The cosmic background radiation II:The WMAP results

Alexander Schmah 27.01.05

General Aspects

- WMAP measures temperatue fluctuations of the CMB around 2.726 K - Reason for the temperature fluctuations are density fluctuation in the early universe

- The CMB comes from the age of the decoupling of the photons from the matter

- The CMB data is described with cosmological models

WMAP: Overview

Wilkinson Microwave Anisotropy Probe: WMAP

-Named after Dr. David Wilkinson, pioneer in the study of CMB and member of the science team, died in September 2002

- WMAP weight: 840 kg

-Angular resolution: 0.3°

- Sensitivity: 20 K/(0.3°)2

Launch

Launch of the Delta II rocket on 30 June 2001

Measuring position

Orbit around the second Lagrange point (L2) of the Earth-Sun system

- 1.5 million km away from earth- scans ~30% of the sky per day- full sky coverage after ½ year

WMAP: Detectors I

WMAP: Detectors II

-Two back to back symmetric telescopes

-Differential microwave radiometers

- Angle between opposite feed horns: ~ 141°

Frequency Bands

K-band: ~22 GHz (13.6 mm) (1)Ka-band: ~30 GHz (10.0 mm) (1)Q-band: ~40 GHz (7.5 mm) (2)V-band: ~60 GHz (5.0 mm) (2)W-band: ~90 GHz (3.3 mm) (4)

Thermal spectrum

K-band

W-band

Cosmic Backgroundcharged particles interacting with magnetic fields

hot gas(thermal Bremsstrahlung)

thermalemission

Map making

DT=T A −T B Measured signal

T 1 A =DT 1T B1T 2 A =DT 2T B2 ..T n A =DT nT Bn

T A =DTT B Absolute temperature

⟨T A ⟩=1n∑i=1

n

T i A

estimated

Iterative procedure

Map projection

Scan strategy

Observation Map

Galactic Plane Map

Dipole Map

K-band Map (23 GHz)

Ka-band Map (33 GHz)

Q-band Map (41 GHz)

V-band Map (61 GHz)

W-band Map (94 GHz)

Final Map

Comparison COBE-WMAP

53 GHz

94 GHz(30 times finer)

Difference Map

Spherical harmonics

Power Spectrum I

T n =∑l∑m=−l

l

almY lm n

C Θ ≡⟨T n1⋅T n2 ⟩ n1⋅n2=cos Θ

∑m=−l

l

Y lm¿ n1⋅Y lm n2 =

2 l14π

P l n1⋅n2

C Θ = 14π∑l

al2 P l cos Θ al

2=∑m

∣alm∣2

Power Spectrum II

C l=⟨∣alm∣2⟩m=

12 l1∑m

∣alm∣2= 1

2 l1al

2

C Θ = 14π∑l

2 l1 C l P l cos Θ

ΔT l=C l l l1 /2π

Power Spectrum III

Θ~πl

Primordial fluctuation region

Θ2°↔ lldec≈90

Angular scales larger than the causal horizon size at decouplingas observed today (primordial fluctuation spectrum)

Acoustic Peak Region

2°>Θ0 . 2°↔90l900

This region can be described by the physics of a 3000 K plasmawith a number density of ne=300 cm-3 responding to fluctuation in the gravitational potential of dark matter (acoustic peak region)

Silk Damping Tail

Θ0 . 2°↔ l900

The structure is produced by the diffusion of the photons fromthe potential fluctuations, and the washing out of the net observedfluctuations by the large number of cold and hot regions along the line of sight (Silk damping tail)

Interpretation of the peaksInterpretation in terms of a flat adiabatic ΛCDM-cosmological-model

Only the position of the peaks and their ratios are considered

Physics of the acoustic peaks may be understood in terms of:

ωb ,ωm , ns , τ ,Θ A

mh2bh

2

ωm=ωbωc

baryondensity

matter density

angular scale of thesound horizon atdecouplingspectral

index

optical depth atreionization

Peak ratios

For l>40 the peak ratios are insensitive to the intrinsic amplitudeof the power spectrum and τ due to:

Scattering of free electrons from reionization (z=20)with CMB photons -> lowering the fluctuation by nearly a constant factor

The first acoustic peak- The peaks arise from adiabatic compression of the photon-baryon-fluid as it falls into preexisting wells in the gravitaional potential

- The potential wells are the result of some primordial field fluctuation (e.g. inflation field)

- The wells are enhanced by the dark matter (does not scatter off the baryons and photons)

- The first peak corresponds to the scale of the mode that has compressed once in the age of the universe (the photons decoupled from the electrons, t=379 kyr after Big Bang)

Angular scale of the peaks

Θ A=r s zdec d A zdec

comoving size of the soundhorizon at decoupling

angular diameter distanceto the decoupling surface

Geometric degeneracy

ωm , ωb Are well measured (affect the spectrum at early times)

Geometric degeneracy: Same A for different ωm , ωb

ωm=mh2

ωb=bh2

and h

It can be shown that A is the same for constant mh3 . 4

(assumption: flat geometry)

Age of the Universe

b fixed to 0.023 (1region) (position of the first peak)

b fixed to 0.023 (2region) (position of the first peak)

1 limits on m

1 and 2 region of the full analysis

mh3 . 4=const ΘA

Seperation of m and h

isochrons

t0=6 .52h−1 1−m −1/ 2

ln 11−m

m [Gyr ]

Basic Results

0.02

0.04

0.004

0.04

95% CL

0.002

1

0.04

0.2

8

+220 (-80)

1.02

0.73

0.044

0.27

<0.015

2.725

1089

0.71

13.7

379

180

tot

b

m

tcmb

zdec

h

t0

tdec

tr

Total density

Dark energy density

Baryon density

Matter density

Light neutrino density

CMB Temperature (K)

Redshift at decoupling

Hubble constant

Age of universe (Gyr)

Age at decoupling (kyr)

Age at reionization (Myr)

UncertaintyValueSymbolDescription

mν0 . 23 eV

Standard model of cosmology: flat -dominated universe seeded by a nearly scale-invariant adiabatic Gaussian fluctuation fits the data

Future: Planck

- Start in the first quarter of 2007

- Frequencies from 30 GHz to 857 GHz

-Angular resolution: 5.0 arcmin to 33 arcmin (WMAP: 13.8 arcmin – 55.8 arcmin)

References- The Cosmic Microwave Background Data and their Implications for Cosmology, V.Tudose, Romanian Reports in Physics, Volume 55, Number 2, P.116-142, 2003

- First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results, C.L. Bennett et al. Astrophysical Journal

- Two-Point Correlations in the COBE DMR Four-Year Anisotropy Maps, G. Hinshaw et al. Astrophysical Journal, 464:L25-L28, 1996 June 10

- First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Interpretation of the TT and TE Angular Power Spectrum Peaks, L. Page et al. Astrophysical Journal

- WMAP-Homepage: http://map.gsfc.nasa.gov

- PLANCK-Homepage: http://www.rssd.esa.int/index.php?project=PLANCK

- First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: The Angular Power Spectrum, G. Hinshaw et al. Astrophysical Journal

- First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters

Angular scale of the peaks II

r s zdec =3997 ωγ

ωmωb

ln1RdecRdecReq

1Req

R z =3 ρb z /4 ργ z

1zeq=5464 ωm /0 .135 T CMB /2.725 4 1 ρν / ργ

redshift at matter-radiation equality

Angular scale of the peaks III

d A=∫0

zdec H 0−1dz

r 1z 4m 1z 3Λ

Λ=1−m−r

matter densitycurrent radiation density

angular diameter distance to the decoupling surface for a flat geometry

Age of the Universe I

r s=147±2 Mpc

- First acoustic peak in the CBM power spectrum: known acoustic size:

at redshift: zdec=1089±1

Age: t0=13.7±0 . 2 Gyr

d A=14 .0−0 . 30 . 2 GpcDecoupling surface:

t0=6.52h−1 1−m −1/ 2

ln 11−m

m [Gyr ]