Sunspot simulations with MURaM -- I. Parameter study using potential field initial conditions

Abstract

Context. Existing sunspot simulations fail to reproduce the observed magnetic field distribution due to an artificially increased $B_{hor}$ at the upper boundary. Aims. We explore alternative ways to better reproduce the magnetic and dynamic properties of observed sunspots. Methods. We used the radiative MHD code MURaM. As initial conditions, we placed a potential magnetic field into small-scale dynamo simulations and used potential-field extrapolation at the top. Results. We find that: (1) Simulations with increasing initial magnetic field strengths (20, 40, 80, and 160 kG) show larger spots, umbrae, and penumbrae. (2) Penumbral-to-spot sizes are smaller than those measured in observed sunspots. (3) In none of the runs are pure Evershed (radially outward) flows. Instead, bi-directional flows with inflows in the inner penumbra and outflows in the outer penumbra were measured, consistent with to early observations of penumbra formation for runs with $\ge 80$ kG at 96/32 km resolution, whereas runs with $\le 40$ kG or less showed pure inflows. (4) Simulations with 160 kG at 32/16 km resolution contain filaments with bi-directional and Evershed flows. (5) Simulations with fluxes $>10^{22}$ Mx show unrealistically strong fields in the umbra. (6) The best runs with 160 kG and $10^{22}$ Mx give realistic radial profiles of $B_z$ and $B_r$, although stronger fields than observed. (7) Increasing the width of the box and reducing the overall flux by subtracting a uniform opposing vertical field have little influence on internal spot dynamics and fields, but change the mean vertical field beyond the spot. Conclusions. Simulations of small ($10^{22}$) sunspots with an initial potential field and intensified bottom magnetic field strength best reproduce observations of the initial stages of sunspot formation. Numerical resolution may be critical for achieving fully developed penumbrae.

submitted to Astronomy & Astrophysics; 10 pages, 8 figures, 3 tables, incl. appendix; abstract shortened compared to PDF; v2: published version, changes by language editor and typesetter

References in corpus (27)

• Radiative MHD simulation of sunspot structure
• Numerical simulations of quiet Sun magnetism: On the contribution from a small-scale dynamo
• Simulation of the Formation of a Solar Active Region
• Extension of the MURaM radiative MHD code for coronal simulations
• Penumbral structure and outflows in simulated sunspots
• Numerical sunspot models: Robustness of photospheric velocity and magnetic field structure
• MHD simulations of penumbra fine structure
• Structure of sunspot penumbral filaments: a remarkable uniformity of properties
• Emergence of magnetic flux generated in a solar convective dynamo. I: Formation of Sunspots and Active regions, and Origin of Their Asymmetries
• Convection and the origin of Evershed flows in sunspot penumbrae
• A 3-D sunspot model derived from an inversion of spectropolarimetric observations and its implications for the penumbral heating
• Properties of sunspot umbrae observed in Cycle 24
• The role of emerging bipoles in the formation of a sunspot penumbra
• Variation in sunspot properties between 1999 and 2011 as observed with the Tenerife Infrared Polarimeter
• On rising magnetic flux tube and formation of sunspots in a deep domain
• 3D Radiative MHD simulations of starspots
• Correlations between sunspots and their moat flows
• Magnetic properties of a long-lived sunspot - Vertical magnetic field at the umbral boundary
• Orphan penumbrae: Submerging horizontal fields
• Sunspot simulations: penumbra formation and the fluting instability
• Characterization of magneto-convection in sunspots -- The Gough & Tayler stability criterion in MURaM sunspot simulations
• A distinct magnetic property of the inner penumbral boundary III. Analysis of simulated sunspots
• The role of the chromospheric magnetic canopy in the formation of a sunspot penumbra
• Onset of penumbra formation
• The formation of a penumbra as observed with the German VTT and SoHO/MDI
• 3D Radiative MHD Simulations of Starspots II: Large-scale Structure
• The magnetic origin of the outer boundaries of sunspots