R. H. Cameron

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.

Solar Cycle Prediction Using Precursors and Flux Transport Models

We study the origin of the predictive skill of some methods to forecast the strength of solar activity cycles. A simple flux transport model for the azimuthally averaged radial magnetic field at the solar surface is used, which contains a source term describing the emergence of new flux based on observational sunspot data. We consider the magnetic flux diffusing over the equator as a predictor, since this quantity is directly related to the global dipole field from which a Babcock-Leighton dynamo generates the toroidal field for the next activity cycle. If the source is represented schematically by a narrow activity belt drifting with constant speed over a fixed range of latitudes between activity minima, our predictor shows considerable predictive skill, with correlation coefficients up to 0.95 for past cycles. However, the predictive skill is completely lost when the actually observed emergence latitudes are used. This result originates from the fact that the precursor amplitude is determined by the sunspot activity a few years before solar minimum. Since stronger cycles tend to rise faster to their maximum activity (known as the Waldmeier effect), the temporal overlapping of cycles leads to a shift of the minimum epochs that depends on the strength of the following cycle. This information is picked up by precursor methods and also by our flux transport model with a schematic source. Therefore, their predictive skill does not require a memory, i.e., a physical connection between the surface manifestations of subsequent activity cycles.

Simulations of the solar near-surface layers with the CO5BOLD, MURaM, and Stagger codes

Context. Radiative hydrodynamic simulations of solar and stellar surface convection have become an important tool for exploring the structure and gas dynamics in the envelopes and atmospheres of late-type stars and for improving our understanding of the formation of stellar spectra. Aims. We quantitatively compare results from three-dimensional, radiative hydrodynamic simulations of convection near the solar surface generated with three numerical codes (CO 5 BOLD, MURaM, and Stagger) and different simulation setups in order to investigate the level of similarity and to cross-validate the simulations. Methods. For all three simulations, we considered the average stratifications of various quantities (temperature, pressure, flow velocity, etc.) on surfaces of constant geometrical or optical depth, as well as their temporal and spatial fluctuations. We also compared observables, such as the spatially resolved patterns of the emerging intensity and of the vertical velocity at the solar optical surface as well as the center-to-limb variation of the continuum intensity at various wavelengths. Results. The depth profiles of the thermodynamical quantities and of the convective velocities as well as their spatial fluctuations agree quite well. Slight deviations can be understood in terms of differences in box size, spatial resolution and in the treatment of non-gray radiative transfer between the simulations. Conclusions. The results give confidence in the reliability of the results from comprehensive radiative hydrodynamic simulations.

SURFACE FLUX TRANSPORT MODELING FOR SOLAR CYCLES 15-21: EFFECTS OF CYCLE-DEPENDENT TILT ANGLES OF SUNSPOT GROUPS

We model the surface magnetic field and open flux of the Sun from 1913 to 1986 using a surface flux transport model, which includes the observed cycle-to-cycle variation of sunspot group tilts. The model reproduces the empirically derived time evolution of the solar open magnetic flux and the reversal times of the polar fields. We find that both the polar field and the axial dipole moment resulting from this model around cycle minimum correlate with the strength of the following cycle.

The crucial role of surface magnetic fields for the solar dynamo

Sunspot cycle driven by linked fields Sunspots indicate magnetic flux emerging at the Suns surface. Sunspots change over an 11-year time scale, which depends on the behavior of the probable magnetic dynamo within. Cameron et al. suggest that the flux revealed by sunspot activity is effectively driven by the magnetic field strength at the Suns poles. Their mathematical reasoning explains why the polar field activity can predict the sunspot cycle. Science, this issue p. 1333 Whether poloidal magnetic flux crosses the Sun’s surface determines its effect on the toroidal field flux at lower latitudes. Sunspots and the plethora of other phenomena occurring in the course of the 11-year cycle of solar activity are a consequence of the emergence of magnetic flux at the solar surface. The observed orientations of bipolar sunspot groups imply that they originate from toroidal (azimuthally orientated) magnetic flux in the convective envelope of the Sun. We show that the net toroidal magnetic flux generated by differential rotation within a hemisphere of the convection zone is determined by the emerged magnetic flux at the solar surface and thus can be calculated from the observed magnetic field distribution. The main source of the toroidal flux is the roughly dipolar surface magnetic field at the polar caps, which peaks around the minima of the activity cycle.

The effect of activity-related meridional flow modulation on the strength of the solar polar magnetic field

We studied the effect of the perturbation of the meridional flow in the activity belts detected by local helioseismology on the development and strength of the surface magnetic field at the polar caps. We carried out simulations of synthetic solar cycles with a flux transport model, which follows the cyclic evolution of the surface field determined by flux emergence and advective transport by near-surface flows. In each hemisphere, an axisymmetric band of latitudinal flows converging toward the central latitude of the activity belt was superposed onto the background poleward meridional flow. The overall effect of the flow perturbation is to reduce the latitudinal separation of the magnetic polarities of a bipolar magnetic region and thus diminish its contribution to the polar field. As a result, the polar field maximum reached around cycle activity minimum is weakened by the presence of the meridional flow perturbation. For a flow perturbation consistent with helioseismic observations, the polar field is reduced by about 18% compared to the case without inflows. If the amplitude of the flow perturbation depends on the cycle strength, its effect on the polar field provides a nonlinearity that could contribute to limiting the amplitude of a Babcock-Leighton type dynamo.

Vortices in simulations of solar surface convection

We report on the occurrence of small-scale vortices in simulations of the convective solar surface. Using an eigenanalysis of the velocity gradient tensor, we find the subset of high-vorticity regions in which the plasma is swirling. The swirling regions form an unsteady, tangled network of filaments in the turbulent downflow lanes. Near-surface vertical vortices are underdense and cause a local depression of the optical surface. They are potentially observable as bright points in the dark intergranular lanes. Vortex features typically exist for a few minutes, during which they are moved and twisted by the motion of the ambient plasma. The bigger vortices found in the simulations are possibly, but not necessarily, related to observations of granular-scale spiraling pathlines in “cork animations” or feature tracking.

Are the strengths of solar cycles determined by converging flows towards the activity belts

It is proposed that the observed near-surface inflows towards the active regions and sunspot zones provide a nonlinear feedback mechanism that limits the amplitude of a Babcock-Leighton-type solar dynamo and determines the variation of the cycle strength. This hypothesis is tested with surface flux transport simulations including converging latitudinal flows that depend on the surface distribution of magnetic flux. The inflows modulate the build-up of polar fields (represented by the axial dipole) by reducing the tilt angles of bipolar magnetic regions and by affecting the cross-equator transport of leading-polarity magnetic flux. With flux input derived from the observed record of sunspot groups, the simulations cover the period between 1874 and 1980 (corresponding to solar cycles 11 to 20). The inclusion of the inflows leads to a strong correlation of the simulated axial dipole strength during activity minimum with the observed amplitude of the subsequent cycle. This in agreement with empirical correlations and in line with what is expected from a Babcock-Leighton-type dynamo. The results provide evidence that the latitudinal inflows are a key ingredient in determining the amplitude of solar cycles.

Modeling the Sun's open magnetic flux and the heliospheric current sheet

By coupling a solar surface flux transport model with an extrapolation of the heliospheric field, we simulate the evolution of the Suns open magnetic flux and the heliospheric current sheet (HCS) based on observational data of sunspot groups since 1976. The results are consistent with measurements of the interplanetary magnetic field near Earth and with the tilt angle of the HCS as derived from extrapolation of the observed solar surface field. This opens the possibility for an improved reconstruction of the Suns open flux and the HCS into the past on the basis of empirical sunspot data.

Radiative magnetohydrodynamic simulations of solar pores

Context. Solar pores represent a class of magnetic structures intermediate between small-scale magnetic flux concentrations in intergranular lanes and fully developed sunspots with penumbrae. Aims. We study the structure, energetics, and internal dynamics of pore-like magnetic structures by means of exploratory numerical simulations. Methods. The MURaM code has been used to carry out several 3D radiative MHD simulations for pores of various sizes and with different boundary conditions. Results. The general properties of the simulated pores (morphology, continuum intensity, magnetic field geometry, surrounding flow pattern, mean height profiles of temperature, pressure, and density) are consistent with observational results. No indications for the formation of penumbral structure are found. The simulated pores decay by gradually shedding magnetic flux into the surrounding pattern of intergranular downflows (“turbulent erosion”). When viewed under an angle (corresponding to observations outside solar disc center), granules behind the pore appear brightened. Conclusions. Radiative MHD simulations capture many observed properties of solar pores.