Polarized Radiation from Aligned Dust

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Polarized Radiation from Aligned Dust
Solving 60 year old problem

• A Lazarian
• Astronomy Department and CMSO
• UW-Madison

Collaboration T. Hoang UW-Madison
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Aligned grains dominate polarization of CMB
foreground for frequencies larger than 100 GHz
Example

Emission by aligned grains
By Hiroshi Sugimoto
By Dotson et al. 00
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Theory of grain alignment is essential to both
quantitatively model polarization and interpret
the observations
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This presentation describes the present state of
grain alignment theory and its implications
Problem of grain alignment
Helicity of irregular grains
Motivation
Modeling polarization
Modern theory
Implications
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Differential extinction results in linear
polarization of transmitted light
How well do aligned grains trace magnetic fields?
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No Theory No Trust in Dust
Polarimetry. L. Spitzer
wanted us to have the theory.
Rao et al. 98


Does magnetic field or alignment change direction?
We need theory to interpret polarization in
terms of B!
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The textbook solution, namely, paramagnetic
alignment is inefficient for typical ISM grains
Davis-Greenstein mechanism
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B
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Grains get aligned with rotation axis parallel to
B (grain 1)
For ISM
tDGgttgas for paramagnetic grains
Marginal alignment
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Paramagnetic alignment may be important for very
small grains, e.g. spinning dust
The degree of alignment of thermally rotating
grains scales as a-1 and dominates for alt10-6cm.
Lazarian Draine 00
10-7cm
Polarization degree
10-5cm
Resonance Relaxation process can align PAHs
PAHs according to Draine Lazarian 98 provide
spinning dust foreground component.
Constraining magnetic intensity UV polarimetry
shows that 3x10-6cm are poorly aligned, so
magnetic fields cannot be gt10-5G.
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Dolginov Mytrophanov 76 radiative torques can
align twisted grains. How important is it?
Irregular ISM grain
Dolginov Mytrophanov 76 considered difference
in scattering of left and right circular
polarized photons by twisted grain and
discovered radiative torque (RAT) alignment.
Claim of the RAT importance was not proven.
Bradley et al. 95
Incorrect statements oblate and
prolate grains align oppositely (corrected in
Lazarian 95), wavelength
dependence is incorrect (corrected in Lazarian
Hoang 07), analytical model is
incorrect (shown in Hoang Lazarian 08).
Mechanism was ignored for 20 years!
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Bruce Draine modified DDSCAT code to calculate
radiative torques (RATs)
Numerical studies
Draine Weingartner 96 DDSCAT calculations of
RATs and conjecture of RAT importance.
Draine Weingartner 97 RATs can align on their
own, but the treatment of grain dynamics is
problematic.
Angle between B and light direction
Weingartner Draine 03 study of RAT alignment
in the presence of thermal fluctuations for a
single direction of radiation and a single
wavelength.
Draine Weingrartner 97
L. Spitzer Alignment torques are not universal.
How can a universal alignment exist?
Fallacy in literature RATs act like Purcells
torque to spin up grains, while DG aligns grains
How many grain shapes should be studied at how
many wavelengths to predict the degree of
alignment?
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Our goal is to formulate analytical predictive
theory of radiative torque alignment
Based on 6 papers Lazarian Hoang 07ab, 08
Hoang Lazarian 08abc
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Analytical model (AMO) provides quantitative
insight into RAT alignment
Qe2
Qe1

Qe3
e2
?
a1
?
e1
k
mirror
a1 is grain max inertia axis k is light
direction
e3

Only projections Qe1 and Qe2 matter, Qe3 causes
grain precession only.
Lazarian Hoang 07
Simple analytical expressions are available for
AMOs torques.
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Grains being left- and right- handed and this
induces dramatic differences in torques

Why do the shapes of torques differ?
Note the alignment and spin up studied by
DW97 are even more different.
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Our model (AMO) represents RATs of irregular
grains very well!
Deviations from AMO for irregular grains
Model
The functional forms of torques of irregular
grains are similar to AMO. The ratio of
Qe1max/Qe2max changes from grain to grain.
Lazarian Hoang 07
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New effect RATs can stop grain rotation!
Detailed treatment of crossovers confirms this
Beam of light
a
k

B
is angle between magnetic field and
radiation
is angle between a and magnetic field
Cyclic phase trajectories above are artifacts of
incorrect treatment of crossovers.
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When angular momentum is parallel to magnetic
field the alignment torques vanish
Q Why alignment is right? A J parallel or
anti-parallel to B is a stationary point
J
Magnetic field
B
Stationary points are either attractor or repellor
Light beam
Additional stationary points can exist.
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AMO predicts when RATs only stop grain rotation
and when they also spin grains up
Ratio Qe1max/Qe2max is as important for
polarimetry as the grain axis ratio
RATs can only impede grain rotation
Angle between k and B
Lazarian Hoang 07
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Thermal wobbling kills wrong alignment, namely,
alignment with long axes parallel to B
wrong alignment for a narrow range of angles
No wobbling wrong alignment
Makes interpretation of polarimetry reliable.
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Both gaseous collisions and superparamagnetic
inclusions may increase the degree of alignment
New effect Superparamagnetic inclusions induce
fast grain rotation!
Lazarian Hoang 08
No inclusions, no attractor point
Inclusions induce attractor point
Another new effect Gaseous bombardment moves
grains from low to high attractor point,
increasing alignment!
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A similar mechanism can align irregular grains
drifting subsonically in respect to gas
Irregular grains should experience regular
torques similar to RATs. This induces alignment
with long axes perpendicular to B.
Lazarian Hoang 08
Yan Lazarian 03
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Quantitative modeling of polarization base on the
alignment theory is only starting. Testing with
observations is essential.
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For the first time we have a cookbook to model
dust polarization
Axis ratio, Qe1max/Qe2max, k and B angle,
radiation field, gas damping
Predicted polarization
Theory
Hoang Lazarian 08
Lazarian Hoang 07
Max rotational rate
Qe1max/Qe2max
Alignment is present
40 alignment
No alignment
k and B angle
RATs efficiency
RATs increase with aeff
100 alignment
Questions to address Are grains supermagnetic?
k and B angle
Is it OK to use mean Qe1max/Qe2max ratio?
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RATs align grains in starless cores as grain
sizes increase there and so do RATs
L43 starless dark core
Challenge to Theory How can grains be aligned at
Av10?
Ward-Thompson et al. 00
Solution As grain size grows external radiation
aligns grains in dark cores (Cho Lazarian 05).
Simulated cloud
Further modeling is in Pelkonen et al. 07 and
Bethell et al. 07.
Av10
Bethell et al. 07
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Large grains, e.g. Zodi and comet dust, should be
aligned
photon beam
Circular polarization observations and
predictions
Hoang Lazarian 08

Scattering by aligned grains results in circular
polarization. Would be good to test with the
Zodiacal dust.
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Good alignment of grains justifies relating
extinction to emission polarization
Starlight polarization
star
Spectrum of degree of starlight polarization
observer
For aligned grains
Fosalba, Lazarian, Prunet Tauber 01
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To relate extinction and emission polarization,
one must understand observations of turbulence
At angles, less than L/dmax the observed
fluctuations reveals the underlying turbulence
spectrum
angle1/l
Predictions of emission depend whether stars are
at large or small distances to the observer
(Lazarian 95, Cho Lazarian 02).
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Starlight polarization data is consistent with
the model of Kolmogorov magnetic turbulence
For Kolmogorov and stars being the nearby ones,
one can explain the data
Cho Lazarian 02 prediction for emission
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In summary, radiative torques are responsible for
ISM grain alignment. We have an analytical model
of RATs.

• Analytical model for RAT alignment exists.
• RAT alignment explains the existing data.
• The theory is important for foreground studies.

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Change of polarization with optical depth is
consistent with the RAT predictions
Molecular cloud interface
Future observations should determine whether
superparamagnetic inclusions are necessary.
AV 3
AV 0
Line of sight
Polarization in the presence of turbulence
Hoang, Lazarian Jones 08
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Next stage is to include detailed alignment
prescriptions in simulated polarization maps
Falceta-Goncalvez et al. 08 finds that C-F
technique can provide 20 accuracy if the
alignment is known.
How does C-F technique of determining magnetic
field strength is affected by incomplete
alignment?
Falceta-Goncalvez, Lazarian Kowal 08
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Grain alignment happens with long axes // or
to B due to fast Larmor precession
Internal alignment for 10-5 cm grain Barnett
relaxation is 107 s (Purcell 79) Nuclear
relaxation is 10 s (Lazarian Draine 99)
Exception Alignment or change of B on the scales
less than the precession time.
Must know
When is the alignment parallel or perpendicular
to B? When is there no alignment?