CMB Polarization
• Theory: yet another Holy Grail
– Origin of CMB polarization
– Q,U, E, B & all that
• The heroic past
– Discovery of CMB polarization (2003-2009)
• Challenges
– Systematics
– Calibration
– Foregrounds
• Future ambitions
14th March 2010
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Generation of polarized CMB radiation by Thomson
scattering (Hu)
Scalar quadupole
moment
Tensor
quadrupole
moment
14th March 2010
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Scalar Polarization
• Naturally produced by adiabatic fluctuations at last
scattering
• “Large” polarization: photons travel significant
distance between scatterings (!)
• Only on causally-connected angular scales (< 1°)
– acoustic peaks when generated at last scattering
– Large scales when generated by re-ionization
• A bit smaller-scale than structure in total intensity:
– driven by gradients in brightness
• Polarized brightness up to 10% of total intensity
fluctuations on small scales.
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Tensor Polarization
• Driven by very-large
scale gravitational
waves, generated at
inflation.
• Tensor-to-scalar power
ratio depends on
inflationary energy
scale:
Planck Energy
r ≈ (V1/4 / 3.3  1017 GeV)4
• Nearly negligible on
‘causal’ scales,
strongest @ ~2°
14th March 2010
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LHC
E-mode vs B-mode
• Polarization pattern on sky
can be separated into two
orthogonal modes:
– E-mode or gradient mode
– B-mode or curl mode
• For plane waves, E-modes
polarized alternately parallel
& perpendicular to wave
vector
• B-modes at 45°
• B-modes have opposite
parity to E-modes
• B-modes only generated by
tensor fluctuations
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• Names based on obscure &
confusing analogy with EM
fields; ignore!
– (Polarization always refers
to electric field
orientation)
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E-mode vs B-mode
Wayne Hu
14th March 2010
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±2Ylm: Spin-2
Spherical Harmonics
• Polarization normally
represented by Stokes
parameters
I  |Ex|2 + |Ey|2
• Total intensity
Q  |Ex|2 – |Ey|2
U  Re(ExEy*)
• Linear poln
V  |ER|2 - |EL|2
• Circular poln
• But depend on coordinate
system defining x and y
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• Polarization is “Spin-2”
quantity
– orientation but no
direction
• Analyse in terms of “spin-2
spherical harmonics” ±2Ylm
• Harmonic coefficients can be
summed & differenced to
yield pure E- and B-modes
• E mode parity (-1)ℓ
• B mode parity (-1)ℓ+1
• almE,B Coefficients coorddependent, but not Cℓ
Rencontres de Moriond 2010
Polarization Cℓ Spectra
•
•
•
•
•
•
E-mode peaks interleave with
total power
E-mode correlated with Temp
(Stokes I), alternately positive &
negative
B-mode uncorrelated due to
opposite parity
Note bump at ℓ < 10 due to
scattering after re-ionization
Tensor mode only separable
from scalar in B-mode pol (no
scalar contribution)
B-mode amplitude assumes
maximum possible scalar-totensor ratio r
T
E
B
Blens
14th March 2010
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Cosmology
• E-modes:
– Direct probe of last scattering surface
– Best constraint on early re-ionization (z ~ 10)
– Independent check on cosmological model fitted to
Temperature data
– (Nearly) independent of temperature pattern: eventually
reduces cosmic variance (needs better SNR)
• Gravitational lensing B-modes:
– Sensitive probe of mass distribution: σ8, mass vs light, tests of
GR consistency.
• Primordial B-modes:
–
–
–
–
“Holy Grail of Cosmology”.
Relic from inflationary epoch: t = 10-37 s,
Fixes inflation energy scale: big clue to relevant physics
Non-guassian B-modes sensitive test of defects
14th March 2010
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High History of the Holy Grail
(abridged)
•
•
•
•
•
King Arthur inherits kingdom in
anarchy & chaos.
Gathers knights of the round
table, pacifies kingdom,
conquers the Roman Empire,
institutes ideal kingdom.
Knights see vision of Holy Grail
at feast in Camelot, set off to
search for Holy Grail.
Failure, disappointment,
disillusion, death; no knight
finds Grail and returns to tell the
tale.
Fellowship of the Round Table
never recovers. Kingdom
collapses into anarchy & chaos.
14th March 2010
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WMAP, L2, 2003
Discovery!
Cosmic Background
Imager, Chajnantor, 2004
E-modes!
DASI Team
South Pole, 2002
14th March 2010
Boomerang 2003,
Somewhere in Antarctica
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CMB Polarization 2005
14th March 2010
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QUaD
Uses old DASI mount
14th March 2010
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QUaD: E vs B amplitude
E-mode only
Signal!
14th March 2010
B-mode only
Noise!
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QUaD: E-mode Peaks
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South Pole: BICEP1
14th March 2010
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Chiang et al, ApJ, this week
BICEP Polarization
14th March 2010
NB Scale
Difference!
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Current results
Chiang et al, ApJ, this week
• Dominated by
BICEP at ℓ < 300,
QUaD at higher ℓ
• Best limit:
• r < 0.72 (95%)
(BICEP)
• 1 more year of
BICEP, full year of
QUIET data
already taken.
– Expect modest
improvement.
14th March 2010
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Double take
• B-mode limit gives r < 0.72
• …but WMAP claim r < 0.24 (Jarosik et al 2010)??
• Current best limit on tensor amplitude comes from
total intensity (+BAO etc) not B-modes
• But limited by cosmic variance…
• …so tight limits on B-modes needed to do better.
• Current race (Planck vs BICEP2 vs others) is to get
to r = 0.1
• Slow race: energy scale  r1/4
– but B-mode amplitude on sky  r 1/2
14th March 2010
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Challenges of CMB Polarization
•
•
Good news:
1.
Q  |Ex|2 – |Ey|
or vice versa
U  Re(ExEy*)
…differencing and cross-correlation are two good ways
to eliminate systematics
2. Polarization signals are weak, don’t drive systematics
3. Sky rotates around detector: automatic “chopping”
}
Bad news:
1.
2.
3.
Leakage from unpolarized signal
Lack of bright polarized calibrators
4 times more complicated
14th March 2010
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Being systematic about
systematics
• Complex field description
(Jones Matrix):
 E x
e  
 E
 y
  J xx

 J
  yx
J xy   E x

J yy   E y

  Je


• Power description (Mueller
Matrix):
 I    m II

 
 Q    m QI
s  


m UI

U



V   m

  VI
14th March 2010
m IQ
m IU
m QQ
m QU
m UQ
m UU
m VQ
m VU
m IV   I

m QV   Q
m UV   U

m VV   V
•



  Ms



Rencontres de Moriond 2010
•
•
J: 8 real numbers
(including irrelevant
overall phase)
M: 16 real numbers
M allows for incoherent
combination of modes.
Being systematic about
systematics?
• Output at one pixel is whole-sky integral over matrix-valued
beam times sky
• Matrices vary with
–
–
–
–
frequency,
sky position (polarized beam)
time
Often we only have one output signal, not four, i.e. one row of
matrix
• Effective matrix at given sky pixel is weighted response from
many visits with different orientations: “beam” different at each
pixel.
• Each polarimeter architecture has characteristic strengths &
weaknesses, including additive artefacts not included in
matrices.
14th March 2010
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First-order beam artefacts
Graphic: Epic Study
• Hu, Hedman & Zaldarriaga analysis:
– First-order perturbations around gaussian beam
– Monopole, dipole quadrupole terms
– Structure smaller than beam by definition.
14th March 2010
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Trends 2001-2010
• Interferometers give way to large focal plane arrays
– Surface brightness limitations for interferometers
• Very broad-band systems
– Bandpass mis-match major source of leakage from I to
(Q,U): requires careful calibration
• Corrugated horns (for very clean beams) replaced by
focal plane detector arrays
– Requires elaborate baffling to cut out stray light.
• Bolometric systems
14th March 2010
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To amplify or not?
• Amplification: allows replication of signal,
saves √2 or 2 in SNR for polarimetry
• But inevitably adds noise even in ideal case,
especially at hν >~ kTb
• To avoid amplification, need very cold (0.1 K)
detectors, held at very stable temperature.
• Upshot: bolometers best at > 100 GHz,
amplifiers best below 50 GHz.
14th March 2010
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Polarization-Sensitive Bolometers
• Two planes of
absorbing mesh, with
orthogonal wires.
• Each rejects ‘wrong’
polarization with 9095% efficiency
• Used on Boomerang
2003 flight, QUaD
experiment, Planck HFI,
etc.
14th March 2010
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Calibration
• Getting absolute angles
surprisingly difficult
• Astronomers don’t need
angles to absolute
precision better than a
few degrees
• Astronomical
“calibrators” known to
2° at best
• Use physical
polarization reference
BICEP wire-grid Calibrator
14th March 2010
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Foregrounds
• Thermal Dust:
– COBE FIRAS,
Planck HFI, PILOT
• Anomalous Dust:
– COSMOSOMAS,
WMAP, Planck LFI,
QUIJOTE
• Free-free /
Synchrotron:
– Arecibo, C-BASS,
Planck LFI
14th March 2010
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Polarized Foreground SED (???)
RMS Q,U
on 1° scales
(maybe!)
14th March 2010
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Foreground vs CMB signal
• CMB polarization splits
into orthogonal modes:
• E-modes fix optical depth
to re-ionization
– dramatic reduction in
parameter degeneracy
• B-modes define energy
scale of inflation
• Obscured by Galactic
foreground emission
– minimum at ~60 GHz
– synchrotron below
– dust above.
14th March 2010
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C-BASS
E
60 GHz
B
V1/4 = 2×1016 GeV
ESA’s Planck mission
• “Last word” in CMB
temperature observations:
accuracy set by foreground
residuals
• Polarization:
– Not formal mission goal
– Best we can do without
putting extra constraints
on the hardware
• best power spectrum yet
– Low SNR but 12 million
pixels
• First chance of detecting
primordial B-mode
polarization
14th March 2010
WMAP
Planck
Max
resolution
14 arcmin
5 arcmin
Bands:
5, @ 23–
94 GHz
9, @ 30–
857 GHz
Best
Sensitivity
(0.3°)
20 μK
(6 yrs)
3.5 μK
(1.25 yrs)
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Planck mission status
•
Launch: May 18th 2009
•
CPV Phase: July-August
•
Survey started: Aug 13th 2009
•
>95% of sky now covered once
•
Baseline Survey ends: Oct
2010, one year extension
approved.
•
End of proprietary period on 1st
year of data: October 2012.
Planck Cryo Qualification
Model under test at CSL,
Liège.
14th March 2010
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Projects ongoing and planned
• Space
• Ground-based:
– Planck
– CMBPOL/EPIC
– BPOL
• Balloon
– EBEX
– PILOT (Dust)
– SPIDER
14th March 2010
– QUIET1 (40/90 GHz)
– C-BASS (5 GHz)
– QUIJOTE1 (10-18, 30
GHz)
– BICEP2 (150 GHz)
– GEM-P (5 GHz)
– ABS (145 GHz)
– POLARBear (150 GHz)
– QUIET2 (30/40/90)
– QUIJOTE2 (30)
– Keck Array (100/150/220)
– QUBIC
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State-of-the art Receivers
• MIC Amplifiers up to 120 GHz
–
–
–
–
cool to 15K
Tsys=10 K at 33 GHz, state of the art.
Rule of thumb is 1/3 K per GHz.
7 times worse than quantum limits, limited by internal
noise
– 20% bandwidth, defined (not very well) by tuned circuits
• Bolometers 100 GHz to infrared.
–
–
–
–
cooled to 0.1K
30-50% bandwidth
Custom filters (Cardiff University)
7 times worse that quantum limits, limited by losses in
filters etc (nearly perfect detectors)
14th March 2010
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