اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA wavelet-Galerkin algorithm of the E/B decomposition of CMB polarization maps
317
0
0.0
(
0
)
تأليف
Liang Cao
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We develop an algorithm of separating the $E$ and $B$ modes of the CMB polarization from the noisy and discretized maps of Stokes parameter $Q$ and $U$ in a finite area. A key step of the algorithm is to take a wavelet-Galerkin discretization of the differential relation between the $E$, $B$ and $Q$, $U$ fields. This discretization allows derivative operator to be represented by a matrix, which is exactly diagonal in scale space, and narrowly banded in spatial space. We show that the effect of boundary can be eliminated by dropping a few DWT modes located on or nearby the boundary. This method reveals that the derivative operators will cause large errors in the $E$ and $B$ power spectra on small scales if the $Q$ and $U$ maps contain Gaussian noise. It also reveals that if the $Q$ and $U$ maps are random, these fields lead to the mixing of the $E$ and $B$ modes. Consequently, the $B$ mode will be contaminated if the powers of $E$ modes are much larger than that of $B$ modes. Nevertheless, numerical tests show that the power spectra of both $E$ and $B$ on scales larger than the finest scale by a factor of 4 and higher can reasonably be recovered, even when the power ratio of $E$- to $B$-modes is as large as about 10$^2$, and the signal-to-noise ratio is equal to 10 and higher. This is because the Galerkin discretization is free of false correlations, and keeps the contamination under control. As wavelet variables contain information of both spatial and scale spaces, the developed method is also effective to recover the spatial structures of the $E$ and $B$ mode fields.
قيم البحث
اقرأ أيضاً
We present an augmented version of our dual messenger algorithm for spin field reconstruction on the sphere, while accounting for highly non-trivial and realistic noise models such as modulated correlated noise. We also describe an optimization metho
d for the estimation of noise covariance from Monte Carlo simulations. Using simulated Planck polarized cosmic microwave background (CMB) maps as a showcase, we demonstrate the capabilities of the algorithm in reconstructing pure E and B maps, guaranteed to be free from ambiguous modes resulting from the leakage or coupling issue that plagues conventional methods of E/B separation. Due to its high speed execution, coupled with lenient memory requirements, the algorithm can be optimized in exact global Bayesian analyses of state-of-the-art CMB data for a statistically optimal separation of pure E and B modes. Our algorithm, therefore, has a potentially key role in the data analysis of high-resolution and high-sensitivity CMB data, especially with the range of upcoming CMB experiments tailored for the detection of the elusive primordial B-mode signal.
We present new methods for mapping the curl-free (E-mode) and divergence-free (B-mode) components of spin 2 signals using spin directional wavelets. Our methods are equally applicable to measurements of the polarisation of the cosmic microwave backgr
ound (CMB) and the shear of galaxy shapes due to weak gravitational lensing. We derive pseudo and pure wavelet estimators, where E-B mixing arising due to incomplete sky coverage is suppressed in wavelet space using scale- and orientation-dependent masking and weighting schemes. In the case of the pure estimator, ambiguous modes (which have vanishing curl and divergence simultaneously on the incomplete sky) are also cancelled. On simulations, we demonstrate the improvement (i.e., reduction in leakage) provided by our wavelet space estimators over standard harmonic space approaches. Our new methods can be directly interfaced in a coherent and computationally-efficient manner with component separation or feature extraction techniques that also exploit wavelets.
Detailed measurements of the CMB lensing signal are an important scientific goal of ongoing ground-based CMB polarization experiments, which are mapping the CMB at high resolution over small patches of the sky. In this work we simulate CMB polarizati
on lensing reconstruction for the $EE$ and $EB$ quadratic estimators with current-generation noise levels and resolution, and show that without boundary effects the known and expected zeroth and first order $N^{(0)}$ and $N^{(1)}$ biases provide an adequate model for non-signal contributions to the lensing power spectrum estimators. Small sky areas present a number of additional challenges for polarization lensing reconstruction, including leakage of $E$ modes into $B$ modes. We show how simple windowed estimators using filtered pure-$B$ modes can greatly reduce the mask-induced mean-field lensing signal and reduce variance in the estimators. This provides a simple method (used with recent observations) that gives an alternative to more optimal but expensive inverse-variance filtering.
Madam is a CMB map-making code, designed to make temperature and polarization maps of time-ordered data of total power experiments like Planck. The algorithm is based on the destriping technique, but it also makes use of known noise properties in the
form of a noise prior. The method in its early form was presented in an earlier work by Keihanen et al. (2005). In this paper we present an update of the method, extended to non-averaged data, and include polarization. In this method the baseline length is a freely adjustable parameter, and destriping can be performed at a different map resolution than that of the final maps. We show results obtained with simulated data. This study is related to Planck LFI activities.
A persistent signal of power asymmetry on opposite hemispheres of CMB sky was seen in full-sky temperature measurements made so far. This asymmetry was seen in microwave sky from WMAP as well as PLANCK satellites, and calls for attention the larger q
uestion of emph{statistical isotropy}, one of the foundational principles of modern cosmology. In this work we present an analysis of polarized CMB maps from PLANCK 2015 full mission data. We apply the local variance estimator on low resolution $E-$mode maps from PLANCK 2015 polarization texttt{Commander} solution. We find a significant hemispherical power asymmetry in polarization data on large angular scales, at the level of $sim 2.6-3.9%$ depending on the galactic mask, and the circular disc radius used for computing local variance maps. However the direction is found to be pointing broadly towards CMB kinetic dipole direction. Precise measurements of CMB polarization in future will shed light on this apparent discrepancy in the anisotropy axis seen in temperature and polarized CMB sky, and likely influence of systematics on our findings.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
