Transcript Three-year WMAP Observations: Method and Results

Results from ThreeYear WMAP
Observations
Eiichiro Komatsu (UT Austin)
TeV II Particle Astrophysics
August 29, 2006
Why Care About WMAP?
• WMAP observes CMB. This is a conference
about “TeV” particle astrophysics. Why care
about CMB?
– The present-day temperature of CMB is 2.725K, or
2.35 meV.
– The temperature at decoupling (where the most of
CMB is coming from) was ~3000K, or 0.26 eV.
– The temperature at matter-radiation equality was
~9000K, or 0.8 eV.
• CMB is a nuisance for many particle
astrophysicists: it attenuates cosmic-ray
particles traveling through the universe. (GZK)
• Why am I here?
What Can CMB Offer?
• Baryon-to-photon ratio in the universe
– Sound speed and inertia of baryon-photon fluid
• Matter-to-radiation ratio in the universe
– Dark matter abundance
– “Radiation” may include photons, neutrinos as well as any
other relativistic components.
• Angular diameter distance to decoupling surface
– Peak position in l space ~ (Sound horizon)/(Angular
Diameter Distance)
• Time dependence of gravitational potential
– Integrated Sachs-Wolfe Effect, Dark energy
• Primordial power spectrum (Scalar+Tensor)
– Constraints on inflationary models
• Optical depth
– Cosmic reionization
Full Sky Microwave Map
COBE/FIRAS:
T=2.725 K
Uniform, “Fossil” Light from the Big Bang
Cosmic Microwave Background Radiation
COBE/FIRAS, 1990
Perfect blackbody = Thermal equilibrium = Big Bang
COBE/DMR, 1992
Gravity is STRONGER in cold
spots: DT/T~F
The Wilkinson Microwave
Anisotropy 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
polarization modes.
• Temperature anisotropy is measured by single
difference.
• Polarization anisotropy is measured by double
difference.
K band (22GHz)
Ka Band (33GHz)
Q Band (41GHz)
V Band (61GHz)
W Band (94GHz)
The Angular Power Spectrum
• CMB temperature anisotropy is very close to
Gaussian; thus, its spherical harmonic
transform, alm, is also Gaussian.
• Since alm is Gaussian, the power spectrum:
*
l
lm lm
C  a a
completely specifies statistical properties of
CMB.
WMAP 3-yr Power Spectrum
Physics of CMB Anisotropy
• SOLVE GENERAL RELATIVISTIC BOLTZMANN
EQUATIONS TO THE FIRST ORDER IN
PERTURBATIONS
Use temperature fluctuations, Q=DT/T, instead of f:
Expand the Boltzmann equation to the first order in
perturbations:
where
describes the Sachs-Wolfe effect: purely GR fluctuations.
For metric perturbations in the form of:
ds  a
2
2
1 h
00
d
2
 ij  hij dx dx
i
j

Newtonian potential
Curvature perturbations
the Sachs-Wolfe terms are given by
where g is the directional cosine of photon propagations.
1. The 1st term = gravitational redshift
h00/2
2. The 2nd term = integrated Sachs-Wolfe effect
(higher T)
Dhij/2
Small-scale Anisotropy (<2 deg)
Collision term describing
coupling between photons and
baryons via electron scattering.
• When coupling is strong, photons and baryons move
together and behave as a perfect fluid.
• When coupling becomes less strong, the photon-baryon
fluid acquires shear viscosity.
• So, the problem can be formulated as “hydrodynamics”.
(c.f. The Sachs-Wolfe effect was pure GR.)
Boltzmann Equation to
Hydrodynamics
• Multipole expansion
• Energy density, Velocity, Stress
Monopole: Energy density
Dipole: Velocity
Quadrupole: Stress
Photon Transport Equations
CONTINUITY
EULER
Photon-baryon coupling
f2=9/10 (no polarization), 3/4 (with polarization)
FA = -h00/2, FH = hii/2
C=Thomson scattering optical depth
Baryon Transport
Cold Dark Matter
The Strong Coupling Regime
SOUND WAVE!
The Wave Form Tells Us
Cosmological Parameters
Higher baryon density
 Lower sound speed
 Compress more
 Higher peaks at
compression phase
(even peaks)
Amplitude of temperature fluctuations at a given scale, l~p/q
What CMB Measures
Ang.Diam. Distance
ISW
Mat-toRadiation
Ratio
10
Large scales
40
100
200
Baryon-tophoton Ratio
400
800
Multipole moment l~p/q Small scales
CMB to Parameters
Measuring Matter-Radiation Ratio
where g is the directional cosine of photon propagations.
1. The 1st term = gravitational redshift
h00/2
2. The 2nd term = integrated Sachs-Wolfe effect
(higher T)
Dhij/2
During the radiation dominated epoch, even CDM fluctuations
cannot grow (the expansion of the Universe is too fast); thus,
dark matter potential gets shallower and shallower as the
Universe expands --> potential decay --> ISW --> Boost Cl.
Matter-Radiation Ratio
• More extra radiation component means that the equality
happens later.
• Since gravitational potential decays during the radiation
era (free-fall time scale is longer than the expansion time
scale during the radiation era), ISW effect increases
anisotropy at around the Horizon size at the equality.
How Many (Effective) Neutrinos?
So, It’s Been Three Years Since
The First Data Release. What Is
New Now?
POLARIZATION DATA!!
K Band (23 GHz)
Dominated by synchrotron; Note that polarization direction is
perpendicular to the magnetic field lines.
Ka Band (33 GHz)
Synchrotron decreases as n-3.2 from K to Ka band.
Q Band (41 GHz)
We still see significant polarized synchrotron in Q.
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.
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.
Polarized Light
Un-filtered
Polarized Light
Filtered
Seljak & Zaldarriaga (1997); Kamionkowski, Kosowsky, Stebbins (1997)
Jargon: E-mode and B-mode
• Polarization is a rank-2 tensor field.
• One can decompose it into a divergencelike “E-mode” and a vorticity-like “B-mode”.
E-mode
B-mode
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-baryon
fluid, which is generated by velocity gradient.
isotropic
anisotropic
electron
no net polarization
net polarization
Boltzmann Equation
• Temperature anisotropy, Q, can be generated by
gravitational effect (noted as “SW” = Sachs-Wolfe)
• Linear polarization (Q & U) is generated only by scattering
(noted as “C” = Compton scattering).
• Circular polarization (V) would not be generated. (Next
slide.)
Primordial Gravity Waves
• Gravity waves create quadrupolar
temperature anisotropy -> Polarization
• Directly generate polarization without kV.
• Most importantly, GW creates B mode.
Power Spectrum
Scalar T
Tensor T
Scalar E
Tensor E
Tensor B
Polarization From
Reionization
• CMB was emitted at z~1088.
• Some fraction of CMB was re-scattered in a reionized
universe.
• The reionization redshift of ~11 would correspond to
365 million years after the Big-Bang.
IONIZED
z=1088, ～1
NEUTRAL
First-star
formation
REIONIZED
z～11, ～0.1
z=0
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
Ne =
Polarization from Reioniazation
“Reionization
Bump”
Masking Is Not Enough:
Foreground Must Be Cleaned
• Outside P06
– EE (solid)
– BB (dashed)
• Black lines
– Theory EE
• tau=0.09
– Theory BB
• r=0.3
Rough fit to BB
FG in 60GHz
• Frequency =
Geometric mean
of two
frequencies used
to compute Cl
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)
3-sigma
detection
of EE.
The “Gold”
multipoles:
l=3,4,5,6.
BB consistent
with zero after
FG removal.
Parameter Determination:
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
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.
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.
What Should WMAP Say
About Inflation Models?
Hint for ns<1
Zero GW
The 1-d
marginalized
constraint from
WMAP alone is
ns=0.95+-0.02.
GW>0
The 2-d joint
constraint still
allows for ns=1
(HZ).
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.
What Should WMAP Say
About Neutrino Properties?
3.04)
• Understanding of
Summary
– Noise,
– Systematics,
– Foreground, and
• Analysis techniques
• have significantly
improved from the firstyear release.
• A simple LCDM model fits
both the temperature and
polarization data very well.
•
•
CMB offers constraints on:
• Neutrino properties: the number of species and mass
• Dark matter abundance
• Dark matter abundance and properties
• Inflationary models (flatness and spectral index)
• Reionization of the universe
We are now working on the 5-year data…