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Coronal Faraday Rotation ofCoronal Faraday Rotation of Occulted Radio Signals Occulted Radio Signals

M. K. BirdArgelander-Institut für Astronomie, Universität Bonn

International Colloquium on

Scattering and Scintillation in Radio Astronomy

Pushchino, Russia

Monday, 19 June 2006

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OutlineOutline Coronal Faraday Rotation – Definition Coronal FR using Various Radio Sources

– Pulsars

– Extended Continuum Sources

– Spacecraft (Helios E12: 1975-1984)

FR Variations over Different Time Scales– Background Coronal Magnetic Field

– FR Signature of Coronal Mass Ejections

– FR Fluctuations: Alfvén Waves & Quasi-harmonic Oscillations

Coronal FR Mapping – the Future? Summary

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Coronal Faraday Rotation - DefinitionCoronal Faraday Rotation - Definition

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Faraday Rotation Faraday Rotation : Definition: Definition

sBB

N

f

K

dssBsNf

K

s

e

E

H

se

ˆ

)()(2

radians

2.36∙104 in MKS or cgs units

radio frequency (Helios: 2.3 GHz)

electron density

mag field proj. along ray path

with

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Interplanetary Electron Column Density from EarthInterplanetary Electron Column Density from Earth

“Dispersion Measure”Units: hexems

1 hexem = 1016 el/m2

Earth

Sun

analogous plotfor Faraday Rotationdoes not exist!

I = ∫Ne(s) ds

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Polarization Angle MeasurementPolarization Angle Measurement

Electric Vectors (semi-majoraxis of polarization ellipse):

E0 = Source (transmitted)

E = Measured (received)

Angle definitions:q = locally measured

polarization anglep = parallactic angle = Faraday rotation

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Rotation Measure RM:Rotation Measure RM:

rad 2 RM

2-13 m rad ˆ1063.2

where

dssBNRM e

A rotation measure of RM = 1 rad m-2 yields:

= 0.97° at 2.3 GHz (=0.13 m) = 57.3° at 300 MHz (=1.0 m) = 1432° at 60 MHz (=5.0 m)

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Coronal Faraday Rotation MeasurementCoronal Faraday Rotation Measurement

1. can be positive or negative (from polarity of interplanetary magnetic field)

2. Angle ambiguity ( ± m·180°)

3. Contributions from electron density and magnetic field cannot be separated without independent measurements

4. Correction for variable ionosphere necessary if solar offset R > 10 RS

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Ionospheric Faraday RotationIonospheric Faraday Rotation

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Coronal FR using Various Radio SourcesCoronal FR using Various Radio Sources

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Coronal FR with PulsarsCoronal FR with Pulsars

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Pulsars at Conjunction 1978-79Pulsars at Conjunction 1978-79

[Bird et al., Nature 283, 459-460, 1980]

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Pulsar Pulse Profiles: Measurement TechniquePulsar Pulse Profiles: Measurement Technique

PSR 0525+21 PSR 0540+23

intrinsicprofile

modifiedprofile

p-angle:intrinsic

&modified

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Coronal FR of PSR 0525+21 (1978-79)Coronal FR of PSR 0525+21 (1978-79)

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Solwind Images during 1979 Occultation of PSR 0525+21Solwind Images during 1979 Occultation of PSR 0525+21

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Coronal Magnetic Field from RM & DM: 1979Coronal Magnetic Field from RM & DM: 1979

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Coronal FR with Coronal FR with Extended ContinuumExtended Continuum

Sources Sources

3C228

[Spangler, 2005]

A

B

C

1'

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Coronal FR at VLA: 21 Aug 2003Coronal FR at VLA: 21 Aug 2003

RM:62.5 rad/m2

3C228

R = 7.1…6.2 RS

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SOHO/LASCO: 16 AUG 2003SOHO/LASCO: 16 AUG 2003

3C228

3C228

Jupiter Venus

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Coronal FR with HeliosCoronal FR with Helios

Helios – 1– Launch: 10 Dec 1974

– EOM: 15 Mar 1986

– q = 0.31 AU (P = 190 d)

– i = 0°, "spin up"

Helios – 2– Launch: 15 Jan 1976

– EOM: 08 Jan 1981

– q = 0.29 AU (P = 186 d)

– i = 0°, "spin down"

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Earth-Sun Line Fixed: Helios-1Earth-Sun Line Fixed: Helios-1

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Coronal Faraday Rotation: Helios ObservationsCoronal Faraday Rotation: Helios Observations

<FR> = 35.4° FR = 2.1°

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Helios FR: Effelsberg/Goldstone

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Coronal FR: Helios-1, Dec 1981Coronal FR: Helios-1, Dec 1981

180 ambiguity

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FR Variations over Different Time Scales …FR Variations over Different Time Scales …Background Coronal Magnetic FieldBackground Coronal Magnetic Field

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Ballerina Model of HCSBallerina Model of HCS

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Radio Ray Path Geometry in the CoronaRadio Ray Path Geometry in the Corona

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Coronal Faraday Rotation from Sector StructureCoronal Faraday Rotation from Sector Structure

r

RBB

r

RNN S

rS

e ;

Let

00

1

002max

1

2

then

R

RBN

f

KR SS

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Mean Absolute FR: 1975-1976Mean Absolute FR: 1975-1976

|max| R-4.15

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Coronal Electron Density: Coronal Electron Density: Radial ProfilesRadial Profiles

2120

0

m 104.1 2.45,

N

r

RNN S

e

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Mean Coronal Magnetic Mean Coronal Magnetic Field 1975-76Field 1975-76

3 RS < R < 10 RS :

Br = 7.9 R-2.7 G (17) orBr = 6 R-3 + 1.2 R-2 G (18)

[Pätzold et al., Solar Phys. 109, 91, 1987]

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FR Variations over Different Time Scales FR Variations over Different Time Scales … FR Fluctuations: Alfvén Waves & … FR Fluctuations: Alfvén Waves &

Quasi-harmonic OscillationsQuasi-harmonic Oscillations

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FR Fluctuations: Standard Deviation vs. Solar OffsetFR Fluctuations: Standard Deviation vs. Solar Offset

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FR Spectra for FR Spectra for Various Solar Various Solar

Offset DistancesOffset Distances

Andreev et al., [1996]

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FR Spectral Index vs Solar OffsetFR Spectral Index vs Solar Offset

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Two-Station Two-Station Coronal Sounding Coronal Sounding

MeasurementsMeasurements

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Measuring Coronal VelocitiesMeasuring Coronal Velocities

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Coronal Velocities from FR CorrelationsCoronal Velocities from FR Correlations

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Two-Station FR MeasurementsTwo-Station FR Measurements

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Simultaneous FR Spectra with QHCSimultaneous FR Spectra with QHC

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Rapid Sequence of Rapid Sequence of FR SpectraFR Spectra

QHC comes…… and goes!

[Chashei et al., 1999]

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FR Variations over Different Time Scales FR Variations over Different Time Scales … FR Signature of Coronal Mass Ejections … FR Signature of Coronal Mass Ejections

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CME Passing throughCME Passing through Helios-2 Ray Path Helios-2 Ray Path

Solwind CoronagraphImages recorded during Helios Solar Occultations

In Oct/Nov 1979

[Bird et al., 1985]

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CME Height-Time Diagram, 24 Oct 1979CME Height-Time Diagram, 24 Oct 1979

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CME Magnetic Field Estimates, 24 Oct 1979CME Magnetic Field Estimates, 24 Oct 1979

UT Solar Offset

(RS)

I

(hexems)

(deg)

<BS>

(mG)

08:00 5.1 1.8 ±10 ±2

08:30 5.1 1.8 +20 +4

09:00 5.0 1.9 +40 +8

09:30 5.0 1.9 +55 +11

10:00 4.9 2.0 +35 +7

10:30 4.9 2.0 ±5 ±1

11:00 4.8 2.0 -45 -9

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Coronal FR Mapping – the Future?Coronal FR Mapping – the Future?

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One line of sight to a linearly polarized sourceOne line of sight to a linearly polarized source

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Simulated Coronal FR for CR 1751Simulated Coronal FR for CR 1751

[J. Kasper, priv. comm, 2004.]

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Transient Simulations: October 2003 CMEsTransient Simulations: October 2003 CMEs

CME not yet detected Large FR in 20 sources

CME!

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FR Mapping – Conclusions regarding LOFARFR Mapping – Conclusions regarding LOFAR

Expected density of suitably polarized sources: 1 deg-2

FR maps could be used to test models of coronal magnetic topology

FR maps of transient flux ropes could be used to predict the geoeffectivity of the ensuing CME impact at Earth

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Coronal Faraday Rotation: SummaryCoronal Faraday Rotation: Summary

Faraday Rotation measurements provide a unique tool for investigating coronal magnetic structure…– Emperical model for the magnitude and radial dependence of the

background coronal magnetic field

– Evidence for outward (and inward) propagating Alfvén waves

– Evidence for dominance of magnetic fluctuations over density fluctuations

FR Mapping of CMEs is a difficult, but not hopeless, task.