Statistics of gravitational potential perturbations: A novel approach to deriving the X-ray temperature function

Context. While the halo mass function is theoretically a very sensitive measure of cosmological models, masses of dark-matter halos are poorly defined, global, and unobservable quantities. Aims. We argue that local, observable quantities such as the X-ray temperatures of galaxy clusters can be directly compared to theoretical predictions without invoking masses. We derive the X-ray temperature function directly from the statistics of Gaussian random fluctuations in the gravitational potential. Methods. We derive the abundance of potential minima constrained by the requirement that they belong to linearly collapsed structures. We then use the spherical-collapse model to relate linear to non-linear perturbations, and the virial theorem to convert potential depths to temperatures. No reference is made to mass or other global quantities in the derivation. Results. Applying a proper high-pass filter that removes large enough modes from the gravitational potential, we derive an X-ray temperature function that agrees very well with the classical Press-Schechter approach on relevant temperature scales, but avoids the necessity of measuring masses. Conclusions. TThis first study shows that and how an X-ray temperature function of galaxy clusters can be analytically derived, avoiding the introduction of poorly defined global quantities such as halo masses. This approach will be useful for reducing scatter in observed cluster distributions and thus in cosmological conclusions drawn from them.Comment: 10 pages, 5 figures, accepted for publication in A&A. Revision to match the published version. Equation 8 corrected. Notable changes in section 4 including new figure

An analytic approach to number counts of weak-lensing peak detections

We develop and apply an analytic method to predict peak counts in weak-lensing surveys. It is based on the theory of Gaussian random fields and suitable to quantify the level of spurious detections caused by chance projections of large-scale structures as well as the shape and shot noise contributed by the background galaxies. We compare our method to peak counts obtained from numerical ray-tracing simulations and find good agreement at the expected level. The number of peak detections depends substantially on the shape and size of the filter applied to the gravitational shear field. Our main results are that weak-lensing peak counts are dominated by spurious detections up to signal-to-noise ratios of 3--5 and that most filters yield only a few detections per square degree above this level, while a filter optimised for suppressing large-scale structure noise returns up to an order of magnitude more.Comment: 9 pages, 5 figures, submitted to A&

The influence of mergers on the cluster temperature function and cosmological parameters derived from it

We develop a parameter-free analytic model to include the effects of mergers into the theoretical modelling of the X-ray temperature function of galaxy clusters. We include this description into our model for the cluster population based on fluctuations of the gravitational potential, which avoids any reference to mass. Comparisons with a numerical simulation reveal that the theoretical model is in good agreement with the simulation results. We show that building the model on the dynamics of spherical rather than ellipsoidal collapse yields better results if emission-weighted temperatures are used, while ellipsoidal collapse yields good agreement between model and simulation for mass-weighted temperatures. Analysing two different samples of X-ray clusters, we quantify the influence of mergers and a conversion between different temperature definitions on the joint determination of Ωm0 and σ8. If effects of mergers are included, temperature functions based on cluster masses and on the gravitational potential built on spherical collapse are in good agreement with other cosmological probes without any conversion of temperatures