Joint reconstruction of galaxy clusters from gravitational lensing and thermal gas

Abstract

We present a method of estimating the lensing potential from massive galaxy clusters for given observational X-ray data. The concepts developed and applied in this work can be easily combined with other techniques to infer the lensing potential, e.g. weak gravitational lensing or galaxy kinematics, to obtain an overall best-fit model for the lensing potential. After elaborating on the physical details and assumptions the method is based on, we explain how the numerical algorithm itself is implemented with a Richardson-Lucy algorithm as a central part. Our reconstruction method is tested on simulated galaxy clusters with a spherically symmetric NFW density profile filled with gas in hydrostatic equilibrium. We describe in detail how these simulated observational data sets are created and how they need to be fed into our algorithm. We tested the robustness of the algorithm against small parameter changes and estimate the quality of the reconstructed lensing potentials. As it turns out, we achieve a very high degree of accuracy in reconstructing the lensing potential. The statistical errors remain below 2.0%, whereas the systematical error does not exceed 1.0%.

Reconstructing the projected gravitational potential of galaxy clusters from galaxy kinematics

“…In addition, we will focus on unifying the two algorithms presented in Konrad et al (2013) and this paper so as to allow a single, joint reconstruction of the twodimensional potential of galaxy clusters using lensing, X-ray and kinematic data.…”

“…A strength of this method is the presence of a regularisation that helps control the noise. As detailed in Konrad et al (2013), a line of sight-projection g(s) is assumed to be related to a three-dimensional quantity f (r) by…”

“…Provided that g(s), f (r) and K(s|r) are normalised 2 , the following iterative scheme follows from Bayes' theorem (see Lucy 1974;Konrad et al 2013):…”

“…For easier comparison of both potentials, their zero points and normalisations are adjusted 3 . To be consistent with Konrad et al (2013), we decided to normalise both functions to unity and fix φ(r max ) = 0. In Fig.…”

“…Under this assumption, which we find well satisfied in simulations, the effective galaxy pressure is related to the gravitational potential by a Volterra integral equation of the second kind, which can be solved iteratively. We can then proceed as in the previous paper of this series (Konrad et al 2013): We apply the Richardson-Lucy deprojection to the observable line of sight velocity dispersions to obtain a three-dimensional effective galaxypressure profile. This is then converted to the three-dimensional potential, from which the two-dimensional potential is found by projection.…”