Space Storms as Critical Phase Transitions J. A. Wanliss D aytona Beach, Florida 12 May 2005

1. Space Storms as Critical Phase Transitions J. A. WanlissDaytona Beach, Florida12 May 2005

2. INTRODUCTION • Critical behaviour – Ising model -Struggle between order and disorder -eternal problem of the one and the many • Sol and Gaia – the cosmic kiss! • Evidence • Tests – Multifractal models….

3. INTRODUCTION • Critical behaviour – Ising model -Struggle between order and disorder -eternal problem of the one and the many • Sol and Gaia – the cosmic kiss! • Evidence • Tests – Multifractal models….

4. CRITICAL BEHAVIOUR • Power laws • Self-similarity across scales • Sensitivity to small perturbations

5. ISING MODEL • Magnetization of individual elements • State of element i depends on behavior of neighbors, and the forces tending to imitation, K, and disorder, .

6. NEAREST NEIGHBOURS

7. K<Kc

8. K≈Kc

9. At the critical point a singularity occurs because the susceptibility goes as a power law: • The critical scaling exponent • System is highly sensitive to small perturbations, has power laws, and is self-similar across scales

10. K>Kc

11. SPACE WEATHER • A collection of magnetic and electric phenomena that occur in: • Outer space • The upper atmosphere of planets • On the sun

12. Technology is Sensitive to Space Weather • Heaven • Earth

14. WHAT IS A STORM? • Most prominent space weather events • Initial phase: sudden worldwide increase in the B-field by 10s nT (~minutes to hours) • Main phase: 100s of nT reductions in the horizontal component (~day) • Recovery phase: B-field slowly returns to pre-storm values (days)

15. Disordered Imitative

16. CLASSICAL VIEW • Onset is caused by strong magnetospheric convection coupled with CMEs - and/or fast solar wind - and/or pressure pulses - and/or extended periods of southward IMF

17. CORONAL MASS EJECTION

18. FACTS • Classical view substantially correct. • Precise storm trigger is unknown! • CMEs and extreme values of the southward IMF, Bs, are leading factors in storm development although neither of these factors by themselves are sufficient nor necessary for storm occurrence or development.

19. 1995/1/8, 1700 UT 2000/7/5, 0100 UT 1981/3/7, 0300 UT ?? VBs P • Show example of cme and no storm, or storm without cme B Bz

20. SPACE STORMS • Drastic system collapse at onset of storm main phase. • Is the pre-storm magnetosphere state highly disordered ( dominates) until the statistical state of the system passes through a critical point that precipitates the mostly ordered (K dominates) and imitative state of the space storm?

21. HYPOTHESIS • Onset is the result of a first-order-like phase transition between different possible critical states of the magnetosphere. • IF the storm onset is a critical point…

22. IF…THEN • IF the storm onset is a critical point… THEN • …there are important implications because criticality is always associated with some precursory phenomena.

23. L2 C L1 B A

24. MODELING STRATEGIES • 1.) Analytic theories (e.g. Burton et al. 1975) • 2.) Brute force (e.g. MHD) -suffers from inaccurate specification and numerical issues that are important and extreme events -at best we only have one point measurement of solar wind data….

25. LRD and intermittency DST [nT] DST [nT]

26. Power law

27. Fractal dynamics • Are there characteristic differences in nonlinear statistics during quiet (Q) and active (A) times? • Study Q and A periods from 21 years of SYM-H • Compute and compare nonlinear statistics

29. Example: 1985

32. Independent events

33. Results • Averages: • Compare differences between Q and A, using students-t

34. Continuous analysis DST a da

35. Multifractal Modeling • Statistical physics concept to create a partition function • is essentially a variable scale size. The variables q and play a similar role as the inverse of temperature and free energy in thermodynamics.

36. Scaling exponent is defined by and the generalised fractal dimensions of the measure are defined as • If curve is non-linear, the original series is multifractal.

37. Partition function vs scale size

38. Generalised fractal dimension vs q

39. Conclusions • We analyzed Dst series and measure representation for 1981-2002. • Q/A states follow very different scaling laws…FSOC?? • Variations in nonlinear scaling exponent indicates transitions between Q/A states and suggests a predictive scheme • MF analysis indicates intermittency is an important feature in the magnetosphere

40. References • Wanliss, J.A., Fractal properties of SYM-H during quiet and active times, J. Geophys. Res., 2005. • Wanliss, J. A., V. V. Anh, Z.-G. Yu, and S. Watson, Multifractal modelling of magnetic storms via symbolic dynamics analysis, J. Geophys. Res., 2005. • V. V. Anh, Z. G. Yu, J. A. Wanliss, and S. M. Watson, Prediction of magnetic storm events using the Dst index, Nonlin. Proc. Geophys., 2005.

41. RENORMALIZATION GROUP

43. Halo CME storm

44. Halo CME no storm • Show example of cme and no storm, or storm without cme

45. POWER LAWS

46. SELF-SIMILARITY

47. SENSITIVITY TO PERTURBATIONS

48. Movement through critical states • A B – spectral indices change continuously • A C – spectral indices change abruptly (goes through critical point) • If either of these things happen the system is multifractal.