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