We present a search for 183 GHz H_2O(3_13-2_20) emission in the infrared-luminous quasar MG 0751+2716 with the NRAO Very Large Array (VLA). At z=3.200+/-0.001, this water emission feature is redshifted to 43.6 GHz. As opposed to the faint rotational transitions of HCN (the standard high-density tracer at high-z), H_2O(3_13-2_20) is observed with high maser amplification factors in Galactic star-forming regions. It therefore holds the potential to trace high-density star-forming regions in the distant universe. If indeed all star-forming regions in massively star-forming galaxies at z>3 have similar physical properties as e.g. the Orion or W49N molecular cloud cores, the flux ratio between the maser-amplified H_2O(3_13-2_20) and the thermally excited CO(1-0) transitions may be as high as factor of 20 (but has to be corrected by their relative filling factor). MG 0751+2716 is a strong CO(4-3) emitter, and therefore one of the most suitable targets to search for H_2O(3_13-2_20) at cosmological redshifts. Our search resulted in an upper limit in line luminosity of L(H_2O) < 0.6 x 10^9 K km/s pc^2. Assuming a brightness temperature of T_b(H_2O) ~= 500 K for the maser emission and CO properties from the literature, this translates to a H_2O(3_13-2_20)/CO(4-3) area filling factor of less than 1%. However, this limit is not valid if the H_2O(3_13-2_20) maser emission is quenched, i.e. if the line is only thermally excited. We conclude that, if our results were to hold for other high-z sources, H_2O does not appear to be a more luminous alternative to HCN to detect high-density gas in star-forming environments at high redshift.
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