## 2. The completeness of the surveyIn Paper 1 we have discussed in detail the selection of our sample
and the selection effects. In summary, an automated procedure was
applied to the low-resolution digitised objective-prism spectra, based
on two parameters, the slope of the continuum and the "luminosity"of
the integrated spectra (in counts). The selected candidates were
afterwards rescanned with high resolution and the final selected
spectra were visually inspected for the presence of emission-lines.
While the slope of the continuum helps us to preselect very promising
emission-line candidates, the cut in brightness at the faint end of
the photographic plates produces some loss of very faint objects, with
very little continuum and almost all the flux in the emission-lines.
In order to prevent the latter incompleteness we also scanned the
faint end of the photographic plates, and we completed the follow-up
spectroscopy for all the faint candidates. This extra survey was done
only for one of our regions - Region 3 from Paper 1 (a region North to
the Coma Supercluster, , centred around
) and in the following discussion we will refer
only to this subsample. The surface density of the subsample is 0.3
galaxies/deg As the main selection was based on the presence of the [OIII] 5007 line, the corresponding parameters for this line were computed. A complete catalogue with fluxes and equivalent widths (EW) will be published in a following paper. All the spectroscopic parameters calculated here are slit widths measurements. The line flux was measured directly from the slit spectra. The flux in the continuum under the line was calculated as , where is the mean flux per unit of wavelength and is the FW0I (flux width at zero intensity) of the emission-line. is calculated as the ratio between the line flux and the EW of the line, and it can be measured directly from the slit spectra. , where Disp(z) is the reciprocal dispersion
of the objective prism in and R is the spectral
resolution on the objective prism plates. In our case the resolution R
is determined by the slit widths of the PDS machine that was used to
digitise the plates. For the high resolution scans (see Paper 1 for
further details) we used a slit of 0.03 mm and we can assume that this
is also the value of R
The was transformed in a magnitude scale: where the constant is arbitrary. Our sample contains objects with the flux of the [OIII] 5007 emission-line as faint as and as bright as . If we consider the brightness parameter discussed above, namely the sum of the flux in the emission-line and of the continuum under the line, then the range is . The EW values range between 8 and 1700 . The completeness limit was derived based on a test (Schmidt 1968). V is the volume contained in a sphere whose radius is the (redshift) distance to the object and is the volume contained in a sphere whose radius is the maximum distance the galaxy could have and still be in the sample under study, where is the completeness limit and A is the Galactic absorption. The value of is then given by
. The mean value of the ratio
should be 0.5 for a complete sample of objects
uniformly distributed in Euclidian space. In practice the distribution
of galaxies is affected by large scale structure inhomogeneities. As a
first approximation we can consider that our subsample covers enough
volume (415 deg The mean ratios were computed for 99 galaxies in our Region 3 and the results are listed in Table 1. The Column (1) gives the , Column (2) gives the ratios and Column (3) gives the total number of objects brighter than the corresponding . Column (4) specifies the number of objects that need to be added at each level of magnitude in order to keep the average around 0.5 and Column (5) gives the level of completeness, c . The ratios are around 0.5 up to and then they start to decrease. We will take as a completeness limit , where the sample is 77 complete. This corresponds to a flux of erg sec .
In order to determine also the EW limit of our survey we plotted in Figure 1 log(EW) versus . With the vertical line we delimit the complete sample from the incomplete one and with the horizontal line we trace the threshold below which the ELGs are no more seen by our survey. This is a level of 0.9, which means an . There is only one point that falls below the horizontal threshold of 0.9. The corresponding galaxy was selected based on its [OII] 3727 line, one of the few cases that did not use only the [OIII] 5007 line criteria. Its spectrum is typical for a low ionization object, with faint [OIII] 5007 and strong [OII] 3727 emission lines. If one computed the EW for the [OII] 3727 line, the galaxy would fall above the horizontal threshold. One should also mention that all the points that were just above this threshold were galaxies selected as second priority objects (see Paper 1 for a detailed discussion of the selection procedure). The corresponding emission-lines were barely detectable on the digitised spectra, and we had difficulties to decide whether the candidate was real or not. The follow-up spectroscopy was the only method to determine the real nature of the objects. Therefore, removing these points from the plot, the diagram would indicate a slightly higher limit in EW, toward 12 .
The diagram also shows a trend of increasing EW at both the bright and the faint end of the . At the very bright end the galaxies have a strong continuum, and therefore it requires a higher EW for the emission-line to be detected above the continuum. By contrary, at the faint end, the galaxies have a low level continuum and therefore the spectrum is quite noisy. It requires again a high EW for the emission-line to be detected above the noise. In addition the sum between the flux in the emission-line and the continuum flux has to be kept above a certain level of detectability, and as the continuum decreases, the flux in the emission-line has to increase in order to detect the galaxy. In conclusion we can build a complete sample with all the objects brighter than erg sec and having a detectability in equivalent widths EW . Such a sample cannot be compared with a magnitude selected sample, but can be used for statistical calculations. © European Southern Observatory (ESO) 1997 Online publication: April 28, 1998 |