Matthias Rempel

Flux-Transport Dynamos with Lorentz Force Feedback on Differential Rotation and Meridional Flow: Saturation Mechanism and Torsional Oscillations

In this paper we discuss a dynamic flux-transport dynamo model that includes the feedback of the induced magnetic field on differential rotation and meridional flow. We consider two different approaches for the feedback: mean field Lorentz force and quenching of transport coefficients such as turbulent viscosity and heat conductivity. We find that even strong feedback on the meridional flow does not change the character of the flux-transport dynamo significantly; however, it leads to a significant reduction of differential rotation. To a large degree independent of the dynamo parameters, the saturation takes place when the toroidal field at the base of the convection zone reaches between 1.2 and 1.5 T, and the energy converted into magnetic energy corresponds to about 0.1%-0.2% of the solar luminosity. The torsional oscillations produced through Lorentz force feedback on differential rotation show a dominant poleward propagating branch with the correct phase relation to the magnetic cycle. We show that incorporating enhanced surface cooling of the active region belt (as proposed by Spruit) leads to an equatorward propagating branch in good agreement with observations.

Solar differential rotation and meridional flow : The role of a subadiabatic tachocline for the taylor-proudman balance

We present a simple model for the solar differential rotation and meridional circulation based on a mean field parameterization of the Reynolds stresses that drive the differential rotation. We include the subadiabatic part of the tachocline and show that this, in conjunction with turbulent heat conductivity within the convection zone and overshoot region, provides the key physics to break the Taylor-Proudman constraint, which dictates differential rotation with contour lines parallel to the axis of rotation in case of an isentropic stratification. We show that differential rotation with contour lines inclined by 10°-30° with respect to the axis of rotation is a robust result of the model, which does not depend on the details of the Reynolds stress and the assumed viscosity, as long as the Reynolds stress transports angular momentum toward the equator. The meridional flow is more sensitive with respect to the details of the assumed Reynolds stress, but a flow cell, equatorward at the base of the convection zone and poleward in the upper half of the convection zone, is the preferred flow pattern.

Penumbral Structure and Outflows in Simulated Sunspots

Sunspots Before Your Eyes Sunspots have a dark central region, the umbra, surrounded by a region of lighter radial filaments, the penumbra, along which there are outward horizontal mass flows that are still not fully understood despite their discovery 100 years ago. Now Rempel et al. (p. 171, published online 18 June; see the Perspective by Scharmer) present comprehensive numerical simulations of a pair of sunspots that show the development of an outer penumbra with systematic radial outflows along channels of nearly horizontal magnetic field in regions where the average field inclination is greater than 45 degrees. The outflows result from rising hot plasma that turns over and is guided outward by the strong and inclined magnetic field. The simulations reproduce observed properties throughout the entire penumbra and show that the penumbral structure and outflows in sunspots can be understood in terms of convective flow in a magnetic field with varying inclination. Simulations of sunspots show that their structure and outflows can be understood in terms of convection in a magnetic field. Sunspots are concentrations of magnetic field on the visible solar surface that strongly affect the convective energy transport in their interior and surroundings. The filamentary outer regions (penumbrae) of sunspots show systematic radial outward flows along channels of nearly horizontal magnetic field. These flows were discovered 100 years ago and are present in all fully developed sunspots. By using a comprehensive numerical simulation of a sunspot pair, we show that penumbral structures with such outflows form when the average magnetic field inclination to the vertical exceeds about 45 degrees. The systematic outflows are a component of the convective flows that provide the upward energy transport and result from anisotropy introduced by the presence of the inclined magnetic field.

Penumbral Fine Structure and Driving Mechanisms of Large-scale Flows in Simulated Sunspots

We analyze in detail the penumbral structure found in a recent radiative magnetohydrodynamic simulation. Near τ = 1, the simulation produces penumbral fine structure consistent with the observationally inferred interlocking comb structure. Fast outflows exceeding 8 km s–1 are present along almost horizontal stretches of the magnetic field; in the outer half of the penumbra, we see opposite polarity flux indicating flux returning beneath the surface. The bulk of the penumbral brightness is maintained by small-scale motions turning over on scales shorter than the length of a typical penumbral filament. The resulting vertical rms velocity at τ = 1 is about half of that found in the quiet Sun. Radial outflows in the sunspot penumbra have two components. In the uppermost few 100 km, fast outflows are driven primarily through the horizontal component of the Lorentz force, which is confined to narrow boundary layers beneath τ = 1, while the contribution from horizontal pressure gradients is reduced in comparison to granulation as a consequence of anisotropy. The resulting Evershed flow reaches its peak velocity near τ = 1 and falls off rapidly with height. Outflows present in deeper layers result primarily from a preferred ring-like alignment of convection cells surrounding the sunspot. These flows reach amplitudes of about 50% of the convective rms velocity rather independent of depth. A preference for the outflow results from a combination of Lorentz force and pressure driving. While the Evershed flow dominates by velocity amplitude, most of the mass flux is present in deeper layers and likely related to a large-scale moat flow.

A more realistic representation of overshoot at the base of the solar convective envelope as seen by helioseismology

The stratification near the base of the Sun’s convective envelope is governed by processes of convective overshooting and element diffusion, and the region is widely believed to play a key role in the solar dynamo. The stratification in that region gives rise to a characteristic signal in the frequencies of solar p modes, which has been used to determine the depth of the solar convection zone and to investigate the extent of convective overshoot. Previous helioseismic investigations have shown that the Sun’s spherically symmetric stratification in this region is smoother than that in a standard solar model without overshooting, and have ruled out simple models incorporating overshooting, which extend the region of adiabatic stratification and have a more-or-less abrupt transition to subadiabatic stratification at the edge of the overshoot region. In this paper we consider physically motivated models which have a smooth transition in stratification bridging the region from the lower convection zone to the radiative interior beneath. We find that such a model is in better agreement with the helioseismic data than a standard solar model.

Discovery of a 1.6 Year Magnetic Activity Cycle in the Exoplanet Host Star ι Horologii

The Mount Wilson Ca HK survey revealed magnetic activity variations in a large sample of solar-type stars with timescales ranging from 2.5 to 25 years. This broad range of cycle periods is thought to reflect differences in the rotational properties and the depths of the surface convection zones for stars with various masses and ages. In 2007, we initiated a long-term monitoring campaign of Ca II H and K emission for a sample of 57 southern solar-type stars to measure their magnetic activity cycles and their rotational properties when possible. We report the discovery of a 1.6 year magnetic activity cycle in the exoplanet host star ι Horologii and obtain an estimate of the rotation period that is consistent with Hyades membership. This is the shortest activity cycle so far measured for a solar-type star and may be related to the short-timescale magnetic variations recently identified in the Sun and HD 49933 from helioseismic and asteroseismic measurements. Future asteroseismic observations of ι Hor can be compared to those obtained near the magnetic minimum in 2006 to search for cycle-induced shifts in the oscillation frequencies. If such short activity cycles are common in F stars, then NASAs Kepler mission should observe their effects in many of its long-term asteroseismic targets.

The dynamical disconnection of sunspots from their magnetic roots

After a dynamically active emergence phase, magnetic flux at the solar surface soon ceases to show strong signs of the subsurface dynamics of its parent magnetic structure. This indicates that some kind of disconnection of the emerged flux from its roots in the deep convection zone should take place. We propose a mechanism for the dynamical disconnection of the surface flux based upon the buoyant upflow of plasma along the field lines. Such flows arise in the upper part of a rising flux loop during the final phases of its buoyant ascent towards the surface. The combination of the pressure buildup by the upflow and the cooling of the upper layers of an emerged flux tube by radiative losses at the surface lead to a progressive weakening of the magnetic field in several Mm depth. When the field strength has become sufficiently low, convective motions and the fluting instability disrupt the flux tube into thin, passively advected flux fragments, thus providing a dynamical disconnection of the emerged part from its roots. We substantiate this scenario by considering the quasi-static evolution of a sunspot model under the effects of radiative cooling, convective energy transport, and pressure buildup by a prescribed inflow at the bottom of the model. For inflow speeds in the range shown by simulations of thin flux tubes, we find that the disconnection takes place in a depth between 2 and 6 Mm for disconnection times up to 3 days.

A solar mean field dynamo benchmark

Context. The solar magnetic activity and cycle are linked to an internal dynamo. Numerical simulations are an e cient and accurate tool to investigate such intricate dynamical processes. Aims. We present the results of an international numerical benchmark study based on two-dimensional axisymmetric mean field solar dynamo models in spherical geometry. The purpose of this work is to provide the scientific community with reference cases that can be analyzed in detail and that can help in further development and validation of numerical codes that solve such problems. Methods. The results of eight numerical codes solving the induction equation in the framework of mean field theory are compared for three increasingly computationally intensive models of the solar dynamo: an dynamo with constant magnetic di usivity, an dynamo with magnetic di usivity sharply varying with depth and an example of a flux-transport Babcock-Leighton dynamo which includes a non-local source term and one large single cell of meridional circulation per hemisphere. All cases include a realistic profile of di erential rotation and thus a sharp tachocline. Results. The most important finding of this study is that all codes agree quantitatively to within less than a percent for the dynamo cases and within a few percents for the flux-transport case. Both the critical dynamo numbers for the onset of dynamo action and the corresponding cycle periods are reasonably well recovered by all codes. Detailed comparisons of butterfly diagrams and specific cuts of both toroidal and poloidal fields at given latitude and radius confirm the good quantitative agreement. Conclusions. We believe that such a benchmark study will be a very useful tool for the scientific community since it provides detailed standard cases for comparison and reference.

Subsurface Magnetic Field and Flow Structure of Simulated Sunspots

We present a series of numerical sunspot models addressing the subsurface field and flow structure in up to 16?Mm deep domains covering up to two days of temporal evolution. Changes in the photospheric appearance of the sunspots are driven by subsurface flows in several Mm depth. Most of magnetic field is pushed into a downflow vertex of the subsurface convection pattern, while some fraction of the flux separates from the main trunk of the spot. Flux separation in deeper layers is accompanied in the photosphere with light bridge formation in the early stages and formation of pores separating from the spot at later stages. Over a timescale of less than a day we see the development of a large-scale flow pattern surrounding the sunspots, which is dominated by a radial outflow reaching about 50% of the convective rms velocity in amplitude. Several components of the large scale flow are found to be independent from the presence of a penumbra and the associated Evershed flow. While the simulated sunspots lead to blockage of heat flux in the near surface layers, we do not see compelling evidence for a brightness enhancement in their periphery. We further demonstrate that the influence of the bottom boundary condition on the stability and long-term evolution of the sunspot is significantly reduced in a 16 Mm deep domain compared to the shallower domains considered previously.

NUMERICAL SIMULATIONS OF QUIET SUN MAGNETISM: ON THE CONTRIBUTION FROM A SMALL-SCALE DYNAMO

We present a series of radiative MHD simulations addressing the origin and distribution of the mixed polarity magnetic field in the solar photosphere. To this end, we consider numerical simulations that cover the uppermost 2-6 Mm of the solar convection zone and we explore scales ranging from 2 km to 25 Mm. We study how the strength and distribution of the magnetic field in the photosphere and subsurface layers depend on resolution, domain size, and boundary conditions. We find that 50% of the magnetic energy at the τ = 1 level comes from fields with the less than 500 G strength and that 50% of the energy resides on scales smaller than about 100 km. While the probability distribution functions are essentially independent of resolution, properly describing the spectral energy distribution requires grid spacings of 8 km or smaller. The formation of flux concentrations in the photosphere exceeding 1 kG requires a mean vertical field strength greater than 30-40 G at τ = 1. The filling factor of kG flux concentrations increases with overall domain size as the magnetic field becomes organized by larger, longer-lived flow structures. A solution with a mean vertical field strength of around 85 G at τ = 1 requires a subsurface rms field strength increasing with depth at the same rate as the equipartition field strength. We consider this an upper limit for the quiet Sun field strength, which implies that most of the convection zone is magnetized close to the equipartition. We discuss these findings in view of recent high-resolution spectropolarimetric observations of quiet Sun magnetism.