Three-Year WMAP Observations: Polarization Analysis

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Three-Year WMAP Observations Polarization
Analysis

• Eiichiro Komatsu
• The University of Texas at Austin
• Irvine, March 23, 2006

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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 llt23

These are improvements only in the analysis
techniques there are also various improvements
in the polarization map-making algorithm. See
Jarosik et al. (2006)
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K Band (23 GHz)
Dominated by synchrotron Note that polarization
direction is perpendicular to the magnetic field
lines.
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Ka Band (33 GHz)
Synchrotron decreases as n-3.2 from K to Ka band.
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Q Band (41 GHz)
We still see significant polarized synchrotron in
Q.
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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.
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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.
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Polarization Mask (P06)

• Mask was created using
• K band polarization intensity
• MEM dust intensity map

fsky0.743
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Masking Is Not Enough Foreground Must Be Cleaned

• Outside P06
• EE (solid)
• BB (dashed)
• Black lines
• Theory EE
• tau0.09
• Theory BB
• r0.3
• Frequency Geometric mean of two frequencies
  used to compute Cl

Rough fit to BB FG in 60GHz
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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 dont use W band for the three year analysis
  (for other reasons).

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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 DOF4534 (outside P06)

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3-sigma detection of EE.
The Gold multipoles l3,4,5,6.
BB consistent with zero after FG removal.
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• Residual FG unlikely in QV
• Black EE
• Blue BB
• Thick 3-year data coadded
• Thin year-year differences
• Red line upper bound on the residual synchrotron
• Brown line upper bound on the residual dust
• Horizontal Dotted best-fit CMB EE (tau0.09)

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Null Tests

• Its 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 dont expect 3-yr data to detect any BB.

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Data Combination (llt23)

• 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 l7 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-year
  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.

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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 noise
  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)
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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.

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High-l TE Data
Amplitude
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 Blue1yr, Black3yr)

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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.

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Optimal Analysis of the Low-l Polarization Data

• In the likelihood code, we use the TE power
  spectrum data at 23ltllt500, 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 llt23 in the likelihood code.
• In fact, we do not use the EE or BB power
  spectrum data anywhere 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 fact that the pixel data (both signal
  and noise) are Gaussian.

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Exact TE,EE,BB Likelihood
Gaussian Likelihood for T, Q, U
T Factorized
By Rotating the Basis.
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Stand-alone t

• Tau is almost entirely determined by the EE data.
• TE adds very little.
• Black Solid TEEE
• Cyan EE only
• Dashed Gaussian Cl
• Dotted TEEE from KaQVW
• Shaded Kogut et al.s stand-alone tau analysis
  from Cl TE
• Grey lines 1-yr full analysis (Spergel et al.
  2003)

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Tau is Constrained by EE

• The stand-alone analysis of EE data gives
• tau 0.100 - 0.029
• The stand-alone analysis of TEEE 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 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. (Rachel Beans talk)

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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.

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Summary

• Understanding of
• Noise,
• Systematics,
• Foreground, and
• Analysis techniques such as
• Exact likelihood method
• have significantly improved from the first-year
  release.
• Tau0.09-0.03

• 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)