21-cm Observations of Dim Galaxies

Immediately following our original conjecture (Disney 1976) Shostak (1977) looked back at existing 21-cm observations of optical galaxies to see if any ``Iceberg galaxies'' had turned up accidently in the ``off-beams''. Out of several thousand observations there was not a single convincing ``Iceberg'', and this was felt, at the time, to be a very telling argument against the existence of any extensive population of dim galaxies. This inference rested, however, on the implicit assumptions that dim galaxies would have neutral hydrogen columns as high as ``normal'' optical galaxies. But that is surely unreasonable? Dimness presumably corresponds to low surface density, and therefore to low hydrogen columns even in galaxies with normal ratios (the total HI mass to optical B-band luminosity).

The point can be made as follows. Starting from the antenna equation as usual, one can show that for an HI source of solid angle , to be detected with S/N , one requires it to have a column density, :

where K is a numerical factor of order unity, is the system temperature, is the solid angle subtended by the beam, V is the velocity dispersion of the gas, and the integration time.

For sources smaller than the beam, this converts to the usual

where we have taken , (Rohlfs, 1986), K , is the size of the telescope in metres and is the distance of the source. This can be converted to yield the maximum range for detection of:

so that the range r , and hence the volume searched . Thus in a blind survey the number of sources O(t) detected, in observing time , in fixed direction, goes as,

Since O(t) does not rise as fast as , observers with a total time T to spend on a survey have generally made short integrations in order to cover a large area of sky and so to maximize O(t).

Now consider the other limit, i.e. for sources larger than the beam, (1) then converts to

(where we have taken , following tests at Jodrell Bank.) This shows that radio telescopes have surface intensity limits . (The size drops out because larger telescopes have smaller beams and hence see less hydrogen from a given extended source). Because at 21-cm astronomers have rarely used integrations beyond 30 minutes almost nothing is known of the extragalactic world below . According to Briggs (1990): ``the short integration times that typify 21-cm line redshift surveys could not reliably detect 's much less than , even if the emission filled the beam.''

Now consider galaxies. Because an SB of , one can show that:

where is a mean SB over the hydrogen-bearing area. Adjusting (5) for the fact that hydrogen radii are generally larger than optical ones, we obtain the correspondence between mean surface brightness and column density shown in Table 1.

Three conclusions can immediately be drawn from the table:

(a) Existing 21-cm surveys, capable of reaching not far below , set no intensity constraints on the population of low SB and invisible galaxies. Any galaxy they can detect should be visible on existing Schmidt surveys. For instance, Shostak's observations were far too short to pick up ``Iceberg'' galaxies. The ``Crouching Giant'' Malin 1 was picked up so easily at 21-cm only because of its uniquely high . Most such Crouching Giants may have ``normal'' 's of 10 times less, and would be far harder to detect at 21-cm.

(b) An all-sky multibeam survey with short ( sec) integrations per pointing will pick up optically undetected galaxies only if they have ('s of 4 or more.

(c) However, were it possible to reach column densities as low as a new region of parameter space opens up, a region which may contain numerous galaxies too dim to be picked up on either existing optical or indeed 21-cm surveys.

 
Table 1: Surface Brightness (B) versus column density (atoms cm) for different values of .

Key for Table 1:

: visible on POSS

: visible on UK Schmidt.

© Copyright Astronomical Society of Australia 1997