3 Strengthening and normalization to the pseudo-continuum

This phase of the data processing takes the TACOS spectra and delivers order-connected spectra with a constant wavelength step. Both the instrumental and continuum fluxes are evaluated.

The operations follow these steps:

• Strengthen the spectra by dividing them by a de-blazing function;
• Compute the pseudo-continuum normalization and analyze the "shape'' of each order to determine a correction to the diffuse-light subtraction;
• Mask spikes and telluric lines;

• Convolve and rebin with two desired resolutions ($R=10\,000$ and $R=42\,000$) to 1D spectra.

3.1 De-blazing and pseudo-continuum normalization

The instrument, hard- and soft-ware, was mostly designed as a "velocimeter" and hence the spectrophotometric quality was not optimized. The standard flat-field correction and order extraction was applied as described in Baranne et al. (1996). However, the procedure is not sufficient to connect the orders into a single spectrum, because the blaze function is imperfectly corrected. Actually, after the standard correction, each order presents a residual "curvature'' of about 2%. This effect is certainly due to diffuse light within the spectrograph which is imperfectly subtracted by the TACOS program, this is a common difficulty with echelle spectrographs.

To solve this problem we had to analyze this residual curvature on the actual spectra and correct it. Obviously, it is a risky approach since the spectrum itself is used to determine the correction. To minimize possible biases, the residual curvature is modeled with only a few parameters: each order is represented by a second degree polynomial whose coefficients are not independent from order to order, but are themselves second degree polynomials of the order number. The total effect of the diffuse light is modeled by only 3 coefficients.

Practically, we divide the TACOS spectrum by a de-blazing function determined from a tungsten-lamp spectrum (internal flat-field) and corrected using 3 metal-deficient stars (because the blaze function appears to have slight systematic differences between internal flat-field and star).

To analyze the "residual'' curvature of each order, we normalized the spectrum to its pseudo-continuum, defined as a $3^{\rm rd}$ degree spline interpolation from one point in each order. Each point is determined by fitting a second degree polynomial to the order weighted with a mask to avoid as much as possible the stellar lines. The fit is iterated after $\kappa-\sigma$ clipping and the remaining bias due to the weak stellar lines is statistically corrected. The latter correction is based on the analysis of the skewness of the distribution of residuals. The weighting mask is prepared from a previous iteration of the reduction of the whole archive: for each wavelength point it gives the probability of having a stellar line (we started with no weight).

Though the visual inspection of the strengthened spectra appears satisfactory, the (unsuccessful) search for possible biases is presented in Sect. 5.

After the correction for diffuse light was applied, the pseudo-continuum was re-computed. These normalized spectra are scoped for abundance studies, and determination of the atmospheric parameters with TGMET.

All the information permitting calculation of the detected flux (in electrons) is kept in the form of a table extension attached to the FITS image. The S/N of each pixel is also kept in a separate extension. The detailed description of the FITS files is given with the electronic version of the tables and spectra.

3.2 Cosmic rays and telluric lines

The spikes due cosmics and defective pixels and the telluric lines have been masked following the procedure developed by Katz et al. (1998).

3.3 Resampling to 1D spectra

The orders are normalized to their pseudo-continuum and resampled to a 1D spectrum with a wavelength step of 0.005 nm using spline interpolation (the observations are over-sampled by about 20%).

To produce a version of the archive at the resolution 10000 (i.e. 30 kms^-1 at $\lambda$ = 550 nm) the spectra are convolved by a Gaussian function of FWHM = 0.054 nm, and rebinned with a step of 0.02 nm.

The high resolution version has a constant resolution of $R=42\,000$, i.e. the resolution in nm changes with the wavelength. At variance, with the low resolution archive, the wavelength resolution, in nm, is constant throughout the spectra.

Note also that the convolution to produce the low resolution archive is done on the continuum-normalized spectra, which is not formally equivalent to convolving the flux-calibrated spectra. However, the induced difference is absolutely insignificant.