Three-Year WMAP Observations: Polarization Analysis

Eiichiro KomatsuThe 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 algorithm. See Jarosik et al. (2006)

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

fsky=0.743

• Outside P06 EE (solid) BB (dashed)

• Black lines Theory EE

tau=0.09 Theory BB

r=0.3

• Frequency = Geometric mean of two frequencies used to compute Cl

Masking 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 FG removal.

3-sigma detection of EE.

The “Gold” multipoles: l=3,4,5,6.

• Residual FG unlikely in 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 synchrotron

Brown line: upper bound on the residual dust

Horizontal Dotted: best-fit CMB EE (tau=0.09)

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

to detect any BB.

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 the 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 amplifies the EE and BB spectra at particular multipoles. The multipoles and amplitude of noi

se amplification depend on the beam separation, which is different from DA to DA.

Red: white noise model (used in the first-year analysis)

Black: correlated noise model (3-yr model)

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 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 with the prediction from TT data and linear perturbation theory and adiabatic initial conditions. (Left Panel: Blue=1yr, Black=3yr)

Phase Shift

Am

plitu

de

High-l EE Data

• 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.

WMAP: QVW combined

Optimal Analysis of the Low-l Polarization Data

• In the likelihood code, we use the TE power spectrum data at 23<l<500, assuming that the distribution of high-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 spectrum 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

act that the pixel data (both signal and noise) are Gaussian.

Exact TE,EE,BB LikelihoodGaussian Likelihood for T, Q, U

T Factorized…

By Rotating the Basis.

Stand-alone • Tau is almost entirely determined 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 independent of the other parameters, and thus can break massive degeneracies between tau and the other parameters. (Rachel Bean’s talk)

Stand-alone r • Our ability to constrain the amplitude of gravity waves is still coming mostly from TT.

• BB information adds very little.

• EE data (which fix the value of tau) are also important, as r is degenerate with the tilt, which is also degenerate with tau.

• Understanding of Noise, Systematics, Foreground, and

• Analysis techniques such as Exact likelihood me

thod

• have significantly improved from the first-year release.

• Tau=0.09+-0.03• To-do list for the next data release(!)

• Understand W band better• Understand foreground in Ka better

• These improvements, combined with more years of data, would further reduce the error on tau. • 3-yr KaQVW combination gave delta(tau)~0.02• 6-yr KaQVW would give delta(tau)~0.014 (hopefully)

Summary