Free-form modelling of galaxy clusters: a Bayesian and data-driven approach

Abstract

A new method is presented for modelling the physical properties of galaxy clusters. Our technique moves away from the traditional approach of assuming specific parameterised functional forms for the variation of physical quantities within the cluster, and instead allows for a 'free-form' reconstruction, but one for which the level of complexity is determined automatically by the observational data and may depend on position within the cluster. This is achieved by representing each independent cluster property as some interpolating or approximating function that is specified by a set of control points, or 'nodes', for which the number of nodes, together with their positions and amplitudes, are allowed to vary and are inferred in a Bayesian manner from the data. We illustrate our nodal approach in the case of a spherical cluster by modelling the electron pressure profile P e (r) in analyses both of simulated Sunyaev-Zel'dovich (SZ) data from the Arcminute MicroKelvin Imager (AMI) and of real AMI observations of the cluster MACS J0744+3927 in the CLASH sample. We demonstrate that one may indeed determine the complexity supported by the data in the reconstructed P e (r), and that one may constrain two very important quantities in such an analysis: the cluster total volume integrated Comptonisation parameter (Y tot ) and the extent of the gas distribution in the cluster (r max ). The approach is also well-suited to detecting clusters in blind SZ surveys.

Bayesian inflationary reconstructions from Planck 2018 data

“…For simplicity we assume r = 0 for the remainder of this section. This technique has a history of being successfully applied to the primordial power spectrum [5][6][7][8][9], but has also been applied to dark energy equation of state by Hee et al [10] and Vázquez et al [11], to the cosmic reionisation history by Millea and Bouchet [12] and to galaxy cluster profiles by Olamaie et al [13]. Our work differs from previous primordial power spectrum reconstructions in both the data we use, the styling of the priors, and in the application of more modern inference tools such as functional posterior plotting [37], conditional Kullback-Leibler divergences [10] and PolyChord.…”

“…Throughout we adopt a fully Bayesian framework, treating our non-parametric reconstruction functions using priors, posteriors and evidences to marginalize out factors that are irrelevant to physical quantities of interest. We reconstruct both the inflationary potential and the primordial power spectrum directly using spline and feature-based reconstructions, in a manner related but not identical to the existing literature [5][6][7][8][9][10][11][12][13][14].…”

Sunyaev–Zel’dovich profile fitting with joint AMI-Planck analysis

“…the models proposed in Olamaie et al (2012), Javid et al (2018) and Javid et al (2019). We also plan to implement a non-parametric model such as that proposed in Olamaie et al (2018).…”

A semi-parametric approach to fitting gas pressure profiles of galaxy clusters

“…Degeneracy implies that different sets of parameter values can produce models equally consistent with the data. [2] moved away from the traditional approach of assuming a specific parametric form for cluster properties and introduced a more flexible node-based model. This is achieved by representing the radial profile of the cluster using piecewise function defined by a set of control points also called "nodes".…”

“…In this study, we follow and further develop the method introduced by [2] to fit Planck data on the Coma cluster, avoiding a restrictive parameterisation and instead allowing a flexible form for the pressure-radius relationship. Our study diverges from [2] in the treatment of position parameters, where we utilise Dirichlet priors to mitigate node disorder, as opposed to the uniform priors they applied (as mentioned in Section 2.3.1). While piecewise functions have been used to reconstruct pressure profiles in other work, such as [3], where these functions rely on node positions that are fixed and must be predetermined.…”