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Physics 681: Solar Physics and Instrumentation –
Lecture 9
Carsten Denker
NJIT Physics DepartmentCenter for Solar–Terrestrial
Research
September 27, 2005 Center for Solar-Terrestrial Research
Polarimetry Zeeman splitting Assume weak magnetic field (LS or Russel-Saunders
coupling) Quantum numbers: L orbital angular momentum of the
electrons, S spin angular momentum, J total angular momentum, and MJ magnetic quantum number
Landé factor
Displacement of the line in the presence of a magnetic field
Normal Zeeman effect or Lorentz triplet: S = S’ = 0 and ΔMJ = –1, 0, +1 g* = –1, 0, +1
1 1 11
2 1
J J S S L Lg
J J
20 with
4Be
eg B g gM g M
cm
September 27, 2005 Center for Solar-Terrestrial Research
http://w.home.cern.ch/w/wadhwa/www/zeeman.html
Normal and Anomalous Zeeman Effect
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/sodzee.html
September 27, 2005 Center for Solar-Terrestrial Research
Solar spectral lines are broadened by micro- and macro-turbulence and by pressure the components of a Zeeman multiplet are normally not resolved
The triplet consists of two shifted σ-components and an unshifted π-component
Longitudinal Zeeman effect: line-of-sight (LOS) || B σ-components with circular polarization of opposite sense
Transverse Zeeman effect: LOS =|== B π-component (linearly polarized =|== B ) and σ-components (linearly polarized || B )
ΔλB ≈ λ2 ΔλD ≈ λ Polarized light (propagating in the z-direction)
Stokes vector
cos and cosx x y yE E
2 2 2 2
2 cos 2 sinx y x y
x y x y
I Q
U V
2 2 2 2I Q U V
September 27, 2005 Center for Solar-Terrestrial Research
Schlichenmaier and Collados (2002)
September 27, 2005 Center for Solar-Terrestrial Research
Bellot Rubio et al. (2004)
September 27, 2005 Center for Solar-Terrestrial Research
Superposition of a large number of independent waves
Degree of polarization
Stokes profiles I(λ), Q(λ), U(λ), and V(λ) Longitudinal Zeeman triplet
2 2 2 2
2 cos 2 sin
x y x y
x y x y
I Q
U V
2 2 2
2
Q U VP
I
1 / 2
with /
/ 2
C C
B l C
C
I I I
V I
September 27, 2005 Center for Solar-Terrestrial Research
Unno’s Equations
2 2
2
2
with
0 0 , where
0 0
0 0
1 1sin 1 cos
2 41 1
sin cos 22 4
1 1sin sin 2
2 4
1cos
2
I Q U V
Q I
U I
V I
I
Q
U
V
I
Q
U
V
I I - I
I =
September 27, 2005 Center for Solar-Terrestrial Research
Transfer of Polarized Light
Longitudinal magnetic field
Radiative transfer equations
cosd
d
1I
I B
1 10 0, 0, , and
2 2Q U I V
1 1
1 1
I V I
I V I
dI dQI B V Q
d ddV dU
V I B Ud d
September 27, 2005 Center for Solar-Terrestrial Research
Transverse magnetic field
Radiative transfer equations
90 and 0 0 and 0
1 1
2 41 1
2 4
U V
I
Q
U
1
1
1
I Q
I Q
I
dII B Q
ddQ
Q I BddV
Vd
September 27, 2005 Center for Solar-Terrestrial Research
SOLIS