22 research outputs found
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