Estimation of Primordial Spectrum with post-WMAP 3 year data

In this paper we implement an improved (error sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the WMAP 3 year data to determine the primordial power spectrum assuming different points in the cosmological parameter space for a flat LCDM cosmological model. We also present the preliminary results of the cosmological parameter estimation by assuming a free form of the primordial spectrum, for a reasonably large volume of the parameter space. The recovered spectrum for a considerably large number of the points in the cosmological parameter space has a likelihood far better than a `best fit' power law spectrum up to \Delta \chi^2_{eff} \approx -30. We use Discrete Wavelet Transform (DWT) for smoothing the raw recovered spectrum from the binned data. The results obtained here reconfirm and sharpen the conclusion drawn from our previous analysis of the WMAP 1st year data. A sharp cut off around the horizon scale and a bump after the horizon scale seem to be a common feature for all of these reconstructed primordial spectra. We have shown that although the WMAP 3 year data prefers a lower value of matter density for a power law form of the primordial spectrum, for a free form of the spectrum, we can get a very good likelihood to the data for higher values of matter density. We have also shown that even a flat CDM model, allowing a free form of the primordial spectrum, can give a very high likelihood fit to the data. Theoretical interpretation of the results is open to the cosmology community. However, this work provides strong evidence that the data retains discriminatory power in the cosmological parameter space even when there is full freedom in choosing the primordial spectrum.Comment: 13 pages, 4 figures, uses Revtex4, new analysis and results, references added, matches version accepted to Phys. Rev.

A method for spatial deconvolution of spectra

A method for spatial deconvolution of spectra is presented. It follows the same fundamental principles as the ``MCS image deconvolution algorithm'' (Magain, Courbin, Sohy, 1998) and uses information contained in the spectrum of a reference Point Spread Function (PSF) to spatially deconvolve spectra of very blended sources. An improved resolution rather than an infinite one is aimed at, overcoming the well known problem of ``deconvolution artefacts''. As in the MCS algorithm, the data are decomposed into a sum of analytical point sources and a numerically deconvolved background, so that the spectrum of extended sources in the immediate vicinity of bright point sources may be accurately extracted and sharpened. The algorithm has been tested on simulated data including seeing variation as a function of wavelength and atmospheric refraction. It is shown that the spectra of severely blended point sources can be resolved while fully preserving the spectrophotometric properties of the data. Extended objects ``hidden'' by bright point sources (up to 4-5 magnitudes brighter) can be accurately recovered as well, provided the data have a sufficiently high total signal-to-noise ratio (200-300 per spectral resolution element). Such spectra are relatively easy to obtain, even down to faint magnitudes, within a few hours of integration time with 10m class telescopes.Comment: 18 pages, 6 postscript figures, in press in Ap

Evidence for Proportionate Partition Between the Magnetic Field and Hot Gas in Turbulent Cassiopeia A

We present a deep X-ray observation of the young Galactic supernova remnant Cas A, acquired with the ROSAT High Resolution Imager. This high dynamic range (232 ks) image reveals low-surface-brightness X-ray structure, which appears qualitatively similar to corresponding radio features. We consider the correlation between the X-ray and radio morphologies and its physical implications. After correcting for the inhomogeneous absorption across the remnant, we performed a point by point (4" resolution) surface brightness comparison between the X-ray and radio images. We find a strong (r = 0.75) log-log correlation, implying an overall relationship of $\log(\Sigma_{_{\rm X-ray}}) \propto (2.21\pm0.05) \times \log(\Sigma_{_{\rm radio}})$. This is consistent with proportionate partition (and possibly equipartition) between the local magnetic field and the hot gas --- implying that Cas A's plasma is fully turbulent and continuously amplifying the magnetic field.Comment: 8 pages with embedded bitmapped figures, Accepted by ApJ Letters 5/1/9

Singular limit of Hele-Shaw flow and dispersive regularization of shock waves

We study a family of solutions to the Saffman-Taylor problem with zero surface tension at a critical regime. In this regime, the interface develops a thin singular finger. The flow of an isolated finger is given by the Whitham equations for the KdV integrable hierarchy. We show that the flow describing bubble break-off is identical to the Gurevich-Pitaevsky solution for regularization of shock waves in dispersive media. The method provides a scheme for the continuation of the flow through singularites.Comment: Some typos corrected, added journal referenc

Exact Resummations in the Theory of Hydrodynamic Turbulence: I The Ball of Locality and Normal Scaling

This paper is the first in a series of three papers that aim at understanding the scaling behaviour of hydrodynamic turbulence. We present in this paper a perturbative theory for the structure functions and the response functions of the hydrodynamic velocity field in real space and time. Starting from the Navier-Stokes equations (at high Reynolds number Re) we show that the standard perturbative expansions that suffer from infra-red divergences can be exactly resummed using the Belinicher-L'vov transformation. After this exact (partial) resummation it is proven that the resulting perturbation theory is free of divergences, both in large and in small spatial separations. The hydrodynamic response and the correlations have contributions that arise from mediated interactions which take place at some space- time coordinates. It is shown that the main contribution arises when these coordinates lie within a shell of a "ball of locality" that is defined and discussed. We argue that the real space-time formalism developed here offers a clear and intuitive understanding of every diagram in the theory, and of every element in the diagrams. One major consequence of this theory is that none of the familiar perturbative mechanisms may ruin the classical Kolmogorov (K41) scaling solution for the structure functions. Accordingly, corrections to the K41 solutions should be sought in nonperturbative effects. These effects are the subjects of papers II and III in this series, that will propose a mechanism for anomalous scaling in turbulence, which in particular allows multiscaling of the structure functions.Comment: PRE in press, 18 pages + 6 figures, REVTeX. The Eps files of figures will be FTPed by request to [email protected]

Chandra X-ray Observations of the Quadruply Lensed Quasar RX J0911.4+0551

We present results from X-ray observations of the quadruply lensed quasar RX J0911.4+0551 using data obtained with the Advanced CCD Imaging Spectrometer (ACIS) on board the Chandra X-ray Observatory. The 29 ks observation detects a total of ~404 X-ray photons (0.3 to 7.0 keV) from the four images of the lensed quasar. Deconvolution of the aspect corrected data resolves all four lensed images, with relative positions in good agreement with optical measurements. When compared to contemporaneous optical data, one of the lensed images (component A3) is dimmer by a factor of ~6 in X-rays with respect to the 2 brighter images (components A1 and A2). Spectral fitting for the combined images shows significant intrinsic absorption in the soft (0.2 to 2.4 keV) energy band, consistent with the mini-BAL nature of this quasar, while a comparison with ROSAT PSPC observations from 1990 shows a drop of ~6.5 in the total soft bandpass flux. The observations also detect ~157 X-ray photons arising from extended emission of the nearby cluster (peaked ~42" SW of RXJ0911.4+0551) responsible for the large external shear present in the system. The Chandra observation reveals the cluster emission to be complex and non-spherical, and yields a cluster temperature of kT = 2.3^{+1.8}_{-0.8} keV and a 2.0 to 10 keV cluster luminosity within a 1 Mpc radius of L_X = 7.6_{-0.2}^{+0.6} x 10^{43} ergs/s (error bars denote 90% confidence limits). Our mass estimate of the cluster within its virial radius is 2.3^{+1.8}_{-0.7} x 10^{14} solar, and is a factor of 2 smaller than, although consistent with, previous mass estimates based on the observed cluster velocity dispersion.Comment: 16 pages, 3 figures (figure 1 is color ps). Accepted by Ap

Velocity Statistics in the Two-Dimensional Granular Turbulence

We studied the macroscopic statistical properties on the freely evolving quasi-elastic hard disk (granular) system by performing a large-scale (up to a few million particles) event-driven molecular dynamics systematically and found that remarkably analogous to an enstrophy cascade process in the decaying two-dimensional fluid turbulence. There are four typical stages in the freely evolving inelastic hard disk system, which are homogeneous, shearing (vortex), clustering and final state. In the shearing stage, the self-organized macroscopic coherent vortices become dominant. In the clustering stage, the energy spectra are close to the expectation of Kraichnan-Batchelor theory and the squared two-particle separation strictly obeys Richardson law.Comment: 4 pages, 4 figures, to be published in PR

Relative dispersion in fully developed turbulence: The Richardson's Law and Intermittency Corrections

Relative dispersion in fully developed turbulence is investigated by means of direct numerical simulations. Lagrangian statistics is found to be compatible with Richardson description although small systematic deviations are found. The value of the Richardson constant is estimated as $C_2 \simeq 0.55$, in a close agreement with recent experimental findings [S. Ott and J. Mann J. Fluid Mech. {\bf 422}, 207 (2000)]. By means of exit-time statistics it is shown that the deviations from Richardson's law are a consequence of Eulerian intermittency. The measured Lagrangian scaling exponents require a set of Eulerian structure function exponents $\zeta_{p}$ which are remarkably close to standard ones known for fully developed turbulence