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Cold Molecular Gas Along the Cooling X-ray Filament in Abell 1795

We present the results of interferometric observations of the cool core of Abell 1795 at CO(1-0) using the Combined Array for Research in Millimeter-Wave Astronomy. In agreement with previous work, we detect a significant amount of cold molecular gas (3.9 +/- 0.4 x10^9 Msun) in the central ~10 kpc. We report the discovery of a substantial clump of cold molecular gas at clustercentric radius of 30 kpc (2.9 +/- 0.4 x10^9 Msun), coincident in both position and velocity with the warm, ionized filaments. We also place an upper limit on the H_2 mass at the outer edge of the star-forming filament, corresponding to a distance of 60 kpc (<0.9 x10^9 Msun). We measure a strong gradient in the HII/H_2 ratio as a function of radius, suggesting different ionization mechanisms in the nucleus and filaments of Abell1795. The total mass of cold molecular gas (\sim7x10^9 Msun) is roughly 30% of the classical cooling estimate at the same position, assuming a cooling time of 10^9 yr. Combining the cold molecular gas mass with the UV-derived star formation rate and the warm, ionized gas mass, the spectroscopically-derived X-ray cooling rate is fully accounted for and in good agreement with the cooling byproducts over timescales of \sim10^9 yr. The overall agreement between the cooling rate of the hot intracluster medium and the mass of the cool gas reservoir suggests that, at least in this system, the cooling flow problem stems from a lack of observable cooling in the more diffuse regions at large radii.