We have searched for emission from the 557 GHz ortho-water line in the interstellar medium of six nearby starburst galaxies. We used the Odin satellite to observe the 1_10-1_01 transition of o-H2O in the galaxies NGC253, IC342, M82, NGC4258, CenA, and M51. None of the galaxies in our sample was detected. We derive three sigma upper limits to the H2O abundance relative to H2 ranging from 2e-9 to 1e-8. The best of these upper limits are comparable to the measured abundance of H$_2$O in the Galactic star forming region W3. However, if only 10% of the molecular gas is in very dense cores, then the water abundance limits in the cores themselves would be larger by a factor of 10 i.e. 2e-8 to 1e-7. These observations suggest that detections of H2O emission in galaxies with the upcoming Herschel Space Observatory are likely to require on-source integration times of an hour or more except in the very brightest extragalactic targets such as M82 and NGC253.
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