Nico Hamaus

Minimizing the stochasticity of halos in large-scale structure surveys

In recent work (Seljak, Hamaus, and Desjacques 2009) it was found that weighting central halo galaxies by halo mass can significantly suppress their stochasticity relative to the dark matter, well below the Poisson model expectation. This is useful for constraining relations between galaxies and the dark matter, such as the galaxy bias, especially in situations where sampling variance errors can be eliminated. In this paper we extend this study with the goal of finding the optimal mass-dependent halo weighting. We use N-body simulations to perform a general analysis of halo stochasticity and its dependence on halo mass. We investigate the stochasticity matrix, defined as C{sub ij{identical_to}} , where {delta}{sub m} is the dark matter overdensity in Fourier space, {delta}{sub i} the halo overdensity of the i-th halo mass bin, and b{sub i} the corresponding halo bias. In contrast to the Poisson model predictions we detect nonvanishing correlations between different mass bins. We also find the diagonal terms to be sub-Poissonian for the highest-mass halos. The diagonalization of this matrix results in one large and one low eigenvalue, with the remaining eigenvalues close to the Poisson prediction 1/n, where n is the mean halo number density. The eigenmodemorexa0» with the lowest eigenvalue contains most of the information and the corresponding eigenvector provides an optimal weighting function to minimize the stochasticity between halos and dark matter. We find this optimal weighting function to match linear mass weighting at high masses, while at the low-mass end the weights approach a constant whose value depends on the low-mass cut in the halo mass function. This weighting further suppresses the stochasticity as compared to the previously explored mass weighting. Finally, we employ the halo model to derive the stochasticity matrix and the scale-dependent bias from an analytical perspective. It is remarkably successful in reproducing our numerical results and predicts that the stochasticity between halos and the dark matter can be reduced further when going to halo masses lower than we can resolve in current simulations.«xa0less

Going beyond the Kaiser redshift-space distortion formula: A full general relativistic account of the effects and their detectability in galaxy clustering

Institute for Theoretical Physics, University of Zürich, CH-8057 Zürich, Switzerland Lawrence Berkeley National Laboratory, University of Cali fornia, Berkeley, CA 94720, USA Physics Department and Astronomy Department, University o f California, Berkeley, CA 94720, USA Institute for the Early Universe, Ewha Womans University, 1 20-750 Seoul, South Korea and School of Natural Sciences, Institute for Advanced Study, E instein Drive, Princeton, NJ 08540, USAKaiser redshift-space distortion formula describes well the clustering of galaxies in redshift surveys on small scales, but there are numerous additional terms that arise on large scales. Some of these terms can be described using Newtonian dynamics and have been discussed in the literature, while the others require proper general relativistic description that was only recently developed. Accounting for these terms in galaxy clustering is the first step toward tests of general relativity on horizon scales. The effects can be classified as two terms that represent the velocity and the gravitational potential contributions. Their amplitude is determined by effects such as the volume and luminosity distance fluctuation effects and the time evolution of galaxy number density and Hubble parameter. We compare the Newtonian approximation often used in the redshift-space distortion literature to the fully general relativistic equation, and show that Newtonian approximation accounts for most of the terms contributing to velocity effect. We perform a Fisher matrix analysis of detectability of these terms and show that in a single tracer survey they are completely undetectable. To detect these terms one must resort to the recently developed methods to reduce sampling variance and shot noise. We show that in an all-sky galaxy redshift survey at low redshift the velocity term can be measured at a few sigma if one can utilize halos of mass M≥1012h-1Msun (this can increase to 10-σ or more in some more optimistic scenarios), while the gravitational potential term itself can only be marginally detected. We also demonstrate that the general relativistic effect is not degenerate with the primordial non-Gaussian signature in galaxy bias, and the ability to detect primordial non-Gaussianity is little compromised.

Universal density profile for cosmic voids.

We present a simple empirical function for the average density profile of cosmic voids, identified via the watershed technique in ΛCDM N-body simulations. This function is universal across void size and redshift, accurately describing a large radial range of scales around void centers with only two free parameters. In analogy to halo density profiles, these parameters describe the scale radius and the central density of voids. While we initially start with a more general four-parameter model, we find two of its parameters to be redundant, as they follow linear trends with the scale radius in two distinct regimes of the void sample, separated by its compensation scale. Assuming linear theory, we derive an analytic formula for the velocity profile of voids and find an excellent agreement with the numerical data as well. In our companion paper [Sutter et al., arXiv:1309.5087 [Mon. Not. R. Astron. Soc. (to be published)]], the presented density profile is shown to be universal even across tracer type, properly describing voids defined in halo and galaxy distributions of varying sparsity, allowing us to relate various void populations by simple rescalings. This provides a powerful framework to match theory and simulations with observational data, opening up promising perspectives to constrain competing models of cosmology and gravity.

How to suppress the shot noise in galaxy surveys

Galaxy surveys are one of the most powerful means to extract cosmological information and for a given volume the attainable precision is determined by the galaxy shot noise sigma(n);(2) relative to the power spectrum P. It is generally assumed that shot noise is white and given by the inverse of the number density n[over ]. In this Letter we argue one may considerably improve upon this due to mass and momentum conservation. We explore this idea with N-body simulations by weighting central halo galaxies by halo mass and find that the resulting shot noise can be reduced dramatically relative to expectations, with a 10-30 suppression at n[over ] = 4x10(-3) (h/Mpc)(3). These results open up new opportunities to extract cosmological information in galaxy surveys and may have important consequences for the planning of future redshift surveys.

Cosmology with void-galaxy correlations.

Galaxy bias, the unknown relationship between the clustering of galaxies and the underlying dark matter density field is a major hurdle for cosmological inference from large-scale structure. While traditional analyses focus on the absolute clustering amplitude of high-density regions mapped out by galaxy surveys, we propose a relative measurement that compares those to the underdense regions, cosmic voids. On the basis of realistic mock catalogs we demonstrate that cross correlating galaxies and voids opens up the possibility to calibrate galaxy bias and to define a static ruler thanks to the observable geometric nature of voids. We illustrate how the clustering of voids is related to mass compensation and show that volume-exclusion significantly reduces the degree of stochasticity in their spatial distribution. Extracting the spherically averaged distribution of galaxies inside voids from their cross correlations reveals a remarkable concordance with the mass-density profile of voids.

Halo stochasticity from exclusion and nonlinear clustering

The clustering of galaxies in ongoing and upcoming galaxy surveys contains a wealth of cosmological information, but extracting this information is a nontrivial task since galaxies and their host haloes are stochastic tracers of the nonlinear matter density field. This stochasticity is usually modeled as the Poisson shot noise, which is constant as a function of wave number 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 behavior and develop models that explain the behavior of the stochasticity on large scales. First, haloes are extended, nonoverlapping 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 wave number k, decreasing to zero for wave numbers large compared to the inverse exclusion scale. Second, haloes show a nonlinear 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 < 0:1h Mpc-1. 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 (Eulerian space), relative to the initial conditions (Lagrangian space). These corrections vary with halo mass, and we present approximate scalings with halo mass and redshift. We also discuss simple applications of these effects to galaxy samples with nonvanishing 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 modeled properly if we want to extract high precision cosmological information from the upcoming galaxy redshift surveys.

GRAVITY: getting to the event horizon of Sgr A*

We present the second-generation VLTI instrument GRAVITY, which currently is in the preliminary design phase. GRAVITY is specifically designed to observe highly relativistic motions of matter close to the event horizon of Sgr A*, the massive black hole at center of the Milky Way. We have identified the key design features needed to achieve this goal and present the resulting instrument concept. It includes an integrated optics, 4-telescope, dual feed beam combiner operated in a cryogenic vessel; near infrared wavefront sensing adaptive optics; fringe tracking on secondary sources within the field of view of the VLTI and a novel metrology concept. Simulations show that the planned design matches the scientific needs; in particular that 10µas astrometry is feasible for a source with a magnitude of K=15 like Sgr A*, given the availability of suitable phase reference sources.

Sparse sampling, galaxy bias, and voids

To study the impact of sparsity and galaxy bias on void statistics, we use a single large-volume, high-resolution N-body simulation to compare voids in multiple levels of subsampled dark matter, halo populations, and mock galaxies from a Halo Occupation Distribution model tuned to dierent galaxy survey densities. We focus our comparison on three key observational statistics: number functions, ellipticity distributions, and radial density proles. We use the hierarchical tree structure of voids to

Optimal Constraints on Local Primordial Non-Gaussianity from the Two-Point Statistics of Large-Scale Structure

One of the main signatures of primordial non-Gaussianity of the local type is a scale-dependent correction to the bias of large-scale structure tracers such as galaxies or clusters, whose amplitude depends on the bias of the tracers itself. The dominant source of noise in the power spectrum of the tracers is caused by sampling variance on large scales (where the non-Gaussian signal is strongest) and shot noise arising from their discrete nature. Recent work has argued that one can avoid sampling variance by comparing multiple tracers of different bias, and suppress shot noise by optimally weighting halos of different mass. Here we combine these ideas and investigate how well the signatures of non-Gaussian fluctuations in the primordial potential can be extracted from the two-point correlations of halos and dark matter. On the basis of large N-body simulations with local non-Gaussian initial conditions and their halo catalogs we perform a Fisher matrix analysis of the two-point statistics. Compared to the standard analysis, optimal weighting and multiple-tracer techniques applied to halos can yield up to 1 order of magnitude improvements in f{sub NL}-constraints, even if the underlying dark matter density field is not known. In this case one needs to resolve allmorexa0» halos down to 10{sup 10}h{sup -1}M{sub sun} at z=0, while with the dark matter this is already achieved at a mass threshold of 10{sup 12}h{sup -1}M{sub sun}. We compare our numerical results to the halo model and find satisfactory agreement. Forecasting the optimal f{sub NL}-constraints that can be achieved with our methods when applied to existing and future survey data, we find that a survey of 50h{sup -3} Gpc{sup 3} volume resolving all halos down to 10{sup 11}h{sup -1}M{sub sun} at z=1 will be able to obtain {sigma}{sub f{sub N{sub L}}}{approx}1 (68% cl), a factor of {approx}20 improvement over the current limits. Decreasing the minimum mass of resolved halos, increasing the survey volume or obtaining the dark matter maps can further improve these limits, potentially reaching the level of {sigma}{sub f{sub N{sub L}}}{approx}0.1. This precision opens up the possibility to distinguish different types of primordial non-Gaussianity and to probe inflationary physics of the very early Universe.«xa0less

Prospects for testing the nature of Sgr A*'s near-infrared flares on the basis of current very large telescope—and future very large telescope interferometer—observations

Sagittarius A*, the supermassive compact object at the center of the Galaxy, exhibits outbursts in the near infrared and X-ray domains. These flares are likely due to energetic events very close to the central object, on a scale of a few Schwarzschild radii. Optical interferometry will soon be able to provide astrometry with an accuracy of this order (~10 muas). In this article we use recent photometric near infrared data observed with the adaptive optics system NACO at the Very Large Telescope combined with simulations in order to deploy a method to test the nature of the flares and to predict the possible outcome of observations with the Very Large Telescope Interferometer. To accomplish this we implement a hot spot model and investigate its appearance for a remote observer in terms of light curves and centroid tracks, based on general relativistic ray tracing methods. First, we use a simplified model of a small steady source in order to investigate the relativistic effects qualitatively. A more realistic scenario is then being developed by fitting our model to existing flare data. While indications for the spin of the black hole and multiple images due to lensing effects are marginal in the light curves, astrometric measurements offer the possibility to reveal these high-order general relativistic effects. This study makes predictions on these astrometric measurements and leads us to the conclusion that future infrared interferometers will be able to detect proper motion of hot spots in the vicinity of Sagittarius A*.Sagittarius A*, the supermassive compact object at the center of the Galaxy, exhibits outbursts in the near infrared (NIR) and X-ray domains. These flares are likely due to energetic events very close to the central object, on a scale of a few Schwarzschild radii. Optical interferometry will soon be able to provide astrometry with an accuracy of this order (10 μas). In this article, we use recent photometric NIR data observed with the adaptive optics system NACO at the Very Large Telescope combined with simulations in order to deploy a method to test the nature of the flares and to predict the possible outcome of observations with the Very Large Telescope Interferometer. To accomplish this we implement a hot-spot model and investigate its appearance for a remote observer in terms of light curves and centroid tracks, based on general relativistic ray-tracing methods. First, we use a simplified model of a small steady source in order to investigate the relativistic effects qualitatively. A more realistic scenario is then being developed by fitting our model to existing flare data. While indications for the spin of the black hole and multiple images due to lensing effects are marginal in the light curves, astrometric measurements offer the possibility to reveal these high-order general relativistic effects. This study makes predictions on these astrometric measurements and leads us to the conclusion that future infrared interferometers will be able to detect proper motion of hot spots in the vicinity of Sagittarius A*.