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A fundamental goal of extragalactic astronomy is to achieve a thorough census of the matter in the universe. With this knowledge we hope to address the great questions about the existence and nature of dark matter, the formation of large-scale structure, and perhaps the ultimate fate of the universe. Through observations of continuum and line emission over the entire electromagnetic spectrum, we attempt to track down the amount of that matter and its distribution in space. This is complex because the translation from observed emission to mass of material present often depends on unknown temperatures, densities, abundances, distributions, filling factors, etc., but usually astrophysics allows some plausible assumptions that permit us to make reasonable estimates.

In 21-cm astronomy, the good news is that the physics of the line transition is independent of all of these complicating terms under almost all possible conditions, so that HI mass estimates are straightforwardly derived from 21-cm line observations (see Kulkarni & Heiles 1988). However, despite this, the 21-cm census is far from complete. As in all fields of extragalactic observation, we need to account for the selection effects that determine which objects enter our samples and which are detected. Unlike the 1948 U.S. presidential pollsters, we want to make sure we don't determine only the characteristics of "galaxies that we can phone up" and declare that President Dewey has been elected! This brings us to the bad news: extragalactic 21-cm astronomy is probably more limited than any other field by subtle and insidious selection effects.

The problem is that extragalactic 21-cm-line astronomy is almost entirely dependent on observations at other wavelengths to define its domain. For the most part observations are made of objects that have been first identified by their starlight, so any conclusions we try to draw about the HI properties of galaxies have optical selection effects folded in with the HI selection effects. Lately younger fields, like far-infrared astronomy, have provided new source lists for 21-cm observers, but this just adds a different layer of complication. I will briefly review the general emission properties of galaxies in section 2, pointing out that almost every other source of electromagnetic emission is intimately tied to stars and stellar nucleosynthesis. This is another reason why correcting the selection effects in 21 cm line studies is so important to pursue. The 21 cm line provides us with one of the only unique probes of the population of galaxies: the low excitation temperature of the line does not require stars to excite it, and since hydrogen is primordial, none of the processes of stellar nucleosynthesis are necessary for its presence.

One of the discoveries from optically-inspired 21-cm studies is that within individual galaxies the hydrogen frequently extends out to radii where little or no starlight is visible. It appears that star formation in the dense stellar regions has consumed most of the hydrogen. We might speculate whether there could be entire galaxies more comparable to the extended disk material, containing little starlight, but perhaps representing a significant portion of the extragalactic population. In such a scenario, optical selection effects would likely exclude these objects from ever entering our samples.

Just such large, low optical luminosity objects have in fact been encountered by a number of 21 cm observers. These discoveries have occurred mostly by accident, but they hint at the possible presence of a population of objects hitherto ignored. For example, in a calibration "off" scan to observations of a galaxy, I found a 200 kpc diameter HI structure in the Leo region outside the Virgo cluster (see Schneider 1989). This ring of gas contains ~ 2 × 109 Msun of HI, yet it has no detectable optical emission. It seems startling that an object with an angular size twice that of the Full Moon could remain unnoticed but for the accidental placement of a telescope during a calibration sequence. Likewise, Giovanelli & Haynes (1989) found a similarly large HI cloud surrounding a dwarf galaxy (McMahon et al. 1990) in one of their "off" scans.

Another surprise at 21 cm has been objects like "Malin 1," a huge disk galaxy found during a survey of low surface brightness dwarf galaxies in the Virgo Cluster (Bothun et al. 1987). Although this object looked like a dwarf, it proved to be at almost 20 times farther away, with a mass of HI > 1011 Msun! Further studies of objects classified as "dwarfs" have demonstrated that many are instead distant, large low surface brightness objects (Schneider et al. 1990, 1992).

These objects are individually fascinating, but it is unclear whether they are rare freaks or representatives of a large hidden population. To establish how common the HI-rich, optically-poor objects are we need to fully understand the selection effects on our observations and the procedures by which they can be corrected.

We will examine some basic ideas about luminosity functions in section 3, and how selection criteria interact with them to produce our samples of extragalactic objects in section 4. While these ideas are quite general for all wavelengths, HI surveys have some unique characteristics that we will focus on in section 5. We conclude by presenting preliminary results from one of the largest independent HI surveys yet carried out.

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