اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPartial CMB maps: bias removal and optimal binning of the angular power spectrum
138
0
0.0
(
0
)
تأليف
R. Ansari
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We present a semi-analytical method to investigate the systematic effects and statistical uncertainties of the calculated angular power spectrum when incomplete spherical maps are used. The computed power spectrum suffers in particular a loss of angular frequency resolution, which can be written as delta_l ~ pi/gamma_max, where gamma_max is the effective maximum extent of the partial spherical maps. We propose a correction algorithm to reduce systematic effects on the estimated C_l, as obtained from the partial map projection on the spherical harmonic Ylm(l,m) basis. We have derived near optimal bands and weighting functions in l-space for power spectrum calculation using small maps, and a correction algorithm for partially masked spherical maps that contain information on the angular correlations on all scales.
قيم البحث
اقرأ أيضاً
We present a novel application of partial convolutional neural networks (PCNN) that can inpaint masked images of the cosmic microwave background. The network can reconstruct both the maps and the power spectra to a few percent for circular and irregu
larly shaped masks covering up to ~10% of the image area. By performing a Kolmogorov-Smirnov test we show that the reconstructed maps and power spectra are indistinguishable from the input maps and power spectra at the 99.9% level. Moreover, we show that PCNNs can inpaint maps with regular and irregular masks to the same accuracy. This should be particularly beneficial to inpaint irregular masks for the CMB that come from astrophysical sources such as galactic foregrounds. The proof of concept application shown in this paper shows that PCNNs can be an important tool in data analysis pipelines in cosmology.
We revisit the problem of exact CMB likelihood and power spectrum estimation with the goal of minimizing computational cost through linear compression. This idea was originally proposed for CMB purposes by Tegmark et al. (1997), and here we develop i
t into a fully working computational framework for large-scale polarization analysis, adopting WMAP as a worked example. We compare five different linear bases (pixel space, harmonic space, noise covariance eigenvectors, signal-to-noise covariance eigenvectors and signal-plus-noise covariance eigenvectors) in terms of compression efficiency, and find that the computationally most efficient basis is the signal-to-noise eigenvector basis, which is closely related to the Karhunen-Loeve and Principal Component transforms, in agreement with previous suggestions. For this basis, the information in 6836 unmasked WMAP sky map pixels can be compressed into a smaller set of 3102 modes, with a maximum error increase of any single multipole of 3.8% at $ellle32$, and a maximum shift in the mean values of a joint distribution of an amplitude--tilt model of 0.006$sigma$. This compression reduces the computational cost of a single likelihood evaluation by a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust likelihood by implicitly regularizing nearly degenerate modes. Finally, we use the same compression framework to formulate a numerically stable and computationally efficient variation of the Quadratic Maximum Likelihood implementation that requires less than 3 GB of memory and 2 CPU minutes per iteration for $ell le 32$, rendering low-$ell$ QML CMB power spectrum analysis fully tractable on a standard laptop.
The lensing power spectrum from cosmic microwave background (CMB) temperature maps will be measured with unprecedented precision with upcoming experiments, including upgrades to ACT and SPT. Achieving significant improvements in cosmological paramete
r constraints, such as percent level errors on sigma_8 and an uncertainty on the total neutrino mass of approximately 50 meV, requires percent level measurements of the CMB lensing power. This necessitates tight control of systematic biases. We study several types of biases to the temperature-based lensing reconstruction signal from foreground sources such as radio and infrared galaxies and the thermal Sunyaev-Zeldovich effect from galaxy clusters. These foregrounds bias the CMB lensing signal due to their non-Gaussian nature. Using simulations as well as some analytical models we find that these sources can substantially impact the measured signal if left untreated. However, these biases can be brought to the percent level if one masks galaxies with fluxes at 150 GHz above 1 mJy and galaxy clusters with masses above M_vir = 10^14 M_sun. To achieve such percent level bias, we find that only modes up to a maximum multipole of l_max ~ 2500 should be included in the lensing reconstruction. We also discuss ways to minimize additional bias induced by such aggressive foreground masking by, for example, exploring a two-step masking and in-painting algorithm.
We compute the effects induced by the use of small CMB maps on the measurement of the $cl{l}$ coefficients of the angular power spectrum and show that small systematic effects have to be taken into account. We also compute numerically the cosmic vari
ance and covariance of the $cl{l}$ spectrum for various spherical cap like maps. Comparisons with simulations are presented. The calculations are done using the standard method based on the spherical harmonic transform or using the temperature angular correlation spectrum.
A theoretical framework is developed to estimate the optimal binning of X-ray spectra. We derived expressions for the optimal bin size for model spectra as well as for observed data using different levels of sophistication. It is shown that by taking
into account both the number of photons in a given spectral model bin and their average energy over the bin size, the number of model energy bins and the size of the response matrix can be reduced by a factor of $10-100$. The response matrix should then contain the response at the bin centre as well as its derivative with respect to the incoming photon energy. We provide practical guidelines for how to construct optimal energy grids as well as how to structure the response matrix. A few examples are presented to illustrate the present methods.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
