30 research outputs found
Gluing hyperconvex metric spaces
We investigate how to glue hyperconvex (or injective) metric spaces such that
the resulting space remains hyperconvex. We give two new criteria, saying that
on the one hand gluing along strongly convex subsets and on the other hand
gluing along externally hyperconvex subsets leads to hyperconvex spaces.
Furthermore, we show by an example that these two cases where gluing works are
opposed and cannot be combined.Comment: 11 page
Magnetic Wreaths and Cycles in Convective Dynamos
Solar-type stars exhibit a rich variety of magnetic activity. Seeking to
explore the convective origins of this activity, we have carried out a series
of global 3D magnetohydrodynamic (MHD) simulations with the anelastic spherical
harmonic (ASH) code. Here we report on the dynamo mechanisms achieved as the
effects of artificial diffusion are systematically decreased. The simulations
are carried out at a nominal rotation rate of three times the solar value
(3), but similar dynamics may also apply to the Sun. Our previous
simulations demonstrated that convective dynamos can build persistent toroidal
flux structures (magnetic wreaths) in the midst of a turbulent convection zone
and that high rotation rates promote the cyclic reversal of these wreaths. Here
we demonstrate that magnetic cycles can also be achieved by reducing the
diffusion, thus increasing the Reynolds and magnetic Reynolds numbers. In these
more turbulent models, diffusive processes no longer play a significant role in
the key dynamical balances that establish and maintain the differential
rotation and magnetic wreaths. Magnetic reversals are attributed to an
imbalance in the poloidal magnetic induction by convective motions that is
stabilized at higher diffusion levels. Additionally, the enhanced levels of
turbulence lead to greater intermittency in the toroidal magnetic wreaths,
promoting the generation of buoyant magnetic loops that rise from the deep
interior to the upper regions of our simulated domain. The implications of such
turbulence-induced magnetic buoyancy for solar and stellar flux emergence are
also discussed.Comment: 21 pages, 16 figures, accepted for publication in Ap
Global-scale wreath-building dynamos in stellar convection zones
When stars like our Sun are young they rotate rapidly and are very
magnetically active. We explore dynamo action in rapidly rotating suns with the
3-D MHD anelastic spherical harmonic (ASH) code. The magnetic fields built in
these dynamos are organized on global-scales into wreath-like structures that
span the convection zone. Wreath-building dynamos can undergo quasi-cyclic
reversals of polarity and such behavior is common in the parameter space we
have been able to explore. These dynamos do not appear to require tachoclines
to achieve their spatial or temporal organization. Wreath-building dynamos are
present to some degree at all rotation rates, but are most evident in the more
rapidly rotating simulations.Comment: 8 pages, 4 figures. To appear in IAU 271: "Astrophysical Dynamics:
from Stars to Galaxies
Magnetic Cycles in a Convective Dynamo Simulation of a Young Solar-type Star
Young solar-type stars rotate rapidly and many are magnetically active; some
undergo magnetic cycles similar to the 22-year solar activity cycle. We conduct
simulations of dynamo action in rapidly rotating suns with the 3D MHD anelastic
spherical harmonic (ASH) code to explore dynamo action achieved in the
convective envelope of a solar-type star rotating at 5 times the current solar
rotation rate. Striking global-scale magnetic wreaths appear in the midst of
the turbulent convection zone and show rich time-dependence. The dynamo
exhibits cyclic activity and undergoes quasi-periodic polarity reversals where
both the global-scale poloidal and toroidal fields change in sense on a roughly
1500 day time scale. These magnetic activity patterns emerge spontaneously from
the turbulent flow and are more organized temporally and spatially than those
realized in our previous simulations of the solar dynamo. We assess in detail
the competing processes of magnetic field creation and destruction within our
simulations that contribute to the global-scale reversals. We find that the
mean toroidal fields are built primarily through an -effect, while the
mean poloidal fields are built by turbulent correlations which are not
necessarily well represented by a simple -effect. During a reversal the
magnetic wreaths propagate towards the polar regions, and this appears to arise
from a poleward propagating dynamo wave. The primary response in the convective
flows involves the axisymmetric differential rotation which shows variations
associated with the poleward propagating magnetic wreaths. In the Sun, similar
patterns are observed in the poleward branch of the torsional oscillations, and
these may represent poleward propagating magnetic fields deep below the solar
surface. [abridged]Comment: 20 pages, 14 figures, emulateapj format; accepted for publication in
ApJ. Expanded and published version of sections 5-6 from
http://arxiv.org/abs/0906.240
Global magnetic cycles in rapidly rotating younger suns
Observations of sun-like stars rotating faster than our current sun tend to
exhibit increased magnetic activity as well as magnetic cycles spanning
multiple years. Using global simulations in spherical shells to study the
coupling of large-scale convection, rotation, and magnetism in a younger sun,
we have probed effects of rotation on stellar dynamos and the nature of
magnetic cycles. Major 3-D MHD simulations carried out at three times the
current solar rotation rate reveal hydromagnetic dynamo action that yields
wreaths of strong toroidal magnetic field at low latitudes, often with opposite
polarity in the two hemispheres. Our recent simulations have explored behavior
in systems with considerably lower diffusivities, achieved with sub-grid scale
models including a dynamic Smagorinsky treatment of unresolved turbulence. The
lower diffusion promotes the generation of magnetic wreaths that undergo
prominent temporal variations in field strength, exhibiting global magnetic
cycles that involve polarity reversals. In our least diffusive simulation, we
find that magnetic buoyancy coupled with advection by convective giant cells
can lead to the rise of coherent loops of magnetic field toward the top of the
simulated domain.Comment: 4 pages, 3 figures, from IAU 273: The Physics of Sun and Star Spot
Energy Conservation and Gravity Waves in Sound-proof Treatments of Stellar Interiors: Part I Anelastic Approximations
Typical flows in stellar interiors are much slower than the speed of sound.
To follow the slow evolution of subsonic motions, various sound-proof equations
are in wide use, particularly in stellar astrophysical fluid dynamics. These
low-Mach number equations include the anelastic equations. Generally, these
equations are valid in nearly adiabatically stratified regions like stellar
convection zones, but may not be valid in the sub-adiabatic, stably stratified
stellar radiative interiors. Understanding the coupling between the convection
zone and the radiative interior is a problem of crucial interest and may have
strong implications for solar and stellar dynamo theories as the interface
between the two, called the tachocline in the Sun, plays a crucial role in many
solar dynamo theories. Here we study the properties of gravity waves in
stably-stratified atmospheres. In particular, we explore how gravity waves are
handled in various sound-proof equations. We find that some anelastic
treatments fail to conserve energy in stably-stratified atmospheres, instead
conserving pseudo-energies that depend on the stratification, and we
demonstrate this numerically. One anelastic equation set does conserve energy
in all atmospheres and we provide recommendations for converting low-Mach
number anelastic codes to this set of equations.Comment: Accepted for publication in ApJ. 20 pages emulateapj format, 7
figure