Three-Year WMAP Observations:
Polarization Analysis
Eiichiro Komatsu
The University of Texas at Austin
Irvine, March 23, 2006
Summary of Improvements in the Polarization Analysis
• First Year (TE)
Foreground Removal
Done in harmonic space
Null Tests
Only TB
Data Combination
Ka, Q, V, W are used
Data Weighting
Diagonal weighting
Likelihood Form
Gaussian for Cl
Cl estimated by MASTER
• Three Years (TE,EE,BB)
Foreground Removal
Done in pixel space
Null Tests
Year Difference & TB, EB, BB
Data Combination
Only Q and V are used
Data Weighting
Optimal weighting (C-1)
Likelihood Form
Gaussian for the pixel data
Cl not used at l<23
These are improvements only in the analysis techniques: there are also various improvements in the polarization map-making
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 -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 (P06)
• Mask was created using
K band polarization intensity
MEM dust intensity map
f
sky=0.743
•
Outside P06 EE (solid)
BB (dashed)
•
Black lines Theory EE
tau=0.09
Theory BB
r=0.3
•
Frequency = Geo metric mean of tw o frequencies use d to compute ClMasking Is Not Enough:
Foreground Must Be Cleaned
Rough fit to BB FG in 60GHz
Template-based FG Removal
•
The first year analysis (TE) We cleaned synchrotron foreground using the K-band correlation function (also power spectrum) information.
It worked reasonably well for TE (polarized foreground is not correlated with CMB temperature); however, this approach is bound to fail for EE or BB.
•
The three year analysis (TE, EE, BB) We used the K band polarization map to model the polarization foreground from synchrotron in pixel space.
The K band map was fitted to each of the Ka, Q, V, and W maps, to find the best-fit coefficient. The best-fit map was then subtracted from each map.
We also used the polarized dust template map based on the stellar polarization data to subtract the dust contamination.
We found evidence that W band data is contaminated by polarized dust, but dust polarization is unimportant in the other bands.
We don’t use W band for the three year analysis (for other reasons).
It Works Well!!
•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)
BB consistent with zero after 3-sigma
detection of EE.
The “Gold” mu ltipoles: l=3,4, 5,6.
•
Residual FG unlikely i n Q&V Black: EE
Blue: BB
Thick: 3-year data coad ded
Thin: year-year differen ces
Red line: upper boun d on the residual syn chrotron
Brown line: upper boun d on the residual dust
Horizontal Dotted: be st-fit CMB EE (tau=0.0 9)
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
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 frequencies have passed t he null tests, the 3-yr combined power spectrum in W band shows some anomalies.
EE at l=7 is too high. We have not identified the source of this anomalous 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-year (KaQVW) to three-y ear analysis (QV) is not as significant as one might think from naïve extrapolation of the first-year result.
There is also another reason why the three-year error is larger (and more accurate) – next slide.
Correlated Noise
•
At low l, noise is not white.•
1/f noise increases noise at low l See W4 in particular.
•
Scan pattern selectively amplifie s the EE and BB spectra at partic ular multipoles. The multipoles and amplitude of noi se amplification depend on the bea m separation, which is different fro m DA to DA.
Red: white noise model (used in the first- year analysis)
Low-l TE Data: Comparison betwe en 1-yr and 3-yr
• 1-yr TE and 3-yr TE have about the sam e error-bars.
1yr used KaQVW an d white noise model
Errors significantly u nderestimated.
Potentially incomplet e FG subtraction.
3yr used QV and cor related noise model
Only 2-sigma detecti on of low-l TE.
High-l TE Data
•
The amplitude and phases of high-l TE data agree very well wit h the prediction from TT data and linear perturbation theory and adiabatic initial conditions. (Left Panel: Blue=1yr, Black=3yr)Phase Shift
Amplitude
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
Optimal Analysis of the Low-l P olarization Data
• In the likelihood code, we use the TE power spectrum data at 23<l<500, assuming that the distribution of hig h-l TE power spectrum is a Gaussian.
An excellent approximation at high multipoles.
This part is the same as the first-year analysis.
• However, we do not use the TE, EE or BB power spe ctrum data at l<23 in the likelihood code.
In fact, we do not use the EE or BB power spectrum data an ywhere in the likelihood code.
The distribution of power spectrum at low multipoles is highly non-Gaussian.
We use the pixel-based exact likelihood analysis, using the f
Exact TE,EE,BB Likelihood
Gaussian Likelihoo d for T, Q, U
T Factorized…
By Rotating the Basis.
Stand-alone • Tau is almost entirely deter mined by the EE data.
TE adds very little.
•
Black Solid: TE+EE•
Cyan: EE only•
Dashed: Gaussian Cl•
Dotted: TE+EE from KaQVW•
Shaded: Kogut et al.’s stand- alone tau analysis from Cl 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 = 0.093 +- 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 impl ies that the 3-yr polarization data essentially fixes tau i ndependent of the other parameters, and thus can bre ak massive degeneracies between tau and the other p arameters. (Rachel Bean’s talk)
Stand-alone r • Our ability to constrai n the amplitude of gra vity waves is still comi ng mostly from TT.
•
BB information adds v ery little.•
EE data (which fix the value of tau) are also important, as r is deg enerate with the tilt, w hich is also degenerat e with tau.• Understanding of
Noise,
Systematics,
Foreground, and
• Analysis technique s such as
Exact likelihood me
