arXiv subjects

Robert E. Smith

Publications and source records attributed to Robert E. Smith.

At least 37 records · Page 2Linked to original sources

arXiv2015

What is the optimal way to measure the galaxy power spectrum?

Measurements of the galaxy power spectrum contain a wealth of information about the Universe. Its optimal extraction is vital if we are to truly understand the micro-physical nature of dark matter and dark energy. In Smith & Marian (2015) we generalized the power spectrum methodology of Feldman et al. (1994) to take into account the key tenets of galaxy formation: galaxies form and reside exclusively in dark matter haloes; a given dark matter halo may host galaxies of various luminosities; galaxies inherit the large-scale bias associated with their host halo. In this paradigm we derived the optimal weighting and reconstruction scheme for maximizing the signal-to-noise on a given band power estimate. For a future all-sky flux-limited galaxy redshift survey of depth b_J ~22, we now demonstrate that the optimal weighting scheme does indeed provide improved S/N at the level of ~20% when compared to Feldman et al. (1994) and ~60% relative to Percival et al. (2003), for scales of order k~0.5 Mpc/h. Using a Fisher matrix approach, we show that the cosmological information yield is also increased relative to these alternate methods -- especially the primordial power spectrum amplitude and dark energy equation of state.

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arXiv2015

An exploration of galaxy-galaxy lensing and galaxy clustering in the Millennium-XXL simulation

The combination of galaxy-galaxy lensing and galaxy clustering data has the potential to simultaneously constrain both the cosmological and galaxy formation models. In this paper we perform a comprehensive exploration of these signals and their covariances through a combination of analytic and numerical approaches. First, we derive analytic expressions for the projected galaxy correlation function and stacked tangential shear profile and their respective covariances, which include Gaussian and discreteness noise terms. Secondly, we measure these quantities from mock galaxy catalogues obtained from the Millennium-XXL simulation and semi-analytic models of galaxy formation. We find that on large scales (R>10 Mpc/h), the galaxy bias is roughly linear and deterministic. On smaller scales (R<5 Mpc/h) the bias is a complicated function of scale and luminosity, determined by the different spatial distribution and abundance of satellite galaxies present when different magnitude cuts are applied, as well as by the mass dependence of the host haloes on magnitude. Our theoretical model for the covariances provides a reasonably good description of the measured ones on small and large scales. However, on intermediate scales (1<R<10 Mpc/h), the predicted errors are ~2-3 times smaller, suggesting that the inclusion of higher-order, non-Gaussian terms in the covariance will be required for further improvements. Importantly, both our theoretical and numerical methods show that the galaxy-galaxy lensing and clustering signals have a non-zero cross-covariance matrix with significant bin-to-bin correlations. Future surveys aiming to combine these probes must take this into account in order to obtain unbiased and realistic constraints.

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arXiv2015

The Anisotropic Line Correlation Function as a Probe of Anisotropies in Galaxy Surveys

We propose an anisotropic generalisation of the line correlation function (ALCF) to separate and quantify phase information in the large-scale structure of galaxies. The line correlation function probes the strictly non-linear regime of structure formation and since phase information drops out of the power spectrum, the line correlation function provides a complementary tool to commonly used techniques based on two-point statistics. Furthermore, it is independent of linear bias as well as the Gaussian variance on the modulus of the density field and thus may also prove to be advantageous compared to the bispectrum or similar higher-order statistics for certain cases. For future applications it is vital, though, to be able to account for observational effects that cause anisotropies in the distribution of galaxies. Based on a number of numerical studies, we find that our ALCF is well suited to accomplish this task and we demonstrate how the Alcock-Paczynski effect and kinematical redshift-space distortions can in principle be measured via the ALCF.

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arXiv2014

Precision cosmology in muddy waters: Cosmological constraints and N-body codes

Future large-scale structure surveys of the Universe will aim to constrain the cosmological model and the true nature of dark energy with unprecedented accuracy. In order for these surveys to achieve their designed goals, they will require predictions for the nonlinear matter power spectrum to sub-percent accuracy. Through the use of a large ensemble of cosmological N-body simulations, we demonstrate that if we do not understand the uncertainties associated with simulating structure formation, i.e. knowledge of the `true' simulation parameters, and simply seek to marginalize over them, then the constraining power of such future surveys can be significantly reduced. However, for the parameters {n_s, h, Om_b, Om_m}, this effect can be largely mitigated by adding the information from a CMB experiment, like Planck. In contrast, for the amplitude of fluctuations sigma8 and the time-evolving equation of state of dark energy {w_0, w_a}, the mitigation is mild. On marginalizing over the simulation parameters, we find that the dark-energy figure of merit can be degraded by ~2. This is likely an optimistic assessment, since we do not take into account other important simulation parameters. A caveat is our assumption that the Hessian of the likelihood function does not vary significantly when moving from our adopted to the 'true' simulation parameter set. This paper therefore provides strong motivation for rigorous convergence testing of N-body codes to meet the future challenges of precision cosmology.

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arXiv2014

A new method to measure galaxy bias

We present a new approach for modelling galaxy/halo bias that utilizes the full non-linear information contained in the moments of the matter density field, which we derive using a set of numerical simulations. Although our method is general, we perform a case study based on the local Eulerian bias scheme truncated to second-order. Using 200 N-body simulations covering a total comoving volume of 675 (Gpc/h)^3, we measure several 2- and 3-point statistics of the halo distribution to unprecedented accuracy. We use the bias model to fit the halo-halo power spectrum, the halo-matter cross spectrum and the corresponding three bispectra for wavenumbers in the range 0.04 < k < 0.12 h Mpc^-1. We find the constraints on the bias parameters obtained using the full non-linear information differ significantly from those derived using standard perturbation theory at leading order. Hence, neglecting the full non-linear information leads to biased results for this particular scale range. We also test the validity of the second-order Eulerian local biasing scheme by comparing the parameter constraints derived from different statistics. Analysis of the halo-matter cross-correlation coefficients defined for the 2- and 3-point statistics reveals further inconsistencies contained in the second-order Eulerian bias scheme, suggesting it is too simple a model to describe halo bias with high accuracy.

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arXiv2013

On the signature of $z\sim 0.6$ superclusters and voids in the Integrated Sachs-Wolfe effect

Through a large ensemble of Gaussian realisations and a suite of large-volume N-body simulations, we show that in a standard LCDM scenario, supervoids and superclusters in the redshift range $z\in[0.4,0.7]$ should leave a {\em small} signature on the ISW effect of the order $\sim 2 μ$K. We perform aperture photometry on WMAP data, centred on such superstructures identified from SDSS LRGs, and find amplitudes at the level of 8 -- 11$ μ$K -- thus confirming the earlier work of Granett et al 2008. If we focus on apertures of the size $\sim3.6\degr$, then our realisations indicate that LCDM is discrepant at the level of $\sim4 σ$. If we combine all aperture scales considered, ranging from 1\degr--20\degr, then the discrepancy becomes $\sim2σ$, and it further lowers to $\sim 0.6 σ$ if only 30 superstructures are considered in the analysis (being compatible with no ISW signatures at $1.3σ$ in this case). Full-sky ISW maps generated from our N-body simulations show that this discrepancy cannot be alleviated by appealing to Rees-Sciama mechanisms, since their impact on the scales probed by our filters is negligible. We perform a series of tests on the WMAP data for systematics. We check for foreground contaminants and show that the signal does not display the correct dependence on the aperture size expected for a residual foreground tracing the density field. The signal also proves robust against rotation tests of the CMB maps, and seems to be spatially associated to the angular positions of the supervoids and superclusters. We explore whether the signal can be explained by the presence of primordial non-Gaussianities of the local type. We show that for models with $\FNL=\pm100$, whilst there is a change in the pattern of temperature anisotropies, all amplitude shifts are well below $<1μ$K.

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arXiv2013

Halo Mass Function and the Free Streaming Scale

The nature of structure formation around the particle free streaming scale is still far from understood. Many attempts to simulate hot, warm, and cold dark matter cosmologies with a free streaming cutoff have been performed with cosmological particle-based simulations, but they all suffer from spurious structure formation at scales below their respective free streaming scales -- i.e. where the physics of halo formation is most affected by free streaming. We perform a series of high resolution numerical simulations of different WDM models, and develop an approximate method to subtract artificial structures in the measured halo mass function. The corrected measurements are then used to construct and calibrate an extended Press-Schechter (EPS) model with sharp-$k$ window function and adequate mass assignment. The EPS model gives accurate predictions for the low redshift halo mass function of CDM and WDM models, but it significantly under-predicts the halo abundance at high redshifts. By taking into account the ellipticity of the initial patches and connecting the characteristic filter scale to the smallest ellipsoidal axis, we are able to eliminate this inconsistency and obtain an accurate mass function over all redshifts and all dark matter particle masses covered by the simulations. As an additional application we use our model to predict the microhalo abundance of the standard neutralino-CDM scenario and we give the first quantitative prediction of the mass function over the full range of scales of CDM structure formation.

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arXiv2013

Halo Stochasticity from Exclusion and non-linear Clustering

The clustering of galaxies in ongoing and upcoming galaxy surveys contains a wealth of cosmological information, but extracting this information is a non-trivial task since galaxies and their host haloes are stochastic tracers of the matter density field. This stochasticity is usually modeled as Poisson shot noise, which is constant as a function of wavenumber with amplitude given by 1/n, where n is the number density of galaxies. Here we use dark matter haloes in N-body simulations to show evidence for deviations from this simple behaviour and develop models that explain the behaviour of the large scale stochasticity. First, haloes are extended, non-overlapping objects, i.e., their correlation function needs to go to -1 on small scales. This leads to a negative correction to the stochasticity relative to the Poisson value at low wavenumber k, decreasing to zero for wavenumbers large compared to the inverse exclusion scale. Second, haloes show a non-linear enhancement of clustering outside the exclusion scale, leading to a positive stochasticity correction. Both of these effects go to zero for high-k, making the stochasticity scale dependent even for k<0.1 h/Mpc. We show that the corrections in the low-k regime are the same in Eulerian and Lagrangian space, but that the transition scale is pushed to smaller scales for haloes observed at present time, relative to the initial conditions. These corrections vary with halo mass and redshift. We also discuss simple applications of these effects to the galaxy samples with non-vanishing satellite fraction, where the stochasticity can again deviate strongly from the fiducial Poisson expectation. Overall these effects affect the clustering of galaxies at a level of a few percent even on very large scales and need to be modelled properly if we want to extract high precision cosmological information from the upcoming galaxy surveys.

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arXiv2013

Toward an accurate mass function for precision cosmology

Cosmological surveys aim to use the evolution of the abundance of galaxy clusters to accurately constrain the cosmological model. In the context of LCDM, we show that it is possible to achieve the required percent level accuracy in the halo mass function with gravity-only cosmological simulations, and we provide simulation start and run parameter guidelines for doing so. Some previous works have had sufficient statistical precision, but lacked robust verification of absolute accuracy. Convergence tests of the mass function with, for example, simulation start redshift can exhibit false convergence of the mass function due to counteracting errors, potentially misleading one to infer overly optimistic estimations of simulation accuracy. Percent level accuracy is possible if initial condition particle mapping uses second order Lagrangian Perturbation Theory, and if the start epoch is between 10 and 50 expansion factors before the epoch of halo formation of interest. The mass function for halos with fewer than ~1000 particles is highly sensitive to simulation parameters and start redshift, implying a practical minimum mass resolution limit due to mass discreteness. The narrow range in converged start redshift suggests that it is not presently possible for a single simulation to capture accurately the cluster mass function while also starting early enough to model accurately the numbers of reionisation era galaxies, whose baryon feedback processes may affect later cluster properties. Ultimately, to fully exploit current and future cosmological surveys will require accurate modeling of baryon physics and observable properties, a formidable challenge for which accurate gravity-only simulations are just an initial step.

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arXiv2013

Cosmological parameter constraints from galaxy-galaxy lensing and galaxy clustering with the SDSS DR7

Recent studies have shown that the cross-correlation coefficient between galaxies and dark matter is very close to unity on scales outside a few virial radii of galaxy halos, independent of the details of how galaxies populate dark matter halos. This finding makes it possible to determine the dark matter clustering from measurements of galaxy-galaxy weak lensing and galaxy clustering. We present new cosmological parameter constraints based on large-scale measurements of spectroscopic galaxy samples from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7). We generalise the approach of Baldauf et al. (2010) to remove small scale information (below 2 and 4 Mpc/h for lensing and clustering measurements, respectively), where the cross-correlation coefficient differs from unity. We derive constraints for three galaxy samples covering 7131 sq. deg., containing 69150, 62150, and 35088 galaxies with mean redshifts of 0.11, 0.28, and 0.40. We clearly detect scale-dependent galaxy bias for the more luminous galaxy samples, at a level consistent with theoretical expectations. When we vary both σ_8 and Ω_m (and marginalise over non-linear galaxy bias) in a flat LCDM model, the best-constrained quantity is σ_8 (Ω_m/0.25)^{0.57}=0.80 +/- 0.05 (1-sigma, stat. + sys.), where statistical and systematic errors have comparable contributions, and we fixed n_s=0.96 and h=0.7. These strong constraints on the matter clustering suggest that this method is competitive with cosmic shear in current data, while having very complementary and in some ways less serious systematics. We therefore expect that this method will play a prominent role in future weak lensing surveys. When we combine these data with WMAP7 CMB data, constraints on σ_8, Ω_m, H_0, w_{de} and \sum m_ν become 30--80 per cent tighter than with CMB data alone, since our data break several parameter degeneracies.

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arXiv2013

The cosmological information of shear peaks: beyond the abundance

We study the cosmological information of weak lensing (WL) peaks, focusing on two other statistics besides their abundance: the stacked tangential-shear profiles and the peak-peak correlation function. We use a large ensemble of simulated WL maps with survey specifications relevant to future missions like Euclid and LSST, to explore the three peak probes. We find that the correlation function of peaks with high signal-to-noise (S/N) measured from fields of size 144 sq. deg. has a maximum of ~0.3 at an angular scale ~10 arcmin. For peaks with smaller S/N, the amplitude of the correlation function decreases, and its maximum occurs on smaller angular scales. We compare the peak observables measured with and without shape noise and find that for S/N~3 only ~5% of the peaks are due to large-scale structures, the rest being generated by shape noise. The covariance matrix of the probes is examined: the correlation function is only weakly covariant on scales < 30 arcmin, and slightly more on larger scales; the shear profiles are very correlated for theta > 2 arcmin, with a correlation coefficient as high as 0.7. Using the Fisher-matrix formalism, we compute the cosmological constraints for {Om_m, sig_8, w, n_s} considering each probe separately, as well as in combination. We find that the correlation function of peaks and shear profiles yield marginalized errors which are larger by a factor of 2-4 for {Om_m, sig_8} than the errors yielded by the peak abundance alone, while the errors for {w, n_s} are similar. By combining the three probes, the marginalized constraints are tightened by a factor of ~2 compared to the peak abundance alone, the least contributor to the error reduction being the correlation function. This work therefore recommends that future WL surveys use shear peaks beyond their abundance in order to constrain the cosmological model.

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arXiv2012

Measuring primordial non-Gaussianity with weak-lensing surveys

We study the ability of future weak lensing (WL) surveys to constrain primordial non-Gaussianity of the local type. We use a large ensemble of simulated WL maps with survey specifications relevant to Euclid and LSST. The simulations assume Cold Dark Matter cosmologies that vary certain parameters around fiducial values: the non-Gaussianity parameter f_NL, the matter density parameter Omega_m, the amplitude of the matter power spectrum sigma_8, the spectral index of the primordial power spectrum n_s, and the dark-energy equation-of-state parameter w_0. We assess the sensitivity of the cosmic shear correlation functions, the third-order aperture mass statistics, and the abundance of shear peaks to these parameters. We find that each of the considered probes provides unmarginalized constraints of Delta f_NL ~ 20 on f_NL. Marginalized constraints from any individual WL probe are much weaker due to strong correlations between parameters. However, the parameter errors can be substantially reduced by combining information from different WL probes. Combining all WL probes yields the following marginal (68% confidence level) uncertainties: Delta f_NL ~ 50, Delta Omega_m ~ 0.002, Delta sigma_8 ~ 0.004, Delta n_s ~ 0.007, and Delta w_0 ~ 0.03. We examine the bias induced by neglecting f_NL on the constraints on the other parameters. We find sigma_8 and w_0 to be the most affected. Moreover, neglecting non-Gaussianity leads to a severe underestimation of the uncertainties in the other cosmological parameters.

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arXiv2012

How covariant is the galaxy luminosity function?

We investigate the error properties of certain galaxy luminosity function (GLF) estimators. Using a cluster expansion of the density field, we show how, for both volume and flux limited samples, the GLF estimates are covariant. The covariance matrix can be decomposed into three pieces: a diagonal term arising from Poisson noise; a sample variance term arising from large-scale structure in the survey volume; an occupancy covariance term arising due to galaxies of different luminosities inhabiting the same cluster. To evaluate the theory one needs: the mass function and bias of clusters, and the conditional luminosity function (CLF). We use a semi-analytic model (SAM) galaxy catalogue from the Millennium run N-body simulation and the CLF of Yang et al. (2003) to explore these effects. The GLF estimates from the SAM and the CLF qualitatively reproduce results from the 2dFGRS. We also measure the luminosity dependence of clustering in the SAM and find reasonable agreement with 2dFGRS results for bright galaxies. However, for fainter galaxies, L 0.5. Our theory is in good agreement with these measurements. These strong correlations can be attributed to sample variance. For a flux-limited survey of similar volume, the estimates are only slightly less correlated. We explore the importance of these effects for GLF model parameter estimation. We show that neglecting to take into account the bin-to-bin covariances can lead to significant systematic errors in best-fit parameters.

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arXiv2012

Cluster Density Profiles as a Test of Modified Gravity

We present a new test of gravitational interactions at the r\sim(0.2-20)Mpc scale, around the virial radius of dark matter halos measured through cluster-galaxy lensing of maxBCG clusters from the Sloan Digital Sky Survey (SDSS). We employ predictions from self-consistent simulations of f(R) gravity to find an upper bound on the background field amplitude of f_R0<3.5x10^-3 at the 1D-marginalized 95% confidence level. As a model-independent assessment of the constraining power of cluster profiles measured through weak gravitational lensing, we also constrain the amplitude F_0 of a phenomenological modification based on the profile enhancement induced by f(R) gravity when not including effects from the increased cluster abundance in f(R). In both scenarios, dark-matter-only simulations of the concordance model corresponding to f_R0=0 and F_0=0 are consistent with the lensing measurements, i.e., at the 68% and 95% confidence level, respectively.

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arXiv2012

Nonlinear Evolution of Cosmological Structures in Warm Dark Matter Models

The dark energy dominated warm dark matter (WDM) model is a promising alternative cosmological scenario. We explore large-scale structure formation in this paradigm. We do this in two different ways: with the halo model approach and with the help of an ensemble of high resolution N-body simulations. Combining these quasi-independent approaches, leads to a physical understanding of the important processes which shape the formation of structures. We take a detailed look at the halo mass function, the concentrations and the linear halo bias of WDM. In all cases we find interesting deviations with respect to CDM. In particular, the concentration-mass relation displays a turnover for group scale dark matter haloes, for the case of WDM particles with masses of the order ~0.25 keV. This may be interpreted as a hint for top-down structure formation on small scales. We implement our results into the halo model and find much better agreement with simulations. On small scales the WDM halo model now performs as well as its CDM counterpart.

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arXiv2012

Measuring primordial non-Gaussianity through weak lensing peak counts

We explore the possibility of detecting primordial non-Gaussianity of the local type using weak lensing peak counts. We measure the peak abundance in sets of simulated weak lensing maps corresponding to three models f_NL={0, +100, -100}. Using survey specifications similar to those of Euclid and without assuming any knowledge of the lens and source redshifts, we find the peak functions of the non-Gaussian models with f_NL=+-100 to differ by up to 15% from the Gaussian peak function at the high-mass end. For the assumed survey parameters, the probability of fitting an f_NL=0 peak function to the f_NL=+-100 peak functions is less than 0.1%. Assuming the other cosmological parameters known, f_NL can be measured with an error Δf_NL ~ 13. It is therefore possible that future weak lensing surveys like Euclid and LSST may detect primordial non-Gaussianity from the abundance of peak counts, and provide complementary information to that obtained from the cosmic microwave background.

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arXiv2012

Optimized detection of shear peaks in weak lensing maps

We present a new method to extract cosmological constraints from weak lensing (WL) peak counts, which we denote as `the hierarchical algorithm'. The idea of this method is to combine information from WL maps sequentially smoothed with a series of filters of different size, from the largest down to the smallest, thus increasing the cosmological sensitivity of the resulting peak function. We compare the cosmological constraints resulting from the peak abundance measured in this way and the abundance obtained by using a filter of fixed size, which is the standard practice in WL peak studies. For this purpose, we employ a large set of WL maps generated by ray-tracing through N-body simulations, and the Fisher matrix formalism. We find that if low-S/N peaks are included in the analysis (S/N ~ 3), the hierarchical method yields constraints significantly better than the single-sized filtering. For a large future survey such as Euclid or LSST, combined with information from a CMB experiment like Planck, the results for the hierarchical (single-sized) method are: Δn=0.0039 (0.004); ΔΩm=0.002 (0.0045); Δσ8=0.003 (0.006); Δw=0.019 (0.0525). This forecast is conservative, as we assume no knowledge of the redshifts of the lenses, and consider a single broad bin for the redshifts of the sources. If only peaks with S/N >= 6 are considered, then there is little difference between the results of the two methods. We also examine the statistical properties of the hierarchical peak function: Its covariance matrix has off-diagonal terms for bins with S/N <= 6 and aperture mass of M < 3 x 1e+14 Ms/h, the higher bins being largely uncorrelated and therefore well described by a Poisson distribution.

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arXiv2011

Modelling large-scale halo bias using the bispectrum

We study the relation between the halo and matter density fields -- commonly termed bias -- in the LCDM framework. In particular, we examine the local model of biasing at quadratic order in the matter density. This model is characterized by parameters b_1 and b_2. Using an ensemble of N-body simulations, we apply several statistical methods to estimate the parameters. We measure halo and matter fluctuations smoothed on various scales and find that the parameters vary with smoothing scale. We argue that, for real-space measurements, owing to the mixing of wavemodes, no scale can be found for which the parameters are independent of smoothing. However, this is not the case in Fourier space. We measure halo power spectra and construct estimates for an effective large-scale bias. We measure the configuration dependence of the halo bispectra B_hhh and reduced bispectra Q_hhh for very large-scale k-space triangles. From this we constrain b_1 and b_2. Using the lowest-order perturbation theory, we find that for B_hhh the best-fit parameters are in reasonable agreement with one another as the triangle scale is varied, but that the fits become poor as smaller scales are included. The same is true for Q_hhh. The best-fit parameters depend on the discreteness correction. This led us to consider halo-mass cross-bispectra. The results from these statistics support our earlier findings. We develop a test to explore the importance of missing higher-order terms in the models. We prove that low-order expansions are not able to correctly model the data, even on scales k_1~0.04 h/Mpc. If robust inferences are to be drawn from galaxy surveys, then accurate models for the full nonlinear matter bispectrum and trispectrum will be essential.

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