Laura Morales: Anisotropic braiding avalanche model for solar ... - ISSI

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1 Δεκ 2013 (πριν από 3 χρόνια και 9 μήνες)

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Laura F. Morales


Canadian Space Agency /
Agence

Spatiale

Canadienne

Paul Charbonneau
Département

de Physique,
Université

de Montréal

Markus
Aschwanden

Lockheed Martin, Adv. Tec.
Center
,


Solar and Astrophysics Lab
.

Anisotropic braiding

avalanche model

for solar flares:

A new 2D application

Outline

Solar Flares

: Observations + Classical Th. Models

SOC paradigm:

The sandpile model






SOC & Solar Flares:

Lu & Hamilton's classic model


New SOC model for solar flares:


* Cellular Automaton


* Statistical results & Spreading exponents


* Expanding the model capabilities: Temperature
















Density

Sun's Atmosphere

PHOTOSPHERE





CHROMOSPHERE



SOLAR CORONA

Sunspots

Granules

Super
-
granules



Spicules

Filaments


Active regions

Loops

Solar Flares

Etc….

http://
www
-
istp.gsfc.nasa.gov/istp/outreach/images/Solar/Educate/atmos.gif

M
-
Class Flare
-

STEREO

(March, 25 2008)


EUV

http://stereo.gsfc.nasa.gov/img/stereoim
ages/movies/Mflare2008.mpg

X
-
Class Flare
-

SOHO

(November, 4 2003)

http://sohowww.nascom.nasa.gov/gallery/
Movies/EITX27/StormEIT195sm.mpg

“...a solar flare is a process associated with a rapid temporary
release of energy in the solar corona triggered by an instability of
the underlying magnetic field configuration …”

Magnetic


Reconnection

t
onset

~ 1
-
2s
-

t
thermalization

~ 100s

t
diffusion
~ 10
16
-
18

s

in the

solar corona

another

mechanism

http://www.sflorg.com/spacenews/images/imsn051906_01_04.gif

Parker's Model for solar flares

B
0
uniform


High

conductivity

Photospheric motions shuffle


the footpoints of magnetic coronal loops

Spontaneous

Current Sheets in Magnetic Fields: With Applications to Stellar X
-
rays


(Oxford U. Press 1)


Figure 11.2


http://helio.cfa.harvard.edu/REU

/images/TRACE171_991106_023044.gif

Photosphere

Injection of kinetic Energy

Solar Corona

Storage of


Magnetic Energy

Very small



Solar


Flares

Energy


Liberation

Magnetic

reconnection


TURBULENCE OR


SELF ORGANIZED CRITICALITY?

(Dennis 1985, Solar
Phys.,
100
, 465)

Power
law



self
similar

behavior

Energy is
released in


a wide range

of scales

~10
24
-
10
33

ergs

SOC +


Solar Corona

Intermitent release of energy:
Magnetic Reconnection

Statistically stationary state:
the

solar corona is an









statistically stationary state

Slowly driven open system

Photospheric motions



instability

threshold
:





Critical

Angle

t
flare


~ seconds

L
B

~ 10
10

cm

t
photosphere

~ hs

How can we obtain predictions
by using this model?

Integrate MHD aquations

Cellular automaton
-
like simulations



Each node is a measure of the B


B(0)=0


Driving mechanism: add perturbations at some
randomly selected interior nodes


Stability criterion: associated

to the curvature of B

Classic SOC Models

(Charbonneau et al.
SolPhys,

203:321
-
353, 2001)


Time series
of lattice
energy

& energy
released

for the
avalanches

produced by

48 X 48
lattice


(Charbonneau et
al.
SolPhys,
203:321
-
353,
2001)


soc

Probability Distributions

Classic SOC Models: Ups

Successfully reproduced statistical properties
observed in solar flares:











pdf’s

exhibiting

power

law

form





good

predictions

for

exponents
:








a
E
,

a
P
,

a
T


Classic SOC Models:
Downs

1.
No magnetic reconnection

2. Link between CA elements & MHD

If
B
k



B



.B ≠ 0

If
B
k



A



.B ≠ 0 solved &






A

interpreted as a twist in the magnetic field



B
k
2

is no longer a measure of the lattice energy



3. No good predictions for
a
A


Lattice Energy ~ ∑ L
i
(t)
2

i

Lattice +


perturbation

NEW MODEL (2008)

Threshold



=



1

+

2

angle

formed by


2 fieldlines


1


2

E=1.25E
0

Reconnect

+ @ (1,3)

Perturbation
starts again

One
-
step
redistribution

E = 1.22 E
0

Elim/reduce angle

Two
-
step
redistribution

Reconnect

(3,2) unstable

E = 1.32E
0

E=1.4E
0

E=1.19E
0

Perturbation
starts again



(3,1)

E = 1.19E
0

The lattice in action

32 x 32

64 x 64

Lattice Energy & Released Energy


Morales, L. & Charbonneau, P.
ApJ
.
682,(1), 654
-
666.
2008

SOC

P


T

E

T

1.73
-
1.84

a
P

1.63
-
1.71

a
E

New SOC

Classic SOC

Observations

1.54

1.40

1.7

1.79
-
2.11

Morales, L. & Charbonneau, P.
ApJ
.
682,(1), 654
-
666.
2008

1.79
-
1.95

a
T

New SOC

Classic SOC

Observations

1.15


2.93

1.70

Morales, L. & Charbonneau, P.
ApJ
.
682,(1), 654
-
666.
2008

Area covered by an
avalanche: a movie

Area covered by Avalanches

unstable (12,2)

unstable (10,1)

t
0


t
0
+30


t
f
= t
0

+332

t
0
+116 = t
max

t
0
+150

Time integrated

Area

Peak Area

Geometric Properties

New SOC

Classic SOC

EUV


TRACE

0.55
±

0.02

1.02
±

0.06

1.83


2.45

1.93
±

0.07

2.45
±

0.11

a
A
*

a
A

Morales, L. & Charbonneau, P.

GRL., 35, L04108

Spreading Exponents

Number

of
unstable

nodes

at

time t

Probability

of existence
at

t



k

Size of an avalanche

death
’ by t


Probability of an avalanche

to reach a size S

128 x 128


c
=2.5



0.09
±
0.02



1.1
±

0.1

k

1.83
±
0.25



1.70
±
0.2

k
th
=1+



+



2.19
±
0.1


th
=(1+


+2


)/
k
th


1.48
±
0.01

Just an
example


Morales, L. & Charbonneau, P.

GRL., 35, L04108

From a 2D lattice to a loop

fold

bend

Avalanching

strands

in the loop

Projection

Projections

Geometrical properties for the
projected areas

a
A

= 2.39
±

0.05


a
*
A

= 1.84
±

0.07

N

D (stretch=1)

D (stretch=10)

32

1.26
±

0.04

1.21
±

0.04

64

1.21
±

0.04

1.23
±

0.04

128

1.20
±

0.03

1.25
±

0.05

Observations

1


1.93

N=64

N=32

Another way of looking at the simulations

Near vertical
current sheet
that extends


from the

coronal
reconnection
regions to the
photospheric


flare ribbons

mapped into

Temperature & Density Evolution

The maximum loop temperature based on the maximum
heating rate and the loop length for uniform heating case:




Pressure

Density

k = 9.210
-
7

erg s
-
1

K
7/2


(Spitzer conductivity)

E
max

Temperatures

Avalanche
duration:

106 it.

Avalanche
duration:

138 it.

N=64 THR=2

51013 avalanches in 4e5 iterations

Max duration ~ 700 it

Density

]

]

With

the

temperature

T(t)

and

density

evolution

n(t)

of

each

avalanche

we

can

compute

the

resulting

peak

fluxes

and

time

durations

for

a

given

wavelength

filter

in

EUV

or

SXR,

because

for

optically

thin

emission

we

just

have
:


I(t) = ∫ n(t)
2

w R(T)
dT


w

is

the

loop

width

R(T)

is

the

instrumental

response

function
.



We

can

plot

the

frequency

distributions

of

energies
:

W =
E_Hmax

* duration

peak

fluxes

(I_EUV,

I_SXR)

Coming up…..

Conclusions


Every

element

in

the

model

can

be

directly

mapped

to

Parker's

model

for

solar

flares

thus

solving

the

major

problems

of

interpretation

posed

by

classical

SOC

models
.



For

the

first

time

a

SOC

model

for

solar

flares

succeeded

in

reproducing

observational

results

for

all

the

typical

magnitudes

that

characterize

a

SOC

model
:

E,

P,

T,


T

&

the

time

integrated

A

and

the

peak

A
*
.

The

new

cellular

automaton

we

introduced

and

fully

analyzed

represents

a

major

breakthrough

in

the

field

of

self
-
organized

critical

models

for

solar

flares

since
: