How Does a Coronal Loop’s Geometry Relate to its Other Properties?

1. How Does a Coronal Loop’s Geometry Relate to its Other Properties? An Exploration of Non-Thermal Particle Effects on Simulated Loop Structures Chester Curme Dr. Henry (Trae) Winter

2. Outline • Introduction • Coronal Heating Problem • The HyLoop Suite and non-thermal particles • The relevance of loop geometry • Tapering a loop • The heating function • Preliminary results • Future work

3. What is a coronal loop? • The sun’s magnetic field penetrates its surface and loops around in its atmosphere. • Plasma, bound to magnetic field lines, conforms to these tubes of magnetic flux to produce beautiful structures like the one on the right. http://upload.wikimedia.org/wikipedia/commons/9/93/Traceimage.jpg

4. THE BIG QUESTION: What heats the solar corona?

5. Temperature of the corona is in excess of 106 K. • Temperature of the underlying photosphere is approximately 5800 K, several hundred times cooler than the corona. • This is a mystery.

6. One Idea for the Heating Mechanism: Buchlin, E., Aletti, V., Galtier, S., Velli, M. Einaudi, G., and Vial, J.-C., "A simplified numerical model of coronal energy dissipation based on reduced MHD," A&A 406, 1061-1070 (2003).

7. A nanoflare storm also produces “shrapnel” in the form of a population of high-energy non-thermal particles (electrons). This shrapnel further heats the plasma.

8. Nanoflare heating is a popular candidate for the heating of coronal loops. • Hot (T > 2 MK) loops tend to be under-dense with respect to density at static equilibrium, whereas warm (T ≈ 1 MK) loops tend to be over-dense (Klimchuk 2006). • This suggests that the plasma in coronal loops is not in static equilibrium, a phenomenon explained by the nanoflare theory. • Most who simulate loops in nanoflare events employ 1D magnetohydrodynamic (MHD) models, and treat the NT electrons analytically (if at all).

9. HOWEVER

10. Only Dr. Henry (Trae) Winter III models the evolution of NT particles in nanoflare heating events! • Code is called the “HyLoop” suite (“Hy” for hybrid) and involves two interacting programs: • SHrEC, a 1D MHD model which treats the thermal plasma • PaTC (Particle Tracking Codes), which tracks the evolution of NT particle beams. Dr. Winter at the Harpoon Barbeque Championships, 2009

11. The HyLoop Suite Loop coordinate, s In each volume cell, at each timestep, HyLoop solves the differential equations that govern the plasma and NT particles, tracking the evolution of the loop.

12. Why are NT particles important to model? • Non-thermal (NT) particles may leave an important observable signature: • NT particles may deposit their energies in unexpected places as they travel along the loop. • There exists a “mirroring force” proportional to the tapering of the magnetic field (and hence the loop itself, since plasma is contained by the field lines): Where is the KE of the particle transverse to • This force causes high-energy particles to “bounce around” in a tapered loop. • Note that both the radiative signatures and behavior of NT particles vary strongly with loop geometry. • SHrEC energy MHD equation:

13. Why are NT particles important to model? • Non-thermal (NT) particles may leave an important observable signature: • NT particles may deposit their energies in unexpected places as they travel along the loop. • There exists a “mirroring force” proportional to the tapering of the magnetic field (and hence the loop itself, since plasma is contained by the field lines): Where is the KE of the particle transverse to • This force causes high-energy particles to “bounce around” in a tapered loop. • Note that both the behavior of NT particles and their radiative signatures vary strongly with loop geometry. • SHrEC energy MHD equation:

14. This brings us to our question: After taking into account the effects of NT particles, how is a coronal loop’s geometry related to its other properties?  Maximum temperature  Apex density  Average power at apex How geometry correlates (if at all) with these properties can shed light on the validity of the nanoflare theory, once compared with observations.

15. We define a loop’s geometry in terms of the tapering ratio • Construct a semi-circular loop of circular cross-section and linearly taper loop radius by Γ. • Study of 43 soft X-ray loops by Yohkoh reported median Γ of ≈ 1.30 (Klimchuk 1999).

16. The Heating Function • First few minutes constitute a stabilization period: constant flux, uniform heating. • After stabilization: • Each simulated flare has the same amount of total energy. • Energy is divided into a series of nanoflare storms. • At a pre-defined timestep, a storm of nanoflares occurs. Each nanoflare injects a beam of test particles into the loop. • Nanoflares in each storm are of equal power and distributed randomly along the loop coordinate s.

20. Volumetric Heating Rate

21. Volumetric Heating Rate

23. Preliminary Results

25. Mean r: 0.973

31. Mean r: 0.977

38. Mean r: 0.743

40. Mean r: 0.542

41. Conclusions • Tapering loops has an appreciable effect on loop maximum temperature, apex density, and (weakly) apex power. • Contribution of NT particles to this circumstance is unquantified. • Including NT particles in simulations generally lowers the loop’s maximum temperature and apex power, while raising its apex density.

42. Future Work • PaTC treats NT particles stochastically; average results over multiple runs and calculate statistical error (Monte Carlo methods). • Use emission data from simulated loops to produce images as would be viewed by satellites: • Perform similar correlation studies, varying: • Location of nanoflares • Pitch-angle distribution • Ratio of thermal to non-thermal energies • Simulate a multi-stranded loop http://helio.cfa.harvard.edu/REU/2009_REU_Proj_Winter.html

43. Special Thanks • Dr. Winter • Dr. Korreck • Dr. Davey • NSF • And many more!

45. Questions: • Not hydrostatic eq.  use simulations? • Gaussians in heat function more physical? • No e_h from NT part. Collisions in previous codes?

47. What are non-thermal particles? • A population of particles that follows a Maxwell-Boltzmann distribution can be said to have a temperature; the particles are thermal. • Nanoflares may inject high-energy non-thermal (NT) particles into a loop. These particles are said to be non-thermal because they lie on the outer tail of the distribution, which follows a power-law; it is meaningless to ascribe a temperature to a population of NT particles. Maxwellian Number of Particles Power-law NT Tail Energy

48. How is HyLoop stochastic? • PaTC treats the NT particle beam as a series of test particles, and tracks their evolution through the thermal plasma. • Test particles are drawn randomly from probability distributions that correspond to certain types of NT beam. In addition, the equations that govern the particles involve stochastic (random) terms. • Results of simulations, then, will vary with each run. Monte Carlo methods are thus used to average over runs and compute statistical errors.

49. Most ideas for the heating mechanism can be grouped into one of two categories: • Dissipation of waves, or “AC Heating” • Dissipation of magnetic stresses, or “DC Heating.”

50. AC Heating • Some propose that the dissipation of wave energy in the corona (acoustic, Alfvén, magnetosonic, torsional…) is responsible for its extreme temperatures. • Presumably, however, only a small fraction of waves’ energy flux is able to pass through the steep density and temperature gradients in the chromosphere and transition region. • Waves aren’t well-understood (energy flux, spectrum, etc.).