Physics 681: Solar Physics and Instrumentation – Lecture 9

Physics 681: Solar Physics and Instrumentation –

Lecture 9Carsten 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 1J J S S L L

gJ J

20 with

4Be

e g B g gM g Mcm


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



http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/sodzee.html


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 QU V

2 2 2 2I Q U V


Schlichenmaier and Collados (2002)


Bellot Rubio et al. (2004)


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 VPI

1 / 2

with /

/ 2

C C

B l C

C

I I I

V I


Unno’s Equations

2 2

2

2

with

0 0 , where

0 00 0

1 1sin 1 cos2 41 1 sin cos 22 41 1 sin sin 22 4

1 cos2

I Q U V

Q I

U I

V I

I

Q

U

V

IQUV

I I - I

I =


Transfer of Polarized Light

Longitudinal magnetic field

Radiative transfer equations

cos dd

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 Qd ddV dUV I B Ud d


Transverse magnetic field

Radiative transfer equations

90 and 0 0 and 01 12 41 12 4

U V

I

Q

U

1

1

1

I Q

I Q

I

dI I B QddQ Q I BddV Vd


SOLIS

Physics 681: Solar Physics and Instrumentation – Lecture 9

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