3,241 research outputs found
Testing for Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe Data: Minkowski Functionals and the Length of the Skeleton
The three Minkowski functionals and the recently defined length of the
skeleton are estimated for the co-added first-year Wilkinson Microwave
Anisotropy Probe (WMAP) data and compared with 5000 Monte Carlo simulations,
based on Gaussian fluctuations with the a-priori best-fit running-index power
spectrum and WMAP-like beam and noise properties. Several power
spectrum-dependent quantities, such as the number of stationary points, the
total length of the skeleton, and a spectral parameter, gamma, are also
estimated. While the area and length Minkowski functionals and the length of
the skeleton show no evidence for departures from the Gaussian hypothesis, the
northern hemisphere genus has a chi^2 that is large at the 95% level for all
scales. For the particular smoothing scale of 3.40 degrees FWHM it is larger
than that found in 99.5% of the simulations. In addition, the WMAP genus for
negative thresholds in the northern hemisphere has an amplitude that is larger
than in the simulations with a significance of more than 3 sigma. On the
smallest angular scales considered, the number of extrema in the WMAP data is
high at the 3 sigma level. However, this can probably be attributed to the
effect of point sources. Finally, the spectral parameter gamma is high at the
99% level in the northern Galactic hemisphere, while perfectly acceptable in
the southern hemisphere. The results provide strong evidence for the presence
of both non-Gaussian behavior and an unexpected power asymmetry between the
northern and southern hemispheres in the WMAP data.Comment: 17 pages, 10 figures, accepted for publication in Ap
Power filtration of CMB observational data
We propose a power filter Gp for linear reconstruction of the CMB signal from
observational maps. This Gp filter preserves the power spectrum of the CMB
signal in contrast to the Wiener filter which diminishes the power spectrum of
the reconstructed CMB signal. We demonstrate how peak statistics and a cluster
analysis can be used to estimate the probability of the presence of a CMB
signal in observational records. The efficiency of the Gp filter is
demonstrated on a toy model of an observational record consisting of a CMB
signal and noise in the form of foreground point sources.Comment: 17 pages; 4 figures; submitted to International Journal of Modern
Physic
New global stability estimates for the Gel'fand-Calderon inverse problem
We prove new global stability estimates for the Gel'fand-Calderon inverse
problem in 3D. For sufficiently regular potentials this result of the present
work is a principal improvement of the result of [G. Alessandrini, Stable
determination of conductivity by boundary measurements, Appl. Anal. 27 (1988),
153-172]
Squeezars: Tidally powered stars orbiting a massive black hole
We propose that there exists a class of transient sources, "squeezars", which
are stars caught in highly eccentric orbits around a massive (m<10^8 Mo) black
hole (MBH), whose atypically high luminosity (up to a significant fraction of
their Eddington luminosity) is powered by tidal interactions with the MBH.
Their existence follows from the presence of a mass sink, the MBH, in the
galactic center, which drives a flow of stars into nearly radial orbits to
replace those it has destroyed. We consider two limits for the stellar response
to tidal heating: surface heating with radiative cooling ("hot squeezars") and
bulk heating with adiabatic expansion ("cold squeezars"), and calculate the
evolution of the squeezar orbit, size, luminosity and effective temperature.
The squeezar formation rate is only ~0.05 that of tidal disruption flares, but
squeezar lifetimes are many orders of magnitude longer, and so future
observations of squeezars in nearby galaxies can probe the tidal process that
feeds MBHs and the effects of extreme tides on stars. The mean number of
squeezars orbiting the Galactic MBH is estimated at 0.1-1.Comment: ApJ Lett. accepted. 4 pp. 1 fi
General Statistical properties of the CMB Polarization field
The distribution of the polarization of the Cosmic Microwave Background (CMB)
in the sky is determined by the hypothesis of random Gaussian distribution of
the primordial density perturbations. This hypotheses is well motivated by the
inflationary cosmology. Therefore, the test of consistency of the statistical
properties of the CMB polarization field with the Gaussianity of primordial
density fluctuations is a realistic way to study the nature of primordial
inhomogeneities in the Universe. This paper contains the theoretical
predictions of the general statistical properties of the CMB polarization
field. All results obtained under assumption of the Gaussian nature of the
signal. We pay the special attention to the following two problems. First, the
classification and statistics of the singular points of the polarization field
where polarization is equal to zero. Second, the topology of contours of the
value of the degree of polarization. We have investigated the percolation
properties for the zones of ``strong'' and ``weak'' polarization. We also have
calculated Minkowski functionals for the CMB polarization field. All results
are analytical.Comment: Latex, 22 pages, including 5 figure
Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential
For the Schrodinger equation at fixed energy with a potential supported in a
bounded domain we give formulas and equations for finding scattering data from
the Dirichlet-to-Neumann map with nonzero background potential. For the case of
zero background potential these results were obtained in [R.G.Novikov,
Multidimensional inverse spectral problem for the equation
-\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22,
(1988)]
Peculiarities of anisotropy and polarization as an indicator of noises in the CMB maps
We discuss some new problems of the modern cosmology which arose after the
BOOMERANG and MAXIMA-1 successful missions. Statistics of high peaks of the CMB
anisotropy is analyzed and we discuss possible inner structure of such peaks in
the observational data of future MAP and PLANCK missions. We have investigated
geometrical and statistical properties of the CMB polarization around such high
isolated peaks of anisotropy in the presence of a polarized pixel noise and
point sources. The structure of polarization fields in the vicinity of singular
points with zero polarization is very sensitive to the level of pixel noises
and point sources in the CMB maps.Comment: 9 pages, 2 figure
Homogeneous singularities inside collapsing wormholes
We analyze analytically and numerically the origin of the singularity in the
course of the collapse of a wormhole with the exotic scalar field Psi with
negative energy density, and with this field Psi together with the ordered
magnetic field H. We do this under the simplifying assumptions of the spherical
symmetry and that in the vicinity of the singularity the solution of the
Einstein equations depends only on one coordinate (the homogeneous
approximation). In the framework of these assumptions we found the principal
difference between the case of the collapse of the ordinary scalar field Phi
with the positive energy density together with an ordered magnetic field H and
the collapse of the exotic scalar field Psi together with the magnetic field H.
The later case is important for the possible astrophysical manifestation of the
wormholes.Comment: 10 pages, 5 figures each of which has a),b),c),and d) sub-figures. To
be published in "Physical review. D, Particles, fields, gravitation, and
cosmology
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