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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
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320 x 260 Mm2
AIA 171Å ≈ 106 K
constant cross section loops expanding
structures
The corona at ≲≲ 106 K: AIA 171 Å
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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
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expansion vs.
temperature
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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Loops at constant
cross section !?
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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
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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 ?!
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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
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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 )
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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
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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
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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
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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
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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
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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
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Comparing different viewing angles Is it possible to reconstruct loop through stereoscopic reconstruction ?
+ 45°
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Comparing different viewing angles Is it possible to reconstruct loop through stereoscopic reconstruction ?
– 30°
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Comparing different viewing angles Is it possible to reconstruct loop through stereoscopic reconstruction ?
– 90°
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Conclusions
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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 !