Precision MARS Mass Reconstruction of Abell 2744: Synergizing the Largest Strong Lensing and Densest Weak Lensing Datasets from JWST

We present a new high-resolution free-form mass model of Abell 2744, combining both weak-lensing (WL) and strong-lensing (SL) datasets from JWST. The SL dataset comprises 286 multiple images, presenting the most extensive SL constraint to date for a single cluster. The WL dataset, employing photo-$z$ selection, yields a source density of ~ 350 arcmin$^{-2}$, marking the densest WL constraint ever. The combined mass reconstruction enables the highest-resolution mass map of Abell 2744 within the ~ 1.8 Mpc$\times$1.8 Mpc reconstruction region to date, revealing an isosceles triangular structure with two legs of ~ 1 Mpc and a base of ~ 0.6 Mpc. Although our algorithm MAximum-entropy ReconStruction (${\tt MARS}$) is entirely blind to the cluster galaxy distribution, the resulting mass reconstruction remarkably well traces the brightest cluster galaxies with the five strongest mass peaks coinciding with the five most luminous cluster galaxies within $\lesssim 2''$. We do not detect any unusual mass peaks that are not traced by the cluster galaxies, unlike the findings in previous studies. Our mass model shows the smallest scatters of SL multiple images in both source (~0".05) and image (~0".1) planes, which are lower than the previous studies by a factor of ~ 4. Although ${\tt MARS}$ represents the mass field with an extremely large number of ~ 300,000 free parameters, it converges to a solution within a few hours thanks to our utilization of the deep learning technique. We make our mass and magnification maps publicly available.