2,183 research outputs found

    An excursion set model of the cosmic web: The abundance of sheets, filaments and halos

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    We discuss an analytic approach for modeling structure formation in sheets, filaments and knots. This is accomplished by combining models of triaxial collapse with the excursion set approach: sheets are defined as objects which have collapsed along only one axis, filaments have collapsed along two axes, and halos are objects in which triaxial collapse is complete. In the simplest version of this approach, which we develop here, large scale structure shows a clear hierarchy of morphologies: the mass in large-scale sheets is partitioned up among lower mass filaments, which themselves are made-up of still lower mass halos. Our approach provides analytic estimates of the mass fraction in sheets, filaments and halos, and its evolution, for any background cosmological model and any initial fluctuation spectrum. In the currently popular Λ\LambdaCDM model, our analysis suggests that more than 99% of the cosmic mass is in sheets, and 72% in filaments, with mass larger than 1010M⊙10^{10} M_{\odot} at the present time. For halos, this number is only 46%. Our approach also provides analytic estimates of how halo abundances at any given time correlate with the morphology of the surrounding large-scale structure, and how halo evolution correlates with the morphology of large scale structure.Comment: 22 pages, 7 figures, Accepted for publication in Ap

    Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis

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    In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multimodal or exhibit pronounced (curving) degeneracies, which can cause problems for traditional MCMC sampling methods. Second, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive. The nested sampling method introduced by Skilling (2004), has greatly reduced the computational expense of calculating evidences and also produces posterior inferences as a by-product. This method has been applied successfully in cosmological applications by Mukherjee et al. (2006), but their implementation was efficient only for unimodal distributions without pronounced degeneracies. Shaw et al. (2007), recently introduced a clustered nested sampling method which is significantly more efficient in sampling from multimodal posteriors and also determines the expectation and variance of the final evidence from a single run of the algorithm, hence providing a further increase in efficiency. In this paper, we build on the work of Shaw et al. and present three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies; we also present an even more efficient technique for estimating the uncertainty on the evaluated evidence. These methods lead to a further substantial improvement in sampling efficiency and robustness, and are applied to toy problems to demonstrate the accuracy and economy of the evidence calculation and parameter estimation. Finally, we discuss the use of these methods in performing Bayesian object detection in astronomical datasets.Comment: 14 pages, 11 figures, submitted to MNRAS, some major additions to the previous version in response to the referee's comment

    Depolarization regions of nonzero volume in bianisotropic homogenized composites

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    In conventional approaches to the homogenization of random particulate composites, the component phase particles are often treated mathematically as vanishingly small, point-like entities. The electromagnetic responses of these component phase particles are provided by depolarization dyadics which derive from the singularity of the corresponding dyadic Green functions. Through neglecting the spatial extent of the depolarization region, important information may be lost, particularly relating to coherent scattering losses. We present an extension to the strong-property-fluctuation theory in which depolarization regions of nonzero volume and ellipsoidal geometry are accommodated. Therein, both the size and spatial distribution of the component phase particles are taken into account. The analysis is developed within the most general linear setting of bianisotropic homogenized composite mediums (HCMs). Numerical studies of the constitutive parameters are presented for representative examples of HCM; both Lorentz-reciprocal and Lorentz-nonreciprocal HCMs are considered. These studies reveal that estimates of the HCM constitutive parameters in relation to volume fraction, particle eccentricity, particle orientation and correlation length are all significantly influenced by the size of the component phase particles

    The Excursion Set Theory of Halo Mass Functions, Halo Clustering, and Halo Growth

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    I review the excursion set theory (EST) of dark matter halo formation and clustering. I recount the Press-Schechter argument for the mass function of bound objects and review the derivation of the Press-Schechter mass function in EST. The EST formalism is powerful and can be applied to numerous problems. I review the EST of halo bias and the properties of void regions. I spend considerable time reviewing halo growth in the EST. This section culminates with descriptions of two Monte Carlo methods for generating halo mass accretion histories. In the final section, I emphasize that the standard EST approach is the result of several simplifying assumptions. Dropping these assumptions can lead to more faithful predictions and a more versatile formalism. One such assumption is the constant height of the barrier for nonlinear collapse. I review implementations of the excursion set approach with arbitrary barrier shapes. An application of this is the now well-known improvement to standard EST that follows from the ellipsoidal-collapse barrier. Additionally, I emphasize that the statement that halo accretion histories are independent of halo environments is a simplifying assumption, rather than a prediction of the theory. I review the method for constructing correlated random walks of the density field in more general cases. I construct a simple toy model with correlated walks and I show that excursion set theory makes a qualitatively simple and general prediction for the relation between halo accretion histories and halo environments: regions of high density preferentially contain late-forming halos and conversely for regions of low density. I conclude with a brief discussion of this prediction in the context of recent numerical studies of the environmental dependence of halo properties. (Abridged)Comment: 62 pages, 19 figures. Review article based on lectures given at the Sixth Summer School of the Helmholtz Institute for Supercomputational Physics. Accepted for Publication in IJMPD. Comments Welcom

    A hierarchy of voids: Much ado about nothing

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    We present a model for the distribution of void sizes and its evolution in the context of hierarchical scenarios of gravitational structure formation. We find that at any cosmic epoch the voids have a size distribution which is well-peaked about a characteristic void size which evolves self-similarly in time. This is in distinct contrast to the distribution of virialized halo masses which does not have a small-scale cut-off. In our model, the fate of voids is ruled by two processes. The first process affects those voids which are embedded in larger underdense regions: the evolution is effectively one in which a larger void is made up by the mergers of smaller voids, and is analogous to how massive clusters form from the mergers of less massive progenitors. The second process is unique to voids, and occurs to voids which happen to be embedded within a larger scale overdensity: these voids get squeezed out of existence as the overdensity collapses around them. It is this second process which produces the cut-off at small scales. In the excursion set formulation of cluster abundance and evolution, solution of the cloud-in-cloud problem, i.e., counting as clusters only those objects which are not embedded in larger clusters, requires study of random walks crossing one barrier. We show that a similar formulation of void evolution requires study of a two-barrier problem: one barrier is required to account for voids-in-voids, and the other for voids-in-clouds. Thus, in our model, the void size distribution is a function of two parameters, one of which reflects the dynamics of void formation, and the other the formation of collapsed objects.Comment: 23 pages, 9 figures, submitted to MNRA
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