3 Data reduction

In order to avoid, at least for statistical studies, the difficult long-term task of follow-up observations we have built a reduction system based on automatic procedures using MIDAS imaging package developped at ESO (Fig. 2).

We suggest the reader to refer to Paper I for a complete description of the calibrations, redshift determination technique and photometric measurements. We remind that we succeeded in deriving redshifts with an average accuracy of 160 km s^-1, U and R asymptotic magnitudes in Johnson-Cousins system and U-R colors in the Basel system with a mean uncertainty of 0.3 mag. In what follows, we describe the additional data reduction processes used to derive equivalent widths and relative line intensities from the digitized O.P. plates.

To perform spectrophotometry on the O.P. spectra of the ELGs, two preliminary steps are needed: the wavelength calibration and derivation of the instrumental response. Figure 2 displays the complete flow chart of the data processing.

  

Figure 2: Flow chart of the data processing. Large black filled circles show internal calibrations while large grey filled circles show calibrations using external objects (spot sensitometer, standard stars, catalogued galaxies)

3.1 Wavelength transformation

Wavelength calibration of slitless spectra present special difficulties: the absence of calibration lamp spectra or night sky emission line features forbids the use of standard methods designed for slit spectroscopy. The crucial point is to determine some reference wavelength as a reference position, in the galaxy spectrum itself. As in Paper I the CaII H 3968 Å absorption line core, was found to be the best reference because of its almost constant presence and good signal-to-noise in the field stars spectra, these field stars being supposed to have an average null radial velocity.

We use the Eq. (2) of Paper I for the CaII H line core. This equation gives the position that the CaII H absorption line core would occupy at null recession velocity in the spectrum of the galaxy using the position of the CaII H absorption line of field stars whose spectra are located in its immediate vicinity.

The equation leads to:

$$X_{\rm o}(\lambda)\, =\, X_{\rm G}\, +\, \Delta_{\rm Ca}$$ (1)

where:

$X_{\rm o}$ is the position that the CaII H absorption line core would occupy in the galaxy spectrum at null recession velocity,

$X_{\rm G}$ is the position of the centroid of the galaxy R image on the bicolor plate,

$\Delta_{\rm Ca}$ is the average separation along the dispersion direction between the field star R positions on the bicolor plate and the CaII H line core position in their respective spectrum. The origin of the coordinates is arbitrary.

From this reference wavelength and solving the equation:

$$\vert n_{\lambda_2}\,-\,n_{\lambda_1}\vert\,=\,{{\Delta X}\over{f\cdot A}}$$ (2)

where:

$\Delta$X is the separation of two spectral lines along the direction of the prism dispersion, $f\cdot A$, calibrated as described in Paper I, is the product of the focal length of the telescope by the O.P. angle (we remind that we need only to know the local value of this product), n$_{\lambda_i}$ is the prism refractive index for the wavelength $\lambda_i$, one can derive the wavelength of any spectral feature from the spatial separation of this feature from the reference position of the CaII H line. Indeed the value of $n_{\lambda_i}$ depends only on $\lambda_i$. It can be calulated with an accuracy of 10^-5, using a polynomial approximation given in Schott technical notices for the UBK7 material of the prism.

We used Eqs. (1) and (2) to rescale the spectra along a wavelength scale using a non linear rebinning algorithm.

Tests experienced with the field stars show that the mean error is less than the intrinsic uncertainty in measuring the emission or absorption line (basically $\le$ 0.4 Å when measuring H$\gamma$).

To check the internal consistency of the wavelength transformation we derived the redshifts of the objects from the rebinned spectra, and compared them to the values obtained from the methods detailed in Paper I (Fig. 3).

  

Figure 3: Comparison of the apparent recession velocities derived from wavelength rebinned spectra ($V_{\rm r}$) with the apparent recession velocities adopted from Paper I ($V_{\rm nr}$)

We found the wavelength transformation 95% confident considering all spectra (100% is obtained when the difference between each couple of measured recession velocities, for all the objects, are smaller than 1.5 times the intrinsic uncertainty on the adopted velocity value). This confidence level reaches 100% when only taking into account the spectra with a signal to noise ratio larger than 7. (the S/N ratio being defined as the ratio between the peak intensity of the [OIII]$\lambda 5007$ Å line and two times the $\sigma$ value of the noise measured on the continuum between 4400 Å and 4800 Å).

3.2 Instrumental response

We used the A type field stars, which are easily recognized thanks to the presence of the Balmer absorption lines, to correct the rebinned spectra from the telescope-emulsion instrumental response, as follows. A serie of A-type stars with good signal-to-noise spectra is identified on the O.P. plate and their spectra are digitized in the same conditions as the galaxy spectra, calibrated and rebinned in wavelength, and corrected from the airmass using standard La Silla values of the extinction. However, we do not have at our disposal a series of spectra of spectrophotometric standard stars taken with the same instrument. Therefore, we decided to build an "average'' spectrum for each subtype A2V, A3V, A5V and A7V, by means of adding individual spectra of several stars of each type. This average spectrum was further normalized at a continuum intensity of 1 at 5200 Å. The instrumental response is obtained by comparing the averaged stellar spectra with those, of same stellar type, observed by Jacobi et al. (1984) and normalized in the same way. The 4 curves obtained by this way are very similar ($\sigma$ = 0.05) and are used to derive a mean instrumental response shown in Fig. 4.

  

Figure 4: Telescope-emulsion instrumental response, normalized to 1 at 5200 Å

The rebinned galaxy spectra are hence divided by the instrumental response to produce the final corrected spectra (Fig. 5).

  

Figure 5: Up: one dimension galaxy spectrum (13228-1955a) as extracted from the digitized O.P. plate; down: same spectrum, rebinned, and corrected from the instrumental response. The bottom spectrum shows from left to right, [OII] line and H$\beta$ - [OIII] triplet. H$\gamma$, H$\delta$ and [NeIII] are also detected

One can notice the very abrupt drop of the IIIaJ emulsion sensitivity at wavelengths larger than 5200 Å. This well-known characteristic of the IIIaJ emulsion allows to avoid the bright 5577 Å nightsky emission line when making deep photographic imaging but makes spectrophotometry in this spectral region very unsafe, and produces a very large numeric noise on the corrected spectra. A number of ELGs in our sample have a redshift value that pushes the [OIII]$\lambda 5007$ line in this spectral region. An additional correction has been devised for these galaxies and is described below.

3.3 Measurement of the emission line fluxes and equivalent widths

After rebinning and correction of the spectra from the instrumental response, the ranges where emission lines are present have been selected. Locally, these spectral fractions have been fitted with the addition of a third order polynomial representing the continuum with one or several Gaussians representing the emission lines. The fit used the standard least-squares optimization methods of the MIDAS processing package (associated with NAG mathematical subroutine library). This method used by Cananzi (1993) for the H$\beta$ and H$\gamma$ absorption lines, allows a reliable determination of fluxes and equivalent widths, especially for low signal to noise ratio spectra. The line intensity ratios relative to H$\beta$ and equivalent widths of H$\beta$,[OIII]$\lambda\lambda 5007,4959$ and [OII]$\lambda 3728$ emision features were subsequently determined from the Gaussian fits.

From the sample of 92 objects, velocities of which were computed, we measured the R magnitude, U-R color for 66 of them and derived at least one emission line relative flux for 79 of them.

3.4 Intensity correction of the [OIII] lines at high velocities

For velocities larger than 12000 km s^-1, the [OIII] doublet enters in the range of sensitivity drop of the IIIaJ emulsion. In this region, the [OIII]$\lambda 5007$/[OIII]$\lambda 4959$ ratio tends to decrease with velocity, even after instrumental response correction.

The average value of the [OIII] ratio, equal to 2.3 is low with respect to the expected value of 3 given by the theory and is mainly due to the weight of objects with velocities larger than 10000 km s^-1 (Fig. 6).

  

Figure 6: Dependance [OIII] $\lambda 5007$/$\lambda 4959$ ratio on the velocities. The line relies the mean [OIII] ratio value every 1000 km s-1

In order to use the [OIII] line intensity (and especially the [OIII]/H$\beta$ intensity ratio) for further studies, we have corrected these values using a method of two dimensional mapping. The evolution of the [OIII]$\lambda 5007$/[OIII]$\lambda 4959$ ratio versus redshift and signal to noise has been mapped from the subsample of 64 galaxies having an [OIII] line measurement. The resulting two-dimension surface has been smoothed and extrapolated across the range:

$0.\le$ velocity $\le 25000$ km s^-1 - $0.\le S/N \le 20.$

using the following conditions: truecm ${{\rm [OIII]}\lambda 5007 \over {\rm [OIII]}\lambda 4959}$ = 3. for $S\over N$ = 20. and vel = 0 km s^-1 truecm and truecm ${{\rm [OIII]}\lambda 5007 \over {\rm [OIII]}\lambda 4959}$ = 0. for $S\over N$ = 0. and vel = 25000 km s^-1. truecm The limiting value equal to 3. is given by the probabilities of transition for the oxygen ion (Osterbrock 1989). The values of the [OIII] lines intensity have subsequently been corrected using this map. The [OIII] doublet intensity ratio corrected in this way has an average value of 3.1 with a standard deviation ($\sigma$ = 0.71) identical to that obtained with uncorrected values for objects with velocities smaller than 10000 km s^-1.