Tackling the coronal heating problemusing 3D MHD models with spectral

synthesis

Sol

ar e

clip

se, 1

1.8.

1999

, Wen

dy C

arlo

s &

Joh

n K

ern

observational constraints

3D MHD model

spectral synthesis

results: structures Doppler shifts DEM

Hardi Peter, Kiepenheuer-Institut für Sonnenphysik, Freiburg

Boris Gudiksen, Institute for Theoretical Astrophysics, Oslo

Åke Nordlund, Astronomical Observatory, NBIfAFG, Copenhagen

Doppler shifts in the solar transition region

0

10

10

5

5

D

oppl

er

shift

[ km

/s ]

Pet

e r

(19 9

9)

Ap J

516

, 4 9

0

SUMER

105 K 6.5105 K

Hardi PeterKIS

Doppler shifts in the low corona & TR

Peter & Judge (1999) ApJ 522, 1148SUMER

Hardi PeterKIS

mean quiet SunDoppler shiftsat disk center

similar for active region line shifts but higher amplitude

qualitatively similar in solar-like stars – smaller for small activity

Net Doppler shifts in 1D models

Doppler shiftas a function of temperature

line formation temperature log (T [K])

line formation temperature T [K]

(blu

e)

D

oppl

er s

hift

[km

/s]

(

red

)Hardi Peter

KIS

4·105 K

105 K

106 K

104 Kphotosphere

corona

e.g.: asymmetric heating flows or waves

asymmetricheating

shock

higherdensity

A by far incomplete list of suggestionsto understand the red / blueshiftsby using loop models:

Antiochos (1984) ApJ 280, 416 McClymont & Craig (1987) ApJ 312, 402Mariska (1988) ApJ 334, 489Klimchuk & Mariska (1988) ApJ 328, 334Hansteen (1993) ApJ 402, 741Peter & Judge (1999) ApJ 522, 1148Teriaca et. al. (1999) A&A 349, 636

no satisfactory model yet

reproducing the vD vs. T curve

qualitatively and quantitatively!!

Emission measure in the (low) coronaHardi Peter

KIS

EM h =Z

n2e dh

Fline / hºZG(T) n2e dh

atomic physics:– excitation– ionisation ...emission measure:

The problem:

below 105 K T is very steep ( q T5/2 T )

in stratified models:

T is so steep

that EM decreases below 105K !

possible scenarios:

– additional dense cool structures – increased heat-conduction below 105 K – heat transport across the field...

Gab

riel (

1976

)P

hil.

Tra

ns.

R.

Soc

. Lo

n.A

281,

339

A multi–structured low corona

Dowdy et al. (1986)Solar Phys., 105, 35

do we have to dealwith a multitudeof individual structures?

Hardi PeterKIS

only 3D models can helpto understand this!

line formation temperature log (T [K])

line formation temperature T [K]

(blu

e)

D

oppl

er s

hift

[km

/s]

(

red

)

Gudiksen & Nordlund (2002) ApJ 572, L113 2x (2004) ApJ, in press

3D coronal modellingHardi Peter

KIS

horizontal x [ Mm]

ho

rizo

nta

l

y [

Mm

]

MDI magnetogram

vert

ical

z

[ M

m]

synthetic TRACE 171 Å emission measure

vertical z [ Mm]cu

rren

t

log 10

J2

mean B2

mean J2

histogram of currents

3D MHD model for the corona: 50 x 50 x 30 Mm Box (now 1503) – fully compressible; high order – non-uniform staggered mesh

full energy equation (heat conduction, rad. losses)

starting with scaled-down MDI magnetogram – no emerging flux

photospheric driver: foot-point shuffled by convection

braiding of magnetic fields (Galsgaard, Nordlund 1995; JGR 101, 13445)

heating: DC current dissipation (Parker 1972; ApJ 174, 499)

heating rate J2 ~ exp(- z/H )

loop-structured 106K corona

21e ),( AhnTG ione

2

nn

n

el

ion

n

n

e

H

n

n

H

el

n

n

),(),( e2

e212 nTGnAnht x

3m

W

total ionization 0.8

abundance = const.

ionizationexcitation

Assumptions:– equilibrium excitation and ionisation (not too bad...)

– photospheric abundances

use CHIANTI to evaluate ratios (Dere et al. 1997) G depends mainly on T (and weakly on ne) log T [K]

norm

aliz

ed c

ontr

ibut

ion

emissivity in the computational box as a function of T

From the MHD model: – density (fully ionized) ne at each

– temperature T grid point and time

Emissivity from the 3D modelHardi Peter

KIS

Emissivity at each grid point and time step:

Synthetic spectraHardi Peter

KIS

2

2los

0 exp),(th

ItIw

vvx

1) emissivity at each grid point (x,t)

2) velocity along the line-of-sight from the MHD calculation vlos

3) temperature at each grid point T

line profile at each grid point:ion

B ),(2m

tTkth

xwline width correspondingto thermal width

total intensity correspondingto emissivity I0 wth (x,t)

integrate along line-of-sight

maps of spectraas would be obtained by a scanwith an EUV spectrograph, e.g. SUMER

analyse these spectra likeobservations

– calculate moments: line intensity, shift & width– emission measure (DEM) – etc. ...

side views

Coronal evolution

top view

Hardi PeterKIS

large coronal loops connecting active regions

gradual evolution in line intensity (“wriggling tail”)

higher spatial structure and dynamics in Doppler shift signal

it is important to have full spectral information!

Mg X (625 Å)

~106 K

side views

TR evolution: C IV (1548 Å)

top view

Hardi PeterKIS

very fine structured loops – highly dynamic

also small loops connecting to “quiet regions”

cool plasma flows – locks like “plasma injection”

dynamics quite different from coronal material !

C IV (1548 Å)

~105 K

Doppler shiftsHardi Peter

KIS

spatial and temporal averages

– very good match in TR – overall trend vD vs. T quite good

– still no match in low corona boundary conditions? missing physics?

temporal variability

– high variability as observed – for some times almost net blueshifts in low corona!

no “fine-tuning” applied !

best over-all match of models so far

DEM inversion using CHIANTI:

1 – using synthetic spectra derived from MHD model

2 – using solar observations (SUMER, same lines, quiet Sun)

good match to observations!!

DEM increases towards low T in the model !

Emission measureHardi Peter

KIS

T

hnDEM

d

d2e

Si II Mg X

Supporting suggestions thatnumerous cool structures

cause increase of DEM to low T

ConclusionsHardi Peter

KIS

Synthetic spectra from a 3D MHD model of a small active region on the Sun

Smooth evolution in corona, but variable Doppler shifts

highly structured in TR lines

For the first time we get a – reasonable good match to TR and coronal Doppler shifts

– very good match to Emission Measure (especially < 105 K)

good arguments for flux braiding as (the) heating mechanism in moderately active regions

Outlook

Boundary conditions – open field regions

Quiet Sun structures

better chromosphere

non-equilibrium ionisation

additional material:

ioneion

1Cn

||)log(

ˆ)(log1

ionflow

vv

T

T

A note on ionization equilibriumHardi Peter

KIS

ionization equilibrium is a severe assumption for a dynamic environment

flow time:

how long does it take to flow across a temperature difference logT with a velocity v?

(logT)ion= 0.1 according to ion.equilibrium

(log T) and v from MHD calculation

ionization time:

what is the ionisation rate?

ne from MHD calculation

Cion(T) from Arnaud & Rothenflug (1985)

but it is not too bad for the present problem...

Non-thermal line widthsHardi Peter

KIS

roughly right order of magnitude

not right trend

... not really surprising thinking of resolution...

more material:

• ref to DEM curve (Raymond ?)

• ref to stellar TR doppler shifts as fct of T

• title of Gudiksen & Nordlund poster

check the posterGudiksen & Nordlund:

“title”

and some plans…

further diagnostics: – temporal and spatial variability – correlation of emission from different lines – line-of-sight effects / stellar spectra

3D models of coronal structures / Pencil code implementation [Sven Bingert] – quiet Sun structures / network – more/emerging magnetic flux / stellar activity

advanced diagnostics: inclusion of non-equilibrium ionisation [Pia Zacharias]

Long term plans

Photospheric observations as boundary conditions use of evolution of observed maps of velocity and magnetic fields [TESOS / polarimetry]

what to do with the chromosphere ? / “toy” radiative transfer ?

local helioseismology: sub-surface flows for slow evolution of active regions / flare initiation

non-MHD-effects ?