Parameter-free Hubble constant from the quadruply lensed quasar SDSS J1004+4112

Abstract

We present a free-form lens model for the multiply lensed quasar in the galaxy cluster SDSS J$1004+4112$. Our lens model draws minimal assumptions on the distribution of mass in the lens plane. We have paid particular attention to the model uncertainties on the predicted time delay originating from the particular configuration of model variables. Taking into account this uncertainty, we obtained a value of the Hubble constant of $H_0= 74^ parsec $, which is consistent with recent independent estimates. The predicted time delay between the central image E and image C (the first to arrive) is $ E-C 200$ days for the estimated Hubble constant. Future measurements of $ E-C $ will allow for a tighter constraint to be imposed on $H_0$ in this cluster-QSO system.