Primordial non-Gaussianity and extreme-value statistics of galaxy clusters

Chongchitnan, Sirichai; Silk, Joseph

doi:10.1103/physrevd.85.063508

Cited by 33 publications

(31 citation statements)

References 82 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…None of the two clusters is in tension with the CDM cosmology, as discussed in Waizmann et al (2012), and also the GPD-based approach leads to the same conclusion. This result is in agreement with the conclusions drawn in the recent works of Chongchitnan & Silk (2012), Harrison & Coles (2012) and Menanteau et al (2012), who find no tension with CDM for individual clusters. Since SPT-CL J2106, due to its position in the redshift interval, appears to be rarer than ACT-CL J0102, the GEV and GPD approaches deliver very similar probabilities, as it has been discussed above.…”

Section: S U M M a Ry A N D C O N C L U S I O N Ssupporting

confidence: 93%

“…Davis et al (2011) related for the first time the GEV distribution parameters to cosmological quantities and compared the approach to numerical N ‐body simulations. The impact of primordial non‐Gaussianity on the EVS of galaxy clusters has been studied by Chongchitnan & Silk (2011). A direct approach, based on the exact rather than the asymptotic form, has been utilized by Harrison & Coles (2011, 2012) to study the halo mass function and the possibility to use extreme clusters to test cosmological models.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the modelling of the excesses of galaxy clusters over high-mass thresholds

Waizmann¹,

Ettori²,

Moscardini³

2012

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

In this work we present for the first time an application of the Pareto approach to the modelling of the excesses of galaxy clusters over high‐mass thresholds. The distribution of those excesses can be described by the generalized Pareto distribution (GPD), which is closely related to the generalized extreme value (GEV) distribution. After introducing the formalism, we study the impact of different thresholds and redshift ranges on the distributions, as well as the influence of the survey area on the mean excess above a given mass threshold. We also show that both the GPD and GEV approaches lead to identical results for rare, thus high‐mass and high‐redshift, clusters. As an example, we apply the Pareto approach to ACT‐CL J0102−4915 and SPT‐CL J2106−5844 and derive the respective cumulative distribution functions of the exceedance over different mass thresholds. We also study the possibility to use the GPD as a cosmological probe. Since in the maximum likelihood estimation of the distribution parameters all the information from clusters above the mass threshold is used, the GPD might offer an interesting alternative to GEV‐based methods that use only the maxima in patches. When comparing the accuracy with which the parameters can be estimated, it turns out that the patch‐based modelling of maxima is superior to the Pareto approach. In an ideal case, the GEV approach is capable to estimate the location parameter with a per cent level precision for less than ∼100 patches. This result makes the GEV‐based approach potentially also interesting for cluster surveys with a smaller area.

show abstract

Section: S U M M a Ry A N D C O N C L U S I O N Ssupporting

confidence: 93%

Section: Introductionmentioning

confidence: 99%

On the modelling of the excesses of galaxy clusters over high-mass thresholds

Waizmann¹,

Ettori²,

Moscardini³

2012

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

show abstract

“…The most widely encountered distribution in extreme value theory, the Gumbel distribution [79,80], has been frequently employed for climate modeling, including extreme rainfall and flooding [81][82][83][84][85], extreme winds [86], avalanches [87], and earthquakes [88]. The Gumbel distribution has also been found to reasonably characterize the density fluctuations within galaxies [89][90][91] and in certain areas of tokamaks [92][93][94], binding energies in liquids [95], as well as turbulent fluctuations [96,97]. The cumulative distribution function F for the Gumbel case has the well-known form:…”

Section: Results: Extreme-value Statistics Of Turbulent Particle Dispmentioning

confidence: 99%

Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection

et al. 2017

View full text Add to dashboard Cite

We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics capture the asymptotic dispersive behavior of a large group of passive tracer particles. Moreover, convex hull analysis provides additional information on the sub-ensemble of tracers that on average disperse most efficiently in the form of extreme value statistics and flow anisotropy via the geometric properties of the convex hulls. We use the convex hull surface geometry to examine the anisotropy that occurs in turbulent convection. Applying extreme value theory, we show that the maximal square extensions of convex hull vertices are well described by a classic extreme value distribution, the Gumbel distribution. During turbulent convection, intermittent convective plumes grow and accelerate the dispersion of Lagrangian tracers. Convex hull analysis yields information that supplements standard Lagrangian analysis of coherent turbulent structures and their influence on the global statistics of the flow.

show abstract

“…Therefore, it is also interesting to study the expectation for the most massive galaxy cluster in the redshift range of interest of 0.5 ≤ z ≤ 1.0. EVS can also be applied to study the distribution of the most massive halo in a given volume (Chongchitnan & Silk 2012;Davis et al 2011;Harrison & Coles 2011Waizmann et al 2011Waizmann et al , 2012a; we will follow the procedure shown in Waizmann et al (2012a) to compute the distribution function. The results are presented in Fig.…”

Section: The Probability Of Occurrence Of the Critical Curvementioning

confidence: 99%

The strongest gravitational lenses

Waizmann

Redlich

Bartelmann

2012

A&A

View full text Add to dashboard Cite

Context. With the amount and quality of galaxy cluster data increasing, the question arises whether or not the standard cosmological model can be questioned on the basis of a single observed extreme galaxy cluster. Usually, the word extreme refers directly to cluster mass, which is not a direct observable and thus subject to substantial uncertainty. Hence, it is desirable to extend studies of extreme clusters to direct observables, such as the Einstein radius. Aims. We aim to evaluate the occurrence probability of the large observed Einstein radius of MACS J0717.5+3745 within the standard ΛCDM cosmology. In particular, we want to model the distribution function of the single largest Einstein radius in a given cosmological volume and to study which underlying assumptions and effects have the strongest impact on the results. Methods. We obtain this distribution by a Monte Carlo approach, based on the semi-analytic modelling of the halo population on the past lightcone. After sampling the distribution, we fit the results with the general extreme value (GEV) distribution which we use for the subsequent analysis. Results. We find that the distribution of the maximum Einstein radius is particularly sensitive to the precise choice of the halo mass function, lens triaxiality, the inner slope of the halo density profile and the mass-concentration relation. Using the distributions so obtained, we study the occurrence probability of the large Einstein radius of MACS J0717.5+3745, finding that this system is not in tension with ΛCDM. We also find that the GEV distribution can be used to fit very accurately the sampled distributions and that all of them can be described by a (type-II) Fréchet distribution. Conclusions. With a multitude of effects that strongly influence the distribution of the single largest Einstein radius, it is more than doubtful that the standard ΛCDM cosmology can be ruled out on the basis of a single observation. If, despite the large uncertainties in the underlying assumptions, one wanted to do so, a much larger Einstein radius ( > ∼ 100 ) than that of MACS J0717.5+3745 would have to be observed.

show abstract

Primordial non-Gaussianity and extreme-value statistics of galaxy clusters

Cited by 33 publications

References 82 publications

On the modelling of the excesses of galaxy clusters over high-mass thresholds

On the modelling of the excesses of galaxy clusters over high-mass thresholds

Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection

The strongest gravitational lenses

Contact Info

Product

Resources

About