The solar photosphere is a transition region in which the primary energy transport mechanism switches from convection to radiative transfer. At the same time the plasma becomes due to the lower temperatures partially ionized, requiring a more complicated equation of state. Also the role of the magnetic field is changing: while the gas pressure dominates the interior of the sun, in or above the photosphere the magnetic pressure becomes the dominant contribution. Due to the rather short density scale height the photosphere is a highly stratified medium in which convective motions easily steepen up to supersonic flows and shock waves. The combination of all these conditions make numerical modeling of the photosphere challenging, but also extremely interesting due to the strong interaction between convection, magnetic field and radiation and the possibility for in depth comparison with high-resolution observations.

Detailed description of individual projects and links to work published during the last year:

1. High resolution simulations of sunspot fine structure:
During the past year the focus was mostly on the detailed analysis of simulations performed over the past 2 years. The publication “M. Rempel, Penumbral fine structure and driving mechanisms of large-scale flows in simulated sunspots, 2011, ApJ, 729, 5” focused on an in depth analysis of sunspot fine structure, mostly the filamentary structure of the penumbra and the origin of the associated horizontal outflows (Evershed flow). It makes the connection between the penumbral structure present in the photosphere and the subsurface magneto-convection processes that are responsible for filamentation, energy transport and acceleration of the Evershed flow. While a substantial amount of overturning convection is present in simulated penumbrae, the observational evidence is not that clear. To investigate this controversy “L. Bharti, M. Schüssler and M. Rempel, Can overturning motions in penumbral filaments be detected?, 2011, ApJ, 739, 35” computed spectral lines from a simulated penumbra and determined the visibility of convective signatures after a degradation to the typical resolution of observations was performed. It was found that upflows remain visible in most cases, while the visibility of downflows depends strongly on the spectral line used. Overall the level of overturning convection present in numerical simulations does not seem to be in conflict with observations at currently available telescope resolutions.

2. Simulations of the subsurface structure of sunspots:
Numerical simulations at lower resolution, but larger computational domains (up to 16 Mm deep and 75 Mm wide) were performed to study the subsurface magnetic and flow structure of sunspots, including large scale-flows in the surrounding moat region. The main findings were published in “M. Rempel, Subsurface Magnetic Field and Flow Structure of Simulated Sunspots, 2011, ApJ 740, 15”. It was found that changes in the photospheric appearance (deformation, light bridge formation, overall decay) of sunspots have their cause in convective motions in several Mm depth, in particular the longest convective time scales present in the simulation domain determine the life time of sunspots. The dominant large-scale flow system around sunspots is an outflow reaching about 50% of the convective rms velocity. Within the collaboration of the NASA funded SDO Science Center a helioseismic analysis of these simulations was performed by collaborators at CoRA/NWRA. It was found that simulated sunspots show helioseismic signatures comparable to those of observed sunspots. Since at the same time the detailed magnetic and thermal structure is known in simulations it can be determined that the physical origin of these signatures is restricted to the upper most ~2 Mm. These findings were published in “D. C. Braun, A. C. Birch, A. D. Crouch and M. Rempel, The need for physics-based inversions of sunspot structure and flows, 2011, J. Phys.: Conf. Ser. 271, 012010”, a more detailed study is accepted for publication in ApJ.

3. Simulations of flux emergence and sunspot formation:
In collaboration with M. Cheung (LMSAL, Lockheed Martin) numerical simulations of flux emergence in 147x74x16 Mm³ sized domains were performed. It was found that results form previous simulations in smaller domains are robust. Furthermore results do not show a strong dependence on the initial field strength, pointing toward a dominant role of photospheric processes in the determination of sunspot field strengths. Results from this study are currently being analyzed and a publication is in preparation.

4. Studies of solar/stellar structure and magnetic cycles:
In addition to the above photospheric MHD problems, M. Rempel participated in studies addressing stellar magnetic cycles and the structure of overshoot at the base of the solar convection zone. “T.S. Metcalfe and 7 coauthors, Discovery of a 1.6-year magnetic activity cycle in the exoplanet host star Horologii (HD 17051), 2010, ApJ 723, 213” discovered a 1.6 year solar-like magnetic cycle in an F star rotating about 3 times faster as the sun. This is currently the shortest known solar-like activity cycle. “J. Christensen-Dalsgaard, M.J.P.F.G Monteiro, M. Rempel and M.J. Thompson, A more realistic representation of overshoot at the base of the solar convection envelope as seen by helioseismology, 2011, Mon. Not. R. Astron. Soc. 414, 1158” performed a helioseismic analysis of the structure of overshoot at the base of the solar convection zone, motivated by recent models allowing for smoother temperature gradients. It was found that the presence of an extended smooth overshoot region leads to a better agreement with helioseismic data than the solar standard model.

Review articles:
In addition the following refereed review articles on models from the scales of sunspot fine structure to the scale active regions were published:

M. Rempel, "Numerical models of sunspot formation and fine structure", 2011, Invited review Royal Society Phil. Trans., accepted for publication

M. Rempel and R. Schlichenmaier, "Sunspot Modeling: From Simplified Models to Radiative MHD Simulations", 2011, Living reviews in solar physics 8, 3.

Publications

Figure 1: High Resolution

(1) Rempel, M. 2011: Penumbral fine structure and driving mechanisms of large-scale flows in simulated sunspots, ApJ, 729, 5.

Abstract: 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.

Figure 1 caption: Sunspot fine structure at the τ = 1 level. Quantities shown are (a) bolometric intensity, (b) radial and (c) vertical magnetic field, (d) field inclination, (e) radial, and (f) vertical flow velocities. A field inclination of 0° corresponds to vertical field with the same polarity as the umbra, 90° to horizontal, and 180° to vertical field with opposite polarity of the umbra. Radial outflows are displayed by red colors, solid contours indicate regions with more than 10 km s⁻¹ outflow velocity. Vertical upflows are displayed by blue colors, solid contours indicate regions with more than 5 km s⁻¹ downflow velocity.

Figure 2: High resolution

(2) Rempel, M. 2011: Subsurface Magnetic Field and Flow Structure of Simulated Sunspots, ApJ, 740, 15.

Abstract: 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.

Figure 2 caption: Radial and vertical flow velocities at three depth levels underneath a simulated sunspot. The top row shows radial flow velocity and the bottom row shows vertical flow velocity. Left to right the depth levels z = −11.5 Mm, z = −3.3 Mm, and z = −1.3 Mm. The ring-like arrangement of convection cells is present at all depth levels, and the diameter of the region in which the presence of the sunspot modifies the convection pattern is increasing with depth as the intrinsic scale of convection is increasing with pressure scale height.