CMB Polarization

14th March 2010 Rencontres de Moriond 2010

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


Generation of polarized CMB radiation by Thomson scattering (Hu)

Scalar quadupole moment

Tensor quadrupole moment


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.


Tensor Polarization

• Driven by very-large scale gravitational waves, generated at inflation.

• Tensor-to-scalar power ratio depends on inflationary energy scale:r ≈ (V1/4 / 3.3 1017 GeV)4

• Nearly negligible on ‘causal’ scales, strongest @ ~2°

LHC

Planck Energy


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

• Names based on obscure & confusing analogy with EM fields; ignore!– (Polarization always

refers to electric field orientation)


E-mode vs B-mode

Wayne Hu


±2Ylm: Spin-2 Spherical Harmonics

• Polarization normally represented by Stokes parametersI |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

• 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 coord-

dependent, but not Cℓ


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-to-tensor ratio r

T

E

B

Blens


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


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.


Discovery!

DASI Team South Pole, 2002

WMAP, L2, 2003

Cosmic BackgroundImager, Chajnantor, 2004

Boomerang 2003, Somewhere in Antarctica

E-modes!


CMB Polarization 2005


QUaD

Uses old DASI mount


QUaD: E vs B amplitude

E-mode onlySignal!

B-mode onlyNoise!


QUaD: E-mode Peaks


South Pole: BICEP1


BICEP Polarization

NB ScaleDifference!

Chi

ang

et a

l, A

pJ,

this

wee

k


Current results

• 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.

Chiang et al, A

pJ, this week


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


Challenges of CMB Polarization

• Good news:1. Q |Ex|2 – |Ey|

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. Leakage from unpolarized signal2. Lack of bright polarized calibrators3. 4 times more complicated

}or vice versa


Being systematic about systematics

• Complex field description (Jones Matrix):

• Power description (Mueller Matrix):

• J: 8 real numbers (including irrelevant overall phase)

• M: 16 real numbers• M allows for incoherent

combination of modes.

OriginalModified

ss M

V

U

Q

I

mmmm

mmmm

mmmm

mmmm

V

U

Q

I

VVVUVQVI

UVUUUQUI

QVQUQQQI

IVIUIQII

ee J

y

x

yyyx

xyxx

y

x

E

E

JJ

JJ

E

E


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.


First-order beam artefacts

• Hu, Hedman & Zaldarriaga analysis:– First-order perturbations around gaussian

beam– Monopole, dipole quadrupole terms– Structure smaller than beam by definition.

Graphic: Epic Study


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


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.


Polarization-Sensitive Bolometers

• Two planes of absorbing mesh, with orthogonal wires.

• Each rejects ‘wrong’ polarization with 90-95% efficiency

• Used on Boomerang 2003 flight, QUaD experiment, Planck HFI, etc.


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


Foregrounds

• Thermal Dust: – COBE FIRAS,

Planck HFI, PILOT

• Anomalous Dust:– COSMOSOMAS,

WMAP, Planck LFI, QUIJOTE

• Free-free / Synchrotron:– Arecibo, C-BASS,

Planck LFI


Polarized Foreground SED (???)

RMS Q,U on 1° scales

(maybe!)


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. Le

nsin

g

E

B

60 GHz

V1/4 = 2×1016 GeV

C-BASS


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

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)


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.


Projects ongoing and planned

• Space– Planck– CMBPOL/EPIC– BPOL

• Balloon – EBEX– PILOT (Dust)– SPIDER

• Ground-based:– 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


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)

CMB Polarization

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