arXiv subjects

Pavel Naselsky

Publications and source records attributed to Pavel Naselsky.

At least 19 recordsLinked to original sources

arXiv2022

The polarization quaternion and its applications: a joint representation of the Q/U Stokes parameters and E/B mode polarizations

In this work, we point out that the Q/U Stokes parameters and E/B mode polarizations are the four components of a unique quaternion, which describes at the same time the directions and the parity states of spherical linear polarizations. We then point out that, with this polarization quaternion, the mathematical form of all Q/U and E/B transforms are greatly simplified, to an extent that requires only one quaternion multiplication for each transform. A preliminary application of the polarization quaternion is shown as an example to detect peculiar pixel domain patterns within the E- and B-families, which are the former and latter halves of the polarization quaternion.

astro-ph.CO↗

arXiv2021

Ring of attraction: overlapping directions of the dipole modulation of the CMB, the parity asymmetry, and kinematic dipole percolation zone

The largest anisotropy in the cosmic microwave background (CMB) is the 3 mK kinematic dipole reflecting our motion with respect to the CMB frame and pointed in the direction $(l, b) = (264^\circ, +48^\circ)$ in Galactic coordinates. We introduce the concept of the ring of attraction (RA), which is orthogonal to the axis of the kinematic dipole. These directions overlap with the zone of percolation for the kinematic dipole, where its amplitude almost vanishes. We show that along this ring are oriented the directions of the dipole modulation of the CMB, and positions of the peaks responsible for generation of parity asymmetry. This coincidence is peculiar at around the 3 sigma level. We analyzed the "interaction" of low multipoles of the CMB with RA and showed that for odd modes there is a sequence of peaks in the RA direction. These peaks correlate with each other for different multipoles and result in mutual amplification of the odd $\ell$ signal for the first 30 multipoles. Our method sheds new light on the nature of parity asymmetry. It consists of the deficit of symmetrically located and equal in amplitude peaks in the CMB map in comparison with asymmetric peaks.

astro-ph.CO↗

arXiv2021

Asymmetry of the CMB map: local and global anomalies

We investigate the sources of parity asymmetry in the CMB temperature maps using a pixel domain approach. We demonstrate that this anomaly is mainly associated with the presence of two pairs of high asymmetry regions. The first pair of peaks with Galactic coordinates $(l, b) = (212^\circ, -21^\circ)$ and $(32^\circ, 21^\circ)$ is associated with the Northern Galactic Spur and the direction of the dipole modulation of the power spectrum of the CMB anisotropy. The other pair ($(l, b)=(332^\circ, -8^\circ)$ and $(152^\circ, 8^\circ)$) is located within the Galactic plane (the Galactic Cold Spot and its antipodal partner). Similar asymmetric peaks, but with smaller amplitudes, belong to the WMAP/Planck Cold Spot and its partner in the Northern Galactic Spur. These local anomalies increase the odd-multipole power to a level consistent with Gaussian simulations. In contrast, the deficit of symmetric peaks is accompanied by a deficit in the even-multipole power and is the source of the parity asymmetry of the CMB temperature maps at the level of about 3 sigma. We also evaluate the influence of the quadrupole, which is another source of the even-multipole deficit. If the low quadrupole is an intrinsic feature of the theoretical model, it will reduce the significance of the parity asymmetry to around the 2 sigma level. We also investigate the relationship between the asymmetry of the power spectrum and the level of the parity asymmetry in the framework of a model with dipole modulation of a statistically uniform Gaussian signal. We show that these two anomalies are innately linked to each other.

astro-ph.CO↗

arXiv2020

Statistics of non-polarized points in the CMB polarization maps

The non-polarized points (NPP) of the $Q$ and $U$ Stokes parameters of the CMB can be classified according to the geometry of the polarization field. We describe a procedure to identify these points in the pixelized sky and present the shape of the polarization angles in the vicinity of NPPs. We design a test of Gaussianity using the Kullback-Leibler divergence. We show that the total number density of non-polarized points of the E- and B-families is closely related to the presence of lensing and the tensor-to-scalar ratio $r$. We further show that in the absence of lensing, the total number of NPPs of all types does not depend on $r$, while the lensing effect removes this degeneracy. This analysis is applied to the CMB maps from the 2018 Planck release. We show that there is general consistency of SMICA and NILC maps compared to a reference set of Gaussian simulations. The strongest discrepancies are found in the Commander (with corresponding $p$-value $0.07$) and NILC ($p = 0.15$) maps.

astro-ph.CO↗

arXiv2020

Comparison of the Planck 2018 CMB polarization maps in the BICEP2/Keck region

We examine the statistical properties of polarization maps from Planck 2018 within the patch of sky observed by the BICEP2/Keck experiment using the one point distribution function (1PDF), skewness, and kurtosis statistics. Our analysis is performed for the Q and U Stokes parameters and for the corresponding E- and B-modes of the CMB signals. We extend our analysis by studying the correlations between CMB polarization maps and residual maps (the difference between the full signal and the CMB map) for the frequency range of 100--217 GHz with both the Q/U and E/B approaches. Although all the CMB maps reveal almost Gaussian statistical properties for Q/U and E/B domains, we have detected very significant anomalies for cross-correlations with residuals at 100 GHz at the level of $3.7σ$ for the Commander map and $5.2σ$ for NILC, for both the Q and U parameters. Using the NILC--Commander difference, which does not contain a cosmological signal, we find a sub-dominant non-Gaussian component in Q skewness and kurtosis at the level of $4.3σ$ and $10σ$, respectively. For the B-mode we have found a very high level of cross-correlation (0.63--0.69) between the NILC/Commander maps and the 143 GHz total signal, which cannot be associated with the cosmological component. These strong deviations suggest that remnants of foregrounds, systematic effects, and component separation exist in the 2018 Planck CMB polarization maps in the BICEP2 sky area, which is far away from the Galactic plane. Our analysis also demonstrates the preferability of the Q/U domain over E/B for determination of the statistical properties of the derived CMB signals, due to non-locality of the transition Q/U $\rightarrow$ E/B.

astro-ph.CO↗

arXiv2020

Statistics of CMB polarization angles

We study the distribution functions of the CMB polarization angle $ψ$, focusing on the Planck 2018 CMB maps. We extend the model of Preece & Battye (2014) of Gaussian correlated $Q$ and $U$ Stokes parameters to allow nonzero means. When the variances of $Q$ and $U$ are equal and their covariance and means are zero, the polarization angle is uniformly distributed. Otherwise the uniform distribution will be modulated by harmonics with $2ψ$ and $4ψ$ phases. These modulations are visible in the Planck 2018 CMB maps. Furthermore, the mean value of $U$ is peculiar compared to the power spectrum.

astro-ph.CO↗

arXiv2019

Methods for pixel domain correction of EB leakage

In observation of the cosmic microwave background (CMB) polarization, "$EB$~leakage" refers to the artificial $B$-mode signal coming from the leakage of $E$-mode signal when part of the sky is unavailable or excluded. Correction of such leakage is one of the preconditions for detecting primordial gravitational waves via the CMB $B$-mode signal. In this work, we design two independent methods for correcting the $EB$~leakage directly in the pixel domain using standard definitions of the $E$- and $B$-modes. The two methods give consistent results, and both are fast and easy to implement. Tests on a CMB simulation containing zero initial $B$-mode show an efficient suppression of the $EB$ leakage. When combined with the MASTER method to reconstruct the full-sky $B$-mode spectrum in simulations with a relatively simple mask, the error from EB-leakage is suppressed further by more than one order of magnitude at the recombination bump, and up to three orders of magnitude at higher multipoles, compared to a "pure" MASTER scheme under the same conditions. Meanwhile, although the final power spectrum estimation benefits from apodization, the pixel domain correction itself is done without apodization, and thus the methods offer more freedom in choosing an apodization based on specific requirements.

astro-ph.CO↗

arXiv2019

Noise residuals for GW150914 using maximum likelihood and numerical relativity templates

We reexamine the results presented in a recent work by Nielsen et al. [1], in which the properties of the noise residuals in the 40\,ms chirp domain of GW150914 were investigated. This paper confirmed the presence of strong (i.e., about 0.80) correlations between residual noise in the Hanford and Livingston detectors in the chirp domain as previously seen by us [2] when using a numerical relativity template given in [3]. It was also shown in [1] that a so-called maximum likelihood template can reduce these statistically significant cross-correlations. Here, we demonstrate that the reduction of correlation and statistical significance is due to (i) the use of a peculiar template which is qualitatively different from the properties of GW150914 originally published by LIGO, (ii) a suspicious MCMC chain, (iii) uncertainties in the matching of the maximum likelihood (ML) template to the data in the Fourier domain, and (iv) a biased estimation of the significance that gives counter-intuitive results. We show that rematching the maximum likelihood template to the data in the 0.2\,s domain containing the GW150914 signal restores these correlations at the level of $60\%$ of those found in [1]. With necessary corrections, the probability given in [1] will decrease by more than one order of magnitude. Since the ML template is itself problematic, results associated with this template are illustrative rather than final.

astro-ph.IM↗

arXiv2019

From top-hat masking to smooth transitions: P-filter and its application to polarized microwave sky maps

In CMB science, the simplest idea to remove a contaminated sky region is to multiply the sky map with a mask that is 0 for the contaminated region and 1 elsewhere, which is also called a top-hat masking. Although it is easy to use, such top-hat masking is known to suffer from various leakage problems. Therefore, we want to extend the top-hat masking to a series of semi-analytic functions called the P-filters. Most importantly, the P-filters can seamlessly realize the core idea of masking in CMB science, and, meanwhile, guarantee continuity up to the first derivative everywhere. The P-filters can significantly reduce many leakage problems without additional cost, including the leakages due to low-, high-, and band-pass filtering, and the E-to-E, B-to-B, B-to-E, and E-to-B leakages. The workings of the P-filter are illustrated by using the WMAP and Planck polarization sky maps. By comparison to the corresponding WMAP/Planck masks, we show that the P-filter performs much better than top-hat masking, and meanwhile, has the potential to supersede the principal idea of masking in CMB science. Compared to mask apodization, the P-filter is ``outward'', that tends to make proper use of the region that was marked as 0; whereas apodization is ``inward'', that always kills more signal in the region marked as 1.

astro-ph.CO↗

arXiv2018

E and B families of the Stokes parameters in the polarized synchrotron and thermal dust foregrounds

Better understanding of Galactic foregrounds is one of the main obstacles to detection of primordial gravitational waves through measurement of the B mode in the polarized microwave sky. We generalize the method proposed in \cite{2011PhRvD..83h3003B} and decompose the polarization signals into the E and B families directly in the domain of the Stokes $Q$, $U$ parameters as $(Q,U)\equiv(Q_E, U_E)+(Q_B,U_B)$. This also enables an investigation of the morphology and the frequency dependence of these two families, which has been done in the WMAP K, Ka (tracing synchrotron emission) and Planck 2015 HFI maps (tracing thermal dust). The results reveal significant differences in spectra between the E and B families. The spectral index of the E family fluctuates less across the sky than that of the B family, and the same tendency occurs for the polarization angles of the dust and synchrotron channels. The new insight from WMAP and Planck data on the North Polar Spur and BICEP2 zones through our method clearly indicates that these zones are characterized by very low polarization intensity of the B family compared to the E family. We have detected global structure of the B family polarization angles at high Galactic latitudes which cannot be attributed to the cosmic microwave background or instrumental noise. However, we cannot exclude instrumental systematics as a partial contributor to these anomalies.

astro-ph.CO↗

arXiv2018

Degeneracy of gravitational waveforms in the context of GW150914

We study the degeneracy of theoretical gravitational waveforms for binary black hole mergers using an aligned-spin effective-one-body model. After appropriate truncation, bandpassing, and matching, we identify regions in the mass--spin parameter space containing waveforms similar to the template proposed for GW150914, with masses $m_1 = 36^{+5}_{-4} M_\odot$ and $m_2 = 29^{+4}_{-4} M_\odot$, using the cross-correlation coefficient as a measure of the similarity between waveforms. Remarkably high cross-correlations are found across broad regions of parameter space. The associated uncertanties exceed these from LIGO's Bayesian analysis considerably. We have shown that waveforms with greatly increased masses, such as $m_1 = 70 M_\odot$ and $m_2 = 35 M_\odot$, and strong anti-aligned spins ($χ_1=0.95$ and $χ_2=-0.95$) yield almost the same signal-to-noise ratio in the strain data for GW150914.

gr-qc↗

arXiv2018

A blind search for a common signal in gravitational wave detectors

We propose a blind, template-free method for the extraction of a common signal between the Hanford and Livingston detectors and apply it especially to the GW150914 event. We construct a log-likelihood method that maximizes the cross-correlation between each detector and the common signal and minimizes the cross-correlation between the residuals. The reliability of this method is tested using simulations with an injected common signal. Finally, our method is used to assess the quality of theoretical gravitational wave templates for GW150914.

astro-ph.IM↗

arXiv2017

On the time lags of the LIGO signals

To date, the LIGO collaboration has detected three gravitational wave (GW) events appearing in both its Hanford and Livingston detectors. In this article we reexamine the LIGO data with regard to correlations between the two detectors. With special focus on GW150914, we report correlations in the detector noise which, at the time of the event, happen to be maximized for the same time lag as that found for the event itself. Specifically, we analyze correlations in the calibration lines in the vicinity of 35\,Hz as well as the residual noise in the data after subtraction of the best-fit theoretical templates. The residual noise for the other two events, GW151226 and GW170104, exhibits similar behavior. A clear distinction between signal and noise therefore remains to be established in order to determine the contribution of gravitational waves to the detected signals.

astro-ph.IM↗

arXiv2017

Towards understanding the Planck thermal dust models

Understanding the properties of dust emission in the microwave domain is an important premise for the next generation of cosmic microwave background (CMB) experiments, devoted to the measurement of the primordial $B$-modes of polarization. In this paper, we compare three solutions to thermal dust emission by the Planck Collaboration \cite{PlanckDust03,planck_16,planck_com} to point out significant differences between their respective parameters (the spectral index $β$, the optical depth $τ$ and the dust temperature $T_d$). These differences originate from e.g. the priors on the parameters or the contribution of the Cosmic infrared background (CIB).

astro-ph.CO↗

arXiv2016

Critical points of the cosmic velocity field and the uncertainties in the value of the Hubble constant

The existence of critical points for the peculiar velocity field is a natural feature of the correlated vector field. These points appear at the junctions of velocity domains with different orientations of their averaged velocity vectors. Since peculiar velocities are the important cause of the scatter in the Hubble expansion rate, we propose that a more precise determination of the Hubble constant can be made by restricting analysis to a subsample of observational data containing only the zones around the critical points of the peculiar velocity field, associated with voids and saddle points. On large-scales the critical points, where the first derivative of the gravitational potential vanishes, can easily be identified using the density field and classified by the behavior of the Hessian of the gravitational potential. We use high-resolution N-body simulations to show that these regions are stable in time and hence are excellent tracers of the initial conditions. Furthermore, we show that the variance of the Hubble flow can be substantially minimized by restricting observations to the subsample of such regions of vanishing velocity instead of aiming at increasing the statistics by averaging indiscriminately using the full data sets, as is the common approach.

astro-ph.CO↗

arXiv2014

PRISM (Polarized Radiation Imaging and Spectroscopy Mission): An Extended White Paper

PRISM (Polarized Radiation Imaging and Spectroscopy Mission) was proposed to ESA in May 2013 as a large-class mission for investigating within the framework of the ESA Cosmic Vision program a set of important scientific questions that require high resolution, high sensitivity, full-sky observations of the sky emission at wavelengths ranging from millimeter-wave to the far-infrared. PRISM's main objective is to explore the distant universe, probing cosmic history from very early times until now as well as the structures, distribution of matter, and velocity flows throughout our Hubble volume. PRISM will survey the full sky in a large number of frequency bands in both intensity and polarization and will measure the absolute spectrum of sky emission more than three orders of magnitude better than COBE FIRAS. The aim of this Extended White Paper is to provide a more detailed overview of the highlights of the new science that will be made possible by PRISM

astro-ph.CO↗

arXiv2013

Large-scale anomalies of the CMB in the curvaton scenario

We extend the curvaton scenario presented by Erickcek et al. (2008, 2009), to explain how the even-odd multipole asymmetry of the Cosmic Microwave Background (CMB) (also called parity asymmetry, (Kim & Naselsky 2010)) and power anisotropies can be generated by the curvaton field, which acts as an extra component to the spectrum of adiabatic perturbations in the inflationary epoch. Our work provides a possible cosmic explanation to the CMB large-scale asymmetry problems besides systematics and unknown residuals.

astro-ph.CO↗

arXiv2012

How accurately can we measure the hydrogen 2S->1S transition rate from the cosmological data?

Recent progress in observational cosmology, and especially the forthcoming PLANCK mission data, open new directions in so-called precision cosmology. In this paper we illustrate this statement considering the accuracy of cosmological determination of the two-quanta decay rate of 2s hydrogen atom state. We show that the PLANCK data will allow us to measure this decay rate significantly better than in the laboratory experiments.

astro-ph.CO↗