  The galaxy cluster RX J1347-1145 is one of the most X-ray luminous and most
massive clusters known. Its extreme mass makes it a prime target for studying
issues addressing cluster formation and cosmology. In this paper we present new
high-resolution HST/ACS and Chandra X-ray data. The high resolution and
sensitivity of ACS enabled us to detect and quantify several new multiply
imaged sources, we now use a total of eight for the strong lensing analysis.
Combining this information with shape measurements of weak lensing sources in
the central regions of the cluster, we derive a high-resolution,
absolutely-calibrated mass map. This map provides the best available
quantification of the total mass of the central part of the cluster to date. We
compare the reconstructed mass with that inferred from the new Chandra X-ray
data, and conclude that both mass estimates agree extremely well in the
observed region, namely within 400 / h_70 kpc of the cluster center. In
addition we study the major baryonic components (gas and stars) and hence
derive the dark matter distribution in the center of the cluster. We find that
the dark matter and baryons are both centered on the BCG within the
uncertainties (alignment is better than <10 kpc). We measure the corresponding
1-D profiles and find that dark matter distribution is consistent with both NFW
and cored profiles, indicating that a more extended radial analysis is needed
to pinpoint the concentration parameter, and hence the inner slope of the dark
matter profile.
