Bayesian constraints on dark matter halo properties using gravitationally lensed supernovae

Abstract

A hierarchical Bayesian method is applied to the analysis of Type Ia supernovae (SNIa) observations to constrain the properties of the dark matter haloes of galaxies along the SNIa lines of sight via their gravitational lensing effect. The full joint posterior distribution of the darkmatter halo parameters is explored using the nested sampling algorithmMULTINEST, which also efficiently calculates the Bayesian evidence, thereby facilitating robust model comparison. We first demonstrate the capabilities of the method by applying it to realistic simulated SNIa data, based on the real 3-year data release from the Supernova Legacy Survey (SNLS3). Assuming typical values for the parameters in a truncated singular isothermal sphere (SIS) halo model, we find that a catalogue analogous to the existing SNLS3 data set is typically incapable of detecting the lensing signal, but a catalogue containing approximately three times as many SNIa can produce robust and accurate parameter constraints and lead to a clear preference for the SIS halo model over a model that assumes no lensing. In the analysis of the real SNLS3 data, contrary to previous studies, we obtain only a very marginal detection of a lensing signal and weak constraints on the halo parameters for the truncated SIS model, although these constraints are tighter than those typically obtained from equivalent simulated SNIa data sets. This difference is driven by a preferred value of η ≈ 1 in the assumed scaling law α Lη between velocity dispersion and luminosity, which is somewhat higher than the canonical values of η = 14 and η = 13for early and late-type galaxies, respectively. © 2013 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.