Most massive haloes with Gumbel statistics

Davis, Olaf; Devriendt, Julien; Colombi, S.; Silk, Joseph

doi:10.1111/j.1365-2966.2011.18286.x

Cited by 38 publications

(66 citation statements)

References 26 publications

(41 reference statements)

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“…In this work, however, we have included the effects of the bias in the presence of non-Gaussianity. Whilst Davis et al [22] have previously reported that the effects of the bias on the extreme-value distribution are small in the Gaussian case, it remains to be shown if this also holds in the presence of non-Gaussianity, which can introduce a strong scale dependence in the bias [33]. We investigate this problem in this work using the formalism of Valageas [34,35], who showed how the bias can be calculated in real space for a given f NL .…”

Section: Introductionmentioning

confidence: 99%

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

Chongchitnan¹,

Silk

2012

Phys. Rev. D

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What is the size of the most massive object one expects to find in a survey of a given volume? In this paper, we present a solution to this problem using Extreme-Value Statistics, taking into account primordial non-Gaussianity and its effects on the abundance and the clustering of rare objects. We calculate the probability density function (pdf) of extreme-mass clusters in a survey volume, and show how primordial non-Gaussianity shifts the peak of this pdf. We also study the sensitivity of the extreme-value pdfs to changes in the mass functions, survey volume, redshift coverage and the normalization of the matter power spectrum, σ8. For 'local' non-Gaussianity parametrized by f NL , our correction for the extreme-value pdf due to the bias is important when f NL 100, and becomes more significant for wider and deeper surveys. Applying our formalism to the massive high-redshift cluster XMMUJ0044.0-2-33, we find that its existence is consistent with f NL = 0, although the conclusion is sensitive to the assumed values of f sky and σ8. We also discuss the convergence of the extreme-value distribution to one of the three possible asymptotic forms, and argue that the convergence is insensitive to the presence of non-Gaussianity.

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Section: Introductionmentioning

confidence: 99%

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

Chongchitnan¹,

Silk

2012

Phys. Rev. D

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“…3, provides simulated CDFs that are discrete by nature. Due to the complexity of the modelling of the Einstein radius distribution, it is not possible to find analytic relations for the GEV parameters, as can be done for halo masses (Davis et al 2011;Waizmann et al 2011). Hence, we use the limiting GEV distribution from Eq.…”

Section: Gev and The Distribution Of Einstein Radiimentioning

confidence: 99%

“…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

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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.

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“…Neglecting correlations, i.e. the clustering of clusters, (Davis et al 2011), P0(x) is described by a Poisson distribution for zero occurrence. Thus…”

Section: General Extreme Value Statisticsmentioning

confidence: 99%

“…This was already done for the mass function in Davis et al (2011), Waizmann et al (2011), Waizmann et al (2012) and Waizmann et al (2013). This approach has the advantage that only the highest weak lensing peaks are taken into account which are prominent features in weak lensing maps.…”

Section: Introductionmentioning

confidence: 99%

Extreme value statistics of weak lensing shear peak counts

Reischke

Maturi

Bartelmann

2015

Mon. Not. R. Astron. Soc.

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The statistics of peaks in weak gravitational lensing maps is a promising technique to constrain cosmological parameters in present and future surveys. Here we investigate its power when using general extreme value statistics which is very sensitive to the exponential tail of the halo mass function. To this end, we use an analytic method to quantify the number of weak lensing peaks caused by galaxy clusters, large-scale structures and observational noise. Doing so, we further improve the method in the regime of high signal-to-noise ratios dominated by non-linear structures by accounting for the embedding of those counts into the surrounding shear caused by large scale structures. We derive the extreme value and order statistics for both over-densities (positive peaks) and under-densities (negative peaks) and provide an optimized criterion to split a wide field survey into sub-fields in order to sample the distribution of extreme values such that the expected objects causing the largest signals are mostly due to galaxy clusters. We find good agreement of our model predictions with a ray-tracing N -body simulation. For a Euclid-like survey, we find tight constraints on σ 8 and Ω m with relative uncertainties of ∼ 10 −3 . In contrast, the equation of state parameter w 0 can be constrained only with a 10% level, and w a is out of reach even if we include redshift information.

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Most massive haloes with Gumbel statistics

Cited by 38 publications

References 26 publications

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

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

The strongest gravitational lenses

Extreme value statistics of weak lensing shear peak counts

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