6.1 The Basic Reductions of the Spectroscopy

Removal of overscan area.

The readout window for the spectroscopy was [300:700,1:1028], and since the overscan area is what is outside [19:1042,3:1026] in these untrimmed coordinates, the section to keep (what we refer to as the trim section) was [1:401,3:1026] in the coordinates of the readout window. The trimmed spectroscopy images have the dimensions 401 pixels $\times$ 1024 pixels. The spatial direction is x, and the wavelength direction is y.

Subtraction of bias.

The bias frame used for the photometry (cf. Section ) was also used for the spectroscopy^6.0.

Correction for fat zero.

Like the photometry images, the spectroscopy images were affected by fat zero (cf. Section ). The columns affected had the same relative numbers as when reading out the entire CCD for the photometry, e.g. column 291, and the effect must therefore originate from the read out register. However, the effect (i.e. fat zero as function of level) was not the same, and it had to be redetermined from the spectroscopy images themselves. A by-eye fit with 1-4 linear functions was used. The fat zero effect in the spectroscopy images was generally smaller than in the photometry images, except for column 291.

Subtraction of dark current.

The two dark frames used for the photometry (one for night 0-5, one for night 6-14; cf. Section ) were also used for the spectroscopy ^6.1.

Flat field correction for pixel-to-pixel variations.

3 sets of 10 dome flat frames were obtained, with exposure times of 120 sec, 240 sec, and 240 sec, and from night 6, 10, and 13, respectively. After bias and dark subtraction, the images were combined within each set. These 3 flat images were normalized as follows: A 7-piece cubic spline, one per image, was fit to the continuum in the wavelength direction - only the section [40:100,*] was used, in order to avoid edges and low response areas. All columns were then divided by the fit. Note, that this normalization is different from that used for the photometry flats - the idea here is to let the flat field image represent only the pixel-to-pixel variations in sensitivity, not the variations in sensitivity with wavelength, and not the spectral energy distribution of the calibration lamp used to illuminate the dome.

The quotients between the 3 normalized flat images were investigated. The quotient between set 1 and set 3 showed a gradient of 1%, and other variations of $\pm 0.5$% or less. The quotient between set 2 and set 3 showed no gradient, and other variations of $\pm 0.3$%.

The slit profile (cf. below) was taken out of nff2 and nff3, and the mean of the resulting images was used as the final flat field image.

Slit correction.

In order to find the variations in sensitivity in the spatial direction, a slit profile image was constructed from the two dome flats nff2 and nff3 by averaging over the wavelength direction, and then taking the mean of the two images. The resulting image had the dimensions 401 pixels $\times$ 1 pixel. The variation in this image is a combination of two effects: 1. The pixel-to-pixel variations in the sensitivity of the CCD averaged over the y direction. 2. The variation of light throughput through the spectrograph caused by variations in the width of the slit.

Besides dome flats, also 6 sky flat images were obtained. These were reduced as outlined above, and then divided by the above slit profile image. First it was noted, that the position of the slit with respect to the CCD was not the same as for the dome flats - the slit profile image had to be shifted 1.5 pixels to match the 5 steep minima in it (probably caused by 5 grains of dust stuck on the slit)^6.2. Second it was noted, that the slit profile extracted from the combined sky flat was not flat, despite that the images had been divided by the slit profile derived from the dome flats. This is caused by a difference in the way the slit is illuminated when the telescope is pointed at the illuminated dome, and when the telescope is pointed at the sky. The effect was modeled by fitting a linear function to the profile. After being normalized, the variation was from 0.985 to 1.01.

The final slit profile image was constructed as the product of the slit profile image derived from the dome flats, and the correction derived from the sky flats. The slit correction of the science images was performed by division with the slit profile image, shifted with an offset determined from the thorium lamp exposure taken just after the given science frame.

Removal of signal from remanence.

Remanence, i.e. the signal from saturated objects (typically bright stars observed in direct imaging mode) in previous exposures, was also a problem for the spectroscopy images. The remanence signal was removed in the same way as for the photometry images, cf. Section .

Removal of signal from cosmic-ray events.

The same method as in JFK95b was used. The spatial profile of the galaxy was modeled from the galaxy spectrum. This model was subtracted from the galaxy spectrum, scaled to the local intensity of the profile. Pixels that deviated more than 7 times the local standard deviation in the resulting residual image were identified as cosmic-ray events. The values in these pixels were replaced by the model values.

Wavelength calibration and geometrical rectification.

We want to transform our science spectra, so that the spatial axis is perfectly aligned with the x axis, and the dispersion axis is perfectly aligned with the y axis. In addition, we want to wavelength calibrate the dispersion axis, and linearize it in $\log(\lambda/{\rm\AA})$.

During the observations at night, after each science spectrum (of a galaxy or a star), a spectrum of the thorium (Th) calibration lamp was obtained, with the telescope and instrument at the same position. Using a table with wavelengths for the different Th lines (see below), the Th spectra were used to establish the mapping of wavelength in Å as function of position on the CCD, i.e. $\lambda(x,y)$ - this could be done, since the spectral lines are at constant $\lambda$, whereas they extend over the entire spatial direction. The galaxy spectra themselves were used to establish the mapping of spatial coordinate as function of position on the CCD (the S-distortion), i.e. s(x,y) - this could be done, since the center of the galaxy is at one spatial point, whereas the wavelength varies. The above two mappings were established using the tasks identify, reidentify, and fitcoords. Note, that there is one set of mappings for each science spectrum.

The spectra were then geometrically rectified, wavelength calibrated, and linearized in $\log(\lambda/{\rm\AA})$ using the task transform. The output images were specified to have the wavelength range 4954.2-5612.5 Å, which was the common range for the night time Th exposures, and to have 1024 pixels in the wavelength direction. With these 3 figures specified, the output pixel interval is fixed as ${\rm d} \log \lambda = (\log \lambda_2 - \log \lambda_1)/(N-1)$. Note, that the output spectra are still 2-dimensional.

The Th lamp had the advantage of having a high signal, therefore requirering only a short exposure time. It had the disadvantage of having blended lines, so that a line list based on atomic data could not be used. For the helium (He) and neon (Ne) lamps, the opposite was the case. To link Th with He+Ne, high signal-to-noise spectra of all 3 lamps were obtained during the daytime on two occasions. From the He+Ne spectrum the mapping $\lambda(x,y)$ was established using a line list based on atomic data. The rms scatter of this dispersion solution was 0.16 Å. This mapping was used to rectify and wavelength calibrate the two day time high S/N Th spectra. Wavelengths for all the blended Th lines were then determined (rms scatter 0.1-0.15 Å), and the resulting line list was used when identifying lines in the Th spectra obtained at night. The rms scatter of the dispersion solutions for the latter ranged from 0.07 Å to 0.44 Å, with a mean of 0.14 Å = 8.1 km/s ^6.3.

The resolution was determined as $\sigma$ from a Gaussian fit to the 5577 Å night sky line, in averages of 10 columns. The mean value (N=75) was $\sigma$ = 1.358 Å = 79 km/s, with an rms scatter of 0.014 Å = 0.8 km/s. The position of the 5577 Å night sky line had an rms scatter of 0.11 Å = 6.6 km/s, which is a good measure of the accuracy of the wavelength calibration.

Subtraction of the sky background.

The sky background spectrum was determined in an area on each side of the galaxy or star at a distance range of typically 77''-91''. The 2D spectrum was rotated 90$^\circ$ so that x became the wavelength direction and y the spatial one - this is the format that the Fourier fitting program requires (cf. Section ). The extracted 1D sky spectrum was kept in row one in the 2D spectrum (with the galaxy spectrum being centered on row 200) to make it possible to calculate the signal-to-noise ratio.

Determination of the velocity dispersion and the radial velocity.

See Section .

Determination of line indices.

See Section . This includes a relative flux calibration.