An MCMC fitting method for triaxial dark matter haloes

Measuring the 3D distribution of mass on galaxy cluster scales is a crucial test of the Lambda cold dark matter (Lambda CDM) model, providing constraints on the behaviour of dark matter. Recent work investigating mass distributions of individual galaxy clusters (e.g. Abell 1689) using weak and strong gravitational lensing has revealed potential inconsistencies between the predictions of structure formation models relating halo mass to concentration and those relationships as measured in massive clusters. However, such analyses employ simple spherical halo models while a growing body of work indicates that triaxial 3D halo structure is both common and important in parameter estimates. Though lensing is sensitive only to 2D projected structure and is thus incapable of independently constraining 3D models, the very strong assumptions about the symmetry of the lensing halo implied with circular or perturbative elliptical Navarro, Frenk & White (NFW) models are not physically motivated and lead to incorrect parameter estimates with significantly underestimated error bars. We here introduce a Markov Chain Monte Carlo (MCMC) method to fit fully triaxial models to weak lensing data that gives parameter and error estimates that fully incorporate the true uncertainty present in nature. Using weak lensing data alone, the fits are sensitive to the Bayesian priors on axis ratio; we explore the impact of various general and physically motivated priors, and emphasize the need for future work combining lensing data with other data types to fully constrain the 3D structure of galaxy clusters. Applying the MCMC triaxial fitting method to a population of NFW triaxial lenses drawn from the shape distribution of structure formation simulations, we find that including triaxiality cannot explain a population of massive, highly concentrated clusters within the framework of Lambda CDM, but easily explains rare cases of apparently massive, highly concentrated, very efficient lensing clusters. Our MCMC triaxial NFW fitting method is easily expandable to include constraints from additional data types, and its application returns model parameters and errors that more accurately capture the true (and limited) extent of our knowledge of the structure of galaxy cluster lenses.