The first detailed VLA mapping of the neutral hydrogen distribution in the isolated, edge-on spiral galaxy NGC 3044 is presented. Physical parameters determined for this galaxy are typical for galaxies of its morphological class (SBc). We have modelled the HI spectra in order to derive its global density and velocity distributions. An HI scale height of 420 h^(-1) pc is thus found. This can be compared to the 8 kpc radio continuum halo found previously. The present study reveals an asymmetry in the HI distribution as well as numerous high-latitude HI structures at various galactocentric radii. Twelve high-latitude features were catalogued, of which four exhibit the signature of an expanding shell. There is some correlation of these features with features observed in the radio continuum from independent data. The most massive shell (Feature 10) extends out to 6h^(-1) kpc above the galactic disk. The radii and masses of these shells range from 1.2h^(-1) - 2.0h^(-1) kpc and 1.6 10^7 - 5.5 10^7h^(-2) solar masses, respectively. We have investigated the possibility that the supershells could have been produced by external impacting clouds, but conclude that this scenario is unattractive, given the age of the shells, the isolation of the galaxy, and the lack of any observed features sufficiently massive to form the shells in the vicinity of the galaxy. Therefore, an internal origin is suggested. Since the implied input energies from supernovae are extremely high (e.g. from 1.4 10^(53)h^(-20 - 7.4 10^(55)h^(-2) ergs, corresponding to 400 - 74,000 supernovae), we suggest that some additional energy (e.g. from magnetic fields) may be needed to produce the observed supershells.
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