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

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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

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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.

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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

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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

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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:

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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

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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

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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)

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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

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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

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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

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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] x x x x x x x x 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

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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] x x x x x x x x x 10 6 DBcBc dΦ p /dt (ΔU p ) tot B 1AU T 1AU a 1AU [Gauss][Mx/sec][erg][nT][hrs][km] x x x x x x x x x 10 6 Best fit Constant Injected Poloidal Energy

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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] x x x x x x x x x 10 7

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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

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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

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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)

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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)

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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

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

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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

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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)

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NRL Solar Physics Division END

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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.

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