Cosmological Constraints from Galaxy Clustering and the Mass-to-Number Ratio of Galaxy Clusters

We place constraints on the average density (Omega_m) and clustering amplitude (sigma_8) of matter using a combination of two measurements from the Sloan Digital Sky Survey: the galaxy two-point correlation function, w_p, and the mass-to-galaxy-number ratio within galaxy clusters, M/N, analogous to cluster M/L ratios. Our w_p measurements are obtained from DR7 while the sample of clusters is the maxBCG sample, with cluster masses derived from weak gravitational lensing. We construct non-linear galaxy bias models using the Halo Occupation Distribution (HOD) to fit both w_p and M/N for different cosmological parameters. HOD models that match the same two-point clustering predict different numbers of galaxies in massive halos when Omega_m or sigma_8 is varied, thereby breaking the degeneracy between cosmology and bias. We demonstrate that this technique yields constraints that are consistent and competitive with current results from cluster abundance studies, even though this technique does not use abundance information. Using w_p and M/N alone, we find Omega_m^0.5*sigma_8=0.465+/-0.026, with individual constraints of Omega_m=0.29+/-0.03 and sigma_8=0.85+/-0.06. Combined with current CMB data, these constraints are Omega_m=0.290+/-0.016 and sigma_8=0.826+/-0.020. All errors are 1-sigma. The systematic uncertainties that the M/N technique are most sensitive to are the amplitude of the bias function of dark matter halos and the possibility of redshift evolution between the SDSS Main sample and the maxBCG sample. Our derived constraints are insensitive to the current level of uncertainties in the halo mass function and in the mass-richness relation of clusters and its scatter, making the M/N technique complementary to cluster abundances as a method for constraining cosmology with future galaxy surveys.Comment: 23 pages, submitted to Ap

The Aemulus Project III: Emulation of the Galaxy Correlation Function

Using the N-body simulations of the AEMULUS Project, we construct an emulator for the non-linear clustering of galaxies in real and redshift space. We construct our model of galaxy bias using the halo occupation framework, accounting for possible velocity bias. The model includes 15 parameters, including both cosmological and galaxy bias parameters. We demonstrate that our emulator achieves ~ 1% precision at the scales of interest, 0.1<r<10 h^{-1} Mpc, and recovers the true cosmology when tested against independent simulations. Our primary parameters of interest are related to the growth rate of structure, f, and its degenerate combination fsigma_8. Using this emulator, we show that the constraining power on these parameters monotonically increases as smaller scales are included in the analysis, all the way down to 0.1 h^{-1} Mpc. For a BOSS-like survey, the constraints on fsigma_8 from r<30 h^{-1} Mpc scales alone are more than a factor of two tighter than those from the fiducial BOSS analysis of redshift-space clustering using perturbation theory at larger scales. The combination of real- and redshift-space clustering allows us to break the degeneracy between f and sigma_8, yielding a 9% constraint on f alone for a BOSS-like analysis. The current AEMULUS simulations limit this model to surveys of massive galaxies. Future simulations will allow this framework to be extended to all galaxy target types, including emission-line galaxies.Comment: 14 pages, 8 figures, 1 table; submitted to ApJ; the project webpage is available at https://aemulusproject.github.io ; typo in Figure 7 and caption updated, results unchange

The Aemulus Project II: Emulating the Halo Mass Function

Existing models for the dependence of the halo mass function on cosmological parameters will become a limiting source of systematic uncertainty for cluster cosmology in the near future. We present a halo mass function emulator and demonstrate improved accuracy relative to state-of-the-art analytic models. In this work, mass is defined using an overdensity criteria of 200 relative to the mean background density. Our emulator is constructed from the AEMULUS simulations, a suite of 40 N-body simulations with snapshots from z=3 to z=0. These simulations cover the flat wCDM parameter space allowed by recent Cosmic Microwave Background, Baryon Acoustic Oscillation and Type Ia Supernovae results, varying the parameters w, Omega_m, Omega_b, sigma_8, N_{eff}, n_s, and H_0. We validate our emulator using five realizations of seven different cosmologies, for a total of 35 test simulations. These test simulations were not used in constructing the emulator, and were run with fully independent initial conditions. We use our test simulations to characterize the modeling uncertainty of the emulator, and introduce a novel way of marginalizing over the associated systematic uncertainty. We confirm non-universality in our halo mass function emulator as a function of both cosmological parameters and redshift. Our emulator achieves better than 1% precision over much of the relevant parameter space, and we demonstrate that the systematic uncertainty in our emulator will remain a negligible source of error for cluster abundance studies through at least the LSST Year 1 data set.Comment: https://aemulusproject.github.io

The Aemulus Project I: Numerical Simulations for Precision Cosmology

The rapidly growing statistical precision of galaxy surveys has lead to a need for ever-more precise predictions of the observables used to constrain cosmological and galaxy formation models. The primary avenue through which such predictions will be obtained is suites of numerical simulations. These simulations must span the relevant model parameter spaces, be large enough to obtain the precision demanded by upcoming data, and be thoroughly validated in order to ensure accuracy. In this paper we present one such suite of simulations, forming the basis for the AEMULUS Project, a collaboration devoted to precision emulation of galaxy survey observables. We have run a set of 75 (1.05 h^-1 Gpc)^3 simulations with mass resolution and force softening of 3.51\times 10^10 (Omega_m / 0.3) ~ h^-1 M_sun and 20 ~ h^-1 kpc respectively in 47 different wCDM cosmologies spanning the range of parameter space allowed by the combination of recent Cosmic Microwave Background, Baryon Acoustic Oscillation and Type Ia Supernovae results. We present convergence tests of several observables including spherical overdensity halo mass functions, galaxy projected correlation functions, galaxy clustering in redshift space, and matter and halo correlation functions and power spectra. We show that these statistics are converged to 1% (2%) for halos with more than 500 (200) particles respectively and scales of r>200 ~ h^-1 kpc in real space or k ~ 3 h Mpc^-1 in harmonic space for z\le 1. We find that the dominant source of uncertainty comes from varying the particle loading of the simulations. This leads to large systematic errors for statistics using halos with fewer than 200 particles and scales smaller than k ~ 4 h^-1 Mpc. We provide the halo catalogs and snapshots detailed in this work to the community at https://AemulusProject.github.io.Comment: 16 pages, 12 figures, 3 Tables Project website: https://aemulusproject.github.io

Parallel HOP: A Scalable Halo Finder for Massive Cosmological Data Sets

Modern N-body cosmological simulations contain billions ($10^9$) of dark matter particles. These simulations require hundreds to thousands of gigabytes of memory, and employ hundreds to tens of thousands of processing cores on many compute nodes. In order to study the distribution of dark matter in a cosmological simulation, the dark matter halos must be identified using a halo finder, which establishes the halo membership of every particle in the simulation. The resources required for halo finding are similar to the requirements for the simulation itself. In particular, simulations have become too extensive to use commonly-employed halo finders, such that the computational requirements to identify halos must now be spread across multiple nodes and cores. Here we present a scalable-parallel halo finding method called Parallel HOP for large-scale cosmological simulation data. Based on the halo finder HOP, it utilizes MPI and domain decomposition to distribute the halo finding workload across multiple compute nodes, enabling analysis of much larger datasets than is possible with the strictly serial or previous parallel implementations of HOP. We provide a reference implementation of this method as a part of the toolkit yt, an analysis toolkit for Adaptive Mesh Refinement (AMR) data that includes complementary analysis modules. Additionally, we discuss a suite of benchmarks that demonstrate that this method scales well up to several hundred tasks and datasets in excess of $2000^3$ particles. The Parallel HOP method and our implementation can be readily applied to any kind of N-body simulation data and is therefore widely applicable.Comment: 29 pages, 11 figures, 2 table

Corporate Social Responsibility Strategy and its Influence Over Consumer Purchasing Decisions in Financial Institutions

The aim of this research is how CSR activities can influence the purchasing behaviour of consumers when it comes to financial institutions. Whilst there have been significant amounts of literature written on CSR there is still a gap in understanding how CSR activities influence consumers perception. This gap is particularly evident in the financial services sector given they are the largest contributors to CSR in Australia (ACCSR, 2011). There is a further gap in the literature in understanding how perceptions of consumers towards CSR change dependant on situational context. In addressing the research problem, the study focusses on understanding the most influential CSR initiatives, understanding how the influence of CSR initiatives can change depending on situational context and then delves further to understand how demographic attributes can alter perception. Bhattacharya and Sen’s (2004) framework was used to frame the questionnaire that was answered by 1014 respondents, showing to be sufficiently representative of the Australian population. The outcomes of this research were used to develop a comprehensive framework for Australian Financial Institutions to use when developing their CSR strategy. It was clear that across all investment types and situational contexts, Community Support was the most influential form of CSR across the sample. Whilst this was the case, the level of influence differed across demographic groups and changed to varying degrees based on situational context dependent on the respondent. Community Support’s influence as a CSR initiative was clearly ahead of others presented to the respondents followed by Employee Support and Environment Support dependent on the investment method and the situational context. This research also addresses the question of influence of demographics by finding that they are a major factor in what and how CSR initiatives influence a person. This dissertation has led to the development of the CSR Strategic Investment Application (SIA) Framework which can be used by Financial Institutions in the development of an optimal CSR strategy, and a revised version of Bhattacharya and Sen’s (2004) framework leading to the Enhanced CSR Framework Model which can be applied by Australian Financial Institutions in future

Consumer Purchasing Decisions in Financial Institutions: Corporate Social Responsibility Strategy

Whilst there have been significant amounts of literature written on CSR there is still a gap in understanding how CSR activities influence consumers perception. This gap is particularly evident in the financial services sector given they are the largest contributors to CSR in Australia (ACCSR, 2011). The aim of this research is how CSR activities can influence the purchasing behaviour of consumers when it comes to financial institutions. There is a further gap in the literature in understanding how perceptions of consumers towards CSR change dependent on situational context. In addressing the research problem, the study focusses on understanding the most influential CSR initiatives, understanding how the influence of CSR initiatives can change depending on situational context and then delves further to understand how demographic attributes can alter perception. Bhattacharya and Sen’s (2004) framework was used to frame the questionnaire that was answered by 1014 respondents, showing to be sufficiently representative of the Australian population. The outcomes of this research were used to develop a comprehensive framework for Australian Financial Institutions to use when developing their CSR strategy. It was clear that across all investment types and situational contexts, Community Support was the most influential form of CSR across the sample. Whilst this was the case, the level of influence differed across demographic groups and changed to varying degrees based on situational context dependent on the respondent. Community Support’s influence as a CSR initiative was clearly ahead of others presented to the respondents followed by Employee Support and Environment Support dependent on the investment method and the situational context. This research also addresses the question of influence of demographics by finding that they are a major factor in what and how CSR initiatives influence a person. This dissertation has led to the development of the CSR Strategic Investment Application (SIA) Framework which can be used by Financial Institutions in the development of an optimal CSR strategy, and a revised version of Bhattacharya and Sen’s (2004) framework leading to the Enhanced CSR Framework Model which can be applied by Australian Financial Institutions in future

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