The HI Luminosity Function

To conclude on a positive note, we can use the tests described in the last section to correct the number counts and generate an HI luminosity function. In Fig. 3, I show the results using Sorar's (1994) and Spitzak's (1996) data. The counts are corrected based on the and relative HI magnitude tests described in the previous section, which imply a poorer effective sensitivity than assumed in previous analyses of these data (Schneider 1996; Sorar 1994). In addition to simple error bars, I have also included an uncertainty of to allow for small number statistics and to estimate upper limits over mass ranges where no objects were detected. Note that the masses of Sorar's objects may be underestimated by a factor as large as 3-5 because of an unknown offset of up to arcmin from the scan center for these ``main-beam'' detections. Nevertheless there is good agreement between the two data sets.

  
Figure 3: HI luminosity function based on two recent surveys. Sorar's (1994) data are shown with dotted crosses and Spitzak's (1996) data are shown with solid crosses. Schechter luminosity functions with , and (dotted line), (solid line), and (dashed line) are shown for comparison (see text).

It appears that there may be a very high space density of low-mass, HI-selected objects. A Schechter luminosity function (Schechter 1976) with a power law as steep as (with ), as suggested by Impey, Bothun, & Malin (1988), is consistent with the data, as shown by the dashed line in Fig. 3. Such a steep function would spread the integrated HI mass almost equally across logarithmic intervals from the dwarfs to giants (Briggs 1990). However, a much shallower power law like the optical luminosity function derived by Lin et al. (1996; dotted line), is difficult to completely rule out because of the small-number statistics of these two surveys. Note that the dotted line uses the same normalization as Lin et al., but with the same value of as above, so there may be up to four orders of magnitude difference in the counts at the faint end for an HI- vs. an optical-selected sample of galaxies.

Finally, although the small number of objects under consideration do not perhaps warrant much further analysis, I have applied a maximum-likelihood method like that of Sandage, Tammann, & Yahil (1979) to estimate the best-fit parameters of the luminosity function. The method was modified to account for the uncertainty in the beam offsets in Sorar's data. Because the results were so sensitive to the nature of the sensitivity roll-off, I limited the sample to detections brighter than about 20-, where the data should be complete. Both Spitzak's and Sorar's samples then gave consistent values of and . This is shown as a solid curve in Fig. 3.

These results are suggestive that the HI luminosity function is much steeper than its optical counterpart, but they await a much bigger survey for confirmation. Given the various values of examined here, the Parkes Multi-Beam surveys may detect thousands or only a few objects with masses . If the maximum-likelihood fit is correct, this number will be about a hundred. With this large range of outcomes, there should be little concern about small-number statistics dominating the uncertainties like they have in the Arecibo surveys. However, the Parkes surveys will be faced with the challenge of discriminating low mass objects from the larger galaxies that will frequently accompany them. The Parkes surveys will also be able to determine whether the HI luminosity function drops off like the optical distribution function at high masses or if it has its own distinctive behavior. The challenge here will be to develop better algorithms for identifying wide-profile sources in the presence of baseline instabilities. Having answered these challenges, the Parkes surveys should provide us with firm grasp on the shape of the HI luminosity function along with its implications for the nature of extragalactic populations.

© Copyright Astronomical Society of Australia 1997