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Astron. Astrophys. 325, 881-892 (1997)

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2. The completeness of the survey

In 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, [FORMULA], centred around [FORMULA]) and in the following discussion we will refer only to this subsample. The surface density of the subsample is 0.3 galaxies/deg2 and the catalogue of the additional survey will be published elsewhere. For the data analysed in this paper we have completed the spectrophotometry, allowing thus to establish a completeness limit. Our sample was not selected in a traditional way, therefore it is not a continuum magnitude limited sample. Nevertheless we can first give the limits of our survey in continuum blue magnitudes, based on the data from Paper 1 and from the additional survey. Our sample contains objects as faint as [FORMULA], and also intrinsically faint objects, down to [FORMULA]. This indicates that the present survey goes deeper than other surveys and is therefore adequate for a search for faint objects in voids. But for a sample that was selected based on the presence of the emission-lines, the relevant brightness parameters are the sum of the flux in the emission-lines and of the flux in the continuum under the line, and the equivalent widths. A detailed description of this selection procedure is given by Salzer (1989).

As the main selection was based on the presence of the [OIII] [FORMULA] 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 [FORMULA] slit widths measurements. The line flux [FORMULA] was measured directly from the slit spectra. The flux in the continuum under the line was calculated as [FORMULA], where [FORMULA] is the mean flux per unit of wavelength and [FORMULA] is the FW0I (flux width at zero intensity) of the emission-line. [FORMULA] is calculated as the ratio between the line flux and the EW of the line, [FORMULA] and it can be measured directly from the slit spectra.

[FORMULA], where Disp(z) is the reciprocal dispersion of the objective prism in [FORMULA] 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 1. The resulting [FORMULA] as well as the EW of the [OIII] [FORMULA] 5007 lines were computed for each individual object of our sample. For two cases the [FORMULA] was stronger than the [OIII] lines, indicating starburst like galaxies, and therefore H [FORMULA] was measured instead.

The [FORMULA] was transformed in a magnitude scale:

[EQUATION]

where the constant is arbitrary.

Our sample contains objects with the flux of the [OIII] [FORMULA] 5007 emission-line as faint as [FORMULA] and as bright as [FORMULA]. 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 [FORMULA]. The EW values range between 8 [FORMULA] and 1700 [FORMULA].

The completeness limit was derived based on a [FORMULA] test (Schmidt 1968). V is the volume contained in a sphere whose radius is the (redshift) distance to the object and [FORMULA] 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,

[EQUATION]

where [FORMULA] is the completeness limit and A is the Galactic absorption.

The value of [FORMULA] is then given by [FORMULA]. The mean value of the ratio [FORMULA] 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 deg2, v [FORMULA]) to cancel out these effects. Also we will show that the ELGs have a small tendency to be more evenly distributed than the giant galaxies, lying also in some voids or at the rim of the voids, and therefore the approximation of uniformity can be applied as a first guess.

The mean [FORMULA] ratios were computed for 99 galaxies in our Region 3 and the results are listed in Table 1. The Column (1) gives the [FORMULA], Column (2) gives the [FORMULA] ratios and Column (3) gives the total number of objects brighter than the corresponding [FORMULA]. Column (4) specifies the number of objects that need to be added at each level of magnitude in order to keep the average [FORMULA] around 0.5 and Column (5) gives the level of completeness, c [FORMULA]. The [FORMULA] ratios are around 0.5 up to [FORMULA] and then they start to decrease. We will take as a completeness limit [FORMULA], where the sample is 77 [FORMULA] complete. This corresponds to a flux of [FORMULA] erg sec [FORMULA].


[TABLE]

Table 1. The [FORMULA] test.


In order to determine also the EW limit of our survey we plotted in Figure 1 log(EW) versus [FORMULA]. 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 [FORMULA]. There is only one point that falls below the horizontal threshold of 0.9. The corresponding galaxy was selected based on its [OII] [FORMULA] 3727 line, one of the few cases that did not use only the [OIII] [FORMULA] 5007 line criteria. Its spectrum is typical for a low ionization object, with faint [OIII] [FORMULA] 5007 and strong [OII] [FORMULA] 3727 emission lines. If one computed the EW for the [OII] [FORMULA] 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 [FORMULA].

[FIGURE] Fig. 1. A plot of log(EW) versus [FORMULA], where EW are the equivalent widths in [FORMULA] and [FORMULA] is the flux in the emission-line plus the flux in the continuum under the line, transformed in a magnitude scale (see (1)). 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.

The diagram also shows a trend of increasing EW at both the bright and the faint end of the [FORMULA]. 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 [FORMULA] erg sec [FORMULA] and having a detectability in equivalent widths EW [FORMULA]. Such a sample cannot be compared with a magnitude selected sample, but can be used for statistical calculations.

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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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