Transcript Three-Year WMAP Observations: Method and Results

Latest Results from
WMAP: Three-year
Observations
Eiichiro Komatsu (UT Austin)
Texas Symposium in
Melbourne
December 15, 2006
Full Sky Microwave Map
Penzias & Wilson, 1965
Uniform, “Fossil” Light from the Big Bang
-Isotropic
-Unpolarized
Galactic Anti-center
Galactic Center
A. Penzias & R. Wilson, 1965
Helium
Superfluidity
T = 2.17 K
CMB
T = 2.73 K
COBE/FIRAS, 1990
Perfect blackbody = Thermal equilibrium = Big Bang
COBE/DMR, 1992
Isotropic?
Gravity is STRONGER in cold
spots: DT/T~F
COBE, “Followed-up” by WMAP
COBE
1989
COBE
Press Release from
the Nobel Foundation
[COBE’s] measurements
also marked the inception of
cosmology as a precise
science. It was not long
before it was followed up,
for instance by the WMAP
satellite, which yielded
even clearer images of
the background
radiation.
WMAP
2001
WMAP
So, It’s Been Three Years Since
The First Data Release in 2003.
What Is New Now?
POLARIZATION DATA!!
CMB is not only anisotropic, but
also polarized.
The Wilkinson Microwave
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!!
WMAP Three Year Papers
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 (Komatsu et al., 2003); thus, its
spherical harmonic transform, alm, is also
Gaussian.
• Since alm is Gaussian, the power spectrum:
completely specifies statistical properties of
CMB.
WMAP 3-yr Power Spectrum
What Temperature Tells Us
Distance to z~1100
Dark Energy/
New Physics?
Baryonto-Photon
Ratio
Matter-Radiation
Equality Epoch
ns: Tilting Spectrum
ns>1: “Blue
Spectrum”
ns: Tilting Spectrum
ns<1: “Red Spectrum”
CMB to Cosmology
Low Multipoles (ISW)
&Third
Baryon/Photon Density Ratio
Constraints on Inflation Models
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.
Polarization Mask
fsky=0.743
Seljak & Zaldarriaga (1997); Kamionkowski, Kosowsky, Stebbins (1997)
Jargon: E-mode and B-mode
• Polarization has directions!
• One can decompose it into a divergencelike “E-mode” and a vorticity-like “B-mode”.
E-mode
B-mode
Polarized Light
Un-filtered
Polarized Light
Filtered
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.
isotropic
anisotropic
electron
no net polarization
net polarization
Boltzmann Equation
• Temperature anisotropy, Q, can be generated by
gravitational effect (noted as “SW” = Sachs-Wolfe, 1967)
• Linear polarization (Q & U) is generated only by scattering
(noted as “C” = Compton scattering).
• Circular polarization (V) is not generated by Thomson
scattering.
Primordial Gravity Waves
• Gravity waves also create quadrupolar
temperature anisotropy -> Polarization
• 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~1100.
• 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.
eFirst-star
formation
e-
ee-
eeIONIZED
eeNEUTRAL
REIONIZED
eeee-
e- - ee
z=1100, t～1
z～11, t～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
Temperature Damping, and
Polarization Generation
e-t
t2
“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 (ML):
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
Parameter Determination (Mean):
First Year vs Three Years
• ML and Mean agree better for the 3yr data.
– Degeneracy broken!
Low-l TE Data: Comparison
between 1-yr and 3-yr
• 1-yr TE and 3-yr TE
have about the same
error-bars.
– 1yr used KaQVW and
white noise model
• Errors significantly
underestimated.
• Potentially incomplete
FG subtraction.
– 3yr used QV and
correlated noise model
• Only 2-sigma
detection of low-l TE.
Amplitude
High-l TE Data
Phase Shift
• The amplitude and phases of high-l TE data agree very well
with the prediction from TT data and linear perturbation theory
and adiabatic initial conditions. (Left Panel: Blue=1yr,
Black=3yr)
High-l EE Data
WMAP: QVW combined
• When QVW are coadded, the high-l EE amplitude relative to the
prediction from the best-fit cosmology is 0.95 +- 0.35.
• Expect ~4-5sigma detection from 6-yr data.
t1st year vs 3rd year
• Tau is almost entirely
determined by the EE
from the 3-yr data.
– TE adds very little.
• Dotted: Kogut et al.’s
stand-alone tau analysis
from TE
• Grey lines: 1-yr full
analysis (Spergel et al.
2003)
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 = 0.088 +- 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 implies that the
3-yr polarization data essentially fixes tau independent of the
other parameters, and thus can break massive degeneracies
between tau and the other parameters.
Degeneracy Finally Broken:
Negative Tilt & Low Fluctuation
Amplitude
Temperature Data
Constrain “s8exp(-t)”
Degeneracy Line
from Temperature
Data Alone
Polarization
Nailed Tau
Lower t
Lower 3rd peak
Polarization Data
Nailed Tau
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=0.96+-0.02.
GW>0
The 2-d joint
constraint still
allows for ns=1.
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.
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 Mass?
3.04)
• Understanding of
Summary
•Tau=0.09+-0.03
•
– 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.
To-do list for the next data release (now working on the 5-year data)
• 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.