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A significant number of massive, low surface brightness galaxies with sizes approaching that of Malin 1 have recently been identified (Schneider et.\ al.\ 1990, 1992; Schombert and Bothun 1988; Schombert et.\ al.\ 1992). Many of these galaxies have large amounts of atomic gas, yet extremely low stellar surface densities. It has been suggested (van der Hulst et.\ al.\ 1987; Kennicutt 1983, 1989; McGaugh 1992) that star formation may be closely linked to the ability to form molecular clouds from atomic clouds through a critical surface density of HI. Indeed, a VLA map of the prototype LSBG Malin 1, indicates that is has a very extended HI disk with low column densities (Bothun, private communication). Furthermore, low resolution HI maps of dwarf low surface brightness galaxies indicate that their HII regions preferentially lie in high column density regions (McGaugh 1992). The situation is not so obvious for most LSBGs, however. From single-dish observations, these systems do not appear to have HI disks extending well beyond their optical disks (Schneider et.\ al.\ 1991) and their average column densities within the optical disk appear to be about normal for late-type disk galaxies. If, however, the atomic gas is not distributed in a small velocity range perpendicular to the disk, it is possible that the atomic gas would not efficiently collapse to form molecular gas even though its distribution along the disk is similar.
We have mapped the vertical velocity structure of atomic hydrogen in a few massive, low surface brightness galaxies with large angular diameters and nearly face-on optical morphologies using the VLA. These galaxies are gas-rich (M$_{HI} \geq$\kern.03em10$^{10}$\kern.03emM$_{\sun}$) and of similar size to giant spiral galaxies (D$_{25} \geq$\kern.03em30\kern.03emkpc), yet they have extremely low stellar surface densities. We estimate the degree of vertical motion of the gas using the local velocity dispersion and use this to compare with local stellar density to test the critical density hypothesis. We also determine the point-to-point deviations in the mean velocity in the gas to search for indications of warping.
