Polarized Light in the Polarized Light in the Cosmic Microwave Cosmic Microwave Background: WMAP Background: WMAP Three-year Results Three-year Results

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Polarized Light in the Polarized Light in the

Cosmic Microwave Cosmic Microwave Background: WMAP Background: WMAP

Three-year Results Three-year Results

Eiichiro Komatsu (UT Austin) Eiichiro Komatsu (UT Austin) Colloquium at U. of Minnesota Colloquium at U. of Minnesota

November 3, 2006

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Full Sky Microwave Map Full Sky Microwave Map

Penzias & Wilson, 1965

Uniform, “Fossil” Light from the Big Bang

- Isotropic - Unpolarized

Galactic Center Galactic Anti-

center

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A. Penzias & R. Wilson, 1965

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CMB

T = 2.73 K Helium Supe

rfluidity

T = 2.17 K

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COBE/FIRAS, 1990 COBE/FIRAS, 1990

Perfect blackbody = Thermal equilibrium = Big Bang

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COBE/DMR, 1992 COBE/DMR, 1992

Gravity is STRONGER in cold spots: T/T~

Isotropic?

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COBE, “Followed-up” by WMA COBE, “Followed-up” by WMA

P P

COBE

WMAP

COBE 1989

WMAP 2001

[COBE’s] measurements als o marked the inception of co smology as a precise science . It was not long before it was followed up, for instanc e by the WMAP satellite, whi ch yielded even clearer imag es of the background radiati on.

Press Release from

the Nobel Foundatio

n

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David Wilkinson (1935~2002) David Wilkinson (1935~2002)

• Science Team Meeting, July, 2002

• Plotted the “second point” (3.2cm) on the CMB spectrum – The first confirmation of a black-body spectrum (1966)

• Made COBE and MAP happen and be successful

• “Father of CMB Experiment”

• MAP has become WMAP in 2003

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So, It’s Been Three Years Since So, It’s Been Three Years Since

The First Data Release in 2003.

What Is New Now?

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POLARIZATION DATA!!

Not only anisotropic, but also Not only anisotropic, but also

polarized.

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The Wilkinson Microwave The Wilkinson Microwave

Anisotropy Probe Anisotropy Probe

• A microwave satellite working at L2

• Five frequency bands

– K (22GHz), Ka (33GHz), Q (41GHz), V (61GHz), W (94GHz) – Multi-frequency is crucial for cleaning the Galactic emission

• The Key Feature: Differential Measurement

– The technique inherited from COBE – 10 “Differencing Assemblies” (DAs)

– K1, Ka1, Q1, Q2, V1, V2, W1, W2, W3, & W4, each consisting of two radiometers that are sensitive to orthogonal linear polarization modes.

• Temperature anisotropy is measured by single difference.

• Polarization anisotropy is measured by double difference.

POLARIZATION DATA!!

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WMAP Three Year Papers

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K band (22GHz)

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Ka Band (33GHz)

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Q Band (41GHz)

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V Band (61GHz)

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W Band (94GHz)

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The Angular Power Spectrum The Angular Power Spectrum

• CMB temperature anisotropy is very clos e to Gaussian (Komatsu et al., 2003); t hus, its spherical harmonic transform, a

lm

, is also Gaussian.

• Since a

lm

is Gaussian, the power spectru m:

completely specifies statistical proper ties of CMB.

* lm lm

l a a

C 

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WMAP 3-yr Power Spectrum

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What Temperature Tells Us What Temperature Tells Us

Distance to z~1100

Baryon- to-Photon Ratio

Matter-Radiation Equality Epoch Dark Energy/

New Physics?

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CMB to Cosmology CMB to Cosmology

&Third

Baryon/Photon Density Ratio

Low Multipoles (ISW)

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K Band (23 GHz) K Band (23 GHz)

Dominated by synchrotron; Note that polarization direction is

perpendicular to the magnetic field lines.

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Ka Band (33 GHz) Ka Band (33 GHz)

Synchrotron decreases as 

^-3.2

from K to Ka band.

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Q Band (41 GHz) Q Band (41 GHz)

We still see significant polarized synchrotron in Q.

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V Band (61 GHz) V Band (61 GHz)

The polarized foreground emission is also smallest in V band.

We can also see that noise is larger on the ecliptic plane.

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W Band (94 GHz) W Band (94 GHz)

While synchrotron is the smallest in W, polarized dust (hard to

see by eyes) may contaminate in W band more than in V band.

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Polarization Mask Polarization Mask

f

_sky

=0.743

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Jargon: E-mode and B-mode Jargon: E-mode and B-mode

• Polarization has directions!

• One can decompose it into a divergence -like “E-mode” and a vorticity-like

“B-mode”.

E-mode B-mode

Seljak & Zaldarriaga (1997); Kamionkowski, Kosowsky, Stebbins (1997)

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Polarized Light Filtered

Polarized Light

Un-filtered

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Physics of CMB Polarization Physics of CMB Polarization

• Thomson scattering generates polarization, if and only if…

– Temperature quadrupole exists around an electron – Where does quadrupole come from?

• Quadrupole is generated by shear viscosity of photon-baryon fluid.

electron isotropic

anisotropic

no net polarization

net polarization

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Boltzmann Equation Boltzmann Equation

• Temperature anisotropy, , can be generated by gravi tational effect (noted as “SW” = Sachs-Wolfe, 1967)

• Linear polarization (Q & U) is generated only by scat tering (noted as “C” = Compton scattering).

• Circular polarization (V) is not generated by Thomson scattering.

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Primordial Gravity Waves Primordial Gravity Waves

• Gravity waves also create quadrupolar temperature anisotropy -> Polarization

• Most importantly, GW creates B mode.

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Power Spectrum Power Spectrum

Scalar T

Tensor T

Scalar E Tensor E

Tensor B

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Polarization From Reionizati Polarization From Reionizati

on on

• CMB was emitted at z~1100.

• Some fraction of CMB was re-scattered in a reion ized universe.

• The reionization redshift of ~11 would correspon d to 365 million years after the Big-Bang.

z=1100,  ～ 1

z ～ 11,  ～ 0.1

First-star formation

e

^-

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Measuring Optical Depth Measuring Optical Depth

• Since polarization is generated by scattering, the amplitude is given by the number of scattering, or optical depth of Thomson scattering:

which is related to the electron column number

density as

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Polarization from Reioniazation Polarization from Reioniazation

“Reionization Bump”



²

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• Outside P06

– EE (solid) – BB (dashed)

• Black lines

– Theory EE

• tau=0.09

– Theory BB

• r=0.3

• Frequency = Geometri c mean of two freque ncies used to comput e Cl

Masking Is Not Enough:

Foreground Must Be Cleaned Foreground Must Be Cleaned

Rough fit to BB

FG in 60GHz

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Clean FG Clean FG

•Only two-parameter fit!

•Dramatic improvement in chi-squared.

•The cleaned Q and V

maps have the reduced

chi-squared of ~1.02 per

DOF=4534 (outside P06)

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BB consistent with zero after FG removal.

3-sigma detection of EE.

The “Gold” mu

ltipoles: l=3,4,

5,6.

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Parameter Determination:

First Year vs Three Years First Year vs Three Years

• The simplest LCDM model fits the data very well.

– A power-law primordial power spectrum – Three relativistic neutrino species

– Flat universe with cosmological constant

• The maximum likelihood values very consistent

– Matter density and sigma8 went down slightly

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Null Tests Null Tests

• It’s very powerful to have three years of data.

– Year-year differences must be consistent with zero

signal.

• yr1-yr2, yr2-yr3, and yr3-yr1

• We could not do this null test for the first year data.

– We are confident that we understand polarization noise to a couple of

percent level.

• Statistical isotropy

– TB and EB must be consistent with zero.

• Inflation prior…

– We don’t expect 3-yr data

to detect any BB.

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Data Combination (l<23) Data Combination (l<23)

• We used Ka, Q, V, and W for the 1-yr TE analysis.

• We use only Q and V for the 3-yr polarization analysis.

– Despite the fact that all of the year-year differences at all fr equencies have passed the null tests, the 3-yr combined power sp ectrum in W band shows some anomalies.

• EE at l=7 is too high. We have not identified the source of this ano malous signal. (FG is unlikely.)

• We have decided not to use W for the 3-yr analysis.

– The residual synchrotron FG is still a worry in Ka.

• We have decided not to use Ka for the 3-yr analysis.

• KaQVW is ~1.5 times more sensitive to tau than QV.

– Therefore, the error reduction in tau by going from the first-ye ar (KaQVW) to three-year analysis (QV) is not as significant as one might think from naïve extrapolation of the first-year resul t.

– There is also another reason why the three-year error is larger (and more accurate) – next slide.

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Correlated Noise Correlated Noise

• At low l, noise is not white.

• 1/f noise increases noise at low l

– See W4 in particular.

• Scan pattern selectively ampl ifies the EE and BB spectra a t particular multipoles.

– The multipoles and amplitude of noise amplification depend on the beam separation, which is different from DA to DA.

Red: white noise model (used in the first-year analysis)

Black: correlated noise model (3-yr model)

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Low-l TE Data: Comparison betwe Low-l TE Data: Comparison betwe

en 1-yr and 3-yr en 1-yr and 3-yr

• 1-yr TE and 3-yr TE have about the same error-bars.

– 1yr used KaQVW and wh ite noise model

• Errors significantly underestimated.

• Potentially incomple te FG subtraction.

– 3yr used QV and corre lated noise model

• Only 2-sigma detecti on of low-l TE.

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High-l TE Data High-l TE Data

• The amplitude and phases of high-l TE data agree very we ll with the prediction from TT data and linear perturbat ion theory and adiabatic initial conditions. (Left Pane l: Blue=1yr, Black=3yr)

Phase Shift

A m p li tu d e

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High-l EE Data High-l EE Data

• When QVW are coadded, the high-l EE amplitude relative t o the prediction from the best-fit cosmology is 0.95 +- 0.35.

• Expect ~4-5sigma detection from 6-yr data.

WMAP: QVW combined

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  1st year vs 3rd year 1st year vs 3rd year

• Tau is almost entirely determined by the EE fr om the 3-yr data.

– TE adds very little.

• Dotted: Kogut et al.’s stand-alone tau analysi s from TE

• Grey lines: 1-yr full a nalysis (Spergel et al.

2003)

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Tau is Constrained by EE Tau is Constrained by EE

• The stand-alone analysis of EE data gives

– tau = 0.100 +- 0.029

• The stand-alone analysis of TE+EE gives

– tau = 0.092 +- 0.029

• The full 6-parameter analysis gives

– tau = 0.093 +- 0.029 (Spergel et al.; no SZ)

• This indicates that the stand-alone EE analysis has exhausted most of the information on tau contained in the polarization data.

– This is a very powerful statement: this immediately implie s that the 3-yr polarization data essentially fixes tau in dependent of the other parameters, and thus can break mass ive degeneracies between tau and the other parameters.

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Degeneracy Finally Broken:

Negative Tilt & Low Fluctuation Negative Tilt & Low Fluctuation

Amplitude Amplitude

Degeneracy Line from Temperature Data Alone

Polarization Data Nailed Tau

Temperature Data Constrain “

₈

exp(-)”

Lower 

Polarization Nailed Tau

Lower 3rd peak

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Constraints on GW Constraints on GW

• Our ability to constrain the

amplitude of gravity waves is still coming mostly from the

temperature spectrum.

– r<0.55 (95%)

• The B-mode

spectrum adds very little.

• WMAP would have to integrate for at least 15 years to detect the B-mode spectrum from

inflation.

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What Should WMAP Say What Should WMAP Say

About Inflation Models?

Hint for ns<1 Zero GW

The 1-d

marginalized constraint from WMAP alone is ns=0.96+-0.02.

GW>0

The 2-d joint

constraint still

allows for ns=1.

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What Should WMAP Say What Should WMAP Say

About Flatness?

Flatness, or very low Hubble’s

constant?

If H=30km/s/Mpc, a closed universe

with Omega=1.3

w/o cosmological

constant still fits the

WMAP data.

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What Should WMAP Say What Should WMAP Say

About Dark Energy?

Not much!

The CMB data alone cannot constrain w very well.

Combining the large-scale

structure data or supernova data breaks degeneracy

between w and

matter density.

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What Should WMAP Say What Should WMAP Say

About Neutrino Mass?

3.04 )

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• Understanding of

– Noise,

– Systematics, – Foreground, and

• Analysis techniques

• have significantly impro ved from the first-year release.