The Nonlinear Redshift Space Power Spectrum: Omega from Redshift Surveys

We examine the anisotropies in the power spectrum by the mapping of real to redshift space. Using the Zel'dovich approximation, we obtain an analytic expression for the nonlinear redshift space power spectrum in the distant observer limit. For a given unbiased galaxy distribution in redshift space, the anisotropies in the power spectrum depend on the parameter $f(\Omega)\approx \Omega^{0.6}$, where $\Omega$ is the density parameter. We quantify these anisotropies by the ratio, $R$, of the quadrupole to monopole angular moments of the power spectrum. In contrast to linear theory, the Zel'dovich approximation predicts a decline in $R$ with decreasing scale. This departure from linear theory is due to nonlinear dynamics and not a result of incoherent random velocities. The rate of decline depends strongly on $\Omega$ and the initial power spectrum. However, we find a {\it universal} relation between the quantity $R/R_{lin}$ (where $R_{lin}$ the linear theory value of $R$) and the dimensionless variable $k/k_{nl}$, where $k_{nl}$ is a wavenumber determined by the scale of nonlinear structures. The universal relation is in good agreement with a large N-body simulation. This universal relation greatly extends the scales over which redshift distortions can be used as a probe of $\Omega$. A preliminary application to the 1.2 Jy IRAS yields $\Omega\sim 0.4$ if IRAS galaxies are unbiased.Comment: uuencoded compressed postscript. The preprint is also available at http://www.ast.cam.ac.uk/preprint/PrePrint.htm

Radiative Transfer Effect on Ultraviolet Pumping of the 21cm Line in the High Redshift Universe

During the epoch of reionization the 21cm signal is sensitive to the scattering rate of the ultraviolet photons, redshifting across the Lyman_alpha resonance. Here we calculate the photon scattering rate profile for a single ultraviolet source. After taking into account previously neglected natural broadening of the resonance line, we find that photons approach the resonance frequency and experience most scatterings at a significantly smaller distance from the source than naively expected r=(dnu/nu_0)(c/H), where dnu=nu-nu_0 is the initial frequency offset, and the discrepancy increases as the initial frequency offset decreases. As a consequence, the scattering rate P(r) drops much faster with increasing distance than the previously assumed 1/r^2 profile. Near the source (r<1Mpc comoving), the scattering rate of photons that redshift into the Ly_alpha resonance converges to P(r) \propto r^{-7/3}. The scattering rate of Ly_alpha photons produced by splitting of photons that redshift into a higher resonance (Ly_gamma, Ly_delta, etc.) is only weakly affected by the radiative transfer, while the sum of scattering rates of Ly_alpha photons produced from all higher resonances also converges to P(r) \propto r^{-7/3} near the source. At 15<z<35, on scales of ~0.01-20Mpc/h (comoving), the total scattering rate of Ly_alpha photons from all Lyman resonances is found to be higher by a factor of ~1+0.3[(1+z)/20]^{2/3} than obtained without full radiative transfer. Consequently, during the early stage of reionization, the differential brightness of 21cm signal against the cosmic microwave background is also boosted by a similar factor.Comment: 7 pages, 4 figures, submitted to Ap

The impact of galactic winds from LBGs on the Intergalactic Medium

An excess of sight-lines close to Lyman-break galaxies (LBGs) with little or no absorption in QSO absorption spectra has been reported and has been interpreted as the effect of galactic winds on the Intergalactic Medium. We use here numerical simulations to investigate the flux probability function close to plausible sites of LBGs. We show that the flux distribution near our LBGs in the simulation depends strongly on redshift, and is very sensitive to the averaging procedure. We show that a model without galactic winds and a model with a wind bubble size of 0.5Mpc/h (comoving) are equally consistent with the new determination of the conditional flux distribution by Adelberger et al. (2005). Models with the larger bubble sizes suggested by the previous observations of Adelberger et al. (2003) based on a much smaller sample at higher redshift are not consistent with the new data. We therefore argue that the volume filling factor of galactic winds driven by LBGs may be much smaller than previously thought, and that most of the metals responsible for the metal absorption associated with the low column density Lya forest are unlikely to have been ejected by LBGs.Comment: 5 pages, 3 figure

A direct probe of cosmological power spectra of the peculiar velocity field and the gravitational lensing magnification from photometric redshift surveys

The cosmological peculiar velocity field (deviations from the pure Hubble flow) of matter carries significant information on dark energy, dark matter and the underlying theory of gravity on large scales. Peculiar motions of galaxies introduce systematic deviations between the observed galaxy redshifts z and the corresponding cosmological redshifts z_cos. A novel method for estimating the angular power spectrum of the peculiar velocity field based on observations of galaxy redshifts and apparent magnitudes m (or equivalently fluxes) is presented. This method exploits the fact that a mean relation between z_cos and m of galaxies can be derived from all galaxies in a redshift-magnitude survey. Given a galaxy magnitude, it is shown that the z_cos(m) relation yields its cosmological redshift with a 1-sigma error of sigma_z~0.3 for a survey like Euclid (~10^9 galaxies at z<~2), and can be used to constrain the angular power spectrum of z-z_cos(m) with a high signal-to-noise ratio. At large angular separations corresponding to l<~15, we obtain significant constraints on the power spectrum of the peculiar velocity field. At 15<~l<~60, magnitude shifts in the z_cos(m) relation caused by gravitational lensing magnification dominate, allowing us to probe the line-of-sight integral of the gravitational potential. Effects related to the environmental dependence in the luminosity function can easily be computed and their contamination removed from the estimated power spectra. The amplitude of the combined velocity and lensing power spectra at z~1 can be measured with <~5% accuracy.Comment: 22 pages, 3 figures; added a discussion of systematic errors, accepted for publication in JCA

Neonatal sepsis syndrome (early onset)

This issue of eMedRef provides information to clinicians on the pathophysiology, diagnosis, and therapeutics of early onset neonatal sepsis syndrome

Patchy He II reionization and the physical state of the IGM

We present a Monte-Carlo model of He II reionization by QSOs and its effect on the thermal state of the clumpy intergalactic medium (IGM). The model assumes that patchy reionization develops as a result of the discrete distribution of QSOs. It includes various recipes for the propagation of the ionizing photons, and treats photo-heating self-consistently. The model provides the fraction of He III, the mean temperature in the IGM, and the He II mean optical depth -- all as a function of redshift. It also predicts the evolution of the local temperature versus density relation during reionization. Our findings are as follows: The fraction of He III increases gradually until it becomes close to unity at $z\sim 2.8-3.0$. The He II mean optical depth decreases from $\tau\sim 10$ at $z\geq 3.5$ to $\tau\leq 0.5$ at $z\leq 2.5$. The mean temperature rises gradually between $z\sim 4$ and $z\sim 3$ and declines slowly at lower redshifts. The model predicts a flattening of the temperature-density relation with significant increase in the scatter during reionization at $z\sim 3$. Towards the end of reionization the scatter is reduced and a tight relation is re-established. This scatter should be incorporated in the analysis of the Ly$\alpha$ forest at $z\leq 3$. Comparison with observational results of the optical depth and the mean temperature at moderate redshifts constrains several key physical parameters.Comment: 18 pages, 9 figures; Changed content. Accepted for publication in MNRA

Polygon Placement Revisited: (Degree of Freedom + 1)-SUM Hardness and an Improvement via Offline Dynamic Rectangle Union

We revisit the classical problem of determining the largest copy of a simple polygon $P$ that can be placed into a simple polygon $Q$. Despite significant effort, known algorithms require high polynomial running times. (Barequet and Har-Peled, 2001) give a lower bound of $n^{2-o(1)}$ under the 3SUM conjecture when $P$ and $Q$ are (convex) polygons with $\Theta(n)$ vertices each. This leaves open whether we can establish (1) hardness beyond quadratic time and (2) any superlinear bound for constant-sized $P$ or $Q$. In this paper, we affirmatively answer these questions under the $k$SUM conjecture, proving natural hardness results that increase with each degree of freedom (scaling, $x$-translation, $y$-translation, rotation): (1) Finding the largest copy of $P$ that can be $x$-translated into $Q$ requires time $n^{2-o(1)}$ under the 3SUM conjecture. (2) Finding the largest copy of $P$ that can be arbitrarily translated into $Q$ requires time $n^{2-o(1)}$ under the 4SUM conjecture. (3) The above lower bounds are almost tight when one of the polygons is of constant size: we obtain an $\tilde O((pq)^{2.5})$-time algorithm for orthogonal polygons $P,Q$ with $p$ and $q$ vertices, respectively. (4) Finding the largest copy of $P$ that can be arbitrarily rotated and translated into $Q$ requires time $n^{3-o(1)}$ under the 5SUM conjecture. We are not aware of any other such natural $($degree of freedom $+ 1)$-SUM hardness for a geometric optimization problem