1. Active Region Magnetic Fields in the Solar Interior W.P. Abbett UC Berkeley SSL

2. The Importance of Active Region Magnetic Fields Active regions represent the largest concentrations of magnetic flux at the solar surface Many, if not all, space weather events (e.g., SEP events triggered by flares or CME shock fronts) are associated with active regions Jan 15, 1996 CME as captured by the LASCO C3 coronagraphTRACE movie of the coronal response to a rotating structure

3. The magnetic field we observe at the visible surface of the Sun is ultimately governed by forces acting on magnetic structures at and below the photosphere, in the turbulent interior. The evolution of active region magnetic fields at the surface provide important constraints on theories and models of CME initiation, and ultimately provide the lower boundary conditions for large-scale coupled models of the Sun- to-earth system. The Importance of Active Region Magnetic Fields From: V. Abramenko; BBSO 2004 RHESSI Sonoma workshop

4. Outline In this review, I will discuss what has been learned about the evolution of active region magnetic fields deep in the solar interior, what aspects of the observations can be explained in terms of theoretical and computational models, and what remains mysterious. I will then suggest directions for future research in this area

5. Observational Characteristics of Active Region Magnetic Fields Left: SOHO EIT image of coronal plasma at ~1.3MK Right: Timeseries of MDI LOS magnetograms taken between Oct.22 and Nov 15 1998 (a time of heightened solar activity) Roughly speaking, active regions are confined to symmetric latitudinal bands across the solar equator These bands move poleward as the 11-year solar cycle progresses, but on average do not venture farther than ~35 degrees away from mid-latitude

6. On average, the leading polarity of an active region is positioned closer to the equator than the trailing polarity. The mean tilt angle of active regions increases linearly with latitude (Joy’s Law) Leading polarities of active regions in a given hemisphere are the same, and oppose those of the opposite hemisphere Active region bipoles are oriented nearly parallel to the E-W direction (Hale’s Law 1919) Fisher et al. 1995 MDI magnetogram from May 11, 2000

7. Implications of the Observed Behavior of Active Regions Hale’s Law implies that the underlying field geometry is torodial (aligned in the E-W direction) Since Hale’s Law persists over multiple solar cycles, the toroidal layer must lie deep in the interior in a region relatively free from convective turbulence. The natural place for active region magnetic fields to be stored is at or near the place where they are thought to be generated: the tachocline, where the differentially rotating convection zone transitions into the stable radiative layers

8. Interpretations Based on Observations Many active regions emerge as simple bipoles. These structures can be interpreted as the tops of large Omega- shaped flux tubes anchored deep in the convection zone. Active regions exhibiting non-Hale configurations (e.g., delta spots) are often interpreted as twisted, or writhed flux tubes From Fisher et al. 2000

9. A Theoretical Interpretation Derive an equation of motion for a flux tube moving in a field-free background model convection zone given the following constraints: –As the tube moves, it retains its identity; i.e., the tube remains cohesive and does not disperse or fragment –The tube is “thin”; i.e., it’s cross-section is small relative to all other relevant length scales of the problem –Quasi-static pressure balance is maintained across the diameter of the tube at all times

10. The “Thin Flux Tube” Approximation Here, F B refers to the magnetic buoyancy force, F T the force due to magnetic tension, F C the Coriolis force, and F D the force resulting from aerodynamic drag (ρ e and ρ i refer to the gas density external to the tube, and in the tube’s interior respectively) (Spruit 1981, Moreno-Insertis 1986, Ferriz-Mas & Schussler 1993, Caligari et al.1995)

11. Coriolis force deflects tube toward the poles as it tries to rise radially Studies Using the Thin Flux Tube Model From Fan & Fisher 1996

12. Studies Using the Thin Flux Tube Model What is the magnetic field strength of the toroidal layer at the base of the solar convection zone? –Thermally or magnetically unstable toroidal flux rings with field strengths between ~3x10 4 and ~10 5 G at the base of a model convection zone (significantly higher than the equipartition value) give rise to buoyant Omega-loops that emerge at latitudes consistent with observations. What is the physical origin of Joy’s Law? –Thin flux tube simulations have shown that active region tilts could be explained by the Coriolis force acting on rising, expanding flux ropes.

13. What is the physical basis of active region asymmetries? –Plasma entrained in an emerging flux rope will conserve its angular momentum, resulting in a distorted Omega-loop: the leading leg is less vertically inclined than the trailing leg, resulting in a more rapid motion of the leading polarity away from the neutral line. Studies Using the Thin Flux Tube Model From Caligari et al. 1995

14. Beyond the Thin Flux Tube Model MHD simulations of magnetic flux tubes in the solar interior 2D results show that without substantial fieldline twist (far more than is, on average, observed), flux tubes fragment and are unable to reach the surface. Boussinesq simulations of Longcope et al 1996 From Fan et al. 1998

15. 3D MHD Simulations of Flux Tubes Simulations of buoyant magnetic flux tubes in a stratified background model convection zone show –The fragmentation “problem” is a result of the axisymmetric assumption; in 3D only a modest amount of twist is required for the flux tube to remain cohesive From Abbett et al. 2000

16. 3D MHD Simulations of Flux Tubes When Coriolis effects are considered, the amount of twist necessary for emergence is essentially negligible Asymmetries predicted by thin flux tube calculations are borne out by 3D MHD simulations in a rotating, stratified model convection zone From Abbett et al. 2001

17. Highly Twisted Flux Tubes Properties of delta-spot active regions (often the source of the strongest flares and CMEs): –Sunspot umbrae of opposite polarity in a common penumbra –Strong shear along the neutral line –Rotates as it emerges Interpretation: The geometry of a kinked flux rope can explain the rotation and shear observed in delta spot active regions Tanaka 1991, Linton et al. 1999, Fan et al. 1999

18. Active Region Fields in a Convectively Unstable Background State Q: What are the conditions for the tube to retain its cohesion? Fieldline twist is relatively unimportant: what matters is the axial field strength relative to the kinetic energy density of strong downdrafts: Q: Is an active region-scale magnetic flux tube susceptible to flux pumping? From Abbett et al. 2004

19. Turbulent Pumping Images from Tobias et al. 2001 A robust property of compressible, penetrative convection: magnetic flux is preferentially transported to the base of the convection zone at timescales characteristic of convective turnover Tobias et al. 1998, 2001, Dorch & Nordlund 2001

20. From Abbett et al. 2004 Are relatively weak active region-scale magnetic flux tubes susceptible to turbulent pumping in the absence of an overshoot layer?

21. The Transport of Magnetic Flux Over the lifetime of an active region-scale magnetic structure, there seems to be no systematic tendency for a net transport of signed magnetic flux into either the upper or lower half of the model convection zone (in the absence of an overshoot layer)

22. The Transport of Magnetic Flux To qualitatively understand the initial behavior of the simulations, let’s neglect the effects of Lorentz forces and magnetic diffusion, and again consider the ideal MHD induction equation: Applying Stoke’s theorem gives: Since we are interested how signed flux is redistributed through the domain, let’s consider a closed circuit encompassing the lower half of a single vertical slice. Our horizontal boundaries are periodic, and v z and B z are assumed anti-symmetric across the lower boundary. Thus, the line integral becomes:

23. The Transport of Magnetic Flux The initial horizontal magnetic field is constant (of the form B = B 0 x); thus, the only way the total amount of magnetic flux above or below the mid-plane of a vertical slice can change, is by the interaction of vertical flows with the horizontal layer of flux. Then the average time rate of change of signed magnetic flux in the lower half of the domain can initially be expressed as: If there are no bulk flows, or net vertical pulsations in the domain (as is the case in our dynamically relaxed model convection zone), then And we should expect no initial tendency for a horizontal flux layer to be preferentially transported in one direction over the other, solely as a result of the presence of an asymmetric vertical flow field.

24. There are two important time scales to keep in mind: The convective time scale H r / v c The “flux expulsion” timescale --- i.e., the amount of time necessary for the field to reach its equilibrium distribution From Abbett et al. 2004 After the flux distribution becomes significantly non-uniform, there is a net downward transport of flux (a weak pumping mechanism uncorrelated with vertical flow asymmetries) while the flux is redistributed to its equilibrium configuration

25. Dynamic Disconnection Understanding the transition between active region evolution in terms of emerging flux tubes versus active region decay as described by passive flux transport models (Schüssler & Rempel 2005) As magnetic flux breaks through the photosphere, sunspots form and the initial coronal magnetic field is established As the plasma in the spots cools and sinks, and the buoyant plasma from below emerges, the upper parts of these flux tubes are blown apart and are then controlled by convective motions. Passive flux transport models then describe the surface evolution of the active region field

26. Closer to the Surface From Abbett et al. 2003

27. Closer to the Surface The emergence of active region magnetic fields into the solar atmosphere From Magara 2004From Fan 2001

28. Successes of Sub-surface Models Equatorial zone of avoidance of active regions Hale’s law and Joy’s law (active region orientation) The dependence of active region tilt on AR size The dispersion of tilt versus active region size Asymmetric spot motions (leading vs. following) Morphological asymmetry Helicity distribution of active regions with latitude Stability of active region flux tubes (Ω-loops) in 3D The transition between active region flux tube dynamics and flux transport models (new result) δ-spot active regions as highly twisted kinking flux tubes (maybe)

29. Open Questions What triggers the eruption of active regions from the base of the convection zone? Instability, secular heating, convective overshoot, or something else? Most active regions exhibit only small amounts of twist, and are consistent with a tube lying initially at the base of the convection zone with no twist. How then do the island δ-spot regions acquire so much twist? How is the free energy from sub-surface fields transported into the corona?

30. Open Questions What is the magnetic connection between different active regions? Are active regions magnetically connected to each other in the dynamo region, or are they all separate? How do we relate “active longitudes” and “active nests” to a magnetic picture of the large-scale dynamo region at the base of the convection zone? Is the magnetic flux that gives birth to active regions in a smooth, slab-like geometry, or is the flux already pre- existing in the form of tubes?

31. What happens when active region flux tubes collide in the solar interior? What happens when a new active region emerges into an old one? How do active region flux tubes interact with the small scale field in the Quiet Sun? What is the 3D analogue of the surface flux transport models? How does the following polarity from decaying, emerged active regions return to the dynamo regions? What happens to the magnetic roots of an emerged active region once the active region begins decaying? Open Questions

32. Can we infer the sub- surface structure of an active region by studying its surface evolution? Can we predict the emergence of new active regions before it happens, either from helioseismic observation, or from a better knowledge of the physics of magnetic evolution below the photosphere?