3 Preliminary data reduction procedures

Packages in the image processing system IRAF (Tody 1986) were used for the basic reduction of the spectra. The main preliminary reduction steps, which are described in more detail below, are the following: (i) bias subtraction and dividing the data by a flat field; (ii) mapping the wavelength as a function of row and column by using the comparison exposures; (iii) subtracting the sky spectrum; (iv) removing the cosmic-ray hits from the spectra; and (v) extracting one-dimensional spectra from a sum over the aperture.

The bias level for each frame was found from the overscan region. The bias frames were averaged and the residual bias level subtracted pixel-by-pixel from each image. From dark frames with exposures of 2400 s, a level always much less than one count was found. Since the dark current is flat, no dark count corrections were made. The flat field frames were combined to their median value, by using noao.imred.ccdred.flatcombine. This result was then normalized by fitting a cubic spline to the continuum in the wavelength direction and dividing the flat field by this fit to obtain the response function. The rms variation in the resulting flattened response frames was typically less than 0.5%. Each galaxy or star spectral frame was then divided by the response function.

The next step was to transform from pixel coordinates to a two-dimensional spatial scale with wavelength coordinates along the dispersion axis of the CCD image. Tasks in the package noao.twodspec.longslit were used for this. By means of 25 - 50 identified arc lines in the comparison lamp spectra, a polynomial was fitted to the wavelength solution, with an rms residual in the coordinate fit of 0.1 - 0.2  $\mbox{\AA}$. The two-dimensional spectra of stars and galaxies were calibrated in wavelength using the comparison lamp spectra observed before and after each object, and thus transformed to a linear wavelength scale.

The sky was fitted interactively using background, with the sky level found from unoccupied regions of the slit, and the sky background was subtracted. This worked well, since the galaxy occupied a relatively small part of the slit. Cosmic rays were removed by rejection using images.lineclean, with care being taken that absorption lines were unaffected. The final one-dimensional spectra were extracted by summing over an aperture covering the entire visible galaxy. This included tracing the mapping of the slit position across the CCD as a function of row or column. The package kpnoslit.apall was used interactively to fit the traced positions of the apertures. For all runs the trace was found to vary by at most 4 pixels across the CCD, in 1023 pixels. The typical width of the galaxy spectrum was about 20 pixels, so the maximum misalignment resulting from the tilt of the spectrum would be 0.1 pixels.

Figure 1: The distribution of spectra as a function of the mean S/N per $\mbox{\AA}$measured at the wavelength of Mgb

The summed one-dimensional spectra typically have 1000 - 20 000 counts at 5200 $\mbox{\AA}$, near the wavelength of Mgb. The mean value of the S/N per $\mbox{\AA}$ was found for each spectrum, of galaxies and standard stars. The S/N was calculated from the mean number of photon counts in the spectrum in the wavelength range of the continuum bands of the Mgb spectral feature, also including in the noise the contribution of the readout noise and the effect of subtracting the sky spectrum. For most spectra the resulting value of S/N per $\mbox{\AA}$ is in the range of 15- 40. A histogram of the frequency distribution of all the spectra with respect to S/N is shown in Fig. 1. The mean S/N for all spectra is 23.0. For sample galaxies it is 21.4, for Coma galaxies 27.3, and for standard galaxies 26.8. The S/N of a typical stellar observation is 100 - 200, which means that the stellar spectra can be considered to be noiseless.

At this stage the one-dimensional extracted spectra were inspected. Usually the sky subtraction was reasonably accurate, but the spectra were checked for night-sky emission lines, particularly those of [O I] at 5577 $\mbox{\AA}$ and Hg at 5461 $\mbox{\AA}$, and if necessary these lines were removed by hand in cases of imperfect sky subtraction. There were sometimes cosmic rays which had not been removed completely, and these were also removed by hand. Three of the observed galaxies had spectra which were found to contain strong emission lines, and these galaxies were removed from the sample.