1,846 research outputs found

### Helicity and alpha-effect by current-driven instabilities of helical magnetic fields

Helical magnetic background fields with adjustable pitch angle are imposed on
a conducting fluid in a differentially rotating cylindrical container. The
small-scale kinetic and current helicities are calculated for various field
geometries, and shown to have the opposite sign as the helicity of the
large-scale field. These helicities and also the corresponding $\alpha$-effect
scale with the current helicity of the background field. The $\alpha$-tensor is
highly anisotropic as the components $\alpha_{\phi\phi}$ and $\alpha_{zz}$ have
opposite signs. The amplitudes of the azimuthal $\alpha$-effect computed with
the cylindrical 3D MHD code are so small that the operation of an
$\alpha\Omega$ dynamo on the basis of the current-driven, kink-type
instabilities of toroidal fields is highly questionable. In any case the low
value of the $\alpha$-effect would lead to very long growth times of a dynamo
in the radiation zone of the Sun and early-type stars of the order of
mega-years.Comment: 6 pages, 7 figures, submitted to MNRA

### Stratorotational instability in Taylor-Couette flow heated from above

We investigate the instability and nonlinear saturation of
temperature-stratified Taylor-Couette flows in a finite height cylindrical gap
and calculate angular-momentum transport in the nonlinear regime. The model is
based on an incompressible fluid in Boussinesq approximation with a positive
axial temperature gradient applied. While both ingredients itself, the
differential rotation as well as the stratification due to the temperature
gradient, are stable, together the system becomes subject of the
stratorotational instability and nonaxisymmetric flow pattern evolve. This flow
configuration transports angular momentum outwards and will therefor be
relevant for astrophysical applications. The belonging viscosity $\alpha$
coefficient is of the order of unity if the results are adapted to the size of
an accretion disc. The strength of the stratification, the fluids Prandtl
number and the boundary conditions applied in the simulations are well-suited
too for a laboratory experiment using water and a small temperature gradient
below five Kelvin. With such a rather easy realizable set-up the SRI and its
angular momentum transport could be measured in an experiment.Comment: 10 pages, 6 figures, revised version appeared in J. Fluid Mech.
(2009), vol. 623, pp. 375--38

### The angular momentum transport by unstable toroidal magnetic fields

We demonstrate with a nonlinear MHD code that angular momentum can be
transported due to the magnetic instability of toroidal fields under the
influence of differential rotation, and that the resulting effective viscosity
may be high enough to explain the almost rigid-body rotation observed in
radiative stellar cores. Only stationary current-free fields and only those
combinations of rotation rates and magnetic field amplitudes which provide
maximal numerical values of the viscosity are considered. We find that the
dimensionless ratio of the effective over molecular viscosity, $\nu_T/\nu$;,
linearly grows with the Reynolds number of the rotating fluid multiplied with
the square-root of the magnetic Prandtl number - which is of order unity for
the considered red sub-giant KIC 7341231.
For the considered interval of magnetic Reynolds numbers - which is
restricted by numerical constraints of the nonlinear MHD code - there is a
remarkable influence of the magnetic Prandtl number on the relative importance
of the contributions of the Reynolds stress and the Maxwell stress to the total
viscosity, which is magnetically dominated only for Pm $\gtrsim$ 0.5. We also
find that the magnetized plasma behaves as a non-Newtonian fluid, i.e. the
resulting effective viscosity depends on the shear in the rotation law. The
decay time of the differential rotation thus depends on its shear and becomes
longer and longer during the spin-down of a stellar core.Comment: Revised version. 7 pages, 9 figures; accepted for publication in A&

### Angular momentum transport efficiency in post-main sequence low-mass stars

Context. Using asteroseismic techniques, it has recently become possible to
probe the internal rotation profile of low-mass (~1.1-1.5 Msun) subgiant and
red giant stars. Under the assumption of local angular momentum conservation,
the core contraction and envelope expansion occurring at the end of the main
sequence would result in a much larger internal differential rotation than
observed. This suggests that angular momentum redistribution must be taking
place in the interior of these stars. Aims. We investigate the physical nature
of the angular momentum redistribution mechanisms operating in stellar
interiors by constraining the efficiency of post-main sequence rotational
coupling. Methods. We model the rotational evolution of a 1.25 Msun star using
the Yale Rotational stellar Evolution Code. Our models take into account the
magnetic wind braking occurring at the surface of the star and the angular
momentum transport in the interior, with an efficiency dependent on the degree
of internal differential rotation. Results. We find that models including a
dependence of the angular momentum transport efficiency on the radial
rotational shear reproduce very well the observations. The best fit of the data
is obtained with an angular momentum transport coefficient scaling with the
ratio of the rotation rate of the radiative interior over that of the
convective envelope of the star as a power law of exponent ~3. This scaling is
consistent with the predictions of recent numerical simulations of the
Azimuthal Magneto-Rotational Instability. Conclusions. We show that an angular
momentum transport process whose efficiency varies during the stellar evolution
through a dependence on the level of internal differential rotation is required
to explain the observed post-main sequence rotational evolution of low-mass
stars.Comment: 8 pages, 6 figures; accepted for publication in Astronomy &
Astrophysic

### Nonaxisymmetric MHD instabilities of Chandrasekhar states in Taylor-Couette geometry

We consider axially periodic Taylor-Couette geometry with insulating boundary
conditions. The imposed basic states are so-called Chandrasekhar states, where
the azimuthal flow $U_\phi$ and magnetic field $B_\phi$ have the same radial
profiles. Mainly three particular profiles are considered: the Rayleigh limit,
quasi-Keplerian, and solid-body rotation. In each case we begin by computing
linear instability curves and their dependence on the magnetic Prandtl number
Pm. For the azimuthal wavenumber m=1 modes, the instability curves always scale
with the Reynolds number and the Hartmann number. For sufficiently small Pm
these modes therefore only become unstable for magnetic Mach numbers less than
unity, and are thus not relevant for most astrophysical applications. However,
modes with m>10 can behave very differently. For sufficiently flat profiles,
they scale with the magnetic Reynolds number and the Lundquist number, thereby
allowing instability also for the large magnetic Mach numbers of astrophysical
objects. We further compute fully nonlinear, three-dimensional equilibration of
these instabilities, and investigate how the energy is distributed among the
azimuthal (m) and axial (k) wavenumbers. In comparison spectra become steeper
for large m, reflecting the smoothing action of shear. On the other hand
kinetic and magnetic energy spectra exhibit similar behavior: if several
azimuthal modes are already linearly unstable they are relatively flat, but for
the rigidly rotating case where m=1 is the only unstable mode they are so steep
that neither Kolmogorov nor Iroshnikov-Kraichnan spectra fit the results. The
total magnetic energy exceeds the kinetic energy only for large magnetic
Reynolds numbers Rm>100.Comment: 12 pages, 14 figures, submitted to Ap

### The angular momentum transport by standard MRI in quasi-Kepler cylindric Taylor-Couette flows

The instability of a quasi-Kepler flow in dissipative Taylor-Couette systems
under the presence of an homogeneous axial magnetic field is considered with
focus to the excitation of nonaxisymmetric modes and the resulting angular
momentum transport. The excitation of nonaxisymmetric modes requires higher
rotation rates than the excitation of the axisymmetric mode and this the more
the higher the azimuthal mode number m. We find that the weak-field branch in
the instability map of the nonaxisymmetric modes has always a positive slope
(in opposition to the axisymmetric modes) so that for given magnetic field the
modes with m>0 always have an upper limit of the supercritical Reynolds number.
In order to excite a nonaxisymmetric mode at 1 AU in a Kepler disk a minimum
field strength of about 1 Gauss is necessary. For weaker magnetic field the
nonaxisymmetric modes decay. The angular momentum transport of the
nonaxisymmetric modes is always positive and depends linearly on the Lundquist
number of the background field. The molecular viscosity and the basic rotation
rate do not influence the related {\alpha}-parameter. We did not find any
indication that the MRI decays for small magnetic Prandtl number as found by
use of shearing-box codes. At 1 AU in a Kepler disk and a field strength of
about 1 Gauss the {\alpha} proves to be (only) of order 0.005

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