observed by the Ulysses and Voyager 2 spacecraft upstream of shocks in the heliosphere, for which a superdiffusive particle transport has previously been observed. Further, we have jointly studied the electron energy spectra, comparing the values of the spectral indices observed with those predicted by the standard diffusive shock acceleration theory and by a model based on superdiffusive transport. For a number of interplanetary shocks and for the solar wind termination shock, for the first time we obtain the anomalous diffusion constants and the scale at which the probability of particle free paths changes to a power-law...Comment: 5 Figure

The interaction of multiple stellar winds in stellar clusters: potential flow

While several studies have investigated large-scale cluster winds resulting from an intra-cluster interaction of multiple stellar winds, as yet they have not provided details of the bordering flows inside a given cluster. The present work explores the principal structure of the combined flow resulting from the interaction of multiple stellar winds inside stellar clusters. The theory of complex potentials is applied to analytically investigate stagnation points, boundaries between individual outflows, and the hydrodynamic structure of the asymptotic large-scale cluster wind. In a second part, these planar considerations are extended to fully three-dimensional, asymmetric configurations of wind-driving stars. We find (i) that one can distinguish regions in the large-scale cluster wind that are determined by the individual stellar winds, (ii) that there are comparatively narrow outflow channels, and (iii) that the large-scale cluster wind asymptotically approaches spherical symmetry at large distances. The combined flow inside a stellar cluster resulting from the interaction of multiple stellar winds is highly structured.Comment: 8 pages, 8 Figure