Crash-testing the cauldron code for joint lensing and dynamics analysis of early-type galaxies

Abstract

We apply the joint lensing and dynamics code for the analysis of early-type galaxies, ‘Combined Algorithm for Unified Lensing and Dynamics ReconstructiON (cauldron)’, to a rotating N-body stellar system with dark matter halo which significantly violates the two major assumptions of the method, i.e. axial symmetry supported by a two-integral distribution function. The goal is to study how cauldron performs in an extreme case, and to determine which galaxy properties can still be robustly recovered. Three data sets, corresponding to orthogonal lines of sight, are generated from the N-body system and analysed with the identical procedure followed in the study of real lens galaxies, adopting an axisymmetric power-law total density distribution. We find that several global properties of the N-body system are recovered with remarkable accuracy, despite the fact that the adopted power-law model is too simple to account for the lack of symmetry of the true density distribution. In particular, the logarithmic slope of the total density distribution is robustly recovered to within less than 10 per cent (with the exception of the ill-constrained very inner regions), the inferred angle-averaged radial profile of the total mass closely follows the true distribution, and the dark matter fraction of the system (inside the effective radius) is correctly determined within ∼10 per cent of the total mass. Unless the line-of-sight direction is almost parallel to the total angular momentum vector of the system, reliably recovered quantities also include the angular momentum, the V/σ ratio and the anisotropy parameter δ. We conclude that the cauldron code can be safely and effectively applied to real early-type lens galaxies, also providing reliable information for the systems that depart significantly from the method's assumptions.