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Structure and stability of the magnetic solar tachocline
Rather weak fossil magnetic fields in the radiative core can produce the solar tachocline if the field is almost horizontal in the tachocline region, i.e. if the field is confined within the core. This particular field geometry is shown to result from a shallow (≲1 Mm) penetration of the meridional flow existing in the convection zone into the radiative core. Two conditions are thus crucial for a magnetic tachocline theory: (i) the presence of meridional flow of a few metres per second at the base of the convection zone, and (ii) a magnetic diffusivity inside the tachocline smaller than 108 cm 2 s-1. Numerical solutions for the confined poloidal fields and the resulting tachocline structures are presented. We find that the tachocline thickness runs as Bp-1/2 with the poloidal field amplitude falling below 5% of the solar radius for Bp > 5 mG. The resulting toroidal field amplitude inside the tachocline of about 100 G does not depend on the Bp. The hydromagnetic stability of the tachocline is only briefly discussed. For the hydrodynamic stability of latitudinal differential rotation we found that the critical 29% of the 2D theory of Watson (1981 Geophys. Astrophys. Fluid Dyn. 16 285) are reduced to only 21% in 3D for marginal modes of about 6 Mm radial scale. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft
The alpha-effect and current helicity for fast sheared rotators
We explore the alpha-effect and the small-scale current helicity, for the
case of weakly compressible magnetically driven turbulence that is subjected to
the differential rotation. No restriction is applied to the amplitude of
angular velocity, i.e., the derivations presented are valid for an arbitrary
Coriolis number, though the differential rotation itself is assumed to be weak.
The expressions obtained are used to explore the possible distributions of
alpha-effect and current helicity in convection zones (CZ) of the solar-type
stars. The implications of the obtained results to the mean-field dynamo models
are discussed.Comment: 20 pages, 6 figure
The kink-type instability of toroidal stellar magnetic fields with thermal diffusion
The stability of toroidal magnetic fields in rotating radiative stellar zones
is studied for realistic values of both the Prandtl numbers. The two considered
models for the magnetic geometry represent fields with odd and even symmetry
with respect to the equator. In the linear theory in Boussinesq approximation
the resulting complex eigenfrequency (including growth rate and drift rate) are
calculated for a given radial wavenumber of a nonaxisymmetric perturbation with
m=1. The ratio of the Alfven frequency, \Omega_A, to the rate of the basic
rotation, \Omega, controls the eigenfrequency of the solution. For strong
fields with \Omega_A > \Omega the solutions do not feel the thermal diffusion.
The growth rate runs with \Omega_A and the drift rate is close to -\Omega so
that the magnetic pattern will rest in the laboratory system. For weaker fields
with \Omega_A < \Omega the growth rate strongly depends on the thermal
conductivity. For fields with dipolar parity and for typical values of the heat
conductivity the resulting very small growth rates are almost identical with
those for vanishing gravity. For fields with dipolar symmetry the differential
rotation of any stellar radiative zone (like the solar tachocline) is shown as
basically stabilizing the instability independent of the sign of the shear.
Finally, the current-driven kink-type instability of a toroidal background
field is proposed as a model for the magnetism of Ap stars. The recent
observation of a lower magnetic field treshold of about 300 Gauss for Ap stars
is understood as corresponding to the minimum magnetic field producing the
instability.Comment: 11 pages, 7 figures, acc. for publicatio
Cross helicity and turbulent magnetic diffusivity in the solar convection zone
In a density-stratified turbulent medium the cross helicity is
considered as a result of the interaction of the velocity fluctuations and a
large-scale magnetic field. By means of a quasilinear theory and by numerical
simulations we find the cross helicity and the mean vertical magnetic field
anti-correlated. In the high-conductivity limit the ratio of the helicity and
the mean magnetic field equals the ratio of the magnetic eddy diffusivity and
the (known) density scale height. The result can be used to predict that the
cross helicity at the solar surface exceeds the value of 1 Gauss km/s. Its sign
is anti-correlated with that of the radial mean magnetic field. Alternatively,
we can use our result to determine the value of the turbulent magnetic
diffusivity from observations of the cross helicity.Comment: 9 pages, 2 figures, submitted to Solar Physic
The generalized non-conservative model of a 1-planet system - revisited
We study the long-term dynamics of a planetary system composed of a star and
a planet. Both bodies are considered as extended, non-spherical, rotating
objects. There are no assumptions made on the relative angles between the
orbital angular momentum and the spin vectors of the bodies. Thus, we analyze
full, spatial model of the planetary system. Both objects are assumed to be
deformed due to their own rotations, as well as due to the mutual tidal
interactions. The general relativity corrections are considered in terms of the
post-Newtonian approximation. Besides the conservative contributions to the
perturbing forces, there are also taken into account non-conservative effects,
i.e., the dissipation of the mechanical energy. This dissipation is a result of
the tidal perturbation on the velocity field in the internal zones with
non-zero turbulent viscosity (convective zones). Our main goal is to derive the
equations of the orbital motion as well as the equations governing
time-evolution of the spin vectors (angular velocities). We derive the
Lagrangian equations of the second kind for systems which do not conserve the
mechanical energy. Next, the equations of motion are averaged out over all fast
angles with respect to time-scales characteristic for conservative
perturbations. The final equations of motion are then used to study the
dynamics of the non-conservative model over time scales of the order of the age
of the star. We analyze the final state of the system as a function of the
initial conditions. Equilibria states of the averaged system are finally
discussed.Comment: 37 pages, 13 figures, accepted to Celestial Mechanics and Dynamical
Astronom
Time-distance analysis of the emerging active region NOAA 10790
We investigate the emergence of Active Region NOAA 10790 by means of time – distance helioseismology. Shallow regions of increased sound speed at the location of increased magnetic activity are observed, with regions becoming deeper at the locations of sunspot pores. We also see a long-lasting region of decreased sound speed located underneath the region of the flux emergence, possibly relating to a temperature perturbation due to magnetic quenching of eddy diffusivity, or to a dense flux tube. We detect and track an object in the subsurface layers of the Sun characterised by increased sound speed which could be related to emerging magnetic-flux and thus obtain a provisional estimate of the speed of emergence of around 1 km s−1
Active region formation through the negative effective magnetic pressure instability
The negative effective magnetic pressure instability operates on scales
encompassing many turbulent eddies and is here discussed in connection with the
formation of active regions near the surface layers of the Sun. This
instability is related to the negative contribution of turbulence to the mean
magnetic pressure that causes the formation of large-scale magnetic structures.
For an isothermal layer, direct numerical simulations and mean-field
simulations of this phenomenon are shown to agree in many details in that their
onset occurs at the same depth. This depth increases with increasing field
strength, such that the maximum growth rate of this instability is independent
of the field strength, provided the magnetic structures are fully contained
within the domain. A linear stability analysis is shown to support this
finding. The instability also leads to a redistribution of turbulent intensity
and gas pressure that could provide direct observational signatures.Comment: 19 pages, 10 figures, submitted to Solar Physic
Quenching of Meridional Circulation in Flux Transport Dynamo Models
Guided by the recent observational result that the meridional circulation of
the Sun becomes weaker at the time of the sunspot maximum, we have included a
parametric quenching of the meridional circulation in solar dynamo models such
that the meridional circulation becomes weaker when the magnetic field at the
base of the convection zone is stronger. We find that a flux transport solar
dynamo tends to become unstable on including this quenching of meridional
circulation if the diffusivity in the convection zone is less than about 2 *
10^{11} cm^2/s. The quenching of alpha, however, has a stabilizing effect and
it is possible to stabilize a dynamo with low diffusivity with sufficiently
strong alpha-quenching. For dynamo models with high diffusivity, the quenching
of meridional circulation does not produce a large effect and the dynamo
remains stable. We present a solar-like solution from a dynamo model with
diffusivity 2.8 * 10^{12} cm^2/s in which the quenching of meridional
circulation makes the meridional circulation vary periodically with solar cycle
as observed and does not have any other significant effect on the dynamo.Comment: Consistent with the published version. Solar Physics, in pres
Spontaneous formation of flux concentrations in a stratified layer
The negative effective magnetic pressure instability discovered recently in
direct numerical simulations (DNS) may play a crucial role in the formation of
sunspots and active regions in the Sun and stars. This instability is caused by
a negative contribution of turbulence to the effective mean Lorentz force (the
sum of turbulent and non-turbulent contributions) and results in formation of
large-scale inhomogeneous magnetic structures from initial uniform magnetic
field. Earlier investigations of this instability in DNS of stably stratified,
externally forced, isothermal hydromagnetic turbulence in the regime of large
plasma beta are now extended into the regime of larger scale separation ratios
where the number of turbulent eddies in the computational domain is about 30.
Strong spontaneous formation of large-scale magnetic structures is seen even
without performing any spatial averaging. These structures encompass many
turbulent eddies. The characteristic time of the instability is comparable to
the turbulent diffusion time, L^2/eta_t, where eta_t is the turbulent
diffusivity and L is the scale of the domain. DNS are used to confirm that the
effective magnetic pressure does indeed become negative for magnetic field
strengths below the equipartition field. The dependence of the effective
magnetic pressure on the field strength is characterized by fit parameters that
seem to show convergence for larger values of the magnetic Reynolds number.Comment: 14 pages, 8 figures, submitted to special issue "Advances of European
Solar Physics" in Solar Physic
Observation and Modeling of the Solar-Cycle Variation of the Meridional Flow
We present independent observations of the solar-cycle variation of flows
near the solar surface and at a depth of about 60 Mm, in the latitude range
. We show that the time-varying components of the meridional flow
at these two depths have opposite sign, while the time-varying components of
the zonal flow are in phase. This is in agreement with previous results. We
then investigate whether the observations are consistent with a theoretical
model of solar-cycle dependent meridional circulation based on a flux-transport
dynamo combined with a geostrophic flow caused by increased radiative loss in
the active region belt (the only existing quantitative model). We find that the
model and the data are in qualitative agreement, although the amplitude of the
solar-cycle variation of the meridional flow at 60 Mm is underestimated by the
model.Comment: To be published in Solar Physcis Topical Issue "Helioseismology,
Asteroseismology, and MHD Connections