We combine ASCA and ROSAT X-ray data to constrain the radial dark matter distribution in the primary cluster of A2256, free from the isothermality assumption. Both instruments indicate that the temperature declines with radius. The region including the central galaxy has a multicomponent spectrum, which results in a wide range of allowed central temperatures. We find that the secondary subcluster has a temperature and luminosity typical of a rich cluster; however, the ASCA temperature map shows no signs of an advanced merger. It is therefore assumed that the primary cluster is in hydrostatic equilibrium. The data then require dark matter density profiles steeper than rho ~ r^-2.5 in its outer part. Acceptable models have a total mass within r=1.5 Mpc (the virial radius) of 6.0+-1.5 10^14 Msun at the 90% confidence, about 1.6 times smaller than the mass derived assuming isothermality. Near the center, dark matter profiles with and without central cusps are consistent with the data. Total mass inside the X-ray core (r=0.26 Mpc) is 1.28+-0.08 10^14 Msun, which exceeds the isothermal value by a factor of 1.4. Although the confidence intervals above may be underestimates since they do not include possible asymmetry and departures from hydrostatic equilibrium, the behavior of the mass distribution, if applicable to other clusters, can bring into better agreement X-ray and lensing mass estimates, but aggravate the ``baryon catastrophe. The observed considerable increase in the gas content with radius, not anticipated by simulations, may imply that a significant fraction of thermal gas energy comes from sources other than gravity and merger shocks.
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