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Register a new userBandpass mismatch error for satellite CMB experiments I: Estimating the spurious signal
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Future Cosmic Microwave Background (CMB) satellite missions aim to use the $B$ mode polarization to measure the tensor-to-scalar ratio $r$ with a sensitivity of about $10^{-3}$. Achieving this goal will not only require sufficient detector array sensitivity but also unprecedented control of all systematic errors inherent to CMB polarization measurements. Since polarization measurements derive from differences between observations at different times and from different sensors, detector response mismatches introduce leakages from intensity to polarization and thus lead to a spurious $B$ mode signal. Because the expected primordial $B$ mode polarization signal is dwarfed by the known unpolarized intensity signal, such leakages could contribute substantially to the final error budget for measuring $r.$ Using simulations we estimate the magnitude and angular spectrum of the spurious $B$ mode signal resulting from bandpass mismatch between different detectors. It is assumed here that the detectors are calibrated, for example using the CMB dipole, so that their sensitivity to the primordial CMB signal has been perfectly matched. Consequently the mismatch in the frequency bandpass shape between detectors introduces difference in the relative calibration of galactic emission components. We simulate using a range of scanning patterns being considered for future satellite missions. We find that the spurious contribution to $r$ from reionization bump on large angular scales ($ell < 10$) is $approx 10^{-3}$ assuming large detector arrays and 20 percent of the sky masked. We show how the amplitude of the leakage depends on the angular coverage per pixels that results from the scan pattern.
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Future Cosmic Microwave Background (CMB) satellite missions aim at using the B-mode polarisation signal to measure the tensor-to-scalar ratio $r$ with a sensitivity $sigma(r)$ of the order of $leq 10^{-3}$. Small uncertainties in the characterisation of instrument properties such as the spectral filters can lead to a leakage of the intensity signal to polarisation and can possibly bias any measurement of a primordial signal. In this paper we discuss methods for avoiding and correcting for the intensity to polarisation leakage due to bandpass mismatch among detector sets. We develop a template fitting map-maker to obtain an unbiased estimate of the leakage signal and subtract it out of the total signal. Using simulations we show how such a method can reduce the bias on the observed B-mode signal by up to $3$ orders of magnitude in power.
A great deal of experimental effort is currently being devoted to the precise measurements of the cosmic microwave background (CMB) sky in temperature and polarisation. Satellites, balloon-borne, and ground-based experiments scrutinize the CMB sky at multiple scales, and therefore enable to investigate not only the evolution of the early Universe, but also its late-time physics with unprecedented accuracy. The pipeline leading from time ordered data as collected by the instrument to the final product is highly structured. Moreover, it has also to provide accurate estimates of statistical and systematic uncertainties connected to the specific experiment. In this paper, we review likelihood approaches targeted to the analysis of the CMB signal at different scales, and to the estimation of key cosmological parameters. We consider methods that analyze the data in the spatial (i.e., pixel-based) or harmonic domain. We highlight the most relevant aspects of each approach and compare their performance.
The non-Gaussian nature of the epoch of reionization (EoR) 21-cm signal has a significant impact on the error variance of its power spectrum $P({bf textit{k}})$. We have used a large ensemble of semi-numerical simulations and an analytical model to estimate the effect of this non-Gaussianity on the entire error-covariance matrix ${mathcal{C}}_{ij}$. Our analytical model shows that ${mathcal{C}}_{ij}$ has contributions from two sources. One is the usual variance for a Gaussian random field which scales inversely of the number of modes that goes into the estimation of $P({bf textit{k}})$. The other is the trispectrum of the signal. Using the simulated 21-cm signal ensemble, an ensemble of the randomized signal and ensembles of Gaussian random ensembles we have quantified the effect of the trispectrum on the error variance ${mathcal{C}}_{ij}$. We find that its relative contribution is comparable to or larger than that of the Gaussian term for the $k$ range $0.3 leq k leq 1.0 ,{rm Mpc}^{-1}$, and can be even $sim 200$ times larger at $k sim 5, {rm Mpc}^{-1}$. We also establish that the off-diagonal terms of ${mathcal{C}}_{ij}$ have statistically significant non-zero values which arise purely from the trispectrum. This further signifies that the error in different $k$ modes are not independent. We find a strong correlation between the errors at large $k$ values ($ge 0.5 ,{rm Mpc}^{-1}$), and a weak correlation between the smallest and largest $k$ values. There is also a small anti-correlation between the errors in the smallest and intermediate $k$ values. These results are relevant for the $k$ range that will be probed by the current and upcoming EoR 21-cm experiments.
We study the problem of searching for cosmic string signal patterns in the present high resolution and high sensitivity observations of the Cosmic Microwave Background (CMB). This article discusses a technique capable of recognizing Kaiser-Stebbins effect signatures in total intensity anisotropy maps, and shows that the biggest factor that produces confusion is represented by the acoustic oscillation features of the scale comparable to the size of horizon at recombination. Simulations show that the distribution of null signals for pure Gaussian maps converges to a $chi^2$ distribution, with detectability threshold corresponding to a string induced step signal with an amplitude of about 100 $muK$ which corresponds to a limit of roughly $Gmu < 1.5times 10^{-6}$. We study the statistics of spurious detections caused by extra-Galactic and Galactic foregrounds. For diffuse Galactic foregrounds, which represents the dominant source of contamination, we derive sky masks outlining the available region of the sky where the Galactic confusion is sub-dominant, specializing our analysis to the case represented by the frequency coverage and nominal sensitivity and resolution of the Planck experiment.
We test the statistical isotropy (SI) of the $E$-mode polarization of the cosmic microwave background (CMB) radiation observed by the Planck satellite using two statistics, namely, the contour Minkowski Tensor (CMT) and the Directional statistic ($mathcal{D}$ statistic). The parameter $alpha$ obtained from the CMT provides information of the alignment of structures and can be used to infer statistical properties such as Gaussianity and SI of random fields. The $mathcal{D}$ statistic is based on detecting preferred directionality shown by vectors defined by the field. These two tests are complementary to each other in terms of sensitivity at different angular scales. The CMT is sensitive towards small-scale information present in the CMB map while $mathcal{D}$ statistic is more sensitive at large-scales. We compute $alpha$ and $mathcal{D}$ statistic for the observed $E$-mode of CMB polarization, focusing on the SMICA maps, and compare with the values calculated using FFP10 SMICA simulations which contain both CMB and noise. We find good agreement between the observed data and simulations. Further, in order to specifically analyze the CMB signal in the data, we compare the values of the two statistics obtained from the observed Planck data with the values obtained from isotropic simulations having the same power spectrum, and from SMICA noise simulations. We find no statistically significant deviation from SI using the $alpha$ parameter. From $mathcal{D}$ statistic we find that the data shows slight deviation from SI at large angular scales.
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