Host group degeneracy in gravitational lensing time delay determination of H ₀

Abstract Massive elliptical galaxies, that serve as lenses in gravitational lensing time delay measurements of the Hubble parameter H 0 , often reside a host group. We consider degeneracies modeling group halo. When effect on imaging can be summarized by its flexion (the next order term beyond shear tidal expansion), posterior likelihood map develop disjoint local minima, associated with an approximate discrete symmetry dominant term. Monte-Carlo Markov Chain (MCMC) algorithms are not designed to explore rich landscape miss some introducing systematic bias. study mock data and demonstrate bias exceed 10%, pulls inference value above truth value, for reason traced structure mismodeled MCMC cope uncover structure. If is X-ray bright enough, may also help resolve degeneracy, pinpointing group's center mass. Finally, we show implementations literature used inaccurate kinematical prior, mis-modeling velocity dispersion much 20%.