Presentation given to the Solar Physics group at Purple Mountain Observatory, Nanjing.

1. Formation of Helium lines
in solar prominences
Nicolas Labrosse
University of Glasgow, Scotland, UK

2. Outline
•Introduction on solar prominences
•Radiative transfer modelling
–Description of the models
–Influence of the prominence-to-corona transition region
(PCTR) on line profiles and intensities
–Influence of the radial motions of the plasma on line profiles
and intensities
•Conclusions
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3. Solar prominences
prominence
body
T~8000 K
n~1010 cm-3
corona
T≥1-2 MK
n~108 cm-3
SOHO/EIT
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4. Puzzles
•How do prominences form?
–What is the magnetic configuration of filament channels, and
how is this highly sheared structure created?
–Where does their dense material originate, and how is it
maintained?
–How do prominences reach and maintain energy balance with
the ambient corona?
–How are the magnetic structure and the plasma dynamics
linked?
Labrosse et al. (2010), Mackay et al. (2010)
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5. Puzzles
•Prominence fine structure and diagnostics
–What are their detailed thermal and magnetic structures?
–How can we use existing (SOHO, Hinode, STEREO, SDO)
and future (Solar Orbiter) space missions to obtain the best
information on solar prominences?
–Can we construct a prominence model that reproduces the
observed emission in optically thin and optically thick lines?
Labrosse et al. (2010), Mackay et al. (2010)
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6. Puzzles
•Prominence disappearance
–What can observations of heating and activation in
prominences tell us about their disappearance?
–Why do filament channels generate the most energetic solar
eruptions?
–What tools can we develop to forecast prominence eruptions
in a reliable way?
Labrosse et al. (2010), Mackay et al. (2010)
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7. Physical parameters
Patsourakos & Vial (2002), Labrosse et al. (2010).
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8. Plasma parameters
Temperature, density, ionisation, filling factor, ...
Accurate measurements are
crucial to construct realistic models of prominences
difficult to obtain
prominence plasma not in local thermodynamical equilibrium
(non-LTE) because of strong incident radiation coming from
the Sun
Large span of measured values
depending on the observed structure
depending on the technique used
Non-LTE radiative transfer modelling of prominences
sheds light on line formation mechanisms
helps to interpret spectroscopic observations / imaging
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9. Non-LTE radiative transfer
•Line formation
–observations are difficult to
understand
•Necessity to solve
equations
–Statistical equilibrium
–Radiative transfer
including optically thick lines
and continua
•Non linear and non
local coupling between
matter and radiation
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10. H and He EUV resonance lines
Lyman lines of hydrogen form in different parts of the
prominence (Heinzel 2007)
Optically thick core reveals fine structure close to prominence
boundaries
Optically thin wings result from integration of several elements
along LOS
Same for He I and He II resonance lines
He I 584 Å, He I 537 Å, He II 304 Å, He II 256 Å
Plasma out of local thermodynamic equilibrium (LTE)
Plasma diagnostics is complex
Non-LTE radiative transfer calculations with velocity fields
are needed to build realistic prominence models
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11. The prominence model
The prominence model
•1D plane-parallel vertical slab Anzer & Heinzel (1999)
Free parameters
Gas pressure
Temperature
Column mass
Height above the limb
Radial velocity
Equations to solve
Pressure equilibrium, ionisation
and statistical equilibria (SE),
radiative transfer (RT) for H (20
levels)
SE, RT for other elements: He I
(29 levels) + He II (4 levels)

12. Prominence-corona transition region
(PCTR)
Temperature inside the prominence slab for γ=2 (extended PCTR), γ=10, and
γ=20 (narrow PCTR). The column mass is M = 5×10−6 g cm−2 and the central
temperature is 9000 K.
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13. He I model atom
He I: 29 energy levels
He II: 4 energy levels
76 bound-bound
transitions and 33 bound-
free transitions
561 transitions overall
We can now calculate the
emergent radiation.

14. Intensities and physical parameters
He I triplet line intensity ratio depends on prominence altitude
E(10830)/E(D3) vs height above the limb
Labrosse & Gouttebroze (2004)
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15. Influence of PCTR on line profiles
H Lyman α He I 584 Å
model without models with
transition region transition region
Labrosse et al (2002)
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16. Influence of PCTR on He I triplet lines
•PCTR affects formation mechanisms of lines formed
in cool parts of the prominence
–statistical equilibrium of He I atomic states
E(10830)/E(D3) vs optical depth at 504 Å
T<6000 K
T<6000 K
T>16000 K
T>16000 K
Labrosse & Gouttebroze (2004)
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17. Prominence diagnostic with SUMER
BBSO Hα MEDOC campaign #13,
15–16/6/2004
Observed profiles compared
with grid of 4720 computed
models (T, n, ...)
⇩
Ly-β, Ly-ε, and
He I 584 Å
observed by
SUMER/SOHO
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18. Prominence diagnostic with SUMER
● Prominence model: 1D plane-parallel slab
Temperature profile inside prominence slab
(Anzer & Heinzel 1999)
ne = 6 108 cm-3 (surface)
ne = 5 109 cm-3 (center)
Labrosse, Vial, & Gouttebroze (2006)
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19. Prominence diagnostic with EIS
np/nH n(HeII)/n(He)
Surface: 1 Surface: 0.20
Centre: 0.94 Centre: 3.3x10-5
Max = 0.99
See also Heinzel et al. (2008), Labrosse et al. (2011)
Temperature n(He III)/n(He)
Surface: 105 K Surface: 0.8
Centre: 104 K Centre: 0
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20. 2D models
Ionisation degree in cylindrical prominence
H + He ionisation
H ionisation only
Gouttebroze & Labrosse (2009)
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21. 2D models
Variation of the ionisation ratio with T
30000-50000 K
20000 K
15000 K
10000 K
8000 K
6000 K
Gouttebroze & Labrosse (2009)
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22. DiagnosticHe velocity fields
of I model atom
● Imaging measurements
– apparent motion of structure in plane-of-sky
● Doppler shifts in prominence spectra
– velocity along line-of-sight
● Doppler dimming / brightening
– varies with radial velocity
The full velocity vector may be inferred, but
requires at least the radial velocity.
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23. Effects of radial motions
Effects of radial motions
•For a simple 2-level atom with photo-excitation
–Doppler dimming if the incident line is in emission
–Doppler brightening if the incident line is in absorption
•If coupling between several atomic levels
–situation gets more complex: dimming and brightening
–e.g. coupling between first two excited levels of H
•Factors determining effects of radial motions
–line formation mechanism
–details of incident radiation (strength, emission/absorption)
See Heinzel & Rompolt (1987), Gontikakis et al (1997), Labrosse et al (2007,
2008)
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24. V=0 km s-1
V=80 km s-1
T = 8000 K
T = 15000 K
V=200 km s-1
V=400 km s-1
He I 584 He II 304 He I 10830 Labrosse et al. (2007)

25. Plasma motions in prominences
● He II 304 Å line sensitive to Doppler dimming due to
radial motion of prominence plasma
Labrosse et al. (2007)
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26. Results
Effects on Lyman α
Doppler dimming if
Large temperature
gradient in PCTR
Not too dense
Cool plasma
Doppler dimming of Lyman α line less pronounced
when PCTR is extended.
increased contribution in line formation of collisional processes in
higher temperature region relative to narrow PCTR case
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27. Results
Effects on Lyman α
Doppler dimming if
Large temperature
gradient in PCTR
Not too dense
Cool plasma
Increasing column mass with all other parameters kept
constant means more hot material
collisionalcomponent of Ly-α becomes more important ⇒ the line is
less sensitive to Doppler dimming
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28. Results
Effects on Lyman α
Doppler dimming if
Large temperature
gradient in PCTR
Not too dense
Cool plasma
Increasing temperature of main prominence body increases
amount of hot material
collisionalcomponent of Ly-α becomes more important ⇒ the line is
less sensitive to Doppler dimming
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29. Results (5)
Results
Effects on Helium
resonance lines
(Same trend as
Lyman lines)
Doppler dimming
Cool plasma
Not too dense
Large temperature
gradient in PCTR
Effects on Helium subordinate lines
10830, D3, ... are less sensitive to Doppler dimming/brightening
due to weak incident radiation
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30. E(He I 584) vs. radial velocity
(erg s1 cm-2 sr-1 Å-1)
(PCTR = prominence-to-corona transition region)
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31. E(He II 304) vs. radial velocity
(erg s1 cm-2 sr-1 Å-1)
(PCTR = prominence-to-corona transition region)
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32. 2011-06-10
Labrosse & McGlinchey (subm)
2010-09-08
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33. Comparison with observations
Labrosse & McGlinchey (subm)
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34. Conclusions / Future plans
Importance of taking into account PCTR
–Affects plasma diagnostics from most lines in most cases
Calculations provide constraints for determination of
–Opacities
–Ionisation degree
– Variations in ionisation degree along LOS can be important
–Radiative losses for energy balance calculations
Compare 2D calculations with observations
–Models must be constrained by using several lines (H+He)
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