Jaroslav Dudík 1 ,2 Elena Dzifčáková 3 , Jonathan Cirtain 4

1. Area Expansion of MagneticFlux-Tubes in Solar Active Regions Jaroslav Dudík1,2Elena Dzifčáková3, JonathanCirtain4 1– DAMTP-CMS, University of Cambridge 2 – DAPEM, FMPhI, Comenius University, Bratislava, Slovakia 3–Astronomical Institute of the Academy of Sciences, Ondřejov, Czech Republic 4 –NASA MarshallSpaceFlight Center, Huntsville, AL, USA 14th European Solar Physics Meeting Dublin, Ireland, September 9th, 2014

2. Outline • The Active Region Corona: Loops and what else?Observednon-expansion of coronal loopsDo we understand the geometrical effects? Notes on active region modelling • The Case of Quiescent AR 11482 Dudík et al. (2014) ApJ, submitted Hinode/SOT observations Potential extrapolation and approximation by magnetic charges Expansion with height Structure of area expansion factors: steep valleys and flat hills “Fundamental flux-tubes”: linguine rather than spaghetti • Speculations: How to Create Coronal LoopsThe effect of expansion on density and total input heating

3. Coronal Loops: Lack of Expansion Klimchuk et al. (1992), PASJ 44, L181 Klimchuk (2000), SoPh 193, 53 Watko & Klimchuk (2000), SoPh 193, 77 Aschwanden & Nightingale (2005), ApJ 633, 499 Brooks et al. (2007), PASJ 59, 691

4. Hot Core and WarmPeriphery • Closed magnetic flux – loops (widths, temperature profiles) • Spatial structure: – hot, X-Ray AR core, diffuse – warm EUV loops • – EUV moss – “bright points” Could these observations be explained by ONE and UNIVERSAL heating function?

5. Do We Understand the Geometry? DeForest (2007),ApJ 661, 532: Poorly resolved expanding structures may appear to benon-expanding

6. But some loops are resolved… Brooks et al. (2013), ApJ 772, L19 Peter et al. (2013) A&A 556, A104

7. Geometry… Part 2 • Malanushenko & Schrijver (2013), ApJ 775, 120 • No circular cross-sections • Introduces bias in loop selection

9. Expanding Loop: Thermal Struct. • Peter & Bingert (2012), • A&A 457, A1 • MHD model of the solar corona • Magnetic flux-tube with expanding area (cross-section) • Interplay between temperature and density structure • Leads to apparently non-expanding AIA loop • Even if well-resolved

10. Dudík et al. (2011), A&A 531, A115

11. Area Expansion Factor: Structure • SOHO/MDI • 2” spatial resolution • Expansion factor defined as: (flux cons.)

12. Hinode/SOT BZ: 0.3’’ resolution

13. Approximation by 134 charges

14. Area Expansion: General Properties , calculated for every voxel (volume pixel) • Flux-tubes in direct extrapolation expand more strongly • Rate of expansion increases with height of the starting point

15. Area Expansion Factor: Structure direct extrapolation magnetic charges significant structure little structure

16. “Steep Valleys and Flat Peaks” Direct extrapolation Approx. by charges

17. Steep Valleys: Coronal Loops? Periphery AR core

18. “Fundamental Flux-tubes”

19. Highly Squashed Cross-sections

20. Toy model: Density increase • Suppose heating depends on B, and B decreases exponentially: • The definition of the area expansion factor then gives • Electron density in the hydrostatic, steady-heating case can be obtained from the scaling laws: I.e., because of the definition of Γ. • Therefore, two field lines with different Γ1, Γ2 will produce density contrast:

21. Summary • The flux-tube expansion is finely structuredEven in potential fields – other fields likely even more complex. • Steep valleys with width of one or several 0.3’’ pixels • Prediction: Hi-C off limb may NOT see expanding loops • “Fundamental flux-tubes” have highly squashed cross-sections • Linguine rather than spaghetti • Combined with heating as a function of B, a structureof activeregionemission canemerge Dudík et al. (2011), Astron. Astrophys. 531, A115 Dudík et al. (2014), Astrophys. J., submitted

22. Thank you for your attention

23. Hot Core and WarmPeriphery • X-ray “hot” loops • EUV “warm” loops

24. ActiveRegions: TheScaleProblem

25. The Heating Function • Unkown. Assumed to be exponentially decreasing & parametrized: CH0, ρ & τ–free parameters B0– footpoint magnetic field L0–loop half-length sH –heating scale-length • sHis determined from the rate of magnetic field decrease along a loop

26. “DDKK” Generalized Scaling Laws • Non-uniform heating • Non-isothermal loops • Pressure stratification in non-isothermal loops • Parametrized form of radiative losses: R(T) = χT–σne2 Dudíket al. (2009), Astron. Astrophys. 502, 957

27. Loop Temperature Profiles • Voxel position corresponding to a location s along the loop. Define • If the heating has L/sH < 3, then • Else (3 < L/sH< 25) Aschwanden & Schrijver (2002), ApJS 142, 269

28. AR 10963: Observations

30. The Temperature Structure

31. The Role of Heating Scale-Length

32. The Role of Heating Scale-Length

33. The Hinode/SOT Case

34. The Hinode/SOT Case

35. Area Expansion at 0.3’’ resolution Saturated to: Γ = 50 Γ = 150 • XY plane, Z = 100*0.32’’ = 32’’ = 23.2 Mm

36. Area Expansion at 0.3’’ resolution Saturated to: Γ = 50 Γ = 150 YZplane, Xfixed

37. Area Expansion at 0.3’’ resolution Saturated to: Γ = 50 Γ = 150 XZplane, Yfixed

38. Area Expansion at 0.3’’ resolution Volumetric rendering of the Expansion Factor

39. Area Expansion at 0.3’’ resolution Volumetric rendering of the (Expansion Factor)1.5