Uncovering CMB B-modes with Planck
Chris Crowe
ccrowe@ast.cam.ac.uk
With G. Efstathiou, S. Gratton, and the Planck Collaboration
Outline
• The Planck mission
• B-modes and inflation
• Simulating Planck data
• Foreground separation
The Planck Mission
• Launched in Jun 2009
• Helium ran out in January 2012
• 26 papers came out in 2011:
– Performance
– Compact sources
– SZ clusters
– Galactic science
• Cosmology papers come out in January 2013
The Planck Mission
The Planck Mission
The Planck Mission
• The final word in temperature analysis
• Polarization is the next frontier, but….
…foregrounds dominate
B-modes and inflation
• Anisotropic Thomson scattering
sources CMB polarization
• Polarization is at a few % of T
• Pattern can be decomposed into
curl-free E-modes, and divergence-free B-modes
B-modes and inflation
B-modes and inflation
• Harmonic representation
of Q/U as spin-2 fields
• E and B-modes expand
as spin-0 harmonics
• Averaged over
ensembles
B-modes and inflation
B-modes and inflation
B-modes and inflation
• E-pol from scalar, vector and tensor modes
• B-pol only from vector and tensor modes
• Large scale Gaussian B-modes from primordial gravitational waves:
- Constrain the energy scale of inflation via
- rule out most ekpyrotic and pure curvaton/ inhomogeneous reheating
models and others
• Most of B from gravity waves is on large scales l < 300
(for high optical depth most from l < 30)
• Lensing dominates at high-l
– Motivates low-resolution analyses
B-modes and inflation
Credit: J Stolan, 2012
Simulating Planck data – Polarized CMB
Full Q/U
Put in E and B composition of a polarized cmb map TQU
E Contrib.
B Contrib.
Simulating Planck data – Polarized foregrounds
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Dominant foregrounds are the ultimate limit in
our ability to characterise inflationary B-modes
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Synchrotron and dust are significantly polarized
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Possible contribution from spinning dust (<2%?)
Dust
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Aspherical grains align with B field
Can be up to ~40%
Typically 3-10%
Few large scale maps (eg Archeops)
Synchrotron
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Regular+turbulent B-field
Can be up to ~75%
Typically 10-40%
Multiple maps eg WMAP, Haslam
Simulating Planck data – Polarized synchrotron
Synchrotron maps available at
400MHz, 1.4GHz, and WMAP
Haslam 400MHz
Βs from 0.4,1.4,3.23GHz
WMAP 23 GHz Q
WMAP 23 GHz U
Simulating Planck data – Polarized dust
Dust maps available at 100µm, but very little other pol info
astro-ph/9905128
Simulating Planck data – multifrequency maps
Temperature simulations:
30GHz
Simulating Planck data – multifrequency maps
Temperature simulations:
44GHz
Simulating Planck data – multifrequency maps
Temperature simulations:
70GHz
Simulating Planck data – multifrequency maps
Temperature simulations:
100GHz
Simulating Planck data – multifrequency maps
Temperature simulations:
143GHz
Simulating Planck data – multifrequency maps
Temperature simulations:
217GHz
Simulating Planck data – multifrequency maps
Temperature simulations:
353GHz
Simulating Planck data – multifrequency maps
Polarization simulations:
30GHz
Simulating Planck data – multifrequency maps
Polarization simulations:
44GHz
Simulating Planck data – multifrequency maps
Polarization simulations:
70GHz
Simulating Planck data – multifrequency maps
Polarization simulations:
100GHz
Simulating Planck data – multifrequency maps
Polarization simulations:
143GHz
Simulating Planck data – multifrequency maps
Polarization simulations:
217GHz
Simulating Planck data – multifrequency maps
Polarization simulations:
353GHz
Do the simulations look like real data?
Foreground Separation -Parametric Method
Simple mixing model for multifrequency data:
(1)
Low-resolution pixel-based
parametric likelihood:
(2)
Likelihood reaches maximum for:
(3)
(4)
Assume smooth βs, and sub (4)
into (2) for the spectral likelihood:
(5)
• The βs that maximise (5) are found numerically
• Sub into (4) and solve for amplitudes pixel-by-pixel
arXiv:1004.4756, 1203.5285
Foreground Separation -Maps
CMB+noise simulations
Recovery of Q/U required to at least 1-2% for r~0.1
Foreground Separation -Maps
CMB+noise simulations – B-mode
Recovery of Q/U required to at least 1-2% for r~0.1
Foreground Separation -Maps
• Foregrounds also recovered well
• Different frequency subsets can be used to more closely analyse dust/synchrotron
Foreground Separation -r Likelihoods
• Pixel-based likelihood
• Pixel and noise covariance matrices
calculated analytically
• Foreground-free r=0.1 simulations
• Useful handle on spread in
recovered r due to noise
Foreground Separation -r Likelihoods
• Modify likelihood to include spatial correlation of βs
• Reflects physical assumption that βs and βd don’t
vary on very short scales
• Generalise individual pixel priors to covariance matrix:
• Vary correlation length to improve noise tolerance:
Foreground Separation -r Likelihoods
Foreground Separation -Improvements?
• These methods can get down to about r~=0.01
(perhaps lower depending on real Planck sky)
• r=~0.01 – these and similar methods
• r=~0.001 – achievable with extra datasets if we are lucky!
• r=~0.0001 – very difficult/ impossible
C-BASS
• Alternate datasets:
• C-BASS 5 GHz (2012)
• Quijote – 10-30 GHz (2013?)
• Spider – 100,150,220 GHz (2013)
• COrE – Dedicated polarization satellite (2020?)
COrE?
Spider