114 research outputs found

### The Nonlinear Evolution of Instabilities Driven by Magnetic Buoyancy: A New Mechanism for the Formation of Coherent Magnetic Structures

Motivated by the problem of the formation of active regions from a
deep-seated solar magnetic field, we consider the nonlinear three-dimensional
evolution of magnetic buoyancy instabilities resulting from a smoothly
stratified horizontal magnetic field. By exploring the case for which the
instability is continuously driven we have identified a new mechanism for the
formation of concentrations of magnetic flux.Comment: Published in ApJL. Version with colour figure

### On Predicting the Solar Cycle using Mean-Field Models

We discuss the difficulties of predicting the solar cycle using mean-field
models. Here we argue that these difficulties arise owing to the significant
modulation of the solar activity cycle, and that this modulation arises owing
to either stochastic or deterministic processes. We analyse the implications
for predictability in both of these situations by considering two separate
solar dynamo models. The first model represents a stochastically-perturbed flux
transport dynamo. Here even very weak stochastic perturbations can give rise to
significant modulation in the activity cycle. This modulation leads to a loss
of predictability. In the second model, we neglect stochastic effects and
assume that generation of magnetic field in the Sun can be described by a fully
deterministic nonlinear mean-field model -- this is a best case scenario for
prediction. We designate the output from this deterministic model (with
parameters chosen to produce chaotically modulated cycles) as a target
timeseries that subsequent deterministic mean-field models are required to
predict. Long-term prediction is impossible even if a model that is correct in
all details is utilised in the prediction. Furthermore, we show that even
short-term prediction is impossible if there is a small discrepancy in the
input parameters from the fiducial model. This is the case even if the
predicting model has been tuned to reproduce the output of previous cycles.
Given the inherent uncertainties in determining the transport coefficients and
nonlinear responses for mean-field models, we argue that this makes predicting
the solar cycle using the output from such models impossible.Comment: 22 Pages, 5 Figures, Preprint accepted for publication in Ap

### Does the butterfly diagram indicate asolar flux-transport dynamo?

We address the question whether the properties of the observed latitude-time
diagram of sunspot occurence (the butterfly diagram) provide evidence for the
operation of a flux-transport dynamo, which explains the migration of the
sunspot zones and the period of the solar cycle in terms of a deep equatorward
meridional flow. We show that the properties of the butterfly diagram are
equally well reproduced by a conventional dynamo model with migrating dynamo
waves, but without transport of magnetic flux by a flow. These properties seem
to be generic for an oscillatory and migratory field of dipole parity and thus
do not permit an observational distinction between different dynamo approaches.Comment: 4 pages, 1 figur

### Dynamo Action in the Solar Convection Zone and Tachocline: Pumping and Organization of Toroidal Fields

We present the first results from three-dimensional spherical shell
simulations of magnetic dynamo action realized by turbulent convection
penetrating downward into a tachocline of rotational shear. This permits us to
assess several dynamical elements believed to be crucial to the operation of
the solar global dynamo, variously involving differential rotation resulting
from convection, magnetic pumping, and amplification of fields by stretching
within the tachocline. The simulations reveal that strong axisymmetric toroidal
magnetic fields (about 3000 G in strength) are realized within the lower stable
layer, unlike in the convection zone where fluctuating fields are predominant.
The toroidal fields in the stable layer possess a striking persistent
antisymmetric parity, with fields in the northern hemisphere largely of
opposite polarity to those in the southern hemisphere. The associated mean
poloidal magnetic fields there have a clear dipolar geometry, but we have not
yet observed any distinctive reversals or latitudinal propagation. The presence
of these deep magnetic fields appears to stabilize the sense of mean fields
produced by vigorous dynamo action in the bulk of the convection zone.Comment: 4 pages, 3 color figures (compressed), in press at ApJ

### The cross helicity at the solar surface by simulations and observations

The quasilinear mean-field theory for driven MHD turbulence leads to the
result that the observed cross helicity may directly yield the
magnetic eddy diffusivity \eta_{T} of the quiet Sun. In order to model the
cross helicity at the solar surface, magnetoconvection under the presence of a
vertical large-scale magnetic field is simulated with the nonlinear MHD code
NIRVANA. The very robust result of the calculations is that \simeq 2
independent of the applied magnetic field amplitude. The
correlation coefficient for the cross helicity is about 10%. Of similar
robustness is the finding that the rms value of the magnetic perturbations
exceeds the mean-field amplitude (only) by a factor of five. The characteristic
helicity speed u_{\eta} as the ratio of the eddy diffusivity and the density
scale height for an isothermal sound velocity of 6.6 km/s proves to be 1 km/s
for weak fields. This value well coincides with empirical results obtained from
the data of the HINODE satellite and the Swedish 1-m Solar Telescope (SST)
providing the cross helicity component . Both simulations and
observations thus lead to a numerical value of \eta_{T} \simeq 10^12 cm^2 /s as
characteristic for the surface of the quiet Sun.Comment: 6 pages, 6 figure

### Simulations of dynamo action in fully convective stars

We present three-dimensional nonlinear magnetohydrodynamic simulations of the
interiors of fully convective M-dwarfs. Our models consider 0.3 solar-mass
stars using the Anelastic Spherical Harmonic code, with the spherical
computational domain extending from 0.08-0.96 times the overall stellar radius.
Like previous authors, we find that fully convective stars can generate
kG-strength magnetic fields (in rough equipartition with the convective flows)
without the aid of a tachocline of shear. Although our model stars are
everywhere unstably stratified, the amplitudes and typical pattern sizes of the
convective flows vary strongly with radius, with the outer regions of the stars
hosting vigorous convection and field amplification while the deep interiors
are more quiescent. Modest differential rotation is established in hydrodynamic
calculations, but -- unlike in some prior work --strongly quenched in MHD
simulations because of the Maxwell stresses exerted by the dynamo-generated
magnetic fields. Despite the lack of strong differential rotation, the magnetic
fields realized in the simulations possess significant mean (axisymmetric)
components, which we attribute partly to the strong influence of rotation upon
the slowly overturning flows.Comment: Accepted to the ApJ. 20 pages (emulateapj), 4 color figures
compressed to low-resolution; higher-resolution equivalents are available at
http://lcd-www.colorado.edu/~brownim/browning_2007_mstars.pd

### Local models of stellar convection: Reynolds stresses and turbulent heat transport

We study stellar convection using a local three-dimensional MHD model, with
which we investigate the influence of rotation and large-scale magnetic fields
on the turbulent momentum and heat transport. The former is studied by
computing the Reynolds stresses, the latter by calculating the correlation of
velocity and temperature fluctuations, both as functions of rotation and
latitude. We find that the horisontal correlation, Q_(theta phi), capable of
generating horisontal differential rotation, is mostly negative in the southern
hemisphere for Coriolis numbers exceeding unity, corresponding to equatorward
flux of angular momentum in accordance with solar observations. The radial
component Q_(r phi) is negative for slow and intermediate rotation indicating
inward transport of angular momentum, while for rapid rotation, the transport
occurs outwards. Parametrisation in terms of the mean-field Lambda-effect shows
qualitative agreement with the turbulence model of Kichatinov & R\"udiger
(1993) for the horisontal part H \propto Q_(theta phi)/cos(theta), whereas for
the vertical part, V \propto Q_(r phi)/sin(theta), agreement only for
intermediate rotation exists. The Lambda-coefficients become suppressed in the
limit of rapid rotation, this rotational quenching being stronger for the V
component than for H. We find that the stresses are enhanced by the presence of
the magnetic field for field strengths up to and above the equipartition value,
without significant quenching. Concerning the turbulent heat transport, our
calculations show that the transport in the radial direction is most efficient
at the equatorial regions, obtains a minimum at midlatitudes, and shows a
slight increase towards the poles. The latitudinal heat transport does not show
a systematic trend as function of latitude or rotation.Comment: 26 pages, 20 figures, final published version. For a version with
higher resolution figures, see http://cc.oulu.fi/~pkapyla/publ.htm

### Magnetoconvection and dynamo coefficients III: alpha-effect and magnetic pumping in the rapid rotation regime

Aims. The alpha- and gamma-effects, which are responsible for the generation
and turbulent pumping of large scale magnetic fields, respectively, due to
passive advection by convection are determined in the rapid rotation regime
corresponding to the deep layers of the solar convection zone.
Methods. A 3D rectangular local model is used for solving the full set of MHD
equations in order to compute the electromotive force (emf), E = ,
generated by the interaction of imposed weak gradient-free magnetic fields and
turbulent convection with varying rotational influence and latitude. By
expanding the emf in terms of the mean magnetic field, E_i = a_ij , all
nine components of a_ij are computed. The diagonal elements of a_ij describe
the alpha-effect, whereas the off-diagonals represent magnetic pumping. The
latter is essentially the advection of magnetic fields by means other than the
underlying large-scale velocity field. Comparisons are made to analytical
expressions of the coefficients derived under the first-order smoothing
approximation (FOSA).
Results. In the rapid rotation regime the latitudinal dependence of the
alpha-components responsible for the generation of the azimuthal and radial
fields does not exhibit a peak at the poles, as is the case for slow rotation,
but at a latitude of about 30 degrees. The magnetic pumping is predominantly
radially down- and latitudinally equatorward as in earlier studies. The
numerical results compare surprisingly well with analytical expressions derived
under first-order smoothing, although the present calculations are expected to
lie near the limits of the validity range of FOSA.Comment: 14 pages, 12 figures, accepted for publication in Astronomy &
Astrophysic

### In--out intermittency in PDE and ODE models

We find concrete evidence for a recently discovered form of intermittency,
referred to as in--out intermittency, in both PDE and ODE models of mean field
dynamos. This type of intermittency (introduced in Ashwin et al 1999) occurs in
systems with invariant submanifolds and, as opposed to on--off intermittency
which can also occur in skew product systems, it requires an absence of skew
product structure. By this we mean that the dynamics on the attractor
intermittent to the invariant manifold cannot be expressed simply as the
dynamics on the invariant subspace forcing the transverse dynamics; the
transverse dynamics will alter that tangential to the invariant subspace when
one is far enough away from the invariant manifold.
Since general systems with invariant submanifolds are not likely to have skew
product structure, this type of behaviour may be of physical relevance in a
variety of dynamical settings.
The models employed here to demonstrate in--out intermittency are
axisymmetric mean--field dynamo models which are often used to study the
observed large scale magnetic variability in the Sun and solar-type stars. The
occurrence of this type of intermittency in such models may be of interest in
understanding some aspects of such variabilities.Comment: To be published in Chaos, June 2001, also available at
http://www.eurico.web.co

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