We image 19 quasars with 22 damped Lyman alpha (DLA) systems using the F160W filter and the Near-Infrared Camera and Multiobject Spectrograph aboard the Hubble Space Telescope, in both direct and coronagraphic modes. We reach 5 sigma detection limits of ~H=22 in the majority of our images. We compare our observations to the observed Lyman-break population of high-redshift galaxies, as well as Bruzual & Charlot evolutionary models of present-day galaxies redshifted to the distances of the absorption systems. We predict H magnitudes for our DLAs, assuming they are producing stars like an L* Lyman-break galaxy (LBG) at their redshift. Comparing these predictions to our sensitivity, we find that we should be able to detect a galaxy around 0.5-1.0 L* (LBG) for most of our observations. We find only one new possible candidate, that near LBQS0010-0012. This scarcity of candidates leads us to the conclusion that most DLA systems are not drawn from a normal LBG luminosity function nor a local galaxy luminosity function placed at these high redshifts.
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