Systematic effects in cosmic microwave background polarization and
power spectrum estimation
SKA 2010 Postgraduate Bursary Conference, Stellenbosch Institute for Advanced Study 30/11/10
Fidy A. RAMAMONJISOA
University of KwaZulu-Natal
Prof Subharthi Ray
PhD project
supervised by
School of Mathematical Science
Introduction
CMB is a 2.725 K blackbody radiation composing the majority of the radiation of the universe in mm-cm wavelength
CMB photons are emitted from the last scattering surface (LSS) at z=1100 (379 000 yrs)
Radiation is highly isotropic
Temperature fluctuations of the CMB are at 10-5 level
Time
Infl
atio
n
Pre
sen
t
CM
B o
bse
rver
1010 yrs3x105 yrs
LS
S W. Hu 2002
Introduction
Polarization first detected by the Degree Angular Scale Interferometer (DASI) in 2002
Due to Thomson scattering the fluctuations are polarized at 10% level
Polarization is decomposed into
E-mode (scalar/tensor perturbations due to density fluctuations)
B-mode (tensor perturbations due to gravity waves)
Colder
radiation
Hotter radiation
W. Hu 2001
Stokes parameters
CMB polarization are defined by Stokes parameters
For CMB photons: V=0, Q and U characterize linear polarization
Incident waves
Electron
Linea
rly po
larize
d rad
iation
Electric fi
eld
Mukhanov V. 2005
Objectives
Find a semi-analytic formulation of the cross power spectra Cl
TT, ClTE, Cl
EE, ClBB
Compute the cross power spectra using computationally fast pseudo-Cl estimator
Correct systematic effects due to
Non-circularity of instrument beam response
Foreground emissions
Instrumental noise Multipole l=180 °
θ
ClTT
ClTE
ClEE
ClBB (r=0.1)
ClBB (r=10-4)
ClBB (lensing)
CM
B a
ngu
lar
po
we
r sp
ectr
a
Rosset C. 2005
Beam asymmetry
Non-circularity of beam assumption is essential at small angular scales (higher l)
Assume Gaussian window function
(beam ellipticity parameter: deviation of the beam from circularity)
ClTT
ClTE
ClEE
Multipole l
Planck 100 GHz
Errors in power spectrum estimation as a function of beam ellipticity
Folsaba et al. 2002
• Foreground emissions
Foreground emissions
Mask function Instrumental noise
Beam functionMeasured T
True T
Planck first image
Bennett et al. 2003
http://www.scientificamerican.com/media
Methodology
Decompose Stokes parameters into spin-two harmonics
True power spectra Pseudo-Cl estimators
Methodology
The expectation values of pseudo-Cl is given by
(Mitra et al. 2008)
Bias matrix
CPU time for caculating ClTT bias matrix
1000 dual core CPUs
lmax=3000
mbeam=2
Preliminary results
Expectation values of pseudo-Cl estimator for full sky and
non-circular beam
Mitra et al. (2008)
8 weeks CPU time
Preliminary resultsLimiting case of full sky and non-circular beam
Beam distortion parameterClebsch-Gordon coefficients
Wigner-d function
Beam function
3j symbol
Bias matrix for TE power spectra
Bias matrix for EE and BB power spectra
Preliminary resultsLimiting case of full sky and non-circular beam
Future works
Introduce mask function to account for cut-sky
Write codes to compute bias matrix and power spectra
Run our codes using CHPC facilities
Estimate the covariance matrix errors due to beam asymmetry and incomplete sky coverage
Match theory with upcoming Planck data
Conclusion
Pseudo-Cl method provides computationally fast cross power
spectra estimation at small angular scale (lmax=3000)
Systematic effect corrections are crucial for the Planck-like high resolution CMB experiment
Detection of B-mode polarization is a direct probe of gravitational waves predicted by inflationary models
B-mode polarization detection is challenging
References
Acknowledgements
I acknowledge the South African Square Kilometre Array Project for financial support of this project.
