1. CME Eruption at the Sun and Ejecta Magnetic Field at 1 AU Valbona Kunkel Solar Physics Division, Naval Research Laboratory Collaborator: J. Chen vkunkel@gmu.edu April 15 2013 12th Annual International Astrophysics Conference

2. NRL Solar Physics Division Hundhausen (1999) “MAGNETIC FORCES”: MAGNETIC GEOMETRY OF CMEs 3D Geometry of CMEs–3 Part Morphology Illing and Hundhausen (1986) Chen et al (1997) SOHO Dominant consensus from the 1980s and1990s (SMM era): CMEs are dome-like structures with rotational symmetry, not a thin flux rope Neither of the above SMM

3. NRL Solar Physics Division INTRODUCTION: CME-FLARE PHYSICS Key Questions in Coronal Mass Ejection (CME) Physics and New Answers: What forces drive CMEs?—evolution of a CME and its B field from the Sun (to 1 AU) What is the physical connection between CMEs and associated flares? What is the energy source? Open physics issues—quantified A Physical Model of CMEs: The Erupting Flux Rope (EFR) model of CMEs: a quantitative theoretical model that correctly replicates observed CME dynamics—direct comparison with data: –CME position-time data from the Sun to 1 AU (STEREO) –in situ B(t) and plasma measurements of CME ejecta at 1 AU (STEREO, ACE) –CME data and associated flare (GOES) X-ray (SXR) data (near-Sun processes) Theme of This Talk: What extractable physical information do data contain? Theory-data comparison at both ends of the Sun-Earth region and the intervening CME trajectory.

4. NRL Solar Physics Division THEORY-DATA RELATIONSHIP Physics Models: Characteristic Physical Scales MHD is scale invariant—models are distinguished by characteristic scales The EFR model---defined by MHD equations for macroscopic flux-rope dynamics What determines the flux-rope motion?---3D flux-rope geometry and physical scales ‒ Lorentz hoop force: ‒ A 3D plasma structure: and evolve ‒ Stationary footpoints: S f = const and Initial equilibrium conditions: B 0, M T0 Acceleration time scale (Alfvenic) How are these scales manifested in the data? SfSf R a

5. NRL Solar Physics Division Dynamical Scales S f -SCALING OF FLUX-ROPE ACCELERATION Chen, Marque, Vourlidas, Krall, and Schuck (2006) S f – Scaling A geometrical effect – a flux rope at t = 0 and accelerated by the Lorentz hoop force Directly manifested in data—3D geometrical effect

6. NRL Solar Physics Division PHYSICAL INFORMATION IN DATA: Best-Fit Solutions Extract physical information from observations—constrain the model by only the observed height-time data, Z data (t i ), and calculate the best-fit solution, Z th (t i ) ‒ Minimize the average deviation from the data (maximize the goodness of fit) ‒ data, model solution, and uncertainty at the i-th observing time Adjust S f and to minimize D ‒ A “shooting” method ‒ S f and calculated by the best-fit solution are the physical predictions of the EFR model constrained by the height-time data The best-fit solutions can produce other physical predictions that can be tested ‒ Hypothesis:

7. NRL Solar Physics Division INITIAL-VALUE SOLUTIONS Input Parameters Model corona—specified and unchanged ‒ p c (Z), n c (Z), B c (Z), V sw (Z), C d, Observational constraints ‒ S f, Z data (t i ), I SXR (t) Model Outputs Initial field and mass—calculated, intrinsic ‒ Initial equilibrium conditions B 0, M t0, p 0 Initial-value solution ‒ S f, “shooting parameter” ‒ Minimize D S f, are physical predictions SfSf Z

8. NRL Solar Physics Division EMF: CME-FLARE CONNECTION D = 1.3% Z 0 = 2.5 x 10 5 km S f = 4.25 x 10 5 km max = 3.7 V/cm X

9. NRL Solar Physics Division EMF: CME-FLARE CONNECTION Best-fit and good-fit solutions yield in close agreement with X-ray light curve. Predicted S f is consistent with observation. D = 1.3% Z 0 = 2.5 x 10 5 km S f = 4.25 x 10 5 km max = 3.7 V/cm 12 September 2000 Chen and Kunkel (2010)

10. NRL Solar Physics Division SENSITIVITY OF FLUX INJECTION TO HEIGHT DATA D = 1.4% Z 0 = 8 x 10 4 km S f = 2.0 x 10 5 km max ~ 15 V/cm Initial-value solution from Z 0 to 1 AU Chen and Kunkel (2010) The main acceleration phase manifests Alfven timescale B 0 and M T0 Must be internally generated by a model The long-time trajectory is a stringent constraint on

11. NRL Solar Physics Division CME-FLARE CONNECTION Demonstrated for several CME-flare events: ‒ The best-fit solutions constrained by height-time data alone yield —a physical prediction—in close agreement with I SXR (t) (temporal form) ‒ The height-time data contain no information about X-rays—agreement is significant Hypothesis and an interpretation ‒ is a potential drop (super Dreicer) particle acceleration and radiation physical connection between CME and flare particle acceleration Physical implications ‒ The time scale of I SXR (t) is in the height-time data—via the ideal MHD EFR equations ‒ The EFR equations capture the correct physical relationship between “M” and “HD” Test with another observable quantity ‒ Magnetic field at 1 AU as constrained by the observed CME trajectory data

12. NRL Solar Physics Division 6.1 New Start Plasma Physics Division Best-fit solution is within 1% of the trajectory data throughout the field of view If Z data (t) is used to constrain the EFR equations, the model predicts B 1AU (t) correctly Arrival time earlier than observed; in this case, a 3D geometrical effect (Kunkel 2012) B A Observed B 1AU and 3D Geometry STEREO Configuration 2007 Dec 24 [Kunkel and Chen 2010] PROPAGATION OF CME and EVOLUTION OF CME B FIELD Earth

13. NRL Solar Physics Division SENSITIVITY OF B(1AU) TO SOLAR QUANTITIES Dependence of B(1 AU) on injected poloidal energy Total poloidal energy injected: Vary the flux injection profile while keeping U p | inj unchanged DBcBc dΦ p /dt (ΔU p ) tot B(1AU)T(1AU)a(1AU) [Gauss][Mx/sec][erg][nT][UT][km] 0.844.2 x 10 18 9 x 10 31 2261 9.4 x 10 6 2.973.6 x 10 18 9 x 10 31 22619.4 x 10 6 2.614.8 x 10 18 9 x 10 31 22619.4 x 10 6 |B CME | and arrival time at 1AU are not sensitive to the flux injection profile B CME field and arrival time are most sensitive to injected poloidal magnetic energy Kunkel (PhD thesis, 2012) Best fit

14. NRL Solar Physics Division MAGNETIC FIELD AND TIME OF ARRIVAL OF CME AT 1AU Increase the total injected poloidal energy U p | inj by 10% ‒ Calculate the best-fit solution ‒ Calculate B(1 AU) and time of arrival of CME at 1 AU ‒ Determine the goodness of fit for each solution DBcBc dΦ p /dt (ΔU p ) tot B 1AU T 1AU a 1AU [Gauss][Mx/sec][erg][nT][hrs][km] 2.875.6 x 10 18 1 x 10 32 2360 9.3 x 10 6 4.374.9 x 10 18 1 x 10 32 2459 9.1 x 10 6 2.265.5 x 10 18 1 x 10 32 2261 9.4 x 10 6 DBcBc dΦ p /dt (ΔU p ) tot B 1AU T 1AU a 1AU [Gauss][Mx/sec][erg][nT][hrs][km] 0.844.2 x 10 18 9 x 10 31 22619.4 x 10 6 2.973.6 x 10 18 9 x 10 31 22619.4 x 10 6 2.614.8 x 10 18 9 x 10 31 22619.4 x 10 6 Best fit Constant Injected Poloidal Energy

15. NRL Solar Physics Division B(1 AU) AND ARRIVAL TIME AT 1 AU: INFLUENCE OF B c The overlying field B c determines the initial B p, initial energy, and Alfven time Expect the 1 AU arrival time and B(1 AU) to be sensitive to B c SfSf R a DBcBc dΦ p /dt (ΔU p ) tot B 1AU T 1AU a 1AU [Gauss][Mx/sec][erg][nT][hrs][km] 0.844.2 x 10 18 9.0 x 10 31 2261 9.4 x 10 6 3.50-0.55.4 x 10 18 7.2 x 10 31 17.060 8.6 x 10 6 3.36-1.56.8 x 10 18 1.5 x 10 32 26.162 1.0 x 10 7

16. NRL Solar Physics Division SUMMARY The EFR model equations A self-contained description of the unified CME-flare-EP dynamics ‒ Correctly replicates observed CME dynamics to 1 AU—a challenge for any CME model It can be driven entirely by CME data to compute physical quantities: ‒ — coincides with temporal profile of GOES SXR data (Chen and Kunkel 2010) ‒ B field and plasma parameters at 1 AU — in agreement with data (Kunkel and Chen 2010) ‒ B(1 AU) is not sensitive to the temporal form of ; it is sensitive to the total poloidal energy injected (Kunkel, PhD thesis, 2012; Kunkel et al. 2012) Physical interpretations of is the electromotive force—physical connection to flares Implications –Space Weather Given observed CME trajectory (position-time) data, it is possible to predict the magnetic field at 1 AU—there is sufficient information (Kunkel, PhD, 2012) Accurate 1-2 day forecasting is possible if an L5 or L4 monitor exists

17. NRL Solar Physics Division OPEN ISSUES Energy Sources admits two distinct physical interpretations (Chen 1990; Chen and Krall 2003; Chen and Kunkel 2010) ‒ Coronal source: injection of flux from coronal field via reconnection (conventional) ‒ Subphotospheric source: injection of flux from the solar dynamo (Chen 1989, 1996) Neither interpretation has been theoretically or observationally proven ‒ Reconnection: physical dissipation mechanisms and large scale disparity ‒ Subphotospheric mechanism: none has been calculated Both are “external physics” in all current CME/flare models

18. NRL Solar Physics Division OTHER MODELS The EFR model should be applicable to flux ropes with fixed footpoints ‒ models starting with flux ropes (Chen 1989; Wu et al. 1997; Gibson and Low 1998; Roussev et al. 2003; Manchester et al. 2006) ‒ arcade models producing flux ropes (e.g. Antiochos et al. 1999; Amari et al. 2001; Linker et al. 2001; Lynch et al. 2009) Does not apply to axisymmetric flux rope models—e.g., Titov and Demoulin (1999), Lin, Forbes et al. (1998), Kliem and Torok (2006) ‒ They do not correspond to simulations (e.g., Roussev et al. 2003; Torok and Kliem 2008) Mathematically, occurs in arcade models (e.g., Lynch et al. 2009) Titov and Demoulin (1999) Lynch et al. (1999)

19. NRL Solar Physics Division PHOTOSPHERIC SIGNATURES? Assumptions: ‒ Coherent B field (space and time) ‒ No dynamics ‒ Schuck (2010) ‒ Smaller A and longer ‒ Same calculation (no dynamics) AGU Fall (2001) Lin et al. (2003)

20. NRL Solar Physics Division Schuck (2010) ‒ Falsified the “flux injection hypothesis” ‒ Consistent with the “reconnection hypothesis” Starting point ‒ Specified coherent field and time scale ‒ ‒ No subsurface source of poloidal flux ‒ No dynamical equations of motion for “injection” ‒ No gravity (e.g., no Parker instability) ‒ No convection zone medium through which “injection” occurs ‒ No photosphere (i.e., no photospheric signature) ‒ No reconnection physics or dynamics No physical or mathematical basis to support either claim ‒ A “Strawman” argument The calculation is the same as Forbes (2001) OBSERVATIONAL SIGNATURES OF FLUX INJECTION

21. NRL Solar Physics Division POLOIDAL FLUX INJECTION Poloidal magnetic field is mostly in region—incoherent in dynamics Chen (2012, ApJ)

22. NRL Solar Physics Division Initial Simulation: Chen and Huba (2006) ‒ 3D MHD code (Huba 2003) ‒ A uniform vertical flux rope ‒ Increase B field at the bottom ‒ Introduce a horizontal flow (“convection” flow) ‒ No gravity yet DYNAMICS OF POLOIDAL FLUX INJECTION

23. NRL Solar Physics Division PHOTOSPHERIC SIGNATURES Pietarila Graham et al. (2009) –current magnetogram resolution insufficient to resolve small-scale magnetic structures Cheung et al. (2010) –Simulation of an emerging flux rope; synthetic magnetograms ‒ Photospheric data show small bipoles; scales are much smaller than the underlying emerging flux rope Cheung et al. (2010)

24. NRL Solar Physics Division END

25. NRL Solar Physics Division POST-ERUPTION ARCADES Formation of Post-Eruption Arcades Test the hypothesis that reformation of an arcade results from Establishes the physical connection between CME acceleration and flare energy release EUV+H Jc(t)Jc(t) Roussev et al. (2003) Jc(t)Jc(t) Quantities for comparison: temporal profiles v.