Void statistics and hierarchical scaling in the halo model

Fry, J. N.; Colombi, S.

doi:10.1093/mnras/stt745

Cited by 12 publications

(15 citation statements)

References 63 publications

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“…The hierarchical scaling between the count-in-cells measured VPF and volume-averaged correlation functions has been found to follow the negative binomial model (NBM) in z < 1 galaxy surveys (e.g., Croton et al 2004a;Conroy et al 2005;Tinker et al 2008) and in simulations (e.g., Andrew et al 2013). Conroy et al (2005) deduce and Fry & Colombi (2013) confirm that the NBM of clustering scaling is a feature of the underlying dark matter halos. Additionally, the VPF alone has been used to constrain cosmological parameters of large scale structure (ex.…”

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confidence: 59%

“…The NBM can be derived through many methods and has been used to statistically describe phenomena across many fields of science. It is also known as the modified Bose-Einstein distribution (see Fry & Colombi 2013 for a succinct derivation in that context). The NBM was first used a cosmological context by Carruthers & Duong-van (1983) and derived for clustering analysis by Elizalde & Gaztanaga (1992).…”

Section: The Negative Binomial Model For Hierarchical Scalingmentioning

confidence: 99%

“…Although it is an robust description of many galaxy samples, the NBM is arguably not physically motivated. Fry & Colombi (2013) argue that "there is no fundamental reason that galaxies follow the negative binomial scaling curve, but that this follows from typical galaxy parameters" like bias and number density. Some authors find it justified (Carruthers & Duong-van 1983;Elizalde & Gaztanaga 1992;Betancort-Rijo 2000).…”

Section: The Negative Binomial Model For Hierarchical Scalingmentioning

confidence: 99%

“…We discuss the negative binomial model in great detail in §4.3. The bulk of this list and the functional forms of the models come from C05, Cr04, and Fry & Colombi (2013). The order of these models follows the order of their curves in Figure 4, from top to bottom.…”

Section: Appendixmentioning

confidence: 99%

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Void Probability Function of Simulated Surveys of high-redshift Lyman-Alpha Emitters

Perez,

Malhotra,

Rhoads

et al. 2020

Preprint

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We calculate the void probability function (VPF) in simulations of Lyman-α emitters (LAEs) across a wide redshift range (z = 3.1, 4.5, 5.7, 6.6). The VPF measures the zero-point correlation function (i.e. places devoid of galaxies) and naturally connects to higher order correlation functions while being computationally simple to calculate. We explore the Poissonian and systematic errors on the VPF, specify its accuracy as a function of average source density and the volume probed, and provide the appropriate size scales to measure the VPF. At small radii the accuracy of the VPF is limited by galaxy density, while at large radii the VPF is limited by the number of independent volumes probed. We also offer guidelines for understanding and quantifying the error in the VPF. We approximate the error in the VPF by using independent sub-volumes of the catalogs, after finding that jackknife statistics underestimate the uncertainty. We use the VPF to probe the strength of higher order correlation functions by measuring and examining the hierarchical scaling between the correlation functions using count-in-cells. The negative binomial model (NBM) has been shown to best describe the scaling between the two point correlation function and VPF for low-redshift galaxy observations. We further test the fit of the NBM by directly deriving the volume averaged two-point correlation function from the VPF and vice versa. We find the NBM best describes the z = 3.1, 4.5, 5.7 simulated LAEs, with a 1σ deviation from the model in the z = 6.6 catalog. This suggests that LAEs show higher order clustering terms similar to those of normal low redshift galaxies.

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mentioning

confidence: 59%

Section: The Negative Binomial Model For Hierarchical Scalingmentioning

confidence: 99%

Section: The Negative Binomial Model For Hierarchical Scalingmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

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Void Probability Function of Simulated Surveys of high-redshift Lyman-Alpha Emitters

Perez,

Malhotra,

Rhoads

et al. 2020

Preprint

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“…( 16). As shown by Fry & Colombi (2013), this can be explained by the halo model if the distribution of host haloes follows the hierarchical pattern. Moreover, one should expect that different populations of tracers are described by different void scaling relations.…”

Section: Hierarchical Scaling and Random Dilutionsmentioning

confidence: 93%

Ultraviolet background fluctuations with clustered sources

Desjacques

Dizgah

Biagetti

2014

Monthly Notices of the Royal Astronomical Society

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We develop a count-in-cells approach to the distribution of ultraviolet background fluctuations that includes source clustering. We demonstrate that an exact expression can be obtained if the clustering of ionising sources follows the hierarchical ansatz. In this case, the intensity distribution depends solely on their 2-point correlation function. We show that the void scaling function of high redshift mock quasars is consistent with the Negative Binomial form, before applying our formalism to the description of HeII-ionising fluctuations at the end of helium reionization. The model inputs are the observed quasar luminosity function and 2-point correlation at z ∼ 3. We find that, for an (comoving) attenuation length 55 Mpc, quasar clustering contributes less than 30% of the variance of intensity fluctuations so long as the quasar correlation length does not exceed ∼ 15 Mpc. We investigate also the dependence of the intensity distribution on the large-scale environment. Differences in the mean HeII-ionising intensity between low-and high-density regions could be a factor of few if the sources are highly clustered. An accurate description of quasar demographics and their correlation with strong absorption systems is required to make more precise predictions. Recently, Dixon, Furlanetto & Mesinger (2014) have addressed the impact of quasar clustering using a seminumeric method, in which dark matter haloes are identified in realisations of the linear density field using the excursion set approach. They have found a relatively weak effect. However, given the current uncertainties on the demographics of high redshift quasars, it would be desirable to revisit this issue and explore a wider spectrum of quasar clustering amplitudes.In this paper, we will investigate this issue analytically c 0000 RAS

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Significance of the negative binomial distribution in multiplicity phenomena

Tezlaf

2023

Phys. Scr.

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The negative binomial distribution (NBD) has been theorized to express a scale-invariant property of many-body systems and has been consistently shown to outperform other statistical models in both describing the multiplicity of quantum-scale events in particle collision experiments and predicting the prevalence of cosmological observables, such as the number of galaxies in a region of space. Despite its widespread applicability and empirical success in these contexts, a theoretical justification for the NBD from first principles has remained elusive for fifty years. The accuracy of the NBD in modeling hadronic, leptonic, and semileptonic processes is suggestive of a highly general principle, which is yet to be understood. This study demonstrates that a statistical event of the NBD can in fact be derived in a general context via the dynamical equations of a canonical ensemble of particles in Minkowski space. These results describe a fundamental feature of many-body systems that is consistent with data from the ALICE and ATLAS experiments and provides an explanation for the emergence of the NBD in these multiplicity observations. Two methods are used to derive this correspondence: the Feynman path integral and a hypersurface parametrization of a propagating ensemble.

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Void statistics and hierarchical scaling in the halo model

Cited by 12 publications

References 63 publications

Void Probability Function of Simulated Surveys of high-redshift Lyman-Alpha Emitters

Void Probability Function of Simulated Surveys of high-redshift Lyman-Alpha Emitters

Ultraviolet background fluctuations with clustered sources

Significance of the negative binomial distribution in multiplicity phenomena

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