Convective intensification of magnetic fields in the quiet Sun

Kilogauss-strength magnetic fields are often observed in intergranular lanes at the photosphere in the quiet Sun. Such fields are stronger than the equipartition field B_e, corresponding to a magnetic energy density that matches the kinetic energy density of photospheric convection, and comparable with the field B_p that exerts a magnetic pressure equal to the ambient gas pressure. We present an idealised numerical model of three-dimensional compressible magnetoconvection at the photosphere, for a range of values of the magnetic Reynolds number. In the absence of a magnetic field, the convection is highly supercritical and is characterised by a pattern of vigorous, time-dependent, “granular” motions. When a weak magnetic field is imposed upon the convection, magnetic flux is swept into the convective downflows where it forms localised concentrations. Unless this process is significantly inhibited by magnetic diffusion, the resulting fields are often much greater than B_e, and the high magnetic pressure in these flux elements leads to their being partially evacuated. Some of these flux elements contain ultra-intense magnetic fields that are significantly greater than B_p. Such fields are contained by a combination of the thermal pressure of the gas and the dynamic pressure of the convective motion, and they are constantly evolving. These ultra-intense fields develop owing to nonlinear interactions between magnetic fields and convection; they cannot be explained in terms of “convective collapse” within a thin flux tube that remains in overall pressure equilibrium with its surroundings

Magneto-convection in a sunspot umbra

Results from a realistic simulation of 3D radiative magneto-convection in a strong background magnetic field corresponding to the conditions in sunspot umbrae are shown. The convective energy transport is dominated by narrow upflow plumes with adjacent downflows, which become almost field-free near the surface layers. The strong external magnetic field forces the plumes to assume a cusp-like shape in their top parts, where the upflowing plasma loses its buoyancy. The resulting bright features in intensity images correspond well (in terms of brightness, size, and lifetime) to the observed umbral dots in the central parts of sunspot umbrae. Most of the simulated umbral dots have a horizontally elongated form with a central dark lane. Above the cusp, most plumes show narrow upflow jets, which are driven by the pressure of the piled-up plasma below. The large velocities and low field strengths in the plumes are effectively screened from spectroscopic observation because the surfaces of equal optical depth are locally elevated, so that spectral lines are largely formed above the cusp. Our simulations demonstrate that nearly field-free upflow plumes and umbral dots are a natural result of convection in a strong, initially monolithic magnetic field.Comment: Accepted by Astrophysical Journal Letter

Magnetic buoyancy instabilities in the presence of magnetic flux pumping at the base of the solar convection zone

We perform idealized numerical simulations of magnetic buoyancy instabilities in three dimensions, solving the equations of compressible magnetohydrodynamics in a model of the solar tachocline. In particular, we study the effects of including a highly simplified model of magnetic flux pumping in an upper layer (‘the convection zone’) on magnetic buoyancy instabilities in a lower layer (‘the upper parts of the radiative interior – including the tachocline’), to study these competing flux transport mechanisms at the base of the convection zone. The results of the inclusion of this effect in numerical simulations of the buoyancy instability of both a preconceived magnetic slab and a shear-generated magnetic layer are presented. In the former, we find that if we are in the regime that the downward pumping velocity is comparable with the Alfvén speed of the magnetic layer, magnetic flux pumping is able to hold back the bulk of the magnetic field, with only small pockets of strong field able to rise into the upper layer. In simulations in which the magnetic layer is generated by shear, we find that the shear velocity is not necessarily required to exceed that of the pumping (therefore the kinetic energy of the shear is not required to exceed that of the overlying convection) for strong localized pockets of magnetic field to be produced which can rise into the upper layer. This is because magnetic flux pumping acts to store the field below the interface, allowing it to be amplified both by the shear and by vortical fluid motions, until pockets of field can achieve sufficient strength to rise into the upper layer. In addition, we find that the interface between the two layers is a natural location for the production of strong vertical gradients in the magnetic field. If these gradients are sufficiently strong to allow the development of magnetic buoyancy instabilities, strong shear is not necessarily required to drive them (cf. previous work by Vasil & Brummell). We find that the addition of magnetic flux pumping appears to be able to assist shear-driven magnetic buoyancy in producing strong flux concentrations that can rise up into the convection zone from the radiative interior

Magnetic Doppler imaging of the roAp star HD 24712

We present the first magnetic Doppler images of a rapidly oscillating Ap (roAp) star. We deduce information about magnetic field geometry and abundance distributions of a number of chemical elements on the surface of the hitherto best studied roAp star, HD 24712, using the magnetic Doppler imaging (MDI) code, INVERS10, which allows us to reconstruct simultaneously and consistently the magnetic field geometry and elemental abundance distributions on a stellar surface. For this purpose we analyse time series spectra obtained in Stokes I and V parameters with the SOFIN polarimeter at the Nordic Optical Telescope and recover surface abundance structures of sixteen different chemical elements, respectively ions, including Mg, Ca, Sc, Ti, Cr, Fe, Co, Ni, Y, La, Ce, Pr, Nd, Gd, Tb, and Dy. For the rare earth elements (REE) Pr and Nd separate maps were obtained using lines of the first and the second ionization stage. We find and confirm a clear dipolar structure of the surface magnetic field and an unexpected correlation of elemental abundances with respect to this field: one group of elements accumulates solely where the positive magnetic pole is visible, whereas the other group avoids this region and is enhanced where the magnetic equatorial region dominates the visible stellar surface. We also observe relative shifts of abundance enhancement- or depletion regions between the various elements exhibiting otherwise similar behaviour.Comment: 13 pages, 9 figures, to be published in Astronomy and Astrophysic

Dissipation in Compressible MHD Turbulence

We report results of a three dimensional, high resolution (up to 512^3) numerical investigation of supersonic compressible magnetohydrodynamic turbulence. We consider both forced and decaying turbulence. The model parameters are appropriate to conditions found in Galactic molecular clouds. We find that the dissipation time of turbulence is of order the flow crossing time or smaller, even in the presence of strong magnetic fields. About half the dissipation occurs in shocks. Weak magnetic fields are amplified and tangled by the turbulence, while strong fields remain well ordered.Comment: 5 pages, 3 Postscript figures, LaTeX, accepted by Ap.J.Let

Complete High Temperature Expansions for One-Loop Finite Temperature Effects

We develop exact, simple closed form expressions for partition functions associated with relativistic bosons and fermions in odd spatial dimensions. These expressions, valid at high temperature, include the effects of a non-trivial Polyakov loop and generalize well-known high temperature expansions. The key technical point is the proof of a set of Bessel function identities which resum low temperature expansions into high temperature expansions. The complete expressions for these partition functions can be used to obtain one-loop finite temperature contributions to effective potentials, and thus free energies and pressures.Comment: 9 pages, RevTeX, no figures. To be published in Phys. Rev D. v2 has revised introduction and conclusions, plus a few typographical errors are corrected; v3 corrects one typ

First exit times and residence times for discrete random walks on finite lattices

In this paper, we derive explicit formulas for the surface averaged first exit time of a discrete random walk on a finite lattice. We consider a wide class of random walks and lattices, including random walks in a non-trivial potential landscape. We also compute quantities of interest for modelling surface reactions and other dynamic processes, such as the residence time in a subvolume, the joint residence time of several particles and the number of hits on a reflecting surface.Comment: 19 pages, 2 figure

Oscillations and secondary bifurcations in nonlinear magnetoconvection

Complicated bifurcation structures that appear in nonlinear systems governed by partial differential equations (PDEs) can be explained by studying appropriate low-order amplitude equations. We demonstrate the power of this approach by considering compressible magnetoconvection. Numerical experiments reveal a transition from a regime with a subcritical Hopf bifurcation from the static solution, to one where finite-amplitude oscillations persist although there is no Hopf bifurcation from the static solution. This transition is associated with a codimension-two bifurcation with a pair of zero eigenvalues. We show that the bifurcation pattern found for the PDEs is indeed predicted by the second-order normal form equation (with cubic nonlinearities) for a Takens-Bogdanov bifurcation with Z2 symmetry. We then extend this equation by adding quintic nonlinearities and analyse the resulting system. Its predictions provide a qualitatively accurate description of solutions of the full PDEs over a wider range of parameter values. Replacing the reflecting (Z2) lateral boundary conditions with periodic [O(2)] boundaries allows stable travelling wave and modulated wave solutions to appear; they could be described by a third-order system

Dynamics of Interacting Scalar Fields in Expanding Space-Time

The effective equation of motion is derived for a scalar field interacting with other fields in a Friedman-Robertson-Walker background space-time. The dissipative behavior reflected in this effective evolution equation is studied both in simplified approximations as well as numerically. The relevance of our results to inflation are considered both in terms of the evolution of the inflaton field as well as its fluctuation spectrum. A brief examination also is made of supersymmetric models that yield dissipative effects during inflation.Comment: 36 pages, 12 figures. Version published in the Physical Review

Patterns and localized structures in bistable semiconductor resonators

We report experiments on spatial switching dynamics and steady state structures of passive nonlinear semiconductor resonators of large Fresnel number. Extended patterns and switching front dynamics are observed and investigated. Evidence of localization of structures is given.Comment: 5 pages with 9 figure