Evaluating the reconstruction of individual haloes in constrained cosmological simulations

Constrained cosmological simulations play an important role in modelling the local Universe, enabling investigation of the dark matter content of local structures and their formation histories. We introduce a method for determining the extent to which individual haloes are reliably reconstructed between constrained simulations, and apply it to the Constrained Simulations in BORG (CSiBORG) suite of $101$ high-resolution realisations across the posterior probability distribution of initial conditions from the Bayesian Origin Reconstruction from Galaxies (BORG) algorithm. The method is based on the overlap of the initial Lagrangian patch of a halo in one simulation with those in another, and therefore measures the degree to which the haloes' particles are initially coincident. By this metric we find consistent reconstructions of $M\gtrsim10^{14}~M_\odot / h$ haloes across the CSiBORG simulations, indicating that the constraints from the BORG algorithm are sufficient to pin down the masses, positions and peculiar velocities of clusters to high precision. The effect of the constraints tapers off towards lower mass however, and the halo spins and concentrations are largely unconstrained at all masses. We document the advantages of evaluating halo consistency in the initial conditions, describe how the method may be used to quantify our knowledge of the halo field given galaxy survey data analysed through the lens of probabilistic inference machines such as BORG, and describe applications to matched but unconstrained simulations.