Oscillations and instabilities of fast and differentially rotating relativistic stars

We study non-axisymmetric oscillations of rapidly and differentially rotating relativistic stars in the Cowling approximation. Our equilibrium models are sequences of relativistic polytropes, where the differential rotation is described by the relativistic $j$-constant law. We show that a small degree of differential rotation raises the critical rotation value for which the quadrupolar f-mode becomes prone to the CFS instability, while the critical value of $T/|W|$ at the mass-shedding limit is raised even more. For softer equations of state these effects are even more pronounced. When increasing differential rotation further to a high degree, the neutral point of the CFS instability first reaches a local maximum and is lowered afterwards. For stars with a rather high compactness we find that for a high degree of differential rotation the absolute value of the critical $T/|W|$ is below the corresponding value for rigid rotation. We conclude that the parameter space where the CFS instability is able to drive the neutron star unstable is increased for a small degree of differential rotation and for a large degree at least in stars with a higher compactness.Comment: 16 pages, 11 figures; paper accepted for publication in Phys. Rev. D (81.084019

Measuring patchy reionisation with kSZ2^2-21 cm correlations

We study cross-correlations of the kinetic Sunyaev-Zel'dovich effect (kSZ) and 21 cm signals during the epoch of reionisation (EoR) to measure the effects of patchy reionisation. Since the kSZ effect is proportional to the line-of-sight velocity, the kSZ-21 cm cross correlation suffers from cancellation at small angular scales. We thus focus on the correlation between the kSZ-squared field (kSZ$^2$) and 21 cm signals. When the global ionisation fraction is low ($x_e\lesssim 0.7$), the kSZ$^2$ fluctuation is dominated by rare ionised bubbles which leads to an anti-correlation with the 21 cm signal. When $0.8\lesssim x_e<1$, the correlation is dominated by small pockets of neutral regions, leading to a positive correlation. However, at very high redshifts when $x_e<0.15$, the spin temperature fluctuations change the sign of the correlation from negative to positive, as weakly ionised regions can have strong 21 cm signals in this case. To extract this correlation, we find that Wiener filtering is effective in removing large signals from the primary CMB anisotropy. The expected signal-to-noise ratios for a $\sim$10-hour integration of upcoming Square Kilometer Array data cross-correlated with maps from the current generation of CMB observatories with 3.4~$\mu$K arcmin noise and 1.7~arcmin beam over 100~deg$^2$ are 51, 60, and 37 for $x_e=0.2$, 0.5, and 0.9, respectively.Comment: 7pages, 7 figure

Kink Solution in a Fluid Model of Traffic Flows

Traffic jam in a fluid model of traffic flows proposed by Kerner and Konh\"auser (B. S. Kerner and P. Konh\"auser, Phys. Rev. E 52 (1995), 5574.) is analyzed. An analytic scaling solution is presented near the critical point of the hetero-clinic bifurcation. The validity of the solution has been confirmed from the comparison with the simulation of the model.Comment: RevTeX v3.1, 6 pages, and 2 figure

Modeling Intra-Cluster Gas in Triaxial Dark Halos : An Analytical Approach

We present the first physical model for the non-spherical intra-cluster gas distribution in hydrostatic equilibrium under the gravity of triaxial dark matter halos. Adopting the concentric triaxial density profiles of the dark halos with constant axis ratios proposed by Jing & Suto (2002), we derive an analytical expression for the triaxial halo potential on the basis of the perturbation theory, and find the hydrostatic solutions for the gas density and temperature profiles both in isothermal and polytropic equations of state. The resulting iso-potential surfaces are well approximated by triaxial ellipsoids with the eccentricities dependent on the radial distance. We also find a formula for the eccentricity ratio between the intra-cluster gas and the underlying dark halo. Our results allow one to determine the shapes of the underlying dark halos from the observed intra-cluster gas through the X-ray and/or the Sunyaev-Zel'dovich effects clusters.Comment: accepted by ApJ, LaTex file, 22 pages, 8 postscript figure

Leaf area index and topographical effects on turburlent diffusion in a deciduous forest

In order to investigate turbulent diffusion in a deciduous forest canopy, wind velocity measurements were conducted from late autumn of 2009 to early spring of 2010, using an observation tower 20 m in height located in the campus of Kanazawa University. Four sonic anemometers mounted on the tower recorded the average wind velocities and temperatures, as well as their fluctuations, at four different heights simultaneously. Two different types of data sets were selected, in which the wind velocities, wind bearings and atmospheric stabilities were all similar, but the Leaf Area Indexes (LAI's) were different. Vertical profiles of average wind velocities were found to have an approximately exponential profile in each case. The characteristic length scales of turbulence were evaluated by both von Karman's method and the integral time scale deduced from the autocorrelation from time-series analyses. Both methods produced comparable values of eddy diffusivity for the cases with some foliage during late autumn, but some discrepancy in the upper canopy layer was observed when the trees did not have their leaves in early spring. It was also found that the eddy diffusivities generally take greater values at higher positions, where the wind speeds are large. Anisotropy of eddy diffusivities between the vertical and horizontal components was also observed, particularly in the cases when the canopy does not have leaves, when the horizontal eddy diffusivities are generally larger than the vertical ones. On the other hand, the anisotropy is less visible when the trees have some foliage during autumn. The effects of topography on the turbulent diffusion were also investigated, including evaluation of the non-zero time-averaged vertical wind velocities. The results show that the effects are marginal for both cases, and can be neglected as far as diffusion in the canopy is concerned

Hot and cold spots counts as probes of non-Gaussianity in the CMB

We introduce the numbers of hot and cold spots, $n_h$ and $n_c$, of excursion sets of the CMB temperature anisotropy maps as statistical observables that can discriminate different non-Gaussian models. We numerically compute them from simulations of non-Gaussian CMB temperature fluctuation maps. The first kind of non-Gaussian model we study is the local type primordial non-Gaussianity. The second kind of models have some specific form of the probability distribution function from which the temperature fluctuation value at each pixel is drawn, obtained using HEALPIX. We find the characteristic non-Gaussian deviation shapes of $n_h$ and $n_c$, which is distinct for each of the models under consideration. We further demonstrate that $n_h$ and $n_c$ carry additional information compared to the genus, which is just their linear combination, making them valuable additions to the Minkowski Functionals in constraining non-Gaussianity.Comment: 17 pages, accepted for publication in Ap

Position-dependent power spectra of the 21-cm signal from the epoch of reionization

The 21-cm signal from the epoch of reionization is non-Gaussian. Current radio telescopes are focused on detecting the 21-cm power spectrum, but in the future the Square Kilometre Array is anticipated to provide a first measurement of the bispectrum. Previous studies have shown that the position-dependent power spectrum is a simple and efficient way to probe the squeezed-limit bispectrum. In this approach, the survey is divided into subvolumes and the correlation between the local power spectrum and the corresponding mean density of the subvolume is computed. This correlation is equivalent to an integral of the bispectrum in the squeezed limit, but is much simpler to implement than the usual bispectrum estimators. It also has a clear physical interpretation: it describes how the small-scale power spectrum of tracers such as galaxies and the 21-cm signal respond to a large-scale environment. Reionization naturally couples large and small scales as ionizing radiation produced by galactic sources can travel up to tens of Megaparsecs through the intergalactic medium during this process. Here we apply the position-dependent power spectrum approach to fluctuations in the 21-cm background from reionization. We show that this statistic has a distinctive evolution in time that can be understood with a simple analytic model. We also show that the statistic can easily distinguish between simple "inside-out" and "outside-in" models of reionization. The position-dependent power spectrum is thus a promising method to validate the reionization signal and to extract higher-order information on this process.Comment: 24 pages, 10 figures, accepted in JCA

Primordial Non-Gaussianity and Analytical Formula for Minkowski Functionals of the Cosmic Microwave Background and Large-scale Structure

We derive analytical formulae for the Minkowski Functions of the cosmic microwave background (CMB) and large-scale structure (LSS) from primordial non-Gaussianity. These formulae enable us to estimate a non-linear coupling parameter, f_NL, directly from the CMB and LSS data without relying on numerical simulations of non-Gaussian primordial fluctuations. One can use these formulae to estimate statistical errors on f_NL from Gaussian realizations, which are much faster to generate than non-Gaussian ones, fully taking into account the cosmic/sampling variance, beam smearing, survey mask, etc. We show that the CMB data from the Wilkinson Microwave Anisotropy Probe should be sensitive to |f_NL|\simeq 40 at the 68% confidence level. The Planck data should be sensitive to |f_NL|\simeq 20. As for the LSS data, the late-time non-Gaussianity arising from gravitational instability and galaxy biasing makes it more challenging to detect primordial non-Gaussianity at low redshifts. The late-time effects obscure the primordial signals at small spatial scales. High-redshift galaxy surveys at z>2 covering \sim 10Gpc^3 volume would be required for the LSS data to detect |f_NL|\simeq 100. Minkowski Functionals are nicely complementary to the bispectrum because the Minkowski Functionals are defined in real space and the bispectrum is defined in Fourier space. This property makes the Minksowski Functionals a useful tool in the presence of real-world issues such as anisotropic noise, foreground and survey masks. Our formalism can be extended to scale-dependent f_NL easily.Comment: 16 pages, 5 figures, accepted for publication in ApJ (Vol. 653, 2006

Relativistic stars with purely toroidal magnetic fields

We investigate the effects of the purely toroidal magnetic field on the equilibrium structures of the relativistic stars. The master equations for obtaining equilibrium solutions of relativistic rotating stars containing purely toroidal magnetic fields are derived for the first time. To solve these master equations numerically, we extend the Cook-Shapiro-Teukolsky scheme for calculating relativistic rotating stars containing no magnetic field to incorporate the effects of the purely toroidal magnetic fields. By using the numerical scheme, we then calculate a large number of the equilibrium configurations for a particular distribution of the magnetic field in order to explore the equilibrium properties. We also construct the equilibrium sequences of the constant baryon mass and/or the constant magnetic flux, which model the evolution of an isolated neutron star as it loses angular momentum via the gravitational waves. Important properties of the equilibrium configurations of the magnetized stars obtained in this study are summarized as follows ; (1) For the non-rotating stars, the matter distribution of the stars is prolately distorted due to the toroidal magnetic fields. (2) For the rapidly rotating stars, the shape of the stellar surface becomes oblate because of the centrifugal force. But, the matter distribution deep inside the star is sufficiently prolate for the mean matter distribution of the star to be prolate. (3) The stronger toroidal magnetic fields lead to the mass-shedding of the stars at the lower angular velocity. (4) For some equilibrium sequences of the constant baryon mass and magnetic flux, the stars can spin up as they lose angular momentum.Comment: 13 figures, 7 tables, submitted to PR

Temperature and Polarization CMB Maps from Primordial non-Gaussianities of the Local Type

The forthcoming Planck experiment will provide high sensitivity polarization measurements that will allow us to further tighten the f_NL bounds from the temperature data. Monte Carlo simulations of non-Gaussian CMB maps have been used as a fundamental tool to characterize non-Gaussian signatures in the data, as they allow us to calibrate any statistical estimators and understand the effect of systematics, foregrounds and other contaminants. We describe an algorithm to generate high-angular resolution simulations of non-Gaussian CMB maps in temperature and polarization. We consider non-Gaussianities of the local type, for which the level of non-Gaussianity is defined by the dimensionless parameter, f_NL. We then apply the temperature and polarization fast cubic statistics recently developed by Yadav et al. to a set of non-Gaussian temperature and polarization simulations. We compare our results to theoretical expectations based on a Fisher matrix analysis, test the unbiasedness of the estimator, and study the dependence of the error bars on f_NL. All our results are in very good agreement with theoretical predictions, thus confirming the reliability of both the simulation algorithm and the fast cubic temperature and polarization estimator.Comment: 14 pages, 9 figures, revised version accepted by PRD, minor changes and acknowledgements adde