1. He 10830 lecture: some aspects as seen from an observer‘s viewpoint
Andreas Lagg
National Astronomical Observatory of Japan and
Max-Planck-Institut für Sonnensystemforschung, Katlenburg-Lindau, Germany
no quantum theory
no derivation of formulae
no in depth explanation of Hanle theory
no solar physics
phenomenological explanation of effects (Hanle, PB, atomic polarization)
application of formulae to demonstrate influence of CI, geometry, PB, Hanle on Stokes IQUV

2. Lites et al. (1985): report on steady flows (9 km/s, hours to days)
He History
first solar obs. in He 10830: D‘Azambuja (1938), Zirin (1956), Mohler & Goldberg (1956), Namba (1963), Fisher (1964), Milkey et al. (1973)
Harvey & Hall (1971)
Giovanelli & Hall (1977)
Lites et al. (1985): report on steady flows (9 km/s, hours to days)
Avrett (1994): formation of He 10830
He spectropolarimetry: Lin (1995), Lin et al. 1996, 1998
Trujillo-Bueno (2002): atomic polarization in He solved
Giovanelli & Hall (1977)
D‘Azambuja & D‘Azambuja: remarkable spectroheliograms
Lites: steady flows above active tregions.
Lin: first Stokes poalrimetry measurements of a filament, classical formulation to describe magnetic field configuration
Harvey & Sheeley (1977)

3. Para / Ortho Helium
Centeno et al., 2008

4. Ionization / Recombination Scheme
Centeno et al., 2008

5. The He Triplet
Transition 23S1 – 23P2,1,0
absorption depends on:
density and extend of upper chromosphere
coronal radiation in the λ<504 Å continuum
2s 3S level populated by recombination of He II or collisional excitation from 11S
Tr1: Å, f=0.1111, geff=2.00
Tr2: Å, f=0.3333, geff=1.75
Tr3: Å, f=0.5556, geff=1.25

6. The He D3 line Asensio Ramos et al., 2008
Transition 23P2,1,0 - 33D3,2,1
formation mechanism similar to He (CI required)
difference to 10830:
optical thickness of the observed solar plasma structures is weaker  on the solar disk it is much easier to see structures in than in 5876
both lines are clearly seen in emission when observing offlimb structures such as prominences and spicules.
He preferable because:
forward scattering creates measurable linear polarization signals in the lines of the He I when the magnetic field is inclined (Trujillo Bueno et al. 2002)
nearby presence of Si I line  coupling science

7. He 10830 – Formation Height model atmospheres: T-profile pressure
He density 3S1
z 
model atmospheres:
T-profile pressure
models A (cell-center), C (average), F (bright network), P (plage)
CH/CL hi/lo coronal irradiance
comparison: model is similar to ocean as a plane surface, water below, air above. Unrealistic for a surfer but useful for many purposes.
Tr1
Tr2+3
WL 
Avrett et al. (1994)

8. Influence of Height above Limb
He D3 5876
lowest
highest
The interpretation is as follows: the density in the outer layers of the atmosphere (at large distances from the limb) is so low that it cannot produce measurable emission profiles. As we go deeper into the atmosphere, the density increases quickly and so does the emission in the multiplets, until it
reaches a maximum at a height of 2000 km. The extinction of the EUV radiation as it travels inward through the chromosphere leads to a reduction in the number of ionizations in the inner layers. Thus, the emission in the spectral lines of the He i and D3 multiplets starts decreasing again because the PR (photoionization-recombination) mechanism cannot sustain the populations of the triplet system.
FAL-C, nominal CI
Centeno et al., 2008

9. Influence of Coronal Illumination (CI)
He 10830
He D3 5876
Centeno et al., 2008
change of ratio! (additional diagnostic tool)

10. The HeI 10830 diagnostics: Zeeman effect
reliable magnetic field information for B >200 G
simultaneous observation of photosphere (Si) and chromosphere (He)
three (blended) HeI lines ("blue" line + 2 "red" lines)
Atomic Parameters: [Lagg et al., 2007]
explain IQUV, WL-scale!
Line
WL [Å]
Transition
geff
rOS
Si I
4s 3P2 - 4p 3P2
1.50
He Ia
2s 3S1 - 2p 3P0
2.00
0.11
He Ib
2s 3S1 - 2p 3P1
1.75
0.33
He Ic
2s 3S1 - 2p 3P2
1.25
0.56

11. The HeI 10830 diagnostics: Paschen Back effect
The Hamiltonian of an electron in an atom in an external uniform magnetic field:
Weak B
Zeeman effect
Regime
Hamiltonian of the
electron affected by the
Coulomb interaction
Coupling between S and L
The interaction between
the external B and the
magnetic moment of the e
Paschen-Back
effect Regime
Strong B
IPBS Regime

12. The HeI 10830 diagnostics: Paschen Back effect
Positions and strengths of the Zeeman components as a function of the magnetic field
Tr 1
Tr 2
Tr 3
Δλ (Å)
relative strength
LZS
IPBS
Socas-Navarro et al. (2004)

13. Paschen Back Effect: influence on Q, U, V
Sasso et al. (2006)
dashed = w/o PB dotted = with PB

14. Paschen-Back effect: Error on parameters
Sasso et al. (2006)

15. The HeI 10830 diagnostics: Hanle effect
(Trujillo-Bueno, 2002, Landi Degl'Innocenti, 1982)
non magnetic case:
anisotropic illumination of atoms (3 independent, damped oscillators in x,y,z) with unpolarized light
no polarization in forward scattering
complete linear polarization in 90° scattering
The classical oscillator model represents an easy way to understand the scatter polarization.
non magnetic: no magnetic field present -> no preferred direction -> atom can be represented by 3 independent oscillators oscillating with omega_0.
Anisotropic illumination: only x and y oscillator are exited!
-> forward scattering: unpolarized
-> 90° scattering: linearly polarized
normal: upper level atomic polarization. The anisotropic illumination causes an imbalance of the population in the upper level.
Required: lifetime of upper state longer than depolarizing effects (eg. collisions)
Scattering process: Absorption is unpolarized (since lower level cannot be polarized), emission is polarized.
forward scattering: observer does not see polarization since absorption is unpolarized
90° scattering polarized since emission is polarized.
Hanle effect: modification of (atomic) polarization caused by the action of a magnetic field

16. The HeI 10830 diagnostics: Hanle + B
Hanle Effect
(Trujillo-Bueno, 2002, Landi Degl'Innocenti, 1982)
magnetic case:
now the 3 oscillators are not independent:
1 osc. along B (ω0)
2 osc. around B (ω0-ωL ; ω0+ωL )
damped oscillation precesses around B → rosette like pattern → damping time tlife = 1/γ
Assumption: B along +y axis.
oscillators are not 'free': one along B + 2 counter-rotating, circular oscillators around B
Important: Hanle effect produces detectable signal in the range where the Zeeman sublevels still overlap.
(Zeeman splitting (=prop to B, expressed by omega_L) comparable to natural width of atomic level (=1/t_life))l
-> 2 complementory measurement techniques for weak and strong fields!
ωL ≈ 1/tlife
LP in forward scattering: weaker, but still ±y
90° scattering: lin.pol. in Q, U, smaller than in non-magnetic case
ωL >> 1/tlife
LP in forward scattering: max. polarization along ±y
90° scattering: no polarization

17. Atomic Polarization: the quantum picture
'normal‘ (scattering) case: upper level atomic polarization  polarization only in emission (90° scattering)  no polarization in absorption (forward scattering)
Transition:
JL = 0 → JU = 1

18. The HeI 10830 diagnostics: Atomic Polarization
Hanle Effect, the He case
Trujillo-Bueno, 2001
'normal‘ (scattering) case: upper level atomic polarization
Transition:
JL = 0 → JU = 1
He Blue Line (JL=1, JU=0): degenerate lower level
upper level cannot carry atomic polarization
→ emitted beam to (1) unpolarized
→ transmitted beam (2) has excess of linear polarization ┴ to B (=dichroism)
classical oscillator model represents situation for J = 0 -> 1 -> 0.
excess of linpol perp to horizontal B because dM=0 (=p transitions) absorb more efficiently than dM=1 (s transitions).
This selective absorption mechanism is called dichroism.
red line: polarization signal in prominence case weaker than

19. The HeI 10830 diagnostics: Atomic Polarization
Hanle Effect, the He case
Trujillo-Bueno, 2001
'normal‘ (scattering) case: upper level atomic polarization
Transition:
JL = 0 → JU = 1
He Red Lines (JL=1, JU=1 or 2): degenerate upper & lower level
both levels carry atomic polarization
→ emitted beam to (1) polarized
→ transmitted beam (2) has excess of linear polarization ┴ to B
classical oscillator model represents situation for J = 0 -> 1 -> 0.
excess of linpol perp to horizontal B because dM=0 (=p transitions) absorb more efficiently than dM=1 (s transitions).
This selective absorption mechanism is called dichroism.
red line: polarization signal in prominence case weaker than

20. linear polarization only in red line
The prominence case
90° scattering:
linear polarization only in red line
Trujillo-Bueno, 2001

21. linear polarization in red & blue line
The filament case
forward scattering:
linear polarization in red & blue line
Trujillo-Bueno, 2001

22. Hanle effect saturation
Hanle effect sensitive
linear polarization signal depends on
magnetic field strength
magnetic field direction
(around B = 10−2 G, the density matrix elements start to be affected by the magnetic field caused by a feedback effect that the alteration of the lower-level polarization has on the upper levels)
↑ < 8 Gauss ↑ ↓ > 8 Gauss ↓
Hanle saturation regime
linear polarization signal depends on
magnetic field direction
(coherences are negligible and the atomic alignment values of the lower and upper levels are insensitive to the strength of the magnetic field)
Application: disk center, horizontal field: tan(2*AZI) = Q/U
0 – 8 Gauss
Gauss

23. Ambiguities of Hanle effect
solid lines: INC=const, AZI=(-90,90) dashed lines: AZI=±90, INC=(0,-90) B=25 Gauss, off-limb, red comp.
polarization diagram:
same QU diagram
for:
INC  180-INC and AZI  -AZI
and
AZI  180-AZI (but: different V)
(traditional ambiguities)
Van Vleck ambiguity
Van-Vleck angle (THETA_vv = 54.73°, which corresponds to cos^2(THETA_vv) = 1/3)
Hanle
saturated regime
Merenda et al., 2006

24. Ambiguities: van Vleck ambiguity + traditional ambiguity
Merenda et al., 2006
INC=80°, AZI=-46°, B=22G or INC=40°, AZI=19°, B=25G
plus traditional 180° ambiguity: INC=100°, AZI=46°, B=22G or INC=140°, AZI=-19°, B=25G
The Van Vleck ambiguity occurs only for some combinations of the inclinations and azimuths. Moreover, it occurs mainly in the saturation regime of the Hanle effect.
The Van Vleck ambiguity occurs only for some combinations of the inclinations and azimuths. Moreover, it occurs mainly in the saturation regime of the Hanle effect.

25. Dependence of LP on optical thickness of He slab
Asensio Ramos et al., 2008
 no change in ratio!

26. Dependence of Hanle signal on inclination and observing angle
B=10G, h=3”
Q/I
μ=1
μ=1
Q/I
blue comp.
cos2(ΘVV)=1/3
μ=0.1
red comp.
U/I
U/I
The calculations have been obtained assuming that a constant-property slab of helium atoms at a height of 3 arcseconds is permeated by a magnetic field of 10 G with an inclination θB with respect to the solar local vertical direction. The slab’s optical thickness at the wavelength of the red blended component is τred = 0.1. The positive reference direction for Stokes Q is along the projection of the magnetic field vector on the solar surface, which makes an angle of 90◦ with any of the considered line-ofsights.
μ=0.1
Asensio Ramos et al., 2008

27. Dependence of Stokes Q on magnetic field strength
Trujillo Bueno and Asensio Ramos, 2007
ULL = unpolarized Lower Level

28. Dependence of Stokes Q on magnetic field strength
Trujillo Bueno and Asensio Ramos, 2007
ULL = unpolarized Lower Level

29. Dependence of Stokes Q on magnetic field strength
Trujillo Bueno and Asensio Ramos, 2007
ULL = unpolarized Lower Level

30. Dependence of Stokes Q on magnetic field strength
Trujillo Bueno and Asensio Ramos, 2007
ULL = unpolarized Lower Level
atomic polarization must not be neglected even for strong fields!

31. Dependence of Stokes Q on magnetic field strength
Trujillo Bueno and Asensio Ramos, 2007
ULL = unpolarized Lower Level

32. Some pitfalls for Zeeman-used scientists
Zeeman: total linear polarization is proportional to transversal field
blue: INC=54° (more horizontal) green: INC=44° red: INC=34° (more vertical)
disk center B=500G

33. Some pitfalls for Zeeman-used scientists
Zeeman: total linear polarization is proportional to transversal field
Hanle: not at all! (van Vleck angle)
blue: INC=54° (more horizontal) green: INC=44° red: INC=34° (more vertical)
disk center B=50G

34. Some pitfalls for Zeeman-used scientists
Zeeman: ratio between linear and circular polarization is proportional to inlination
Hanle: not at all! (van Vleck angle) (same example)
blue: INC=54° (more horizontal) green: INC=44° red: INC=34° (more vertical)
disk center B=50G

35. Some pitfalls for Zeeman-used scientists
Zeeman: strength of polarization signal is a measure of strength of magnetic field
Hanle: not for very weak fields! (Hanle depolarizes)
saturation regime (10-100G): strength of linear polarization does not depend on B
blue: B=100G (strongest) green: B=25G red: B=1G (weakest)
disk center INC=60°

36. Conclusions
Strong fields (active region, plage fields):
reliable measurements for B > 200 G (100 G for special geometries)
Paschen-Back effect important for correct determination of |B|
atomic polarization important for B < 1.5 kG
10-3 polarization signal sufficient
Weak fields:
10 – 100 G: saturated Hanle regime: LP determined by direction of B
<10 G: Hanle sensitive regime: LP depends on direction and on strength of B
averaging: weak fields do not cancel out!
good: 4x10-4 polarization signal, ideal: 1x10-4
Hanle: additional complications in analysis of data
Ambiguities:
180° Hanle ambiguity
Van Vleck ambiguity
Computation:
x as compared to Zeeman only