Flat field correction and straightening of each order

The ELODIE reduction software provides a flat field correction, separated in two components. The first one is the response correction, that takes into account pixel to pixel sensitivity differencies. The extracted spectra we are using underwent this correction. The second one is a division of each order by the response of the tungsten lamp spectrum of the same order, to correct the spectra from the modulation of the blaze profile.

We decided not to use the same procedure to straighten the orders, because of the presence of a coloured filter in the beam. This filter is necessary to balance the exposures at the red end and the violet end of the tungsten lamp. But it implies that the spectrum is not flat along the wavelength coordinate. Therefore, polynomials of order 7 to 19 were fitted to the continuum of four very metal-poor (almost line-free) stars : HD 221170, [Fe/H] = -2.10, HD 216143, [Fe/H] = -2.15, HD 108317, [Fe/H] = -2.36, HD 140283, [Fe/H] = -2.53 (Soubiran et al. 1998, paper II). For each order k, the response curve B_k(x) is given by the polynomial which is less affected by the spectral lines, with respect to the three others. Instead of using the tungsten response, the observed spectra are straightened by dividing their flux, order by order, pixel by pixel, by B_k(x), normalized at 1 at its maximum. For further uses all the pixels that correspond to a response value lower than 0.5 at the edges of the orders are rejected by giving them the flag value -100.0.

Orders 138 to 157 (the bluest spectral orders) were rejected, because they were underilluminated with respect to the rest of the orders, and too much degraded by noise.

  

Figure: Order 100 of HD 25329 ($T_\mathrm{eff}$ = 4787 K, $\log g$ = 4.58, [Fe/H] = -1.72, S/N = 141) before (top) and after straightening (bottom) and the response curve $B_{100} (\lambda)$ which has been used to straighten the order (middle).

If the spectral energy distribution (SED) of the target star is very similar to that of the star which was used for straightening the order, no significant slope in the SED of the straightened order is expected. If the two stars have different colours, a residual slope is expected. Initially, the adjustement of the slope between the target and a reference star was performed in the least square fit of the flux levels. However a better consistency was attained in removing this adjustment. In practice the slope remains very small over an order: about 1% from edge to edge for a 1200 K difference in effective temperature. The ``successful'' comparison star has of course a temperature difference considerably smaller than this, with respect to the target star, so the slope adjustment is not necessary. Indeed it is even unwise, because if slope adjustment is provided, the software try to compensate the presence of a strong line at the edge of an order in a comparison star, by inventing an unphysical strong slope in the target star, when the line is non-existent or much weaker in the target star (or vice versa). Figure 1 shows order 100 of HD 25329 before and after straightening.