arXiv subjects

Bhuvnesh Jain

Publications and source records attributed to Bhuvnesh Jain.

At least 145 records · Page 8Linked to original sources

arXiv2004

Cosmological Parameters from Eigenmode Analysis of Sloan Digital Sky Survey Galaxy Redshifts

We present estimates of cosmological parameters from the application of the Karhunen-Loeve transform to the analysis of the 3D power spectrum of density fluctuations using Sloan Digital Sky Survey galaxy redshifts. We use Omega_m*h and f_b = Omega_b/Omega_m to describe the shape of the power spectrum, sigma8 for the (linearly extrapolated) normalization, and beta to parametrize linear theory redshift space distortions. On scales k < 0.16 h/Mpc, our maximum likelihood values are Omega_m*h = 0.264 +/-0.043, f_b = 0.286 +/- 0.065, sigma8 = 0.966 +/- 0.048, and beta = 0.45 +/- 0.12. When we take a prior on Omega_b from WMAP, we find Omega_m*h = 0.207 +/- 0.030, which is in excellent agreement with WMAP and 2dF. This indicates that we have reasonably measured the gross shape of the power spectrum but we have difficulty breaking the degeneracy between Omega_m*h and f_b because the baryon oscillations are not resolved in the current spectroscopic survey window function.

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arXiv2003

Cross-correlation Tomography: Measuring Dark Energy Evolution with Weak Lensing

A cross-correlation technique of lensing tomography is presented to measure the evolution of dark energy in the universe. The variation of the weak lensing shear with redshift around massive foreground objects like bright galaxies and clusters depends solely on ratios of angular diameter distances. Use of the massive foreground halos allow us to compare relatively high, linear shear values in the same part of the sky, thus largely eliminating the dominant source of systematic error in cosmological weak lensing measurements. The statistic we use does not rely on knowledge of the foreground mass distribution and is only shot-noise limited. We estimate the constraints that deep lensing surveys with photometric redshifts can provide on the dark energy density Omega, the equation of state parameter w and its redshift derivative w'. The accuracies on w and w' are: sigma(w) ~ 0.02 fsky^{-1/2} and sigma(w') ~ 0.05 fsky^{-1/2}, where fsky is the fraction of sky covered by the survey and sigma(Omega)=0.03 is assumed in the marginalization. Combining our cross-correlation method with standard lensing tomography, which has complementary degeneracies, will allow measurement of the dark energy parameters with significantly better accuracy.

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arXiv2003

Quasar-Galaxy and Galaxy-Galaxy Cross-Correlations: Model Predictions with Realistic Galaxies

Several measurements of QSO-galaxy correlations have reported signals much larger than predictions of magnification by large-scale structure. We find that the expected signal depends stronly on the properties of the foreground galaxy population. On arcminute scales it can be either larger or smaller by a factor of two for different galaxy types in comparison with a linearly biased version of the mass distribution. Thus the resolution of some of the excess measurements may lie in examining the halo occupation properties of the galaxy population sampled by a given survey; this is also the primary information such measurements will provide. We use the halo model of clustering and simulations to predict the magnification induced cross-correlations and errors for forthcoming surveys. With the full Sloan Digital Sky Survey the statistical errors will be below 1 percent for the galaxy-galaxy correlations and significantly larger for QSO-galaxy correlations. Thus accurate constraints on parameters of the galaxy halo occupation distribution can be obtained from small scale measurements and on the bias parameter from large scales. Since the lensing induced cross-correlation measures the first moment of the halo occupation number of galaxies, these measurements can provide the basis for interpreting galaxy clustering measurements which measure the second and higher order moments.

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arXiv2003

Three-Point Correlations in Weak Lensing Surveys: Model Predictions and Applications

We use the halo model of clustering to compute two- and three-point correlation functions for weak lensing, and apply them in a new statistical technique to measure properties of massive halos. We present analytical results on the eight shear three-point correlation functions constructed using combination of the two shear components at each vertex of a triangle. We compare the amplitude and configuration dependence of the functions with ray-tracing simulations and find excellent agreement for different scales and models. These results are promising, since shear statistics are easier to measure than the convergence. In addition, the symmetry properties of the shear three-point functions provide a new and precise way of disentangling the lensing E-mode from the B-mode due to possible systematic errors. We develop an approach based on correlation functions to measure the properties of galaxy-group and cluster halos from lensing surveys. Shear correlations on small scales arise from the lensing matter within halos of mass M > 10^13 solar masses. Thus the measurement of two- and three-point correlations can be used to extract information on halo density profiles, primarily the inner slope and halo concentration. We demonstrate the feasibility of such an analysis for forthcoming surveys. We include covariances in the correlation functions due to sample variance and intrinsic ellipticity noise to show that 10% accuracy on profile parameters is achievable with surveys like the CFHT Legacy survey, and significantly better with future surveys. Our statistical approach is complementary to the standard approach of identifying individual objects in survey data and measuring their properties.

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arXiv2003

The Three-Point Correlation Function in Cosmology

With the advent of high-quality surveys in cosmology the full three-point correlation function will be a valuable statistic for describing structure formation models. It contains information on cosmological parameters and detailed halo properties that cannot be extracted from the two-point correlation function. We use the halo clustering model to analytically calculate the three-point correlation function (3PCF) for general cosmological fields. We present detailed results for the configuration dependence of the 3-dimensional mass and galaxy distributions and the 2-dimensional cosmic shear field. We work in real space, where higher order correlation functions on small scales are easier to measure and interpret, but halo model calculations get rapidly intractable. Hence we develop techniques for accurate evaluations of the 1, 2 and 3-halo contributions to the 3PCF. The 3PCF violates the hierarchical ansatz in both its scale and configuration dependence. We study the behavior of the coefficient Q in the hierarchical expansion from large, quasilinear scales down to about 20 kpc. We find that the nonlinear 3PCF is sensitive to the halo profile of massive halos, especially its inner slope. We model the distribution of galaxies in halos and show that the 3PCF of red galaxies has a weaker configuration and scale dependence than the mass, while for blue galaxies it is very sensitive to the parameters of the galaxy formation model. The 3PCF from weak lensing on the other hand shows different scalings due to projection effects and a sensitivity to cosmological parameters.

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arXiv2002

The last stand before MAP: cosmological parameters from lensing, CMB and galaxy clustering

Cosmic shear measurements have now improved to the point where they deserve to be treated on par with CMB and galaxy clustering data for cosmological parameter analysis, using the full measured aperture mass variance curve rather than a mere phenomenological parametrization thereof. We perform a detailed 9-parameter analysis of recent lensing (RCS), CMB (up to Archeops) and galaxy clustering (2dF) data, both separately and jointly. CMB and 2dF data are consistent with a simple flat adiabatic scale-invariant model with Omega_Lambda=0.72+/-0.09, omega_cdm=0.115+/- 0.013, omega_b=0.024+/-0.003, and a hint of reionization around z~8. Lensing helps further tighten these constraints, but reveals tension regarding the power spectrum normalization: including the RCS survey results raises sigma8 significantly and forces other parameters to uncomfortable values. Indeed, sigma8 is emerging as the currently most controversial cosmological parameter, and we discuss possible resolutions of this sigma8 problem. We also comment on the disturbing fact that many recent analyses (including this one) obtain error bars smaller than the Fisher matrix bound. We produce a CMB power spectrum combining all existing experiments, and using it for a "MAP versus world" comparison next month will provide a powerful test of how realistic the error estimates have been in the cosmology community.

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arXiv2002

The Three-Point Correlation Function for Spin-2 Fields

The three-point correlation function (3PCF) of the spin-2 fields, the cosmic shear and cosmic microwave background polarization fields, is a statistical measure of non-Gaussian signals. At each vertex of a triangle, the shear field has two independent components. The resulting eight possible 3PCFs were recently investigated by Schneider & Lombardi (2002) and Zaldarriaga & Scoccimarro (2002). Using rotation and parity transformations they addressed the question: how many non-zero components for the shear 3PCF exist? We address this question using an analytical model and measurements from ray-tracing simulations. We show that all the eight 3PCFs are generally non-zero and have comparable amplitude. These eight 3PCFs can be used to improve the signal-to-noise from survey data and their configuration dependence can be used to separate the contribution from E and B-modes. We estimate the signal-to-noise for measuring the shear 3PCF from weak lensing surveys using simulated maps that include the noise due to intrinsic ellipticities. A deep lensing survey with area exceeding 10 square degrees would allow for the detection of the shear 3PCFs, but a survey area of order 100 square degrees is needed for accurate measurements.

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arXiv2002

Magnification effects as measures of large-scale structure

The magnification effects of clustered matter produce variations in the image sizes and number density of galaxies across the sky. This paper advocates the use of these effects in wide field surveys to map large-scale structure and the profiles of galaxy and cluster sized halos. The magnitude of the size variation as a function of angular scale is computed and the signal-to-noise is estimated for different survey parameters. Forthcoming surveys, especially well designed space-based imaging surveys, will have high signal-to-noise on scales of about 0.1 arcminute to several degrees. Thus the clustering of matter could be measured on spatial scales of about 50 Kpc to 100 Mpc. The signal-to-noise is dominated by sample variance rather than shot-noise due to the finite number density of galaxies, hence the accuracy of the measurements will be limited primarily by survey area, sampling strategy and possible systematics. Methods based on magnification are compared with the use of shape distortions and the contrasts and complementarities are discussed. Future work needed to plan survey strategy and interpret measurements based on magnification is outlined.

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arXiv2002

Substructure and the halo model of large-scale structure

We develop the formalism to include substructure in the halo model of clustering. Real halos are not likely to be perfectly smooth, but have substructure which has so far been neglected in the halo model -- our formalism allows one to estimate the effects of this substructure on measures of clustering. We derive expressions for the two-point correlation function, the power-spectrum, the cross-correlation between galaxies and mass, as well as higher order correlation functions. Simple forms of the formulae are obtained for the limit in which the size of the subclumps and mass fraction in them is small. Inclusion of substructure allows for a more accurate analysis of the statistical effects of gravitational lensing. It can also bring the halo model predictions into better agreement with the small-scale structure seen in recent high resolution simulations of hierarchical clustering.

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arXiv2002

The Kurtosis of the Cosmic Shear Field

We study the fourth-order moment of the cosmic shear field using the dark matter halo approach to describe the nonlinear gravitational evolution of structure in the universe. Since the third-order moment of the shear field vanishes because of symmetry, non-Gaussian signatures in its one-point statistics emerge at the fourth-order level. We argue that the shear kurtosis parameter S_4 = / ^3 may be more directly applicable to realistic data than the well-studied higher-order statistics of the convergence field, since obtaining the convergence requires a non-local reconstruction from the measured shear field. We compare our halo model predictions for the variance, skewness and kurtosis of lensing fields with ray-tracing simulations of cold dark matter models and find good agreement. The shear kurtosis calculation is made tractable by developing approximations for fast and accurate evaluations of the 8-dimensional integrals needed to obtain the kurtosis. We show that on small scales it is dominated by correlations within halos more massive than 10^14 solar masses. The shear kurtosis is sensitive to the mass density parameter of the universe, Omega, and has relatively weak dependences on other parameters. The approximations we develop for the third- and fourth-order moments allow for accurate halo model predictions for the 3-dimensional mass distribution as well. We demonstrate their accuracy in the small scale regime, below 2 Mpc, where analytical approaches used in the literature so far cease to be accurate.

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arXiv2002

Analysis of Systematic Effects and Statistical Uncertainties in Angular Clustering of Galaxies from Early SDSS Data

The angular distribution of galaxies encodes a wealth of information about large scale structure. Ultimately, the Sloan Digital Sky Survey (SDSS) will record the angular positions of order 10^8 galaxies in five bands, adding significantly to the cosmological constraints. This is the first in a series of papers analyzing a rectangular stripe 2.5x90 degrees from early SDSS data. We present the angular correlation function for galaxies in four separate magnitude bins on angular scales ranging from 0.003 degrees to 15 degrees. Much of the focus of this paper is on potential systematic effects. We show that the final galaxy catalog -- with the mask accounting for regions of poor seeing, reddening, bright stars, etc. -- is free from external and internal systematic effects for galaxies brighter than r* = 22. Our estimator of the angular correlation function includes the effects of the integral constraint and the mask. The full covariance matrix of errors in these estimates is derived using mock catalogs with further estimates using a number of other methods.

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arXiv2002

The Angular Power Spectrum of Galaxies from Early SDSS Data

We compute the angular power spectrum C_l from 1.5 million galaxies in early SDSS data on large angular scales, l<600. The data set covers about 160 square degrees, with a characteristic depth of order 1 Gpc/h in the faintest (21<r<22) of our four magnitude bins. Cosmological interpretations of these results are presented in a companion paper by Dodelson et al (2001). The data in all four magnitude bins are consistent with a simple flat ``concordance'' model with nonlinear evolution and linear bias factors of order unity. Nonlinear evolution is particularly evident for the brightest galaxies. A series of tests suggest that systematic errors related to seeing, reddening, etc., are negligible, which bodes well for the sixtyfold larger sample that the SDSS is currently collecting. Uncorrelated error bars and well-behaved window functions make our measurements a convenient starting point for cosmological model fitting.

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arXiv2001

KL Estimation of the Power Spectrum Parameters from the Angular Distribution of Galaxies in Early SDSS Data

We present measurements of parameters of the 3-dimensional power spectrum of galaxy clustering from 222 square degrees of early imaging data in the Sloan Digital Sky Survey. The projected galaxy distribution on the sky is expanded over a set of Karhunen-Loeve eigenfunctions, which optimize the signal-to-noise ratio in our analysis. A maximum likelihood analysis is used to estimate parameters that set the shape and amplitude of the 3-dimensional power spectrum. Our best estimates are Gamma=0.188 +/- 0.04 and sigma_8L = 0.915 +/- 0.06 (statistical errors only), for a flat Universe with a cosmological constant. We demonstrate that our measurements contain signal from scales at or beyond the peak of the 3D power spectrum. We discuss how the results scale with systematic uncertainties, like the radial selection function. We find that the central values satisfy the analytically estimated scaling relation. We have also explored the effects of evolutionary corrections, various truncations of the KL basis, seeing, sample size and limiting magnitude. We find that the impact of most of these uncertainties stay within the 2-sigma uncertainties of our fiducial result.

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arXiv2001

The Angular Correlation Function of Galaxies from Early SDSS Data

The Sloan Digital Sky Survey is one of the first multicolor photometric and spectroscopic surveys designed to measure the statistical properties of galaxies within the local Universe. In this Letter we present some of the initial results on the angular 2-point correlation function measured from the early SDSS galaxy data. The form of the correlation function, over the magnitude interval 18<r*<22, is shown to be consistent with results from existing wide-field, photographic-based surveys and narrower CCD galaxy surveys. On scales between 1 arcminute and 1 degree the correlation function is well described by a power-law with an exponent of ~ -0.7. The amplitude of the correlation function, within this angular interval, decreases with fainter magnitudes in good agreement with analyses from existing galaxy surveys. There is a characteristic break in the correlation function on scales of approximately 1-2 degrees. On small scales, < 1', the SDSS correlation function does not appear to be consistent with the power-law form fitted to the 1'< theta <0.5 deg data. With a data set that is less than 2% of the full SDSS survey area, we have obtained high precision measurements of the power-law angular correlation function on angular scales 1' < theta < 1 deg, which are robust to systematic uncertainties. Because of the limited area and the highly correlated nature of the error covariance matrix, these initial results do not yet provide a definitive characterization of departures from the power-law form at smaller and larger angles. In the near future, however, the area of the SDSS imaging survey will be sufficient to allow detailed analysis of the small and large scale regimes, measurements of higher-order correlations, and studies of angular clustering as a function of redshift and galaxy type.

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arXiv2001

The 3D Power Spectrum from Angular Clustering of Galaxies in Early SDSS Data

Early photometric data from the Sloan Digital Sky Survey (SDSS) contain angular positions for 1.5 million galaxies. In companion papers, the angular correlation function $w(θ)$ and 2D power spectrum $C_l$ of these galaxies are presented. Here we invert Limber's equation to extract the 3D power spectrum from the angular results. We accomplish this using an estimate of $dn/dz$, the redshift distribution of galaxies in four different magnitude slices in the SDSS photometric catalog. The resulting 3D power spectrum estimates from $w(θ)$ and $C_l$ agree with each other and with previous estimates over a range in wavenumbers $0.03 < k/{\rm h Mpc}^{-1} < 1$. The galaxies in the faintest magnitude bin ($21 < \rstar < 22$, which have median redshift $z_m=0.43$) are less clustered than the galaxies in the brightest magnitude bin ($18 < \rstar < 19$ with $z_m=0.17$), especially on scales where nonlinearities are important. The derived power spectrum agrees with that of Szalay et al. (2001) who go directly from the raw data to a parametric estimate of the power spectrum. The strongest constraints on the shape parameter $Γ$ come from the faintest galaxies (in the magnitude bin $21 < \rstar < 22$), from which we infer $Γ= 0.14^{+0.11}_{-0.06}$ (95% C.L.).

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arXiv2001

The Topology of Weak Lensing Fields

The topology of weak lensing fields is studied using the 2-dimensional genus statistic. Simulated fields of the weak lensing convergence are used to focus on the effect of nonlinear gravitional evolution and to model the statistical errors expected in observational surveys. For large smoothing angles, the topology is in agreement with the predictions from linear theory. On smoothing angles smaller than 10', the genus curve shows the non-Gaussian signatures of gravitational clustering and differs for open and flat cold dark matter models. Forthcoming surveys with areas larger than 10 square degrees should have adequate signal-to-noise to measure the non-Gaussian shape and the $Ω$-dependence of the genus statistic.

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arXiv2000

How Many Galaxies Fit in a Halo? Constraints on Galaxy Formation Efficiency from Spatial Clustering

We study galaxy clustering using halo models, where gravitational clustering is described in terms of dark matter halos. At small scales, clustering statistics are dominated by halo density profiles, whereas at large scales, correlations are the result of combining non-linear perturbation theory with halo biasing. Galaxies are assumed to follow the dark matter profiles, and galaxy formation efficiency is given by the number of galaxies as a function of halo mass. This approach leads to generic predictions: the galaxy power spectrum shows a power-law behavior even though the dark matter does not, and the galaxy higher-order correlations show smaller amplitudes at small scales than their dark matter counterparts, as observed in galaxy catalogs. We find that requiring to fit both the second and third order moments of the APM galaxies provides a strong constraint on galaxy formation models. The data at large scales require that galaxy formation be relatively efficient at small masses, m =10^10 Msun/h, whereas data at smaller scales require that the number of galaxies in a halo scale as the mass to the 0.8th power in the high-mass limit. These constraints are independent of those derived from the luminosity function or Tully-Fisher relation. We also predict the power spectrum, bispectrum, and higher-order moments of the mass density field. Although halo models agree well with measurements of the mass power spectrum and the higher order Sp parameters in N-body simulations, the model assumption that halos are spherical leads to disagreement in the configuration dependence of the bispectrum at small scales. We stress the importance of finite volume effects in higher-order statistics and show how they can be estimated in this approach.

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arXiv2000

Cosmic shear and halo abundances: Analytical versus numerical results

The aperture mass has been shown in a series of recent publications to be a useful quantitative tool for weak lensing studies, ranging from cosmic shear to the detection of a mass-selected sample of dark matter haloes. Quantitative analytical predictions for the aperture mass have been based on a number of simplifying assumptions. In this paper, we test the reliability of these assumptions and the quality of the analytic approximations, using ray-tracing simulations through a cosmological density field generated by very large N-body simulations. We find that those analytic predictions which take into account the non-linear evolution of the matter distribution, such as the dispersion of the aperture mass and the halo abundance, are surprisingly accurately reproduced with our numerical results, whereas the predictions for the skewness, based on quasi-linear theory, are rather imprecise. In particular, we verify numerically that the probability distribution of the aperture mass decreases exponentially for values much larger than the rms. Given the good overall agreement, comparisons between the observed distribution of the aperture mass and the theoretical values provide a powerful tool for testing cosmological models.

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