On a novel approach using massive clusters at high redshifts as cosmological probe

In this work we propose a novel method for testing the validity of the fiducial LCDM cosmology by measuring the cumulative distribution function of the most massive haloes in a sample of subvolumes of identical size tiled on the sky at a fixed redshift. The fact that the most massive clusters probe the high-mass tail of the mass function, where the difference between LCDM and alternative cosmological models is strongest, makes our method particularly interesting as a cosmological probe. We utilise general extreme value statistics (GEV) to obtain a cumulative distribution function of the most massive objects in a given volume. We sample this distribution function according to the number of patches covered by the survey area for a range of different "test cosmologies" and for differently accurate mass estimations of the haloes. By fitting this sample with the GEV distribution function, we can study which parameters are the most sensitive with respect to the test cosmologies. We find that the peak of the probability distribution function of the most massive halo is well suited to test the validity of the fiducial LCDM model, once we are able to establish a sufficiently complete large-area survey with M_lim=10^14.5 M_sun/h (M_lim=10^14 M_sun/h) at redshifts above z=1 (z=1.5). Being of cumulative nature the proposed measure is robust and an accuracy of 20-30% in the cluster masses would be sufficient to test for alternative models. Since one only needs the most massive system in each angular patch, this method would be ideally suited as a first fast consistency check before going into a more complex statistical analysis of the observed halo sample.Comment: 11 pages, 13 figures, 1 Table, MNRAS accepted versio

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

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 the GEV approach 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 percent level precision for less than 100 patches. This result makes the GEV based approach potentially also interesting for cluster surveys with a smaller area.Comment: 10 pages, 8 figures, MNRAS accepted, minor modifications to match the accepted versio

The strongest gravitational lenses: II. Is the large Einstein radius of MACS J0717.5+3745 in conflict with LCDM?

Can the standard cosmological model 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 (ER). We aim to evaluate the occurrence probability of the large observed ER of MACS J0717.5 within the standard LCDM cosmology. In particular, we want to model the distribution function of the single largest ER in a given cosmological volume and to study which underlying assumptions and effects have the strongest impact on the results. 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. We find that the distribution of the maximum ER 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 ER of MACS J0717.5, finding that this system is not in tension with LCDM. 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 Frechet distribution. With a multitude of effects that strongly influence the distribution of the single largest ER, it is more than doubtful that the standard LCDM 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 ER (> 100 arcsec) than that of MACS J0717.5 would have to be observed.Comment: 15 pages, 11 figures, accepted for publication in Astronomy and Astrophysics, minor corrections to match the accepted version, added discussion of the distribution of the largest Einstein radii for the MACS survey area, extended Fig.

Spherical collapse model in dark energy cosmologies

We study the spherical collapse model for several dark energy scenarios using the fully nonlinear differential equation for the evolution of the density contrast within homogeneous spherical overdensities derived from Newtonian hydrodynamics. While mathematically equivalent to the more common approach based on the differential equation for the radius of the perturbation, this approach has substantial conceptual as well as numerical advantages. Among the most important are that no singularities at early times appear, which avoids numerical problems in particular in applications to cosmologies with dynamical and early dark energy, and that the assumption of time-reversal symmetry can easily be dropped where it is not strictly satisfied. We use this approach to derive the two parameters characterising the spherical-collapse model, i.e.~the linear density threshold for collapse $\delta_\mathrm{c}$ and the virial overdensity $\Delta_\mathrm{V}$, for a broad variety of dark-energy models and to reconsider these parameters in cosmologies with early dark energy. We find that, independently of the model under investigation, $\delta_\mathrm{c}$ and $\Delta_\mathrm{V}$ are always very close to the values obtained for the standard $\Lambda$CDM model, arguing that the abundance of and the mean density within non-linear structures are quite insensitive to the differences between dark-energy cosmologies. Regarding early dark energy, we thus arrive at a different conclusion than some earlier papers, including one from our group, and we explain why.Comment: 11 pages, 7 figures, accepted for publications on MNRA

The strongest gravitational lenses: I. The statistical impact of cluster mergers

For more than a decade now, it has been controversial whether or not the high rate of giant gravitational arcs and the largest observed Einstein radii are consistent with the standard cosmological model. Recent studies indicate that mergers provide an efficient mechanism to substantially increase the strong-lensing efficiency of individual clusters. Based on purely semi-analytic methods, we investigated the statistical impact of cluster mergers on the distribution of the largest Einstein radii and the optical depth for giant gravitational arcs of selected cluster samples. Analysing representative all-sky realizations of clusters at redshifts z < 1 and assuming a constant source redshift of z_s = 2.0, we find that mergers increase the number of Einstein radii above 10 arcsec (20 arcsec) by ~ 35 % (~ 55 %). Exploiting the tight correlation between Einstein radii and lensing cross sections, we infer that the optical depth for giant gravitational arcs with a length-to-width ratio > 7.5 of those clusters with Einstein radii above 10 arcsec (20 arcsec) increases by ~ 45 % (85 %). Our findings suggest that cluster mergers significantly influence in particular the statistical lensing properties of the strongest gravitational lenses. We conclude that semi-analytic studies must inevitably take these events into account before questioning the standard cosmological model on the basis of the largest observed Einstein radii and the statistics of giant gravitational arcs.Comment: 23 pages, 18 figures; accepted for publication in Astronomy and Astrophysics; v2: minor corrections (added clarifying comments; added Fig. 19) to match the accepted versio

A Comparison of Algorithms for the Construction of SZ Cluster Catalogues

We evaluate the construction methodology of an all-sky catalogue of galaxy clusters detected through the Sunyaev-Zel'dovich (SZ) effect. We perform an extensive comparison of twelve algorithms applied to the same detailed simulations of the millimeter and submillimeter sky based on a Planck-like case. We present the results of this "SZ Challenge" in terms of catalogue completeness, purity, astrometric and photometric reconstruction. Our results provide a comparison of a representative sample of SZ detection algorithms and highlight important issues in their application. In our study case, we show that the exact expected number of clusters remains uncertain (about a thousand cluster candidates at |b|> 20 deg with 90% purity) and that it depends on the SZ model and on the detailed sky simulations, and on algorithmic implementation of the detection methods. We also estimate the astrometric precision of the cluster candidates which is found of the order of ~2 arcmins on average, and the photometric uncertainty of order ~30%, depending on flux.Comment: Accepted for publication in A&A: 14 pages, 7 figures. Detailed figures added in Appendi

An application of extreme value statistics to the most massive galaxy clusters at low and high redshifts

In this work we present an application of general extreme value statistics (GEV) to very massive single clusters at high and low redshifts. After introducing the formalism, we apply this statistics to four very massive high redshift clusters. Those clusters comprise ACT-CL J0102-4915 with a mass of M_200m=(2.16+/-0.32)x10^{15} M_sun at a redshift of z=0.87, SPT-CL J2106-5844 with a mass of M_200m=(1.27+/-0.21)x10^{15} M_sun at z=1.132 and two clusters found by the XMM-Newton Distant Cluster Project survey: XMMU J2235.32557 with a mass of M_200c= (7.3+/-1.3)x10^{14} M_sun located at a redshift of z=1.4 and XMMU J0044.0-2033 having a mass in the range of M_200c= (3.5-5.0)x10^{14} M_sun at z=1.579. By relating those systems to their corresponding distribution functions of being the most massive system in a given survey area, we find that none of the systems alone is in extreme tension with LCDM. We confront these results with a GEV analysis of four very massive low redshift clusters: A2163, A370, RXJ1347-1145 and 1E0657-558, finding no tendency of the high-z systems to be more extreme than the low-z ones. In addition, we study the extreme quantiles of single clusters at high-z and present contour plots for fixed quantiles in the mass vs. survey area plane for four redshift intervals, finding that, in order to be significantly in conflict with LCDM, cluster masses would have to be substantially higher than the currently observed ones.Comment: 10 pages, 5 figures, 2 tables, MNRAS accepted, major revision, added discussion of the impact of the bias arising from the posterior choice of the redshift intervals, modified figures and structure of manuscrip

Impact of early dark energy on the Planck SZ cluster sample

Context. One science goal of the upcoming Planck mission is to perform a full-sky cluster survey based on the Sunyaev-Zel'dovich (SZ) effect, which leads to the question of how such a survey would be affected by cosmological models with a different history of structure formation than LCDM. One class of these models are early dark energy (EDE) cosmologies, where the dark energy contribution does not vanish at early times. Aims. Since structures grow slower in the presence of EDE, one expects an increase in the number of galaxy clusters compared to LCDM at intermediate and high redshifts, which could explain the reported excess of the angular CMB power spectrum on cluster scales via an enhanced SZ contribution. We study the impact of EDE on Planck's expected cluster sample. Methods. To obtain realistic simulations, we constructed full-sky SZ maps for EDE and LCDM cosmologies, taking angular cluster correlation into account. Using these maps, we simulated Planck observations with and without Galactic foregrounds and fed the results into our filter pipeline based on the spherical multi-frequency matched filters. Results. For the case of EDE cosmologies, we clearly find an increase in the detected number of clusters compared to the fiducial LCDM case. This shows that the spherical multi-frequency matched filter is sensitive enough to find deviations from the LCDM sample, being caused by EDE. In addition we find an interesting effect of EDE on the completeness of the cluster sample, such that EDE helps to obtain cleaner samples.Comment: 12 pages, 10 figures, accepted for publication in A&A, minor language corrections. Notable changes include an added subsection on collapse parameters for EDE models and a discussion of the consequent SZ power spectr