Non-ideal MHD Properties of Magnetic Flux Tubes in the Solar Photosphere

Magnetic flux tubes reaching from the solar convective zone into the chromosphere have to pass through the relatively cool, and therefore non-ideal (i.e. resistive) photospheric region enclosed between the highly ideal sub-photospheric and chromospheric plasma. It is shown that stationary MHD equilibria of magnetic flux tubes which pass through this region require an inflow of photospheric material into the flux tube and a deviation from iso-rotation along the tube axis. This means that there is a difference in angular velocity of the plasma flow inside the tube below and above the non-ideal region. Both effects increase with decreasing cross section of the tube. Although for characteristic parameters of thick flux tubes the effect is negligible, a scaling law indicates its importance for small-scale structures. The relevance of this "inflow effect" for the expansion of flux tubes above the photosphere is discussed.Comment: 17 pages, 9 figures. Comments welcom

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

An exact analytical solution for the weakly magnetized flow around an axially symmetric paraboloid, with application to magnetosphere models

Rotationally symmetric shapes with parabolic cross sections are frequently used to model astrophysical objects such as magnetospheres and other blunt objects immersed in interplanetary or interstellar gas or plasma flows. We present a simple formula for the potential flow of an incompressible fluid around an elliptic paraboloid whose axis of symmetry coincides with the direction of incoming flow. We then derive an exact analytical solution to the induction equation of ideal magnetohydrodynamics, thereby obtaining explicit expressions for an initially homogeneous magnetic field of arbitrary orientation being passively advected in this flow. The solution procedure employs Euler potentials and the method of Cauchy's Integral based on the flow's stream function and its isochrones. Furthermore, a novel renormalization procedure allows us to generate more general analytic expressions modeling the deformation experienced by arbitrary scalar or vector-valued fields embedded into the flow as they are advected first towards and then past the parabolic obstacle. Finally, the flow field is generalized from incompressible to mildly compressible velocities, where the associated density distribution is found from Bernoulli's principle.Comment: 12 pages; to be submitted to Ap

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

An Exact, Time-dependent Analytical Solution for the Magnetic Field in the Inner Heliosheath

We derive an exact, time-dependent analytical magnetic field solution for the inner heliosheath, which satisfies both the induction equation of ideal magnetohydrodynamics in the limit of infinite electric conductivity and the magnetic divergence constraint. To this end, we assume that the magnetic field is frozen into a plasma flow resembling the characteristic interaction of the solar wind with the local interstellar medium. Furthermore, we make use of the ideal Ohm's law for the magnetic vector potential and the electric scalar potential. By employing a suitable gauge condition that relates the potentials and working with a characteristic coordinate representation, we thus obtain an inhomogeneous first-order system of ordinary differential equations for the magnetic vector potential. Then, using the general solution of this system, we compute the magnetic field via the magnetic curl relation. Finally, we analyze the well-posedness of the corresponding Dirichlet boundary value problem, specify compatibility conditions for the boundary values, and outline the implementation of boundary conditions.Comment: 14 page

Cosmic-ray propagation around the Sun: investigating the influence of the solar magnetic field on the cosmic-ray Sun shadow

The cosmic-ray Sun shadow, which is caused by high-energy charged cosmic rays being blocked and deflected by the Sun and its magnetic field, has been observed by various experiments, such as Argo-YBJ, HAWC, Tibet, and IceCube. Most notably, the shadow's size and depth was recently shown to correlate with the 11-year solar cycle. The interpretation of such measurements, which help to bridge the gap between solar physics and high-energy particle astrophysics, requires a solid theoretical understanding of cosmic-ray propagation in the coronal magnetic field. It is the aim of this paper to establish theoretical predictions for the cosmic-ray Sun shadow in order to identify observables that can be used to study this link in more detail. To determine the cosmic-ray Sun shadow, we numerically compute trajectories of charged cosmic rays in the energy range of 5-316 TeV for five different mass numbers. We present and analyze the resulting shadow images for protons and iron, as well as for typically measured cosmic-ray compositions. We confirm the observationally established correlation between the magnitude of the shadowing effect and both the mean sunspot number and the polarity of the magnetic field during the solar cycle. We also show that during low solar activity, the Sun's shadow behaves similarly to that of a dipole, for which we find a non-monotonous dependence on energy. In particular, the shadow can become significantly more pronounced than the geometrical disk expected for a totally unmagnetized Sun. For times of high solar activity, we instead predict the shadow to depend monotonously on energy, and to be generally weaker than the geometrical shadow for all tested energies. These effects should become visible in energy-resolved measurements of the Sun shadow, and may in the future become an independent measure for the level of disorder in the solar magnetic field.Comment: 18 pages, 88 figure