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 makes minimal assumptions about the distribution of mass in the lens plane. We pay 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 obtain a value of the Hubble constant of $H_0= 74^{+9}_{-13}$km s$^{-1}$ Mpc$^{-1}$, consistent with independent recent estimates. The predicted time delay between the central image E and image C (the first to arrive), is $\Delta T_{E-C}=3200\pm 200$ days. Future measurements of $\Delta T_{E-C}$ will allow to impose a tighter constrain on $H_0$ from this cluster-QSO system.