Achieved Survey Sensitivities

Most HI surveys to date have quoted some sort of sensitivity based on the rms noise in their spectra, often along the lines of equation (3). A 5- limit as suggested there sounds like a reasonable expectation, but all of the surveys have allowed various degrees of user intervention to reject ``unlikely'' signals or to pick the best cases for follow-up. The simple 5- limit also ignores subtle effects like baseline subtraction, which may mask signals. It is important to test the surveys in other ways to determine their actual sensitivity. The recent Arecibo surveys have detected large enough numbers of objects to carry out statistical tests on their level of completeness.

In Fig. 2, the line widths and observed fluxes of HI features detected by Sorar (1994) and Spitzak (1996) are plotted on scales in the same ratio as their rms baseline noise levels. The points for Sorar exclude objects that were detected in the sidelobe. The points for Spitzak include several objects undetected in the survey, but which had previously-measured redshifts. The 5- line appears to represent a fairly good lower bound on the detectable fluxes for both samples even though the surveys were carried out and analyzed in quite different fashions.

  
Figure 2: Observed fluxes vs. line widths of objects detected by Sorar (1994) and Spitzak (1996) relative to the 5- width-dependent detection limit. In addition, known objects undetected by Spitzak, but measured in deeper integrations are also shown with open triangles.

This is not the whole story, though. One would expect the number density of sources to increase rapidly as the limiting-flux line is approached; instead the number density seems to drop slightly near this limit. This could be because the HI surveys are volume-limited by their upper limiting redshifts, but it might also be caused by a roll-off in sensitivity near the flux limit. Note that because the fluxes here are ``as observed,'' this is distinct from the problem of sensitivity decline when sources are not at the beam center. There are several methods of testing the actual survey sensitivity.

One probe of a survey's completeness is a test. Each source has a limiting distance to which it can be detected, either determined by equation (3) or by the limiting redshift of the survey. On average, the distance to an object ought to be half way into its detectable volume. Therefore, the volume in front of a detected source, , should average half of the maximum possible volume in which the object could be detected . Both samples have average values of of only 0.35, and both require an effective limiting flux about 70% higher than 5- to give the correct mean of 0.5. Unfortunately, because of large scale structure within the surveyed regions, this test is somewhat uncertain, although Sorar's survey covers nearly 24 hours in right ascension, so it should be less affected by local structures.

The roll-off in detections is also apparent using a second test, which is the analog of the optical - test. We can define a ``relative HI magnitude'' as (flux/minimum flux), where the minimum flux is based on the 5- limit for the signal's line width. In subsets of the data which are nominally sensitivity limited, the distribution of counts should rise by a factor of 2 in each half-magnitude fainter bin, as is well-known optically. Both Spitzak's and Sorar's samples show the expected rise in number counts until the faintest half-magnitude bin above the nominal sensitivity limit where the counts drop. This indicates that several times fewer galaxies are being detected than should be within a factor of about two of the nominal 5- limit.

These indications that HI signal detection procedures are not as effective as we think are a little disappointing, but hardly surprising. The nominal 5- detection limits would only be attained for spectra that required no baseline fitting, were free of interference, and in which a single (smoothed) channel would be sufficient to declare a detection. Moreover, simply choosing a higher limit does not adequately describe the surveys' sensitivity since some objects are detected down to 5- as seen in Fig. 2.

For the best determination of the HI luminosity function, what is needed is a detailed knowledge of the sensitivity roll-off as a function of the HI line width. A method that we are employing in reducing the Arecibo dual-beam survey data is to introduce artificial HI signals close to our suspected sensitivity limit, ranging from the undetectable to the obvious. We generate these randomly all over the sky and over our entire bandpass range, with widths that span the full observed range of galaxies. These artificial sources are inserted into the raw data before any signal processing is attempted and then subjected to all of the baselining and interference filtering schemes we use. Our initial results suggest that we are even less sensitive to wide-profile sources than equation (3) implies. I would recommend a similar procedure for determining the sensitivity of the Parkes surveys.

© Copyright Astronomical Society of Australia 1997