MHD Simulations of Sunspot Structure
Matthias Rempel((HAO/NCAR)
M. Schüssler (MPS), M. Knölkerl(HAO)High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR)H
The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Researchunder sponsorship of the National Science Foundation. An Equal Opportunity/Affirmative Action Employer.

The problem
 No fundamental progress in our
understanding of sunspots for decades Why?
– Insufficient resolution of fine structure– No information about subsurfacestructure– Insufficient computational power forsimulations from first principles
 Recently progress on all 3 fronts:– AO, images selection & reconstruction,
spectropolarimetry from space (Hinode)– Local helioseimology– Massively parallel computers

Recent progress

Schüssler & Vögler (2006)

Heinemann et al. (2007)

Rempel et al. (2009)

Last 4 months

1.8x1022 Mx sunspot in 50x50x6 Mm domain

Intensity

VrInclination

Vz

Vertical cuts along the filament

Results
 Separated filaments with observed properties– Filaments with dark cores– Almost horizontal field, horizontal flow of ~ 2 - 3 km/s– Important: horizontal flow in magnetized region (required toexplain observed circular polarisation)

 No dense penumbra (yet)– Interface umbra/penumbra– Evershed flow on average too weak ~2 - 3 km/s, peak flows ~9km/s

 Common magneto-convective origin of umbral dots andpenumbral filaments– Overturning convection central element– Umbral dots: almost field free upflow plumes– Penumbral filaments: presence of horizontal field leads topreferred direction

Gaps or flux tubes?
 Overall structure looks like ‘gaps’, but– no intrusion of field free plasma from ‘outside’– ‘gaps’ open within strong field due to magneto- convection– ‘gaps’ filled with mainly horizontal field Photospheric appearance ‘tube’-like, but– description of entire structure as tube not very meaningful(variation over cross section ~ variation along axis)

 Basic agreement with conclusions from Hinodeobservations

Not yet settled questions
 Observational evidence for overturning convection?
– Ichimoto et al (2007)• ‘twisting’ motions in filaments– Rimmele (2008); Zakharov et al. (2008); Bharti et al.
(2007):• Direct observation of overturning motions– More evidence in umbral dots?
– Several other studies looked for signature, but couldn’t
detect it!
 Need improvement (resolution) of simulations!
– Are flows hidden from visible layers?
 More observations needed?
– High resolution observations of deep photospheric lines
with narrow contribution function– 50cm telescope likely not enough for that

Not yet settled questions
 Evershed flow
– Preferred outflow along filaments, but amplitude tooweak Role for energy transport?
– Energy primarily transported by overturning motions• 1-2Mm deep reaching upflows ~1km/s– Role of horizontal flow potentially underestimated Issue likely to be settled through improvement(resolution) of simulations

Primary uncertainty in simulation setup
 Subsurface structure and lower magnetic boundary
condition– Vertical field @ bottom– No velocity in strong field regions– Monolithic self-similar initial field Ways to improvement– Simulate formation of sunspots• Challenging task, unlikely to happen soon

– Constraints through local helioseismology• Combine simulations as forward modeling tool withhelioseismic inversions to improve inversion and models• Downward extension of current simulations (~16 Mm)• SDO/HMI

Prospects for an upward extension(chromosphere) Complicated physics (generic for chromosphere)– NLTE, non-equilibrium ionization (see talk by M.
Carlsson)– Non-MHD effects (low ionization level)– Complicated Ohms law– Balance between detailed description and feasible
numerical approach– Will need solid observational constraints to verify
required simplifications (Solar C, Plan B)

Prospects for an upward extension(chromosphere) Challenges of strong field region– Robust numerical scheme• High order TVD based artificial diffusivities– Low beta stability• Currently: isothermal EOS for beta < 10-4
• Future: right compromise between conservative andnon-conservative treatment of energy equation– High Alfven velocity (> 3000 km/s)• Currently artificial limitation through Lorentz force
reduction (saves factor 100)!
– Problematic if study Alfven waves primary focus, in 10 years
computing power sufficient for direct approach– Likely OK for field guided shocks (running penumbral waves,Bloomfield et al. 2007)

Summary Realistic numerical simulations of sunspots feasible today
 Qualitative agreement with observations
 Not yet resolved issues– Presence/visibility of overturning motions• High resolution, 50cm telescope likely insufficient– Role/amplitude of Evershed flow
– Outer penumbra, filament density

 Future directions– Higher resolution– Deeper down, subsurface structure• Local helioseismology, SDO/HMI– Further up• Detailed observational constraints needed (Solar C, Plan B)