I.

Observations and Observational Testof Coronal Magnetic Fields
II. High Throughput Multi-Slit
Spectropolarimeter
Hao Sheng Lin
Institute for Astronomy
University of Hawaii

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Direct observation of coronal B is highly relevant to the
Science Mission of Solar-C.
 Coronal magnetic field can be reliably measured
 Coronal B observations do provide useful information about thesolar corona• Quantitative observational test of models possible•…
•…
 Space is a very good place for coronal B observations
 Efficient, high-throughput spectropolarimeter design meeting
the requirement of Solar-C science mission exists

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

I. Coronal Magnetic Fields
 The polarization of forbidden coronal emission lines– Saturated Hanle Effect– Coronal Zeeman Effect Diagnostic capability of Coronal Polarimetry– What can we measure?
– Ambiguity– What cannot be measured?
• Complemented by Alfvén Wave Observations
 Observational Challenges
 What can we learn from Coronal Magnetometry?
– Observational test of coronal magnetic field models– Reconstruction of 3-D coronal magnetic field structure What can be done in space?

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Polarization Mechanism of Forbidden
Coronal Emission Lines
The Coronal Zeeman Effect and theSaturated Hanle EffectSolar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

The Saturated Hanle Effect
The saturated Hanle effect describes the properties of the linear
polarization of the coronal emission lines (CELs) due to theresonant scattering of the photospheric radiation by the highly
ionized atoms in the corona, in the presence of the coronalmagnetic fields
 Linear Polarization (LP)• LP of the CELs is either parallel or perpendicular to thedirection of the direction of the coronal magnetic fieldprojected in the plane of the sky.
• Linear polarization is not sensitive to the amplitude of thecoronal magnetic field.
 Circular Polarization (CP) – Zeeman effect• CP is proportional to the strength of the longitudinalcomponent of the coronal magnetic field.

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

The necessary conditions for saturated Hanle effect
1. Optically-thin atmosphere – single scattering
2. Anisotropic illumination
3. ‘Strong’ magnetic field
The effects
1. Alignment of LP to B⊥.
2. Sensitivity of CP to B||.

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

The necessary ingredients:
1. Optically-thin atmosphere
2. Anisotropic illumination–
Prominence/filament/corona• Far away from the solar surface• Large anisotropy• High degree of polarization–
High photosphere/low chromosphere• Close to solar surface• Small anisotropy• Low degree of polarization due to geometricaldepolarization
3. ‘Strong’ magnetic field

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

The necessary ingredients:
1. Optically thin atmosphere
2. Anisotropic illumination
3. ‘Strong’ magnetic field

ωBAωB >> A (Einstein’s A coefficient)The natural line width of the spectral line (in the rest
frame of the atom) is proportional to A
If the Zeeman splitting ωB is much larger than the naturalline width of the spectral line, then there is no coherency
between the magnetic substates
For forbidden transition,– A ≈ 101 to 102/sec– B0 ~ mG satisfies the strong field condition.
For permitted lines,– A ≈ 106 to 108/sec– B0 ~ 10 – 100 G, depending on the spectral line
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

ωB

In comparison…
Weak field regime – Hanle effectA	ωB << AFor the permitted lines…

Large Einstein’s A coefficient → broad natural line widths.
Strong interference between the magnetic substatesIn the upper solar photosphere where there are sufficientanisotropy, the Hanle effect can be used to diagnose weakturbulent magnetic fields.

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Forbidden Lines(M1 Transition)

Permitted Lines(E1 Transition)e.g. , Fe XIII 1074.7 nm, Si IX 3934.6 nm for thesolar Corona

e.g., He I 1083.0 nm, O VI 103.2 nm

Strong field regime:wB >> A (≈ 101 to 102 sec-1),


Weak field regime:ωB ≤ A (≈ 106 to 108 sec-1),

Weak interference between themagnetic substates,
Incoherent superposition of themagnetic sub-states,Strong interference between themagnetic substates,
Coherent superposition of themagnetic sub-states,|E|2 = |E -1|2 + |E 0|2 + |E+1|2|E|2 = |E –1 + E 0 + E+1|2

ωB

ωB

A

A

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Diagnostics Capability of Forbidden
Coronal Emission Line Polarimetry

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Diagnostic Capabilities of CEL Polarimetry

Circular Polarization– B|| – line-of-sight magnetic fieldstrength…with an alignment
effect correctionLinear Polarization– χ –Azimuth direction of B

–
–

y

B

Direction of B projected in theplane of the sky containing suncenter.
No sensitivity to |B |the van Vleck effect
90 degree ambiguity in theazimuth direction of B,
depending on Ψ

γ

Ψ

B⊥
χ

B||
x

z

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

The van Vleck EffectΨ > θvv

 van Vleck AngleΨ < θvvθvv = 54.7 deg– Ψ < θvv , then LP // B
– Ψ > θvv , then LP ⊥ B

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Alfvén Wave Diagnostics of Corona B
Next Talk
Measurement of Alfvén speed yields transverse coronal |B |projected in the POS
 CEL Doppler measurements– Sensitive to motion along the line of sight.
– Tomczyk et al. 2007
 CEL LP direction oscillation– Sensitive to motion perpendicular to the line of sight.
– Keil et al. (unpublished results)

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Vector Coronal Magnetometryγ

 B|| : Longitudinal |B |– CEL Circulation Polarizationy B⊥ : Tranverse |B |Alfvén Waves in– CEL Doppler images– CEL LP orientation oscillations

Bγ χ : Transverse B direction– CEL Linear Polarization

Ψ

B⊥
χ

B||
x

z

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Observational Challenges

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Circular Polarziation
 Best spectral line for coronal B measurement– Fe XIII 1075 nm
 Amplitude of CP– Solar Maximum: ~ 10-3
– Solar Mimumum: ~ 10-4
 With a 50-cm coronagraph on the ground– 20” pixel~ 30 × 10-6 Ic scattered light~ 1 hr integration time
→ 3 G (3 σ) sensitivity @ 1.1 Rsun

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Circular Polarziation, Low Activity Period

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Coronal Magnetogram, April 6, 2004
Transverse field orientation

Longitudinal Field Strength

Contour plot of the line-of-sightmagnetogram over-plotted on the
SOHO/EIT FeXVI 284 A image. The
contours are 5G, 3G, and 1G.
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

SOLARC – Solar Observatory for the Limb and Active
Region Coronae – J. R. Kuhn
PI—Jeff Kuhn (IfA)• 50 cm aperture off-axis gregorian
telescope• No secondary mirror and spider
structure in the optical path forcoronagraphic performance
SOLARC and its dome on the summit of Haleakala, Maui.

Secondary mirror
Prime focus inverse occulter/field stop

Re-imaging lens
LCVR Polarimeter
Input array of fiber optics bundle

Primary mirror
Optical Configuration of SOLARC and OFIS
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

OFIS: A True Imaging Spectropolarimeter••••

NICMOS3 IR Camera
16 × 8 => 2 × 64 optical fiberbundle
160 × 308 mm, 79 lines/mm
echelle grating with 63.5 blazeangle
f = 800 mm, Φ = 150 mm (F/5.3)
collimator and camera lensEchelle Grating
Camera Lens

NICMOS3 IR camera

Collimator

Fiber Bundle

The coherent optical fiber-bundle rearrange the 2dimensional image sampled by the 16 × 8 input array to
two linear array (2 × 64 ). The two linear arrays act as
the slits of the spectrograph, thus allowing for thesimultaneous recording of the spectra from all the field
points in the 2-D image plane.
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Sample CEL Spectra from OFISOne 64-fiber column illuminated
16 × 4 pixels area coverage

Two 64-fiber columns illuminated
16 × 8 pixels area coverage

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

What Can We Learn From Coronal
Magnetometry?
1. Build a Coronal Magnetic Field Model
2. Validating Coronal Magnetic Field Model
3. …

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Can we build a coronal magnetic field modelfrom the polarimetry data?

?
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

The Coronal B Inversion Problem
The coronal atmosphere is optically thinThe observed coronal polarization signals may not originate
from a single localized source along the line of sight.

There are many independent parameters in the model, but only
a few observables…
The inversion problem is severely under constrained!
⇒ Currently, there are no tested and reliable inversion methods
for the reconstruction of the 3D coronal B structure using
polarization measurements…
⇒ Vector tomography looks promising…

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Can we build a coronal magnetic field modeland reproduce the polarimetry data?

?
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Forward Modeling…
 Yes! In principle…
If we know the 3-dimensional• magnetic field B• Density ne• Temperature Te
structure of the corona, then we can synthesize the LP and CP
signals emerging from the observed coronal atmosphere forcomparison with the observed polarization signals…

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Coronal B Extrapolation
In reality…
 Extrapolations yield magnetic field configuration only.
There are no information about n and T.
⇒ n and T has to be derived, inferred, assumed, or guessed byother means…
 The photospheric and coronal observations are not co-temporal…
– Uncertainties due to evolution of the active region.
 Potential and force-free assumption may not be valid at thephotosphere.

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Testing Potential Field Extrapolation with
SOLARC Observations

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

About AR 10581 AND 10582…

Time of SOLARC
coronal B observation

 Flaring activities in AR10582
ceased about 5 days before
our coronal B observation…
Potential field
extrapolation may be
OK?
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Potential Field Modelof AR 10581 and 10582

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008 Since the thickness ofthe new source
function is small, we
computed thesynthesized LP map
as a function of
position along theLine of Sight…

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Comparison with Judge’s Synthesis Code
 Phil Judge’s code
includes collisional
depolarization
effect…
 We really can’t tellwhich code is betterfrom this comparison.
But Judge’s code
includes more
physics…

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Judge’s code
Lin’s synthesis code

Sourcefunction of
the best-fit
layer

LOS direction σp: rms error indegree of linear
polarization, σχ: rms error of
azimuth angle of LP,
 σLP: combined rms
error of the degreeof polarization andthe azimuth angleof the LP.

Photospheric B along the LOS
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Circular Polarization
 B||(h), the longitudinal B as afunction of height h, arecalculated for each layer.

• The height of B|| reversal agrees
with the observed value at twolayers.
• B||(h) at layer 130 fits the observed
one better.

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Source location of
the FeXIII 1075 nm
CEL…

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Is this a coincidences?
NO!
 Two independent parameters– the degree of linear polarization, and– azimuth angle of linear polarization
have minimum at about the same location
 Synthesized B(h) matches the observed circular polarization
signals at roughly the same location
 The polarization signals originate from the corona above thestrongest photospheric magnetic field feature of the AR.

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Conclusions
 Potential field extrapolation of AR 10582 has reproduced
the observed coronal linear and circular polarization
maps.
– The LP and CP source functions are close to the location of
the sunspot of the active region.
– The locations of the LP and CP source functions are not theexactly the same…
– The inferred LP and CP source functions are fairly
localized!
⇒ Single-source inversion (Judge 2007) might be possible…
⇒ Potential field extrapolation may be a good 0th orderapproximation for the coronal magnetic field model

Liu & Lin, 2008, ApJ, 680, 1496
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

What’s Next?
More observations (if the Sun cooperates) andmore comparisons with models…
 Is potential-field extrapolation really OK?
 Does force-free extrapolations provide bettermodel?
 MHD models should come with information
about n and T…
Collaboration with T. Wieglemann & B. Inhester⇒ Direct comparison can be performed
without guessing where the source islocated.
 Vector Tomography
Collaboration with M. Kramar

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Direct Spectropolarimetry of Coronal B
can provide important, quantitative
constraints for coronal modeling.

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

What can be done in space?

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Background-Limited Observations
 Coronal B sensitivity depends on thetelescope– aperture– scattered light• Instrumental scatter• Sky
 Ground-based coronagraphs are ‘dustlimited’.
– SOLARC: ~ 25 x 10-6 Isun @ 1.25 Rsun
– HAO Mk4: ~ 6 x 10-6 Isun @ 1.25 Rsun
 The Space is sky and dust-free– 2 x 10-7 Isun for COR1 & COR2 inner
field–

Thompson et al., 2005, GSFC internal report
5 x 10-7 Isun @ ~1 Rsun

Korendyke & Socker, 1996, Opt. Eng., Vol.
35, 1170
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

The Coronal Aperture

A factor of 100 (10-5 → 10-7 Ic) improvement in scattered light ispossible in the dust-free space environment→ A 25 cm coronagraph with 1 x 10-7 Isun scattered light inspace is equivalent to a 250 cm telescope on the groundwith 1 x 10-5 Isun scattered light.

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

25-cm Space Coronagraph @ 1 AU
Estimated Performance
Assumptions
 1 x 10-7 Isun scattered light– a factor of 300 improvement from SOLARC
 10% system efficiency

B|| (3σ )20”~ 1 G in 5 min @ 1.1 Rsun

5”

~ 1.3 G in 60 min @ 1.1 Rsun

B⊥

S. Tomczyk – Coronal Alfvén Wave, next presentation

χhigh resolution and cadence with high sensitivity

Ne

Fe XIII 350, 1075, and 1080 nm

Te

Fe XVI 530, Fe X 890, and FeXIII 1075 nm
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

II. High Throughput Mulit-Slit
SpectroPolarimeter
Efficient use of modern large-format focal
plane arrays for Fast Scanning True-imaging

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008 Principle of Multi-Slit Spectropolarimetry
 Current Development– FIRS– True-imaging spectropolarimeters• Conventional fiber-optic array• Birefringent Fiber-Optic Image Slicer

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Multiple-Slit Spectroscopy and SpectroPolarimetry
In conventional long-slit spectrograph, modern large array
detectors are under-utilized, unless we do something
different…
Solar spectropolarimetry typically requires measurement of
selected spectral lines with very high spectral resolution andfidelity, but only in a very small spectral window.
For examples,– Fe I 630.15/630.25 nm line pair:• Δλ = 0.2 nm @ 1.5 pm/pixel ⇒ ~130 pixels in spectral
direction– Fe I 1564.8/1565.3 nm line pair:• Δλ = 0.8 nm @ 6 pm/pixel ⇒ ~130 pixels in spectral
direction– Fe XIII 1075 nm Coronal Emission line:• Δλ = 1 nm @ 10 pm/pixel ⇒ ~ 100 pixels in spectral
direction

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

DWDM-Style Filters
 DWDM (Dense Wavelength Division Multiplexing) filters developed
for fiber-optic communication are ideal for multi-slit spectroscopy

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Custom 630 nm and 1565 nm DWDM Filters

Visible DWDM needs improvements

FeI 1565 nm DWDM Filter
Flat top, 90% transmission

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Full-Stokes 4-Slit Spectropolarimetry@ Fe I 1565 nm
Stokes I

2

3

4

1

2

Stokes U

3

4

Stokes V

Spatial Direction

1

Stokes Q

Dual Beam

Wavelength λSolar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Fast 4-Slit Scanning

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

FIRS: The Facility IR Spectropolarimeter for theDunn Solar Telescope
Up to 4 lines simultaneouslyFirst Focus,
Spectral Mask

First Focus,
Spectral Mask

FeI 630.1/630.2 nm
mid photosphere

CaII 854.2 nm
Mid chromosphereHigh ChromosphereFirst Focus,
Spectral Mask

HeI 1083.0 nm

FeI 1564.8/1565.3 nm
Low photosphere
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Current FIRS Capabilitis
 A complete scan in ~ 10 - 60 minutes (sensitivity dependent)– F/36 feed, 150” x 75” coverage now, 150” x 150” in the future– F/108 feed, 50” x 25” FOV now, 50” x 50” in the future
 Simultaneous observation of– Fe I 630 nm, 1565 nm (FIRS), and CaII 854 nm (IBIS)– Fe I 630 nm, He I 1083 nm (FIRS), and CaII 854 nm (IBIS)

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Simultaneous FeI 630 and 1565 nm
Observations
Fe I 1565 nm

Fe I 630 nm

 Showing only
maps fromone slit

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Limitations of Multi-Slit Scanning
No speed-up of scan for field smaller than theseparation between adjacent slits
Solutions: Change the plate scale on the slits to scan a smaller FOV withwider slits – e.g. DLSP at Dunn Solar Telescope Use True-Imaging Spectropolarimeter– Reflecting Image Slicer – MUSE,– Microlens Array – Tiger– Fiber-Optic Integral Field Unit (IFU) – SOLARC/OFIS,
GMOS, VIRUS
1. Conventional Optical Fibers
2. Birefringent Rectangular Fiber-Optic Ribbon

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

1. Conventional Fiber-Optic IFU
Use standard fused silica
low-loss fibers

cladding• The geometry of conventional
optical fiber prevents highdensity packing necessary forlarge FOV coverage…
• 50% pixel utilization ispossible.

Solar-C Science Definition Meeting, ISAS, JAPANcore

dead space

Nov. 18 – 22, 2008

A 64 x 32 – 8 x 256 Coherent Fiber-Optic Array With new large-format focal plane arrays pushing, it is now
possible to build large-format (102 x 102) true-imaging
spectropolarimeters for solar observation

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

2. Birefringent Fiber-Optic Image Slicer
Fiber-optic ribbon constructed with rectangular optical fibers• Linear polarization of the guided waves is preserved – DualBeam Polarimetry possible through the fibers• Low-cost fabrication

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

BiFOIS Prototype Input and Output Arrays
New ribbon, 2008

Output Array: 2 x 20.48 mm x 0.04 mm linear array, equivalent to two continuous long slits.
Input Array:• 32 x 1.280 mm x 0.040
mm ribbons,• equivalent of 32 x 32
square array with 40 um
pixel size.
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

I

Q

U

Solar-C Science Definition Meeting, ISAS, JAPANV

Nov. 18 – 22, 2008

IRIS Prototype Time Sequence






10” x 10” FOV0.3”/pixel spatial sampling with
low-order AO
10 second time resolution
15 minutes
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

High-Throughput Imaging Spectropolarimeters Fast-scanning multi-slit spectropolarimeter can greatly
enhance the temporal resolution of large-area scan

– Active region size scan for ~ 10 minutes
 True-imaging spectropolarimeter can observe a modest field ofview with very high temporal resolution– ~10” x 10” with less than 10 sec cadence on solar
disk– Spectropolarimetry for the solar corona
Both Fast-Scanning and Fiber-Optic Feed Can be
Accommodated by a Single Spectrograph.

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

True-Imaging Multi-Spectral-LineSpectropolarimetry
What can we do with a true-imaging spectropolarimeterthat covers a substantial FOV with diffraction-limited
performance, and four or five spectral lines
simultaneously ?
– Dynamics of the chromosphere– Small-scale dynamo– Jets– Reconnection– Penumbra filaments– Dynamics of the filaments– ???
Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008

Direct observation of coronal B is highly relevant to the
Science Mission of Solar-C.
 Coronal magnetic field can be reliably measured
 Coronal B observations do provide useful information about thesolar corona• Quantitative observational test of models possible•…
•…
 Space is a very good place for coronal B observations
 Efficient, high-throughput spectropolarimeter design meeting
the requirement of Solar-C science mission exists

Solar-C Science Definition Meeting, ISAS, JAPANNov. 18 – 22, 2008