A Small-Scale Modification to the Lensing Kernel

Calculations of the Cosmic Microwave Background lensing power implemented into the standard cosmological codes such as CAMB and CLASS usually treat the surface of last scatter as an infinitely thin screen. However, since the CMB anisotropies are smoothed out on scales smaller than the diffusion length due to the effect of Silk damping, the photons which carry information about the small-scale density distribution come from slightly earlier times than the standard recombination time. The dominant effect is the scale dependence of the mean redshift associated with the fluctuations during recombination. We find that fluctuations at $k = 0.01 {\rm \ Mpc^{-1}}$ come from a characteristic redshift of $z \approx 1090$, while fluctuations at $k = 0.3 {\rm \ Mpc^{-1}}$ come from a characteristic redshift of $z \approx 1130$. We then estimate the corrections to the lensing kernel and the related power spectra due to this effect. We conclude that neglecting it would result in a deviation from the true value of the lensing kernel at the half percent level at small CMB scales. For an all-sky, noise-free experiment, this corresponds to a $\sim 0.1 \sigma$ shift in the observed temperature power spectrum on small scales ($2500 \lesssim l \lesssim 4000$).Comment: 5 pages, 5 figure

The Coyote Universe I: Precision Determination of the Nonlinear Matter Power Spectrum

Near-future cosmological observations targeted at investigations of dark energy pose stringent requirements on the accuracy of theoretical predictions for the clustering of matter. Currently, N-body simulations comprise the only viable approach to this problem. In this paper we demonstrate that N-body simulations can indeed be sufficiently controlled to fulfill these requirements for the needs of ongoing and near-future weak lensing surveys. By performing a large suite of cosmological simulation comparison and convergence tests we show that results for the nonlinear matter power spectrum can be obtained at 1% accuracy out to k~1 h/Mpc. The key components of these high accuracy simulations are: precise initial conditions, very large simulation volumes, sufficient mass resolution, and accurate time stepping. This paper is the first in a series of three, with the final aim to provide a high-accuracy prediction scheme for the nonlinear matter power spectrum.Comment: 18 pages, 22 figures, minor changes to address referee repor

The Lyman-alpha forest at redshifts 0.1 -- 1.6: good agreement between a large hydrodynamic simulation and HST spectra

We give a comprehensive statistical description of the Lyman-alpha absorption from the intergalactic medium in a hydrodynamic simulation at redshifts 0.1-1.6, the range of redshifts covered by HST spectra of QSOs. We use the ENZO code to make a 76 comoving Mpc cube simulation using 75 kpc cells, for a Hubble constant of 71 km/s/Mpc. The best prior work, by \citet{dave99},used an SPH simulation in a 15.6 Mpc box with an effective resolution of 245 kpc and slightly different cosmological parameters. At redshifts z=2 this simulation is different from data. \citet{tytler07b} found that the simulated spectra at z=2 have too little power on large scales, Lyman-alpha lines are too wide, there is a lack high column density lines, and there is a lack of pixels with low flux. Here we present statistics at z<1.6, including the flux distribution, the mean flux, the effective opacity, and the power and correlation of the flux. We also give statistics of the lyman alpha lines including the line width distribution, the column density distribution, the number of lines per unit equivalent width and redshift, and the correlation between the line width and column density. We find that the mean amount of absorption in the simulated spectra changes smoothly with redshift with DA(z)=0.01(1+z)^{2.25}. Both the trend and absolute values are close to measurements of HST spectra by \citet{kirkman07a}. The column density and line width distributions are also close to those measured from HST spectra by \citet{janknecht06a}, except for the mode of the line width distribution which is smaller in the HST spectra. Although some differences that we saw at z=2 are too subtle to be seen in existing HST spectra, overall, the simulation gives an good description of HST spectra at 0.1<z<1.6

Searching for hidden mirror symmetries in CMB fluctuations from WMAP 7 year maps

We search for hidden mirror symmetries at large angular scales in the WMAP 7 year Internal Linear Combination map of CMB temperature anisotropies using global pixel based estimators introduced for this aim. Two different axes are found for which the CMB intensity pattern is anomalously symmetric (or anti-symmetric) under reflection with respect to orthogonal planes at the 99.84(99.96)% CL (confidence level), if compared to a result for an arbitrary axis in simulations without the symmetry. We have verified that our results are robust to the introduction of the galactic mask. The direction of such axes is close to the CMB kinematic dipole and nearly orthogonal to the ecliptic plane, respectively. If instead the real data are compared to those in simulations taken with respect to planes for which the maximal mirror symmetry is generated by chance, the confidence level decreases to 92.39 (76.65)%. But when the effect in question translates into the anomalous alignment between normals to planes of maximal mirror (anti)-symmetry and these natural axes mentioned. We also introduce the representation of the above estimators in the harmonic domain, confirming the results obtained in the pixel one. The symmetry anomaly is shown to be almost entirely due to low multipoles, so it may have a cosmological and even primordial origin. Contrary, the anti-symmetry one is mainly due to intermediate multipoles that probably suggests its non-fundamental nature. We have demonstrated that these anomalies are not connected to the known issue of the low variance in WMAP observations and we have checked that axially symmetric parts of these anomalies are small, so that the axes are not the symmetry ones.Comment: 18 pages, 10 figures, 2 tables. Consideration and discussion expanded, 5 figures and 1 table added, main conclusions unchange

Sunyaev Zel'dovich Effect Observations of Strong Lensing Galaxy Clusters: Probing the Over-Concentration Problem

We have measured the Sunyaev Zel'dovich (SZ) effect for a sample of ten strong lensing selected galaxy clusters using the Sunyaev Zel'dovich Array (SZA). The SZA is sensitive to structures on spatial scales of a few arcminutes, while the strong lensing mass modeling constrains the mass at small scales (typically < 30"). Combining the two provides information about the projected concentrations of the strong lensing clusters. The Einstein radii we measure are twice as large as expected given the masses inferred from SZ scaling relations. A Monte Carlo simulation indicates that a sample randomly drawn from the expected distribution would have a larger median Einstein radius than the observed clusters about 3% of the time. The implied overconcentration has been noted in previous studies with smaller samples of lensing clusters. It persists for this sample, with the caveat that this could result from a systematic effect such as if the gas fractions of the strong lensing clusters are substantially below what is expected.Comment: submitte

On the Baryon Fractions in Clusters and Groups of Galaxies

We present the baryon fractions of 2MASS groups and clusters as a function of cluster richness using total and gas masses measured from stacked ROSAT X-ray data and stellar masses estimated from the infrared galaxy catalogs. We detect X-ray emission even in the outskirts of clusters, beyond r_200 for richness classes with X-ray temperatures above 1 keV. This enables us to more accurately determine the total gas mass in these groups and clusters. We find that the optically selected groups and clusters have flatter temperature profiles and higher stellar-to-gas mass ratios than the individually studied, X-ray bright clusters. We also find that the stellar mass in poor groups with temperatures below 1 keV is comparable to the gas mass in these systems. Combining these results with individual measurements for clusters, groups, and galaxies from the literature, we find a break in the baryon fraction at ~1 keV. Above this temperature, the baryon fraction scales with temperature as f_b \propto T^0.20\pm0.03. We see significantly smaller baryon fractions below this temperature, and the baryon fraction of poor groups joins smoothly onto that of systems with still shallower potential wells such as normal and dwarf galaxies where the baryon fraction scales with the inferred velocity dispersion as f_b \propto \sigma^1.6. The small scatter in the baryon fraction at any given potential well depth favors a universal baryon loss mechanism and a preheating model for the baryon loss. The scatter is, however, larger for less massive systems. Finally, we note that although the broken power-law relation can be inferred from data points in the literature alone, the consistency between the baryon fractions for poor groups and massive galaxies inspires us to fit the two categories of objects (galaxies and clusters) with one relation.Comment: 21 pages, 5 figures, ApJ in pres

Constraining the Scatter in the Mass-Richness Relation of maxBCG Clusters With Weak Lensing and X-ray Data

We measure the logarithmic scatter in mass at fixed richness for clusters in the maxBCG cluster catalog, an optically selected cluster sample drawn from SDSS imaging data. Our measurement is achieved by demanding consistency between available weak lensing and X-ray measurements of the maxBCG clusters, and the X-ray luminosity--mass relation inferred from the 400d X-ray cluster survey, a flux limited X-ray cluster survey. We find \sigma_{\ln M|N_{200}}=0.45^{+0.20}_{-0.18} (95% CL) at N_{200} ~ 40, where N_{200} is the number of red sequence galaxies in a cluster. As a byproduct of our analysis, we also obtain a constraint on the correlation coefficient between \ln Lx and \ln M at fixed richness, which is best expressed as a lower limit, r_{L,M|N} >= 0.85 (95% CL). This is the first observational constraint placed on a correlation coefficient involving two different cluster mass tracers. We use our results to produce a state of the art estimate of the halo mass function at z=0.23 -- the median redshift of the maxBCG cluster sample -- and find that it is consistent with the WMAP5 cosmology. Both the mass function data and its covariance matrix are presented.Comment: 14 pages, 6 figures, submitted to Ap

Cosmological Constraints from the SDSS maxBCG Cluster Catalog

We use the abundance and weak lensing mass measurements of the SDSS maxBCG cluster catalog to simultaneously constrain cosmology and the richness--mass relation of the clusters. Assuming a flat \LambdaCDM cosmology, we find \sigma_8(\Omega_m/0.25)^{0.41} = 0.832\pm 0.033 after marginalization over all systematics. In common with previous studies, our error budget is dominated by systematic uncertainties, the primary two being the absolute mass scale of the weak lensing masses of the maxBCG clusters, and uncertainty in the scatter of the richness--mass relation. Our constraints are fully consistent with the WMAP five-year data, and in a joint analysis we find \sigma_8=0.807\pm 0.020 and \Omega_m=0.265\pm 0.016, an improvement of nearly a factor of two relative to WMAP5 alone. Our results are also in excellent agreement with and comparable in precision to the latest cosmological constraints from X-ray cluster abundances. The remarkable consistency among these results demonstrates that cluster abundance constraints are not only tight but also robust, and highlight the power of optically-selected cluster samples to produce precision constraints on cosmological parameters.Comment: comments welcom

A combined measurement of cosmic growth and expansion from clusters of galaxies, the CMB and galaxy clustering

Combining galaxy cluster data from the ROSAT All-Sky Survey and the Chandra X-ray Observatory, cosmic microwave background data from the Wilkinson Microwave Anisotropy Probe, and galaxy clustering data from the WiggleZ Dark Energy Survey, the 6-degree Field Galaxy Survey and the Sloan Digital Sky Survey III, we test for consistency the cosmic growth of structure predicted by General Relativity (GR) and the cosmic expansion history predicted by the cosmological constant plus cold dark matter paradigm (LCDM). The combination of these three independent, well studied measurements of the evolution of the mean energy density and its fluctuations is able to break strong degeneracies between model parameters. We model the key properties of cosmic growth with the normalization of the matter power spectrum, sigma_8, and the cosmic growth index, gamma, and those of cosmic expansion with the mean matter density, Omega_m, the Hubble constant, H_0, and a kinematical parameter equivalent to that for the dark energy equation of state, w. For a spatially flat geometry, w=-1, and allowing for systematic uncertainties, we obtain sigma_8=0.785+-0.019 and gamma=0.570+0.064-0.063 (at the 68.3 per cent confidence level). Allowing both w and gamma to vary we find w=-0.950+0.069-0.070 and gamma=0.533+-0.080. To further tighten the constraints on the expansion parameters, we also include supernova, Cepheid variable and baryon acoustic oscillation data. For w=-1, we have gamma=0.616+-0.061. For our most general model with a free w, we measure Omega_m=0.278+0.012-0.011, H_0=70.0+-1.3 km s^-1 Mpc^-1 and w=-0.987+0.054-0.053 for the expansion parameters, and sigma_8=0.789+-0.019 and gamma=0.604+-0.078 for the growth parameters. These results are in excellent agreement with GR+LCDM (gamma~0.55; w=-1) and represent the tightest and most robust simultaneous constraint on cosmic growth and expansion to date.Comment: 14 pages, 5 figures, 1 table. Matches the accepted version for MNRAS. New sections 3 and 6 added, containing 2 new figures. Table extended. The results including BAO data have been slightly modified due to an updated BAO analysis. Conclusions unchange