SHINE 2019 – Session 4. Force, Momentum, and Energy Distribution in Solar Eruptions

• How are the force, momentum, and energy distributed in different layers of the solar atmosphere during eruptions?

• What is the momentum partition in solar eruptions like? How does it compare with the energy partition?

• How important are the high-energy particles and the lower-atmosphere responses?

• What new and existing observations can we use to improve our understanding?

• How can data-driven simulations help interpret the observations?

Hugh Hudson vs. 1. Space Sciences Laboratory, UC Berkeley 2. University of Glasgow

Guillaume Aulanier1. Paris Observatory

Scene-setting speakers:

Our session met SHINE’s long standing tradition of polite, constructive, and collaborative discussion to further the physical insight and understanding of the

fundamental issues of force, momentum, energy distribution and evolution in eruptive flare systems

Our session met SHINE’s long standing tradition of polite, constructive, and collaborative discussion to further the physical insight and understanding of the

fundamental issues of force, momentum, energy distribution and evolution in eruptive flare systems

Discussion

• Photosphere : magnetic field increases

• Heliosphere : CME kinetic energies

• Corona : contracting loops

• Some theory : standard models & conjectures

• Lorentz force impulse/stepwise changes in the photosphericmagnetic field during the impulsive phase of eruptive flares imply the fields become more horizontal

• Seen basically everywhere now

• Including in all MHD simulations

• But we had lively discussion about how useful the forceformulation is --- or what it is actually measuring.

The actual MHD Lorentz force densities don’t really give you these patterns?!Contracting loop motions explained by vortex flows during eruptionMagnetic energy density in flare arcade increases during eruption – NO IMPLOSION?!

Impulse and force• The lower boundary of our coronal

disturbances provides lots of diagnostics• DKIST is upon us and flares will happen

• Sudol & Harvey (2005) LOS field

• Fisher et al. (2012) force analysis:

SHINE 2019 20

2.2. Increase of photospheric BhMagnetic field : obs. vs MHD

Barc

zyns

ki, A

ulan

ier,

Mas

son

& W

heat

land

(201

9)

Sun , Hoeksema, Liu, Kazachenko & Chen (2017)

+ 400

G

+ 0.8 Bunit

B unit = 600 Gfor Bz

max = 2 kG

- 200 G

- 0.3 B unit

2.2. Increase of photospheric BhMagnetic field : obs. vs MHD

Barc

zyns

ki, A

ulan

ier,

Mas

son

& W

heat

land

(201

9)

Sun , Hoeksema, Liu, Kazachenko & Chen (2017)

+ 400

G

+ 0.8 Bunit

B unit = 600 Gfor Bz

max = 2 kG

- 200 G

- 0.3 B unit

between

thefootpoints

ofthe

newly

formed

post-flareloops

increasesduring

thesim

ulation.Hence,the

post-flareloops

thatare

createdatthe

startofthe

eruptionare

shorterthan

thepost-

flareloops

thatformed

attheend

ofthe

simulation.T

henew

lyform

edpost-flare

loopsare

rootedat

theouter

edgeof

thecurrentribbon,butpreviously

formed

post-flareloops

stillexistwhere

thenew

loopsare

created.Hence,

thecurrent

ribbonis

wider

with

time(Section

3.1).Letus

nowfocus

onthe

magnetic

fieldevolution

aroundthe

straightpart

ofthe

currentribbons

(Section3.1)

duringthe

flare.The

horizontalmagnetic

fieldin

ROIs

swept

bythe

currentribbon

firstquickly

decreases(e.g.,

forROI-8

from=

tt

164Ato

=t

t170

A ),which

isrelated

tothe

Bxdecrease

becauseByis

almost

constantat

thissam

etim

eand

place.Before

theeruption,

thegeom

etryof

theloops

overlyingthe

fluxrope

givesapositive

Bx .T

heBhdecrease

isdom

inatedby

theBxdecrease,caused

bythe

straighteningof

theinnerlegs

ofthe

pre-flareloops,

asshow

nby

Aulanier

etal.(2012).

Then,

Bhreaches

minim

um,and

finally,Bhincreases

(e.g.,forROI-8

from=

tt

170A )

untilthe

endof

thesim

ulation.Bhincreases

afterthe

reconnectiontook

placeand

createdthe

post-flareloops.

The

post-flareloops

areshort

andlow

lyingand

aretherefore

significantlymore

horizontal(lower

inclinationangle

with

respectto

thesolar

surface)than

thelonger

andhigher

loopsthatform

edlater.T

heBhgrow

thisdue

tothe

increasein

themagnetic

fieldparallelto

thePIL

(roughlyBy ,Section

3.2).This

iscaused

bythe

reconnection,which

transfersthe

differentmagnetic

shearfrom

thepre-flare

loopsto

thepost-flare

loops(A

ulanieret

al.2012).A

tthe

beginningof

thesim

ulation,the

anglebetw

eenthe

mean

PILand

thesegm

entthatjoinsthe

two

footpoints,called

theshear

angle,islow

(largeshear).

During

theflare,the

shearangleslow

lyincreases

(theshear

decreases).The

spatialdistributionof dB

hshow

saclearasym

metry

with

respectto

thePIL

.The

additionalconcentration

ofthe

horizontalmagnetic

fieldoccurs

onthe

rightside

ofthe

positivecurrent

ribbon,at

aroundof

[x;y]≈

[0.5;0.5]

(Section3.1).

This

effectis

dueto

theCME

deflection

(seeFigure

1),which

isa

resultof

thesystem

asymmetry

(Zuccarello

etal.

2015).The

CME

isdeflected

toward

thenegative

x-axis(Figure

1),thereforeBx ,initially

negativein

thisarea,increases

at[x;y]≈

[0.5;0.5]

(seeSection

2).Furtherm

ore,the

horizontalmagnetic

fielddecreases

atthe

centerof

themagnetic

polarities(Section

3.2).This

resultis

consistentwith

observations(Petrie

2013;Sun

etal.

2017).Moreover,the

timedifference

between

thebeginning

ofthe

increaseof-

jzand

Bhgrow

swith

time.T

hisisdue

tothe

factthat

theshorter

loopsneed

lesstim

eto

relaxthan

thelonger

post-flareloops.

To

compare

theobservation

andthe

simulation,

wealso

focuson

thetim

escales.Wesuggestthatour

simulation

coversarelatively

shorterphysical

timerange

thanin

theobserva-

tionalreports,which

presentthemagnetic

fieldand

thecurrent

variabilityseveral

hoursafter

theflare

(e.g.,Petrie

2013).To

illustratethis,

wescale

thedim

ensionlessmodel

tophysical

dimensions

toestim

atethe

durationof

oursim

ulationin

realtim

e.Weconsider

twopossibilities:

first,ayoung

activeregion

with

asize

of50

Mm

(see,e.g.,

AR11158;

Schrijveret

al.2011)

andacoronal

Alfvén

speedof

cA =

1000km

s −1,

andthen

anold

activeregion

with

asize

of200

Mm

andcA =

400km

s −1.The

simulation

showsaspatial

scaleof

ouractive

regionof

aboutfive

spatialunits,the

latterL=

1being

defined

asthe

distancebetw

eenthe

PILand

thecenter,the

onemagnetic

polarityat

z=0.

Based

onthis

information,

we

obtainthe

Alfvén

timeunit

==

tL

c10

AA

sfor

ayoung

activeregion

(likeAR11158),

and100

sfor

anold

spotlessdecaying

activeregion.

These

valuessuggest

thatthe

time

between

thestartof

theeruption

(t=165tA )

andthe

endof

thesim

ulation(=

tt

244A )

isapproxim

ately15

minutes

and2hr

forayoung

andan

oldactive

region,respectively.Ourm

odeledduration

ofabout

15minutes

isconsistent

with

theobserved

durationof

theBhincrease

ofabout30

minutes

asreported

forAR11158

(seeFigure

2of

Sunet

al.2017).

Figure

4.Magnitude

ofthehorizontalm

agneticfield

changesatthree

differenttimes

duringthe

eruption.The

changein

absolutevalue

ofthehorizontalm

agneticfield

d=

()

Bz

0.1h

isdefined

bythe

colorcode.

The

arrowsare

thesam

eas

inFigure

3.The

solidcontour

linesmark

theelectric

currentdensity

atlevels

==

-(

)j

z0.1

2.2,z

−0.4,

1.6,and2.7

(seejzmaps

inFigure

3).The

animation

beginsat

=t

t164

Aand

endsat

=t

t244

A .

(Ananim

ationof

thisfigure

isavailable.)

6

TheAstroph

ysicalJou

rnal,877:67

(16pp),2019

June1

Barczynski

etal.

we obtain

¶¶

= = ( )Bt

B0 const, 11zz

¶¶

= -¶¶

^=^^ ( )B

tB

uz

x ywhere , . 12z

Based on Equations (11)–(12), we study the temporal evolutionof the variables. Figure 11 shows the evolution of the currentdensity (∣ ∣j ), the y-component of the horizontal magnetic field(By), and the spatial partial derivative of the flow (¶ ¶u zz ) inthe vertical (x, z) plane.

Immediately before the eruption (Figure 11(a)), we note thecharacteristic “filled Ω-shaped” structure of a high currentdensity concentration that surrounds the pre-eruptive flux rope([x; z]≈[−0.3; 2]). Inside this structure, the current density iseven higher and has a teardrop-shaped structure. During theeruption (Figure 11(b)), the usual cusp shape has been formedat around =t t208 A with the clearly visible flare current sheet([x; z]≈[−0.5; 1.5] at =t t208 A). Later, the cusp expandsupward (Figure 11(c)), and its footpoints are cospatial with thecurrent ribbons (Figures 1 and 4).

Initially, a high concentration of negative By (xä[−1; 0.4]and zä[0; 3] ) is observed in the region between the currentribbons and near the flux rope (Figure 11(d)). The Byconcentration near the current ribbons ([x; z]≈[0.3; 0.1])continuously increases during the eruption (Figures 11(e), (f)).Before the eruption, the By concentration around the flux rope

([x; z]≈[−0.3; 2]) forms the teardrop-shaped structure, thenmoves upward and at the same time decreases (Figure 11(d)).Finally, this By concentration moves out of our FOV(Figure 11(e)). In general, the strong increase in Bh (and By)and therefore the magnetic field energy density (although wedo not show it in this paper) exists in the whole cusp, hence allalong the flare loops. Conversely, the Bz distribution variessignificantly less strongly in the cusp.Before the eruption (Figure 11(g)), the ¶ ¶u zz map shows a

Y-shaped structure of ¶ ¶ >u z 0z , below the flux rope(x≈−0.3 and z<2) that is related to the current densityconcentration (black or white contours, in Figure 11). When theeruption starts, the cusp ([x; z]≈[−0.5; 0.5]) with¶ ¶ <u z 0z appears below the Y-shaped structure(Figure 11(h)). This cusp is roughly cospatial with the currentdensity concentration (Figure 11(b)). It expands further andcreates a double Y-shaped structure (Figure 11(i)). On the leftand right side of the current sheet (black contours, inFigure 11), ¶ ¶u zz is positive, but above and below thecurrent sheet, ¶ ¶u zz is negative. The expansion of the doubleY-shape continues until the end of the simulation(Figure 11(i)).

5.2. Amplification of Horizontal Fields

After the flare has started, the magnetic field reconnects atthe HFT, leading to the formation of post-flare loops. Thepileup of the magnetic field lines below the HFT is the result of

Figure 10. Comparison of the Lorentz force density fz (a)–(c) and the alternative Lorentz force density szad (d)–(f) at three different times during the eruption phase,

viewed along a vertical cut at y=0. The vertical component is presented in the color scale. Vectors indicate fx, fz (panels (a)–(c)) and sxad, sz

ad (panels (d)–(f)). Vectorsfx, fz are multiplied by a factor of 5. The black contour lines mark the current density at levels =∣ ∣j 1.1, 3.0, and 6.0 (see Figure 11) and show an inverted Y-shape. Allunits are dimensionless. The animation begins at =t t164 A and ends at =t t244 A.

(An animation of this figure is available.)

12

The Astrophysical Journal, 877:67 (16pp), 2019 June 1 Barczynski et al.

• Momentum question kind of still open. Obviously it’s conserved but where does eruptive flare-generated excess go?

• One of the mainapplication is SUNQUAKES

• Not straight-forward through because the physics of the interface region between photosphere/chromosphere/corona has a massive amount of complex physics

The INTERIOR—CORONA Coupling is an great area for future progress !

Momentum: yes, it’s conserved, but how can we learn from that?

Hudson et al. 2012

SHINE 2019 18

The photosphere-corona interface region

• Ion-neutral physics• Jump in plasma beta• Loss of collisionality• Optical depth unity• Big temperature jump• Convection threshold• Flare and transients

Inexplicably, this physics-laden domain(the chromosphere/TR) is often taken as a boundary for numerical simulations!

7

The problem of vertical scale

S. Wedemeyer

SHINE 2019 8

• Thought we had a fairly uncontroversial understanding of the magnetic energy storage and release in eruptive flares... But evidently not????

• Are there correlations btwn

between flare energy and

waiting times? What does that

tell us?

• Observational estimates of CME kinetic energy to flare energy (DM.E.) ~ 3

• But in all MHD simulations total K.E. (CME+rxn jets) only 10–30% of DM.E....

• Something a little funny about

observational estimates of CME

K.E.? Modelers could analyze

simulation data in the same way

IMPROVING QUANTATIVE ENERGY PARTITION IS STILL AN EXTREMELEY VALUABLE EXERCISE BOTH IN OBSERVATIONS AND MODELING

Dt

DW

DW DW ~ Dt after“Saturation”

DW ~ Dt before“Reset”

Physical origin of relaxation correlations

28

Hudson et al. 1998

Dt

DW

DW DW ~ Dt after“Saturation”

DW ~ Dt before“Reset”

Physical origin of relaxation correlations

28

Hudson et al. 1998

4.2. CME kinetic energies vs. Flare energiesOne obs issue ?

Carley, McAteer, & Gallagher (2012)Vourlidas, Esfandiari, Patsourakos,

Yahsiro & Michalek (2010)

x30 x3

x10

x2

4.2. CME kinetic energies vs. Flare energiesOne obs issue ?

Carley, McAteer, & Gallagher (2012)Vourlidas, Esfandiari, Patsourakos,

Yahsiro & Michalek (2010)

x30 x3

x10

x2