5,103 research outputs found
Effect of detrending on multifractal characteristics
Different variants of MFDFA technique are applied in order to investigate
various (artificial and real-world) time series. Our analysis shows that the
calculated singularity spectra are very sensitive to the order of the
detrending polynomial used within the MFDFA method. The relation between the
width of the multifractal spectrum (as well as the Hurst exponent) and the
order of the polynomial used in calculation is evident. Furthermore, type of
this relation itself depends on the kind of analyzed signal. Therefore, such an
analysis can give us some extra information about the correlative structure of
the time series being studied.Comment: Presented by P. O\'swi\k{e}cimka at FENS2012 conference, 17 pages, 9
figure
Testing physical models for dipolar asymmetry with CMB polarization
The cosmic microwave background (CMB) temperature anisotropies exhibit a
large-scale dipolar power asymmetry. To determine whether this is due to a
real, physical modulation or is simply a large statistical fluctuation requires
the measurement of new modes. Here we forecast how well CMB polarization data
from \Planck\ and future experiments will be able to confirm or constrain
physical models for modulation. Fitting several such models to the \Planck\
temperature data allows us to provide predictions for polarization asymmetry.
While for some models and parameters \Planck\ polarization will decrease error
bars on the modulation amplitude by only a small percentage, we show,
importantly, that cosmic-variance-limited (and in some cases even \Planck)
polarization data can decrease the errors by considerably better than the
expectation of based on simple -space arguments. We project
that if the primordial fluctuations are truly modulated (with parameters as
indicated by \Planck\ temperature data) then \Planck\ will be able to make a
2 detection of the modulation model with 20--75\% probability,
increasing to 45--99\% when cosmic-variance-limited polarization is considered.
We stress that these results are quite model dependent. Cosmic variance in
temperature is important: combining statistically isotropic polarization with
temperature data will spuriously increase the significance of the temperature
signal with 30\% probability for \Planck.Comment: 18 pages, 11 figures, 2 tables. Version updated to match PRD versio
Correlating Fourier phase information with real-space higher order statistics
We establish for the first time heuristic correlations between harmonic space
phase information and higher order statistics. Using the spherical full-sky
maps of the cosmic microwave background as an example we demonstrate that known
phase correlations at large spatial scales can gradually be diminished when
subtracting a suitable best-fit (Bianchi-) template map of given strength. The
weaker phase correlations lead in turn to a vanishing signature of anisotropy
when measuring the Minkowski functionals and scaling indices in real-space and
comparing them with surrogate maps being free of phase correlations. Those
investigations can open a new road to a better understanding of signatures of
non-Gaussianities in complex spatial structures by elucidating the meaning of
Fourier phase correlations and their influence on higher order statistics.Comment: 6 pages plus 1 supplemental page, 4 figures, submitte
On coupling consistant dependence of Gauge fields
Classical gauge fields (pure, coupled to the Dirac, scalar and gravitational fields) are investigated in the weak-coupling and strong-coupling limits. Several results concerning coupling constant dependence of fields in these regions are given. In particular, validity of the weak-coupling perturbative techniques is questioned for dynamical and non-singular solutions to the field equations
Measuring Planck beams with planets
Aims. Accurate measurement of the cosmic microwave background (CMB) anisotropy requires precise knowledge of the instrument beam. We explore how well the Planck beams will be determined from observations of planets, developing techniques that are also appropriate for other experiments.
Methods. We simulate planet observations with a Planck-like scanning strategy, telescope beams, noise, and detector properties. Then we employ both parametric and non-parametric techniques, reconstructing beams directly from the time-ordered data. With a faithful parameterization of the beam shape, we can constrain certain detector properties, such as the time constants of the detectors, to high precision. Alternatively, we decompose the beam using an orthogonal basis. For both techniques, we characterize the errors in the beam reconstruction with Monte Carlo realizations. For a simplified scanning strategy, we study the impact on estimation of the CMB power spectrum. Finally, we explore the consequences for measuring cosmological parameters, focusing on the spectral index of primordial scalar perturbations, n_s.
Results. The quality of the power spectrum measurement will be significantly influenced by the optical modeling of the telescope. In our most conservative case, using no information about the optics except the measurement of planets, we find that a single transit of Jupiter across the focal plane will measure the beam window functions to better than 0.3% for the channels at 100–217 GHz that are the most sensitive to the CMB. Constraining the beam with optical modeling can lead to much higher quality reconstruction.
Conclusions. Depending on the optical modeling, the beam errors may be a significant contribution to the measurement systematics for n_s
The scalar perturbation spectral index n_s: WMAP sensitivity to unresolved point sources
Precision measurement of the scalar perturbation spectral index, n_s, from
the Wilkinson Microwave Anisotropy Probe temperature angular power spectrum
requires the subtraction of unresolved point source power. Here we reconsider
this issue. First, we note a peculiarity in the WMAP temperature likelihood's
response to the source correction: Cosmological parameters do not respond to
increased source errors. An alternative and more direct method for treating
this error term acts more sensibly, and also shifts n_s by ~0.3 sigma closer to
unity. Second, we re-examine the source fit used to correct the power spectrum.
This fit depends strongly on the galactic cut and the weighting of the map,
indicating that either the source population or masking procedure is not
isotropic. Jackknife tests appear inconsistent, causing us to assign large
uncertainties to account for possible systematics. Third, we note that the WMAP
team's spectrum was computed with two different weighting schemes: uniform
weights transition to inverse noise variance weights at l = 500. The fit
depends on such weighting schemes, so different corrections apply to each
multipole range. For the Kp2 mask used in cosmological analysis, we prefer
source corrections A = 0.012 +/- 0.005 muK^2 for uniform weighting and A =
0.015 +/- 0.005 muK^2 for N_obs weighting. Correcting WMAP's spectrum
correspondingly, we compute cosmological parameters with our alternative
likelihood, finding n_s = 0.970 +/- 0.017 and sigma_8 = 0.778 +/- 0.045 . This
n_s is only 1.8 sigma from unity, compared to the ~2.6 sigma WMAP 3-year
result. Finally, an anomalous feature in the source spectrum at l<200 remains,
most strongly associated with W-band.Comment: 9 pages, 10 figures, 3 tables. Submitted to Ap
Testing the Gaussianity of the COBE-DMR data with spherical wavelets
We investigate the Gaussianity of the 4-year COBE-DMR data (in HEALPix
pixelisation) using an analysis based on spherical Haar wavelets. We use all
the pixels lying outside the Galactic cut and compute the skewness, kurtosis
and scale-scale correlation spectra for the wavelet coefficients at each scale.
We also take into account the sensitivity of the method to the orientation of
the input signal. We find a detection of non-Gaussianity at per cent
level in just one of our statistics. Taking into account the total number of
statistics computed, we estimate that the probability of obtaining such a
detection by chance for an underlying Gaussian field is 0.69. Therefore, we
conclude that the spherical wavelet technique shows no strong evidence of
non-Gaussianity in the COBE-DMR data.Comment: latex file 7 pages, 6 figures, submitted to MNRA
Markov Chain Beam Randomization: a study of the impact of PLANCK beam measurement errors on cosmological parameter estimation
We introduce a new method to propagate uncertainties in the beam shapes used
to measure the cosmic microwave background to cosmological parameters
determined from those measurements. The method, which we call Markov Chain Beam
Randomization, MCBR, randomly samples from a set of templates or functions that
describe the beam uncertainties. The method is much faster than direct
numerical integration over systematic `nuisance' parameters, and is not
restricted to simple, idealized cases as is analytic marginalization. It does
not assume the data are normally distributed, and does not require Gaussian
priors on the specific systematic uncertainties. We show that MCBR properly
accounts for and provides the marginalized errors of the parameters. The method
can be generalized and used to propagate any systematic uncertainties for which
a set of templates is available. We apply the method to the Planck satellite,
and consider future experiments. Beam measurement errors should have a small
effect on cosmological parameters as long as the beam fitting is performed
after removal of 1/f noise.Comment: 17 pages, 23 figures, revised version with improved explanation of
the MCBR and overall wording. Accepted for publication in Astronomy and
Astrophysics (to appear in the Planck pre-launch special issue
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