Faà di Bruno’s formula and spatial cluster modelling

AbstractThe probability generating functional (p.g.fl.) provides a useful means of compactly representing point process models. Cluster processes can be described through the composition of p.g.fl.s, and factorial moment measures and Janossy measures can be recovered from the p.g.fl. using variational derivatives. This article describes the application of a recent result in variational calculus, a generalisation of Faà di Bruno’s formula, to determine such results for cluster processes

Piece‐wise constant cluster modelling of dynamics of upwelling patterns

A comprehensive approach is presented to analyse season's coastal upwelling represented by weekly sea surface temperature (SST) image grids. Our three-stage data recovery clustering method assumes that the season's upwelling can be divided into shorter periods of stability, ranges, each to be represented by a constant core and variable shell parts. Corresponding clustering algorithms parameters are automatically derived by using the least-squares clustering criterion. The approach has been successfully applied to real-world SST data covering two distinct regions: Portuguese coast and Morocco coast, for 16 years each.LA/P/0101/2020info:eu-repo/semantics/publishedVersio

Bayesian modelling of clusters of galaxies from multi-frequency pointed Sunyaev--Zel'dovich observations

We present a Bayesian approach to modelling galaxy clusters using multi-frequency pointed observations from telescopes that exploit the Sunyaev--Zel'dovich effect. We use the recently developed MultiNest technique (Feroz, Hobson & Bridges, 2008) to explore the high-dimensional parameter spaces and also to calculate the Bayesian evidence. This permits robust parameter estimation as well as model comparison. Tests on simulated Arcminute Microkelvin Imager observations of a cluster, in the presence of primary CMB signal, radio point sources (detected as well as an unresolved background) and receiver noise, show that our algorithm is able to analyse jointly the data from six frequency channels, sample the posterior space of the model and calculate the Bayesian evidence very efficiently on a single processor. We also illustrate the robustness of our detection process by applying it to a field with radio sources and primordial CMB but no cluster, and show that indeed no cluster is identified. The extension of our methodology to the detection and modelling of multiple clusters in multi-frequency SZ survey data will be described in a future work.Comment: 12 pages, 7 figures, submitted to MNRA

X-ray modelling of galaxy cluster gas and mass profiles

We present a parametric analysis of the intracluster medium and gravitating mass distribution of a statistical sample of 20 galaxy clusters using the phenomenological cluster model of Ascasibar and Diego. We describe an effective scheme for the estimation of errors on model parameters and derived quantities using bootstrap resampling. We find that the model provides a good description of the data in all cases and we quantify the mean fractional intrinsic scatter about the best-fit density and temperature profiles, finding this to have median values across the sample of 2 and 5 per cent, respectively. In addition, we demonstrate good agreement between r500 determined directly from the model and that estimated from a core-excluded global spectrum. We compare cool core and non-cool core clusters in terms of the logarithmic slopes of their gas density and temperature profiles and the distribution of model parameters and conclude that the two categories are clearly separable. In particular, we confirm the effectiveness of the logarithmic gradient of the gas density profile measured at 0.04 r500 in differentiating between the two types of cluster.Comment: 8 pages, 7 figures, accepted for publication in MNRA

High Energy Phenomena in Clusters of Galaxies

Several phenomena in high energy astrophysics have been recently related to clusters of galaxies and to cosmic ray interactions occurring inside these structures. In many of these phenomena the observable effects depend on the energy density of cosmic rays confined in the Intra Cluster (IC) medium, which is a poorly known quantity. We propose here that useful indications about this quantity can be obtained from present and future observations of galaxy clusters in the radio and hard X-ray frequency ranges.Comment: 5 pages, 3 Figures, Latex (using espcrc2,epsfig), to appear in the Proceedings of the TAUP97, Eds. A. DiCredico et al., in press. Send comments to S.Colafrancesco: [email protected]