Statistics of structures in the gravitational potential - a possible way to constrain halo populations without reference to mass
Final Report Abstract
During this project, we developed a novel approach for the derivation of the cluster temperature function from the statistics of Gaussian random fields applied to the cosmic gravitational potential. No reference to mass was made during the derivation and therefore, we avoided the inclusion of this problematic global quantity. Consequently, our approach has no need for any empirical scaling relations which are needed to relate the mass to observables like the X-ray temperature or luminosity, but which also induce an additional scatter. Since a comparison of preliminary results to different mass functions suggested that including ellipsoidal collapse might remove discrepancies to mass functions calibrated by numerical simulations, we decided to include ellipsoidal-collapse dynamics also into our approach. As a consequence, we have refined the ellipsoidal-collapse model by Bond & Myers (1996). Using the results of our ellipsoidal-collapse study, we replaced spherical- by ellipsoidalcollapse dynamics in the derivation of the cluster temperature function and compared both alternatives to temperature functions from a numerical simulation based on different temperature definitions. Since increasing discrepancies occurred between the theoretical prediction and the results from the numerical simulation for increasing redshifts, which we attributed to the influence of more and more frequent merger events, we developed an analytic and fully parameter-free merger model. Incorporating this into our theoretical description, we found a good agreement between model and simulation for all redshifts. Furthermore, we studied the influence of mergers on the joint determination of the cosmological parameters Ωm and σ8 . Furthermore, we used the statistics of Gaussian random fields to develop an analytic model predicting the influence of cosmic large-scale structures and shot noise on weak-lensing number counts. We were able to predict the number density of detections as a function of signal-to-noise ratio for various weak-lensing filters used in the literature and found agreement with results from a numerical simulation at the expected level. With our work, we showed that it is possible to derive analytical models from the statistics of Gaussian random fields which provide an improved understanding of the physical mechanisms behind structure formation and which are additionally able to compete with results from numerical simulations, both for the cluster temperature function and for the analysis of weak-lensing convergence maps without having to rely on empirical scaling relations. Future applications of our approach promise to reduce the scatter in the statistics of collapsed cosmological objects substantially as any reference to the unobservable mass can be avoided in its theoretical interpretation.
Publications
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2009, Statistics of gravitational potential perturbations: A novel approach to deriving the X-ray temperature function, A&A, 494, 461
Angrick, C. & Bartelmann, M.
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2010, Triaxial collapse and virialisation of darkmatter haloes, A&A, 518, A38
Angrick, C. & Bartelmann, M.
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An analytic approach to number counts of weak-lensing peak detections, 2010, A&A, 519, A23
Maturi, M., Angrick, C., Pace, F., & Bartelmann, M.
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2011, PhD dissertation, On the derivation of an X-ray temperature function without reference to mass and the prediction of weak-lensing number counts from the statistics of Gaussian random fields, Ruprecht-Karls-Universitat Heidelberg
Angrick, C.
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2012, The influence of mergers on the cluster temperature function and cosmological parameters derived from it, A&A, 538, A98
Angrick, C. & Bartelmann, M.
