Three-Year WMAP ObserThree-Year WMAP Observations: vations: Method and ResultsMethod and Results

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Three-Year WMAP Obser Three-Year WMAP Obser

vations:

Method and Results Method and Results

Eiichiro Komatsu Eiichiro Komatsu

Department of Astronomy

HEP Seminar, April 27, 2006

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

• Science Team Meeting, July, 2002

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The Wilkinson Microwave Anisotr The Wilkinson Microwave Anisotr

opy Probe opy Probe

• A microwave satellite working at L2

• Five frequency bands

– K (22GHz), Ka (33GHz), Q (41GHz), V (61GHz), W (94GHz)

• 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 polari zation modes.

• Temperature anisotropy is measured by single differenc e.

• Polarization anisotropy is measured by double differenc e.

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WMAP WMAP Spacecraft Spacecraft

MAP990422

thermally isolated instrument cylinder

secondary reflectors

focal plane assembly feed horns back to back Gregorian optics, 1.4 x 1.6 m primaries

upper omni antenna line of sight

deployed solar array w/ web shielding medium gain antennae

passive thermal radiator

warm spacecraft with:

- instrument electronics - attitude control/propulsion - command/data handling - battery and power control

60K

90K

300K

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WMAP Focal Plane WMAP Focal Plane

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• 10 DAs (K, Ka, Q1, Q2, V1, V2, W1-W4)

• Beams measured by observing Jupiter.

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WMAP Goes To L2 WMAP Goes To L2

• June 30, 2001

– Launch

– Phasing loop

• July 30, 2001

– Lunar Swingby

• October 1, 2001

– Arrive at L2

• October 2002

– 1st year data

• February 11, 2003

– 1^st data release

• October 2003

– 2nd year data

• October 2004

– 3rd year data

• March 16, 2006

– 2^nd data release

0.010

0.005

0.000

-0.005

-0.010

1.000 1.005 1.010

X (AU)

Earth L2

Y (AU)

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K band (22GHz) K band (22GHz)

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

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

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

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

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Intensity Mask Intensity Mask

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The Angular Power Spectrum The Angular Power Spectrum

• CMB temperature anisotropy is very clos e to Gaussian; thus, its spherical harm onic 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 WMAP 3-yr Power Spectrum

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Physics of CMB Anisotropy Physics of CMB Anisotropy

• SOLVE GENERAL RELATIVISTIC BOLTZMANN SOLVE GENERAL RELATIVISTIC BOLTZMANN EQUATIONS TO THE FIRST ORDER IN

EQUATIONS TO THE FIRST ORDER IN PERTURBATIONS

PERTURBATIONS

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Use temperature fluctuations, =T/T, instead of f:

Expand the Boltzmann equation to the first order in perturbat ions:

where

describes the Sachs-Wolfe effect: purely GR ﬂuctuations.

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For metric perturbations in the form of:

€

ds

²

= a

²

[ ( −1+ h

₀₀

) dτ

²

+ ( δ

_ij

+ h

_ij

) dx

ⁱ

dx

^j

]

the Sachs-Wolfe terms are given by

where  is the directional cosine of photon propagations.

Newtonian potential Curvature perturbations

1. The 1st term = gravitational redshift

2. The 2nd term = integrated Sachs-Wolfe effect

h₀₀/2

h_ij/2

(higher T)

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• When coupling is strong, photons and baryons move togethe r and behave as a perfect fluid.

• When coupling becomes less strong, the photon-baryon flui d acquires shear viscosity.

• So, the problem can be formulated as “hydrodynamics”.

(c.f. The Sachs-Wolfe effect was pure GR.)

Small-scale Anisotropy (<2 d Small-scale Anisotropy (<2 d

eg) eg)

Collision term describing coupling between photons and baryons

via electron scattering.

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Boltzmann Equation to Hydro Boltzmann Equation to Hydro

dynamics dynamics

Monopole: Energy density Dipole: Velocity

Quadrupole: Stress

• Multipole expansion

• Energy density, Velocity, St

ress

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Photon Transport Equations Photon Transport Equations

f₂=9/10 (no polarization), 3/4 (with polarization)

_A= -h₀₀/2, _H= h_ii/2

_C=Thomson scattering optical depth

CONTINUITY EULER

Photon-baryon coupling

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Baryon Transport Baryon Transport

Cold Dark Matter

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The Strong Coupling Regime The Strong Coupling Regime

SOUND WAVE!

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The Wave Form Tells Us Cosmolog The Wave Form Tells Us Cosmolog

ical Parameters ical Parameters

Higher baryon density

 Lower sound speed

 Compress more

 Higher peaks at com pression phase (eve n peaks)

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Weighing Dark Matter Weighing Dark Matter

where  is the directional cosine of photon propagations.

1. The 1st term = gravitational redshift

2. The 2nd term = integrated Sachs-Wolfe effect

h₀₀/2

h_ij/2

(higher T)

During the radiation dominated epoch, even CDM fluctuations c annot grow (the expansion of the Universe is too fast); thus, dar k matter potential gets shallower and shallower as the Universe expands --> potential decay --> ISW --> Boost C_l.

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Weighing Dark Matter Weighing Dark Matter

• Smaller dar k matter de nsity

• More time f or potentia l to decay

• Higher firs

t peak

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Measuring Geometry Measuring Geometry

Sound cross. length

θ

220 ~ or deg

1 ~ l

θ

220 or

deg

1 >

< l

θ

• ^=

• ^<

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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 is a rank-2 tensor field.

• 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…

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

• Quadrupole is generated by shear viscosity of photon-bar yon fluid, which is generated by velocity gradient.

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)

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

• Circular polarization (V) would not be generated. (Ne xt slide.)

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Sources of Polarization Sources of Polarization

• Linear polarizat ion (Q and U) wi ll be generated from 1/10 of tem perature quadrup ole.

• Circular polariz ation (V) will N OT be generated.

No source term,

if V was initial

ly zero.

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Photon Transport Equation Photon Transport Equation

f₂=3/4

_A= -h₀₀/2, _H= h_ii/2

_C=Thomson scattering optical depth

Monopole Dipole

Quadrupole

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Primordial Gravity Waves Primordial Gravity Waves

• Gravity waves create quadrupolar tempe rature anisotropy -> Polarization

• Directly generate polarization without kV.

• 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 Reioniz Polarization From Reioniz

ation ation

• CMB was emitted at z~1088.

• 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=1088,  ～ 1

z ～ 11,  ～ 0.1

First-star formation

z=0 IONIZED

REIONIZED NEUTRAL

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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”

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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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Constraints on GW Constraints on GW

• Our ability to con strain the amplitu de of gravity wave s is still coming mostly from the te mperature spectru m.

– r<0.55 (95%)

• The B-mode spectru m adds very littl e.

• WMAP would have to integrate for at l east 15 years to d etect the B-mode s pectrum from infla tion.

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What Should WMAP Say About What Should WMAP Say About

Inflation Models?

Hint for ns<1 Zero GW

The 1-d margin alized constrain t from WMAP al one is ns=0.95 +-0.02.

GW>0

The 2-d joint co nstraint still allo ws for ns=1 (H Z).

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What Should WMAP Say About What Should WMAP Say About

Flatness?

Flatness, or very l ow Hubble’s const ant?

If H=30km/s/Mpc, a closed universe wit h Omega=1.3 w/o c osmological consta nt still fits the WMA P data.

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What Should WMAP Say About What Should WMAP Say About

Dark Energy?

Not much!

The CMB data alone cannot c onstrain w very well. Combinin g the large-scal e structure data or supernova d ata breaks deg eneracy betwe en w and matte r density.

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What Should WMAP Say About What Should WMAP Say About

Neutrino Mass?

WMAP alone (95%):

- Total mass < 2eV

WMAP+SDSS (95%) - Total mass < 0.9eV

WMAP+all (95%)

- Total mass < 0.7eV

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• Understanding of

– Noise,

– Systematics, – Foreground, and

• Analysis techniques

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

• A simple LCDM model fits both the temperature and polarization data very w

•

To-do list for the next data release: ell.

•

Understand FG and noise better.

•

We are still using only 1/2 of the polarization data.

•

These improvements, combined with more years of data, would further reduce the error on tau.

•

Full 3-yr would give delta(tau)~0.02

•

Full 6-yr would give delta(tau)~0.014 (hopefully)

•

This will give us a better estimate of the tilt, and better constraints on inflation.

Three-Year WMAP ObserThree-Year WMAP Observations: vations: Method and ResultsMethod and Results