Constant cross section of loops

Hardi Peter

Sven Bingert

Max-Planck-Institut für Sonnensystemforschung

Katlenburg-Lindau

or more accurately:

Magnetic expansion and thermal structure of loops

synthesized AIA 171 Å image

320 x 260 Mm2

AIA 171Å ≈ 106 K

constant cross section loops expanding

structures

The corona at ≲≲ 106 K: AIA 171 Å

3D MHD box model of the corona

The Pencil Code Brandenburg & Dobler (2002) Comp Phys Comm 147, 471

► high-order finite-difference modular code for compressible 3D MHD ► horizontal motions in photosphere as driver → field line braiding (Parker 1972)

► start with observed photospheric magnetogram

► energy dissipation through Ohmic heating ~ η j2

► concept similar to Gudiksen & Nodlund (2002, 2005a,b) ► full energy equation (heat conduction, rad. losses) → important for coronal pressure (spectral diagnostics)

photospheric magnetic field

formation height of 105 K emission

density cut

Bin

gert

& h

p (2

011)

A&

A 53

0, A

112

expansion vs.

temperature

Expansion of moss structures Expansion of hot loops very close to their footpoints

0.0

0.2

0.4

0.6

0.8

1.0

Are

a

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.5

1.0

1.5

2.0

Tem

pera

ture

(M

K)

Fe IX

Fe X

Fe XI

Fe XII

Fe XIII

Mg V

Mg VI

Mg VIISi VII

Si X

ConstantExpanding

0 1 2 3 4Distance Along the Loop (Mm)

109

1010

1011

Den

sity

(cm

−3 )

Fe IX

Fe X

Fe XI Fe XII

Fe XIII

Mg V

Mg VI

Mg VII

Si VII

Si X

105 106

Temperature (K)

0.0

0.2

0.4

0.6

0.8

1.0

Are

a

Fe IX

Fe X

Fe XI

Fe XII

Fe XIII

Mg V Mg VI

Mg VII

Si VII

Si X

Warren et al (2010) ApJ 711, 228

– use 1D loop model with variable cross section to match observed structure of density and temperature

→ (magnetic) expansion of loop as function of temperature

→ relation of magnetic to thermal structure

Expansion in the transition region O III

Ne VI

Mg IX

measurement of structure sizes based on observations alone (autocorrelation) expansion of emission structures from 105 K to 106 K by factor 2 → area expansion by factor 4 not necessarily magnetic expansion!

Patsourakos+al (1999) ApJ 522, 540

Expansion cooler smaller loops

O III

Ne VI

Mg IX B

Expansion of cooler and hotter structures

105 106

Temperature (K)

0.0

0.2

0.4

0.6

0.8

1.0

Are

a

Fe IX

Fe X

Fe XI

Fe XII

Fe XIII

Mg V Mg VI

Mg VII

Si VII

Si X

– small transition region structures: area expansion by ≈4 well below 105 K

– footpoints of large hot loops: area expansion by ≈5 above 106 K

fit to Patsourakos et al (1999)

Warren et al (2010)

Expansion: 3D MHD vs. observations

hot dense loops log Tmin > 6.15 log Nmin > 8.5

→ good match to Warren et al (hot loops from moss)

3D MHD model: conservation of magnetic flux Φ = ∫ B da → area expansion ~ 1/B compare to Patsourakos et al (1999) – small loops and Warren et al (2010) – large hot loops

Expansion: 3D MHD vs. observations

short loops L < 20 Mm

→ good match to Patsourakos et al (small loops from network)

3D MHD model: conservation of magnetic flux Φ = ∫ B da → area expansion ~ 1/B compare to Patsourakos et al (1999) – small loops and Warren et al (2010) – large hot loops

Expansion: 3D MHD vs. observations

“midrange” loops 35 Mm < L < 50 Mm

→ in-between the other two types…

3D MHD model: conservation of magnetic flux Φ = ∫ B da → area expansion ~ 1/B compare to Patsourakos et al (1999) – small loops and Warren et al (2010) – large hot loops

Expansion “in the first 5 Mm”

3D MHD model contains fieldlines with (magnetic) expansion as found in observations correspondence as expected: ► short fieldlines: ≙ loops hosting TR structures in the network (Patsourakos et al. 1999) ► fieldlines with hot dense plasma: ≙ hot AR loops with moss emission at footpoints (Warren et al. 2010) ► also expansion in-between these extremes is possible

Loops at constant

cross section !?

Constant cross section of loops: T > 106 K

Klim

chuk

(200

0) S

ol.P

hys.

193

, 53

radius

std.dev.

intensity

Yohkoh SXT, 11.Aug.1992, 145”x140”

Wat

ko &

Klim

chuk

(200

0) S

ol.P

hys.

193

, 77

► many X-ray and most EUV loops have constant cross section! (not only post-flare loops)

TRACE △ 171 Å ♢ 195 Å ✳ 284 Å

Constant cross section: the problem a potential-like magnetic field which expands with height.

SXT TRACE

loop seen in coronal emission with constant cross section

► if the plasma is confined within magnetic flux tubes, how can this be ?!

Constant cross section: suggestions

twisted flux tube surrounded by untwisted expanding field

hypothetical ribbon-like loop that is twisted

from Klimchuk (2000) Sol.Phys. 193, 53

these and other suggestions fail…

evidence for twisted flux tubes in “quiet corona” is missing

evidence for “knots” is missing

Coronal loop in 3D MHD model synthetic AIA 171 Å (106 K)

AIA PSF applied AIA pixel size

horizontally integrated through computational box background subtracted

loop has cross section comparable to AIA PSF width ! ( ≈1.3” ≈ 2.5 pxl )

Synthesized loop and magnetic field lines

loop seen in synthesized emission

→ is aligned with magnetic field lines

→ and has constant cross section despite the expansion of the magnetic field

AIA 171 Å (106 K)

magnetic field lines

Quantitative analysis ► visible loop is really almost constant cross section ► area expansion: visible loop ≈ factor 1.2 … 1.4 magnetic field: ≈ factor 5 ► radius expansion: visible loop ≈ factor 1.1 … 1.2 magnetic field: ≈ factor 2.5 What causes this effect of constant cross section? → still to be determined

AIA 171 Å (106 K)

cross sectional intensity profiles

area expansion along loop B

loop

AIA images of “loop” integrated through box rotate data cube so that loop is aligned with major axis

Investigate: (1) vertical cut along X ≈ 14 Mm (2) vertical profile at (X,Y) ≈ (14,28) Mm

A vertical cut AIA emission: approx constant width density: expanding loop temperature: overall mostly vertical ∇T

→ constant width in emission due to convolution of density and temperature

Vertical profiles te

mpe

ratu

re [

MK

]

dens

ity [

109

cm-3

]

AIA

171

[ a

rb.u

nits

]

temperature

AIA peak T

density: FW 80% M ≈ 5Mm

AIA: FW 80% M ≈ 3Mm

► density structure relatively wide ► ∇T across dense region

→ only part of dense structure contributes to AIA 171 emission

→ emission in AIA 171 relatively narrow

The “loop” with its “central field line” Do we really always see the same loop ?!

synthesized AIA 171 images (integrated through box) count rates: linear scaling ≈ 0…1500 DN / pxl / s

Comparing different viewing angles Is it possible to reconstruct loop through stereoscopic reconstruction ?

+ 45°

Comparing different viewing angles Is it possible to reconstruct loop through stereoscopic reconstruction ?

– 30°

Comparing different viewing angles Is it possible to reconstruct loop through stereoscopic reconstruction ?

– 90°

Conclusions

Conclusions

Constant cross section of loops !?

► magnetic expansion in 3D MHD model can match – small TR structures – footpoint expansion of hot AR loops ► synthesized coronal emission shows loops at constant cross section ► possible explanation: 1) expanding magnetic field (“fluxtube”) is homogeneously filled with plasma (N ≈ const) 2) upper fieldlines of bundles are hotter (→ RTV) → ∇T across B in upper part of loop 3) contribution to coronal emission only in part of upper plasma loop → coronal emission is at ≈ constant cross section ► there is more to this… 3D line-of-sight integration plays important role !