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Title: Lens covariance effects on likelihood analyses of CMB power spectra

Publication Date:
Sponsoring Org.:
OSTI Identifier:
Grant/Contract Number:
FG02-13ER41958; SC0009924
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 96; Journal Issue: 10; Related Information: CHORUS Timestamp: 2017-11-15 10:05:11; Journal ID: ISSN 2470-0010
American Physical Society
Country of Publication:
United States

Citation Formats

Motloch, Pavel, and Hu, Wayne. Lens covariance effects on likelihood analyses of CMB power spectra. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.96.103517.
Motloch, Pavel, & Hu, Wayne. Lens covariance effects on likelihood analyses of CMB power spectra. United States. doi:10.1103/PhysRevD.96.103517.
Motloch, Pavel, and Hu, Wayne. 2017. "Lens covariance effects on likelihood analyses of CMB power spectra". United States. doi:10.1103/PhysRevD.96.103517.
title = {Lens covariance effects on likelihood analyses of CMB power spectra},
author = {Motloch, Pavel and Hu, Wayne},
abstractNote = {},
doi = {10.1103/PhysRevD.96.103517},
journal = {Physical Review D},
number = 10,
volume = 96,
place = {United States},
year = 2017,
month =

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on November 15, 2018
Publisher's Accepted Manuscript

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  • Microwave background temperature and polarization observations are a powerful way to constrain cosmological parameters if the likelihood function can be calculated accurately. The temperature and polarization fields are correlated, partial-sky coverage correlates power spectrum estimators at different l, and the likelihood function for a theory spectrum given a set of observed estimators is non-Gaussian. An accurate analysis must model all these properties. Most existing likelihood approximations are good enough for a temperature-only analysis, however they cannot reliably handle temperature-polarization correlations. We give a new general approximation applicable for correlated Gaussian fields observed on part of the sky. The approximation modelsmore » the non-Gaussian form exactly in the ideal full-sky limit and is fast to evaluate using a precomputed covariance matrix and set of power spectrum estimators. We show with simulations that it is good enough to obtain correct results at l > or approx. 30 where an exact calculation becomes impossible. We also show that some Gaussian approximations give reliable parameter constraints even though they do not capture the shape of the likelihood function at each l accurately. Finally we test the approximations on simulations with realistically anisotropic noise and asymmetric foreground mask.« less
  • High-frequency quasi-periodic oscillations (QPOs) from weakly magnetized neutron stars display rapid frequency variability (second timescales) and high coherence with quality factors up to at least 200 at frequencies about 800-850 Hz. Their parameters have been estimated so far from standard min({chi}{sup 2}) fitting techniques, after combining a large number of power density spectra (PDS), to have the powers normally distributed (the so-called Gaussian regime). Before combining PDS, different methods to minimize the effects of the frequency drift to the estimates of the QPO parameters have been proposed, but none of them relied on fitting the individual PDS. Accounting for themore » statistical properties of PDS, we apply a maximum likelihood method to derive the QPO parameters in the non-Gaussian regime. The method presented is general, easy to implement, and can be applied to fitting individual PDS, several PDS simultaneously, or their average, and is obviously not specific to the analysis of kHz QPO data. It applies to the analysis of any PDS optimized in frequency resolution and for low-frequency variability or PDS containing features whose parameters vary on short timescales, as is the case for kHz QPOs. It is equivalent to the standard {chi}{sup 2} minimization fitting when the number of PDS fitted is large. The accuracy, reliability, and superiority of the method is demonstrated with simulations of synthetic PDS, containing Lorentzian QPOs of known parameters. Accounting for the broadening of the QPO profile, due to the leakage of power inherent to windowed Fourier transforms, the maximum likelihood estimates of the QPO parameters are asymptotically unbiased and have negligible bias when the QPO is reasonably well detected. By contrast, we show that the standard min({chi}{sup 2}) fitting method gives biased parameters with larger uncertainties. The maximum likelihood fitting method is applied to a subset of archival Rossi X-ray Timing Explorer data of the neutron star X-ray binary 4U1608-522, for which we show that the lower kHz QPO parameters can be measured on timescales as short as 8 s. To demonstrate the potential use of the results of the maximum likelihood method, we show that in the observation analyzed the time evolution of the frequency is consistent with a random walk. We then show that the broadening of the QPO due to the frequency drift scales as {radical}T, as expected from a random walk (T is the integration time of the PDS). This enables us to estimate the intrinsic quality factor of the QPO to be {approx}260, whereas previous analysis indicated a maximum value around 200.« less
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