CME Eruption at the Sun and Ejecta Magnetic Field at 1 AU Valbona Kunkel Solar Physics Division, Naval Research Laboratory Collaborator: J. Chen [email protected]

CME Eruption at the Sun and Ejecta Magnetic

Field at 1 AU

Valbona Kunkel

Solar Physics Division, Naval Research Laboratory

Collaborator: J. Chen

[email protected]

April 15 2013 12th Annual International Astrophysics Conference

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


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.


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: Sf = const and

• Initial equilibrium conditions:

B0, MT0 Acceleration time scale (Alfvenic)

• How are these scales manifested in the data?

2 2 2 2/ 0, / 0d Z dt d a dt

Sf

R

a

2 2( ) / ( ) / ( ) ln(8 / ) / 2 / /p p c pdV t dt t L t R a R a B B

2 2/ ( , , )a t pd a dt F B B p

2 2( ) / 4 / 2 ( )fR t Z S Z t

( ) ln 8 /L t R R a


Dynamical Scales

Sf -SCALING OF FLUX-ROPE ACCELERATION

Chen, Marque, Vourlidas, Krall, and Schuck (2006)

22

2 ln (8 / )f

f

Sd Z

R R adt

Sf – Scaling

A geometrical effect – a flux rope at t = 0 and accelerated by the Lorentz hoop force

Directly manifested in data—3D geometrical effect/ /R Ap paR V R B


PHYSICAL INFORMATION IN DATA: Best-Fit Solutions

• Extract physical information from observations—constrain the model by only the

observed height-time data, Zdata(ti), and calculate the best-fit solution, Zth(ti)

‒ Minimize the average deviation from the data (maximize the goodness of fit)

‒ data, model solution, and uncertainty at the i-th observing time

• Adjust Sf and to minimize D

‒ A “shooting” method

‒ Sf 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:

1

| ( ) ( ) |1 Ndata i th i

ii

Z t Z tD

T Z

( ), ( ),data i th i iZ t Z t Z

( ) /pd t dt

( ) /pd t dt

( ) (1/ ) ( ) /pemf t c d t dt ( ) ( )SXRemf t I t


INITIAL-VALUE SOLUTIONS

Input Parameters

• Model corona—specified and unchanged

‒ pc(Z), nc(Z), Bc(Z), Vsw(Z), Cd ,

• Observational constraints

‒ Sf, Zdata(ti), ISXR(t)

Model Outputs

• Initial field and mass—calculated, intrinsic

‒ Initial equilibrium conditions B0, Mt0, p0

• Initial-value solution

‒ Sf, “shooting parameter”

‒ Minimize D Sf, are physical predictions

Sf

p

Z

( ) /pd t dt

( ) /pd t dt

1.18


EMF: CME-FLARE CONNECTION

D = 1.3% Z0 = 2.5 x 105 km Sf = 4.25 x 105 km <E>max = 3.7 V/cm

X

1

| ( ) ( ) |1 Ndata i th i

ii

Z t Z tD

T Z


EMF: CME-FLARE CONNECTION

• Best-fit and good-fit solutions yield in close agreement with X-ray light curve.

• Predicted Sf is consistent with observation.

D = 1.3% Z0 = 2.5 x 105 km Sf = 4.25 x 105 km <E>max = 3.7 V/cm

( ) /pd t dt

12 September 2000

Chen and Kunkel (2010)


SENSITIVITY OF FLUX INJECTION TO HEIGHT DATA

D = 1.4% Z0 = 8 x 104 km Sf = 2.0 x 105 km

<E>max ~ 15 V/cm

Initial-value solution from Z0 to 1 AU

Chen and Kunkel (2010)

The main acceleration phase manifests

Alfven timescale B0 and MT0

Must be internally generated by a model

The long-time trajectory is a stringent

constraint on ( ) /pd t dt


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 ISXR(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 ISXR(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

( ) /pd t dt

(1/ ) ( ) /pemf c d t dt


6.1 New Start Plasma Physics Division

• Best-fit solution is within 1% of the trajectory data throughout the field of view

• If Zdata(t) is used to constrain the EFR equations, the model predicts B1AU(t) correctly

• Arrival time earlier than observed; in this case, a 3D geometrical effect (Kunkel 2012)

BA

Observed B1AU and 3D Geometry

STEREO Configuration 2007 Dec 24

[Kunkel and Chen 2010]

PROPAGATION OF CME and EVOLUTION OF CME B FIELD

Earth


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 Up|inj unchanged

2 0

( ') ( ')1| '

( ') 'p p

p injt d t

U d tL t d tc

D Bc dΦp/dt (ΔUp)totB(1AU) T(1AU) a(1AU)

[Gauss] [Mx/sec] [erg] [nT] [UT] [km]

0.84 -1.0 4.2 x 1018 9 x 1031 22 61 9.4 x 106

2.97 -1.0 3.6 x 1018 9 x 1031 22 61 9.4 x 106

2.61 -1.0 4.8 x 1018 9 x 1031 22 61 9.4 x 106

• |BCME| and arrival time at 1AU are not sensitive to the flux injection profile

• BCME field and arrival time are most sensitive to injected poloidal magnetic energy

Kunkel (PhD thesis, 2012)

Best fit


MAGNETIC FIELD AND TIME OF ARRIVAL OF CME AT 1AU

• Increase the total injected poloidal energy Up|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

D Bc dΦp/dt (ΔUp)tot B1AU T1AU a1AU

[Gauss] [Mx/sec] [erg] [nT] [hrs] [km]

2.87 -1.0 5.6 x 1018 1 x 1032 23 60 9.3 x 106

4.37 -1.0 4.9 x 1018 1 x 1032 24 59 9.1 x 106

2.26 -1.0 5.5 x 1018 1 x 1032 22 61 9.4 x 106



0.84 -1.0 4.2 x 1018 9 x 1031 22 61 9.4 x 106

2.97 -1.0 3.6 x 1018 9 x 1031 22 61 9.4 x 106

2.61 -1.0 4.8 x 1018 9 x 1031 22 61 9.4 x 106

Best fit

Constant Injected Poloidal Energy


B(1 AU) AND ARRIVAL TIME AT 1 AU: INFLUENCE OF Bc

• The overlying field Bc determines the initial Bp, initial energy, and Alfven time

• Expect the 1 AU arrival time and B(1 AU) to be sensitive to Bc

Sf

R

a



0.84 -1.0 4.2 x 1018 9.0 x 1031 22 61 9.4 x 106

3.50 -0.5 5.4 x 1018 7.2 x 1031 17.0 60 8.6 x 106

3.36 -1.5 6.8 x 1018 1.5 x 1032 26.1 62 1.0 x 107

0 0 0 0 0 0 0( / ) ln(8 / ),p c pB R a B R a


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

( ) /pd t dt

(1/ ) ( ) /pemf c d t dt

( ) /pd t dt

( ) /pd t dt


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

( ) /pd t dt


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)( ) /pd t dt

Titov and Demoulin (1999) Lynch et al. (1999)


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)

1/V A t

t


• 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

/ 4 , /c c S E B E V B 0


POLOIDAL FLUX INJECTION

• Poloidal magnetic field is mostly in region—incoherent in dynamics1

Chen (2012, ApJ)(1/ ) 0

0( )

c p

p

J B

J B


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


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)


END


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)

(1/ ) ( ) /emf pE c d t dt

Roussev et al. (2003)

( ) /pd t dtJc(t)

Quantities for comparison: temporal profiles

v. 22( ) ( )EUV c pI t J t d dt ( ) /SXR pI t d dt

Documents

CME Eruption at the Sun and Ejecta Magnetic Field at 1 AU Valbona Kunkel Solar Physics Division, Naval Research Laboratory Collaborator: J. Chen [email protected]