Cylinders out of a top hat: counts-in-cells for projected densities

Uhlemann, Cora; Codis, Sandrine; L’Huillier, Benjamin; Kim, Juhan; Bernardeau, Francis; Park, Changbom; Prunet, S.

doi:10.1093/mnras/sty664

Cited by 29 publications

(38 citation statements)

References 69 publications

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“…The derivation of that value uses a spherical collapse approximation which may not be appro- priate for our cylindrical apertures. Substituting spherical with cylindrical collapse one arrives at ν = 7/5 (Uhlemann et al 2018c). In our situation we find both values for ν to give very similar values of b E 2 (as calculated from b L 1 and b L…”

Section: Halo Bias As a Function Of Mass And Consistency Among Bias M...mentioning

confidence: 99%

“…the matter density field is typically incorporated through an Eulerian expansion of the conditional expectation value δ halo |δm (see e.g. Efstathiou 1995;Manera & Gaztañaga 2011;Clerkin et al 2017;Friedrich et al 2018;Gruen et al 2018;Salvador et al 2019;Repp & Szapudi 2020, with an exception found in Uhlemann et al 2018c). This is somewhat unnatural, because standard methods to model the matter density PDF are typically built around the symmetric collapse of a leading order (saddle-point) configuration of the density field (e.g.…”

Section: Introductionmentioning

confidence: 99%

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The PDF perspective on the tracer-matter connection: Lagrangian bias and non-Poissonian shot noise

Friedrich,

Halder,

Boyle

et al. 2021

Preprint

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We study the connection of matter density and its tracers from the PDF perspective. One aspect of this connection is the conditional expectation value δ tracer |δ m when averaging both tracer and matter density over some scale. We present a new way to incorporate a Lagrangian bias expansion of this expectation value into standard frameworks for modelling the PDF of density fluctuations and counts-in-cells statistics. Using N-body simulations and mock galaxy catalogs we confirm the accuracy of this expansion and compare it to the more commonly used Eulerian parametrization. For halos hosting typical luminous red galaxies, the Lagrangian model provides a significantly better description of δ tracer |δ m at second order in perturbations. A second aspect of the matter-tracer connection is shot-noise, i.e. the scatter of tracer density around δ tracer |δ m . It is well known that this noise can be significantly non-Poissonian and we validate the performance of a more general, two-parameter shot-noise model for different tracers and simulations. Both parts of our analysis are meant to pave the way for forthcoming applications to survey data.

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Section: Halo Bias As a Function Of Mass And Consistency Among Bias M...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The PDF perspective on the tracer-matter connection: Lagrangian bias and non-Poissonian shot noise

Friedrich,

Halder,

Boyle

et al. 2021

Preprint

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“…One way to circumvent this issue is presented in section 4 below by means of nulling. Note that this approach significantly outperforms a standard lognormal approximation for κ + κmin as shown quantitatively in appendix D. Additionally, our formalism can potentially be applied to jointly model the statistics of lensing convergence considered here and tracer densities in thick redshift slices described in Uhlemann et al (2018c), a situation where the log-normal approximation has been shown to fail.…”

Section: Weak-lensing Convergence Pdfsmentioning

confidence: 86%

“…In the spirit of previous work done involving the density filtered in spherical cells, the parametrisation of ζ(τ ) in ν is taken so as to reproduce the value of the tree-order skewness for cylindrical symmetry as computed with perturbation theory. We shall then take ν = 1.4 (Uhlemann et al 2018c). See Appendix B for more details.…”

Section: Cumulants In Cylinders From Theorymentioning

confidence: 99%

A nulling strategy for modelling lensing convergence in cones with large deviation theory

Barthelemy

Codis

Uhlemann

et al. 2020

Monthly Notices of the Royal Astronomical Society

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The distribution of the cosmic convergence field is modelled from first principles using a large deviation principle. The geometry of the past light cone is accounted for by constructing the total weak-lensing signal from contributions of the matter density in thin disk slices. The prediction of this model is successfully tested against numerical simulation with ray tracing, and found to be accurate within at least 5 per cent in the tails at redshift 1 and opening angle of 10 arcmin and even more so with increasing source redshift and opening angle. An accurate analytical approximation to the theory is also provided for practical implementation. The lensing kernel that mixes physical scales along the line-of-sight tends to reduce the domain of validity of this theoretical approach compared to the three dimensional case of cosmic densities in spherical cells. This effect is shown to be avoidable if a nulling procedure is implemented in order to localise the lensing line-of-sight integrations in a tomographic analysis. Accuracy in the tails is thus achieved within a percent for source redshifts between 0.5 and 1.5 and an opening angle of 10 arcmin. Applications to future weak-lensing surveys like Euclid and the specific issue of shape noise are discussed.

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“…Perturbative methods [1,2,[19][20][21][22][23], and the large deviation statistics-formalism developed in Refs. [24,25] are better suited in such a situation. In terms of physical input, our formalism is quite similar to the stochastic numerical method developed in Refs.…”

Section: Introductionmentioning

confidence: 99%

Accurate analytic model for the thermal Sunyaev-Zel’dovich one-point probability distribution function

2019

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Non-Gaussian statistics of late-time cosmological fields contain information beyond that captured in the power spectrum. Here we focus on one such example: the one-point probability distribution function (PDF) of the thermal Sunyaev-Zel'dovich (tSZ) signal in maps of the cosmic microwave background (CMB). It has been argued that the one-point PDF is a near-optimal statistic for cosmological constraints from the tSZ signal, as most of the constraining power in tSZ N -point functions is contained in their amplitudes (rather than their shapes), which probe differently-weighted integrals over the halo mass function. In this paper, we develop a new analytic halo model for the tSZ PDF, discarding simplifying assumptions made in earlier versions of this approach. In particular, we account for effects due to overlaps of the tSZ profiles of different halos, as well as effects due to the clustering of halos. We verify the accuracy of our analytic model via comparison to numerical simulations. We demonstrate that this more accurate model is necessary for the analysis of the tSZ PDF in upcoming CMB experiments. The novel formalism developed here may be useful in modeling the one-point PDF of other cosmological observables, such as the weak lensing convergence field.

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Cylinders out of a top hat: counts-in-cells for projected densities

Cited by 29 publications

References 69 publications

The PDF perspective on the tracer-matter connection: Lagrangian bias and non-Poissonian shot noise

The PDF perspective on the tracer-matter connection: Lagrangian bias and non-Poissonian shot noise

A nulling strategy for modelling lensing convergence in cones with large deviation theory

Accurate analytic model for the thermal Sunyaev-Zel’dovich one-point probability distribution function

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