Void Probability Research Articles

VOID ANALYSIS OF TARGET RESIDUES AT SPS ENERGY

This paper presents new data on void analysis of target residues in ultrarelativistic nucleus–nucleus interaction. The study reveals a set of interesting observations. Void probability shows a scaling behavior at high energy (32 S –AgBr interactions at 200 A GeV) in both forward and backward hemisphere. Whereas such behavior is absent at low energy (16 O –AgBr interactions at 60 A GeV) in backward hemisphere.

Pionization at AGS and SPS energies ― degree of coherence and its target excitation dependence

The target excitation dependence of the higher order cumulant correlation of pions is studied in the present work in the framework of void probability scaling. The data set of pions produced for16O–AgBr interactions at 2.1 AGeV and32S–AgBr interactions at 200 AGeV was divided into three sets depending upon the number of grey tracks ng. The different sets of ngcorrespond to different degrees of target excitation. Analysis was carried out for each set in different pseudorapidity intervals. For the lower projectile energy the void probability scaling is observed only for low target excitation for all pseudorapidity intervals. For the comparatively higher projectile energy, scaling is observed for all pseudorapidity intervals and all target excitation. In other words, for higher projectile energy, scaling is almost independent of the target excitation. The results are interpreted from the point of view of the two source model of particle production.

THE VOID PHENOMENON EXPLAINED

We use high-resolution N-body simulations, combined with a halo occupation model of galaxy bias, to investigate voids in the galaxy distribution. Our goal is to address the phenomenon of Peebles, which presents the observed dearth of faint galaxies in voids as a challenge to current cosmology. In our model, galaxy luminosity is determined only as a function of dark matter halo mass. With this simple assumption, we demonstrate that large, empty voids of ~15 h –1 Mpc in diameter are expected even for galaxies seven magnitudes fainter than L *. The predictions of our model are in excellent agreement with several statistical measures: (i) the luminosity function of galaxies in underdense regions, (ii) nearest-neighbor statistics of dwarf galaxies, and (iii) the void probability function of faint galaxies. In the transition between filaments and voids in the dark matter, the halo mass function changes abruptly, causing the maximum galaxy luminosity to decrease by ~5 magnitudes over a range of ~ 1 h –1 Mpc. Thus, the boundary between filaments and voids in the galaxy distribution is nearly as sharp for dwarfs as for ~L * objects. These results support a picture in which galaxy formation is driven predominantly by the mass of the host dark matter halo, and is nearly independent of the larger-scale halo environment. Further, they demonstrate that ΛCDM, combined with a straightforward bias model, naturally predicts the existence of the void phenomenon.

Void analysis of pions and its multiplicity dependence at Dubna and SPS energies

This paper investigates the multiplicity dependence of void probability scaling of fluctuation of pions (i.e. classifying fluctuation patterns of pions on the basis of their number, ns) for a wide range of projectile energy from 4.5 to 200 A GeV. The study reveals that void probability scaling is dependent on pion multiplicity at all energies. At comparatively lower projectile energy the scaling becomes poor with increase in average multiplicity, however at high energy the scaling is found to be independent of multiplicity.

Statistical analysis of galaxy surveys - III. The non-linear clustering of red and blue galaxies in the 2dFGRS

We present measurements of the higher order clustering of red and blue galaxies as a function of scale and luminosity made from the two-degree field galaxy redshift survey (2dFGRS). We use a counts-in-cells analysis to estimate the volume-averaged correlation functions, ⁠, as a function of scale up to the order of p= 5, and also the reduced void probability function. Hierarchical amplitudes are constructed using the estimates of the correlation functions: ⁠. We find that (i) red galaxies display stronger clustering than blue galaxies at all orders measured; (ii) red galaxies show values of Sp that are strongly dependent on luminosity whereas blue galaxies show no segregation in Sp within the errors; this is remarkable given the segregation in the variance; (iii) the linear relative bias shows the opposite trend to the hierarchical amplitudes, with little segregation for the red sequence and some segregation for the blue; (iv) faint red galaxies deviate significantly from the ‘universal’ negative binomial reduced void probabilities followed by all other galaxy populations. Our results show that the characteristic colour of a galaxy population reveals a unique signature in its spatial distribution. Such signatures will hopefully further elucidate the physics responsible for shaping the cosmological evolution of galaxies.

Void Statistics in Large Galaxy Redshift Surveys: Does Halo Occupation of Field Galaxies Depend on Environment?

We use measurements of the projected galaxy correlation function w_p and galaxy void statistics to test whether the galaxy content of halos of fixed mass is systematically different in low density environments. We present new measurements of the void probability function (VPF) and underdensity probability function (UPF) from Data Release Four of the Sloan Digital Sky Survey, as well as new measurements of the VPF from the full data release of the Two-Degree Field Galaxy Redshift Survey. We compare these measurements to predictions calculated from models of the Halo Occupation Distribution (HOD) that are constrained to match both w_p and the space density of galaxies. The standard implementation of the HOD assumes that galaxy occupation depends on halo mass only, and is independent of local environment. For luminosity-defined samples, we find that the standard HOD prediction is a good match to the observations, and the data exclude models in which galaxy formation efficiency is reduced in low-density environments. More remarkably, we find that the void statistics of red and blue galaxies (at L ~ 0.4L_*) are perfectly predicted by standard HOD models matched to the correlation function of these samples, ruling out assembly bias models in which galaxy color is correlated with large-scale environment at fixed halo mass. We conclude that the luminosity and color of field galaxies are determined predominantly by the mass of the halo in which they reside and have little direct dependence on the environment in which the host halo formed. In broader terms, our results show that the sizes and emptiness of voids found in the distribution of L > 0.2L_* galaxies are in excellent agreement with the predictions of a standard cosmological model with a simple connection between galaxies and dark matter halos. (abridged)

Evidence of azimuthal void probability scaling in relativistic and ultra relativistic nuclear interactions

A study of azimuthal angle void probability of produced pions has been carried out in relativistic and ultra relativistic nucleus–nucleus interactions (32S–AgBr interactions at 200 A GeV, 16O–AgBr interactions at 60 A GeV , 24Mg–AgBr interactions at 4.5 A GeV and 12C–AgBr interactions at 4.5 A GeV). The study reveals a very interesting observation-void probability showing scaling behaviour at significantly lower energy (24Mg–AgBr interactions at 4.5 A GeV and 12C–AgBr interactions at 4.5 A GeV) whereas the behaviour is not so pronounced at higher energy in 16O–AgBr interactions at 60 A GeV and the data do not reveal scaling behaviour at all in case of 32S–AgBr interactions at 200 A GeV.

Signature of void probability scaling in jet-like events in 16O–AgBr interactions at 60 GeV/n

This paper presents the analysis of jet-like and ring-like events to study the rapidity gap probability of pions produced in 16O–AgBr interactions at 60 A GeV. The study reveals the scaling behavior of the void probability for the jet-like events. However for ring-like events, the rapidity gap probability does not obey the scaling law.

Cosmic Voids and Galaxy Bias in the Halo Occupation Framework

(Abridged) We investigate the power of void statistics to constrain galaxy bias and the amplitude of dark matter fluctuations. We use the halo occupation distribution (HOD) framework to describe the relation between galaxies and dark matter. After choosing HOD parameters that reproduce the mean space density n_gal and projected correlation function w_p measured for galaxy samples with M_r<-19 and M_r<-21 from the Sloan Digital Sky Survey (SDSS), we predict the void probability function (VPF) and underdensity probability function (UPF) of these samples by populating the halos of a large, high-resolution N-body simulation. If we make the conventional assumption that the HOD is independent of large scale environment at fixed halo mass, then models constrained to match n_gal and w_p predict nearly identical void statistics, independent of the scatter between halo mass and central galaxy luminosity or uncertainties in HOD parameters. Models with sigma_8=0.7 and sigma_8=0.9 also predict very similar void statistics. However, the VPF and UPF are sensitive to environmental variations of the HOD in a regime where these variations have little impact on w_p. For example, doubling the minimum host halo mass in regions with large scale (5 Mpc/h) density contrast delta<-0.65 has a readily detectable impact on void probabilities of M_r<-19 galaxies, and a similar change for delta<-0.2 alters the void probabilities of M_r<-21 galaxies at a detectable level. The VPF and UPF provide complementary information about the onset and magnitude of density- dependence in the HOD. By detecting or ruling out HOD changes in low density regions, void statistics can reduce systematic uncertainties in the cosmological constraints derived from HOD modeling, and, more importantly, reveal connections between halo formation history and galaxy properties.

The DEEP2 Galaxy Redshift Survey: The Evolution of Void Statistics fromz∼ 1 toz∼ 0

We present measurements of the void probability function (VPF) at z~1 using data from the DEEP2 Redshift Survey and its evolution to z~0 using data from the Sloan Digital Sky Survey (SDSS). We measure the VPF as a function of galaxy color and luminosity in both surveys and find that it mimics trends displayed in the two-point correlation function, $\xi$; namely that samples of brighter, red galaxies have larger voids (i.e. are more strongly clustered) than fainter, blue galaxies. We also clearly detect evolution in the VPF with cosmic time, with voids being larger in comoving units at z~0. We find that the reduced VPF matches the predictions of a `negative binomial' model for galaxies of all colors, luminosities, and redshifts studied. This model lacks a physical motivation, but produces a simple analytic prediction for sources of any number density and integrated two-point correlation function, \bar{\xi}. This implies that differences in the VPF across different galaxy populations are consistent with being due entirely to differences in the population number density and \bar{\xi}. The robust result that all galaxy populations follow the negative binomial model appears to be due to primarily to the clustering of dark matter halos. The reduced VPF is insensitive to changes in the parameters of the halo occupation distribution, in the sense that halo models with the same \bar{\xi} will produce the same VPF. For the wide range of galaxies studied, the VPF therefore does not appear to provide useful constraints on galaxy evolution models that cannot be gleaned from studies of \bar{\xi} alone. (abridged)

Tracing the nature of dark energy with galaxy distribution

Dynamical dark energy (DE) is a viable alternative to the cosmological constant. Constructing tests to discriminate between Λ and dynamical DE models is difficult, however, because the differences are not large. In this paper we explore tests based on the galaxy mass function, the void probability function (VPF), and the number of galaxy clusters. At high z, the number density of clusters shows large differences between DE models, but geometrical factors reduce the differences substantially. We find that detecting a model dependence in the cluster redshift distribution is a significant challenge. We show that the galaxy redshift distribution is potentially a more sensitive characteristic. We do this by populating dark matter haloes in N-body simulations with galaxies using well-tested halo occupation distributions. We also estimate the VPF and find that samples with the same angular surface density of galaxies, in different models, exhibition almost model-independent VPF which therefore cannot be used as a test for DE. Once again, geometry and cosmic evolution compensate each other. By comparing VPFs for samples with fixed galaxy mass limits, we find measurable differences.

Linking halo mass to galaxy luminosity

In this paper we present a new, essentially empirical, model for the relation between the mass of a dark matter halo/subhalo and the luminosity of a galaxy hosted in it. To estimate this, we replace the assumption of linearity between light and mass fluctuations with the assumption of monotonicity between galaxy light and halo or subhalo mass. We are enabled to proceed with this less restrictive ansatz by the availability of new, very high resolution dark matter simulations and more detailed and comprehensive global galactic luminosity functions. We find that the relation between halo/subhalo mass and hosted galaxy luminosity is fairly well fit by a double power law, while that between halo mass and group luminosity is fairly well fit by a two branch function, with both branches double power laws. Both relations asymptote to $L\propto M^4$ at low $M$, while at high mass the former follows $L\propto M^{0.28}$ and the latter $L\propto M^{0.9}$. We also derive results for the occupation number, luminosity function of cluster galaxies, group luminosity function and multiplicity function. Then, using some additional assumptions, we further derive results for biasing between mass and light and mass and galaxy number, light distribution function and the void probability distribution. Our results for the most part seem to match well with observations and previous expectations. We feel this is a potentially powerful way of modelling this relation, since the main inputs are readily testable against dark matter simulation results and galaxy surveys. (abridged)

The 2dF Galaxy Redshift Survey: voids and hierarchical scaling models

We measure the redshift space reduced void probability function (VPF) for 2dFGRS volume limited galaxy samples covering the absolute magnitude range M_bJ-5logh=-18 to -22. Theoretically, the VPF connects the distribution of voids to the moments of galaxy clustering of all orders, and can be used to discriminate clustering models in the weakly non-linear regime. The reduced VPF measured from the 2dFGRS is in excellent agreement with the paradigm of hierarchical scaling of the galaxy clustering moments. The accuracy of our measurement is such that we can rule out, at a very high significance, popular models for galaxy clustering, including the lognormal distribution. We demonstrate that the negative binomial model gives a very good approximation to the 2dFGRS data over a wide range of scales, out to at least 20h-1Mpc. Conversely, the reduced VPF for dark matter in a LambdaCDM universe does appear to be lognormal on small scales but deviates significantly beyond \approx 4h-1Mpc. We find little dependence of the 2dFGRS reduced VPF on galaxy luminosity. Our results hold independently in both the north and south Galactic pole survey regions.

Voids in the Two‐Degree Field Galaxy Redshift Survey

We present an analysis of voids in the 2dF Galaxy Redshift Survey (2dFGRS). This analysis includes identification of void regions and measurement of void statistics. The 2dFGRS is the largest completed redshift survey to date, including a total of 245,591 galaxies covering 1500 deg2 to a median depth of zmed ~ 0.11. We use the voidfinder algorithm to identify a total of 289 voids in the 2dFGRS with radius larger than 10 h-1 Mpc. These voids have an average effective radius, the radius of a sphere with the same volume as the void, of h-1 Mpc in the North Galactic Pole region (NGP) and h-1 Mpc in the South Galactic Pole region (SGP). These voids are extremely underdense, with average density contrast of δρ/ρ = -0.94 ± 0.02. The centers of voids are even emptier, because the few galaxies within the voids typically lie close to the edges. The total volume of the universe filled by these void regions is approximately 40%. These results are very similar to results found from our analysis of the PSCz survey and the Updated Zwicky Catalog; here we detect almost a factor of 10 more voids. We measure the void probability function (VPF) of the 2dFGRS for volume-limited samples with limiting absolute magnitudes, Mlim - 5 log h, from -16 to -21 in bJ. We measure the underdensity probability function (with density contrast threshold δρ/ρ = -0.8) for samples with limiting absolute magnitudes, Mlim - 5 log h, from -18 to -21. We find that the SGP is more underdense than the NGP for all but the brightest sample under consideration. There is good agreement between the VPFs of the Center for Astrophysics survey and the 2dFGRS. Comparison of VPFs measured for the 2dFGRS with the distribution of simulated dark matter halos of similar number density indicates that voids in the matter distribution in ΛCDM simulations are not empty enough. However, semianalytic models of galaxy formation that include feedback effects yield VPFs that show excellent agreement with the data.

Signature of void probability scaling in multipion production at a few GeV∕nucleon

A study of rapidity gap probability has been carried out in $^{16}\mathrm{O}\text{\ensuremath{-}}\text{AgBr}$ interactions at $2.1A\phantom{\rule{0.3em}{0ex}}\text{GeV}$. The study reveals scaling behavior of the void probability. This analysis also confirms the validity of the linked-pair approximation for the $N$-particle cumulant correlation functions in the low energy regime.

Void probability scaling in target fragmentation of high energy nucleus–nucleus collisions

This study reports the scaling behaviour of void probability in limited phase space during the emission of slow target fragments in 12C–AgBr and 24Mg–AgBr interactions at 4.5 A GeV. This study will also enable us to check the validity of linked pair ansatz.

Observation of Void Probability Scaling of Proton Emission in High Energy Nucleus–Nucleus Collisions

In this paper the study of gap probability of protons has been carried out with 28 Si–AgBr interaction at 14.5 A GeV in emission angle space. The study reveals the scaling behaviour of the void probability which hints towards the outer space–inner space connection. This study also confirms the validity of the linked pair approximation for the N-particle cumulant correlation functions in case of protons.

Analysing large-scale structure — I. Weighted scaling indices and constrained randomization

The method of constrained randomisation, which was originally developed in the field of time series analysis for testing for nonlinearities, is extended to the case of three-dimensional point distributions as they are typical in the analysis of the large scale structure of galaxy distributions in the universe. With this technique it is possible to generate for a given data set so-called surrogate data sets which have the same linear properties as the original data whereas higher order or nonlinear correlations are not preserved. The analysis of the original and surrogate data sets with measures, which are sensitive to nonlinearities, yields valuable information about the existence of nonlinear correlations in the data. On the other hand one can test whether given statistical measures are able to account for higher order or nonlinear correlations by applying them to original and surrogate data sets. We demonstrate how to generate surrogate data sets from a given point distribution, which have the same linear properties (power spectrum) as well as the same density amplitude distribution but different morphological features. We propose weighted scaling indices, which measure the local scaling properties of a point set, as a nonlinear statistical measure to quantify local morphological elements in large scale structure. Using surrogates is is shown that the data sets with the same 2-point correlation functions have slightly different void probability functions and especially a different set of weighted scaling indices. Thus a refined analysis of the large scale structure becomes possible by calculating local scaling properties whereby the method of constrained randomisation yields a vital tool for testing the performance of statistical measures in terms of sensitivity to different topological features and discriminative power.

The Halo Occupation Distribution: Toward an Empirical Determination of the Relation between Galaxies and Mass

We investigate galaxy bias in the framework of the halo occupation distribution (HOD), which defines the bias of a population of galaxies by the conditional probability P(N|M) that a dark matter halo of virial mass M contains N galaxies, together with prescriptions that specify the relative spatial and velocity distributions of galaxies and dark matter within halos. By populating the halos of a cosmological N-body simulation using a variety of HOD models, we examine the sensitivity of different galaxy clustering statistics to properties of the HOD. The galaxy correlation function responds to different aspects of P(N|M) on different scales. Obtaining the observed power-law form of ξg(r) requires rather specific combinations of HOD parameters, implying a strong constraint on the physics of galaxy formation; the success of numerical and semianalytic models in reproducing this form is entirely nontrivial. Other clustering statistics such as the galaxy-mass correlation function, the bispectrum, the void probability function, the pairwise velocity dispersion, and the group multiplicity function are sensitive to different combinations of HOD parameters and thus provide complementary information about galaxy bias. We outline a strategy for determining the HOD empirically from redshift survey data. This method starts from an assumed cosmological model, but we argue that cosmological and HOD parameters will have nondegenerate effects on galaxy clustering, so that a substantially incorrect cosmological model will not reproduce the observations for any choice of HOD. Empirical determinations of the HOD as a function of galaxy type from the Two-Degree Field (2dF) and Sloan Digital Sky Survey (SDSS) redshift surveys will provide a detailed target for theories of galaxy formation, insight into the origin of galaxy properties, and sharper tests of cosmological models.

Galaxy voids in cold dark matter universes

We present predictions for numerous statistics related to the presence of voids in the distribution of galaxies in a cold dark matter model of structure formation using a semi-analytic model of galaxy formation. Our study is able to probe galaxies with masses as low as 109h−1 M⊙ corresponding to absolute magnitudes of −5log h=−18.1 and Mr− 5 log h=−18.7. We quantify the void and underdense probability functions, distributions of nearest-neighbour distances and void sizes and compute the density profiles of voids. These results are contrasted with the expectations for dark matter (and the difference examined in terms of the galaxy/dark matter biasing relation) and are compared with analytic predictions and observational data where available. The predicted void probability functions are consistent with those measured from the Centre for Astrophysics redshift surveys given the rather large uncertainties in this relatively small (for studies of voids) observational sample. The size of the observational sample is too small to probe the bias between galaxies and dark matter that we predict. We also examine the predicted properties of galaxies existing within voids and contrast these with the general galaxy population. Our predictions are aimed at forthcoming large galaxy redshift surveys that should for the first time provide statistically accurate measures of the void population.