2 Observations and data reduction

2.1 Hubble Space Telescope observations

HE 0515-4414 was observed with STIS for 31500 s on three occasions between January 31 and February 2, 2000 with the medium resolution NUV echelle mode (E230M) and a $0.2 \times 0.2$ aperture which provides a resolution of $\sim$30000 ( $FWHM \simeq 10\,{\rm km\,s^{-1}}$). We used the HST pipeline data with an additional correction for inter-order background correction (Rosa, private communication). The spectrum covers the range between 2279Å and $\sim$3080Å. The coverage at the red end guarantees overlap with the UVES spectra which extend shortwards to $\sim$3050Å.

2.2 VLT/UVES spectroscopy

Echelle spectra of HE 0515-4414 were obtained during commissioning of UVES at the VLT/Kueyen telescope. The observations were carried out under good seeing conditions (0.5-0.8arcsec) and a slit width of 0.8arcsec was used. A summary of the observations and of the detectors used is given in the ESO web pages http://www.hq.eso.org/instruments/uves.

The spectra were extracted using an algorithm that attempts to reduce the statistical noise to a minimum. After bias-subtracting and flat-fielding of the individual CCD frames, the seeing profiles were fitted with a Gaussian in two steps. In a first step the three parameters of the Gaussian - width, amplitude, and offset from the previously defined orders - were unconstrained; in the second step only the amplitudes were allowed to vary, with width and offset held fixed at values found by a $\kappa\sigma$-clipping fit along the dispersion direction to the values obtained in the first step. Flux values were assigned with a variance according to the Poisson statistics and the read-out noise, while cosmic-ray shots were assigned with infinite variances. Thus, the extraction procedure recovers the total count number even at wavelengths where the spatial profile is partially modified by cosmic-ray hits.

The extracted spectra were wavelength calibrated using as reference Th-Ar spectra taken after each science exposure. All wavelength solutions typically were accurate to better than 1/10 pixel. The wavelength values were converted to vacuum heliocentric values and each spectrum of a given instrumental configuration was binned onto a common linear wavelength scale (of typically 0.04 Å per pixel). Finally, the reduced spectra were added, weighting by the inverse of the flux variances.

2.3 Line profile analysis

Our analysis was carried out using a multiple line fit procedure to determine the parameters $\lambda_{\rm c}$ (line center wavelength), N (column density), and b (line broadening velocity) for each absorption component. We have written a FORTRAN program based on the Levenberg-Marquardt algorithm to solve this nonlinear regression problem (see, e.g., Bevington & Robinson 1992). We have included additional parameters describing the local continuum curvature by a low order Legendre polynomial. A free floating continuum is a prerequisite for an adequate profile decomposition in the case of complex line ensembles.

To improve the numerical efficiency we have to provide adequate initial parameters. In some cases the success of the fitting depends on good starting parameters, since the algorithm tends to converge to the nearest, not necessarily global, minimum of the chi-square merit function. A first approximation can be found neglecting the instrumental profile and converting the flux profile into apparent optical depths using the relation

$$\tau_{\rm a}(\lambda) = \ln [F_{\rm c}(\lambda)/F_{\rm obs}(\lambda)]\,,$$ (1)

where $F_{\rm c}$ and $F_{\rm obs}$ are the continuum level and the observed line flux, respectively. If the instrumental resolution is high compared to the line width, $\tau_{\rm a}(\lambda)$ will be a good representation of the true optical depth $\tau(\lambda)$. However, an ill-defined continuum level or saturation effects may produce large uncertainties. The apparent optical depth can be automatically fitted with a sum of Gaussians, each having a variable position, amplitude, and width. An a priori line identification is not necessary at this stage of the analysis.

Having obtained first-guess parameters we proceed with Doppler profile fitting using artificial test lines with z=0 and f=1, where f is the oscillator strength. It can be shown that most Voigt profiles are well represented by the purely velocity broadened Doppler core. The size of the fit region depends on the complexity and extent of the absorption line ensembles. Indeed, the number of free parameters should be less than 100 to preserve the numerical efficiency. One specific characteristic of our technique is the simultaneous continuum normalization which can reconstruct the true continuum level even in cases, where the background is hidden by numerous lines. The multi component profile is the convolution of the intrinsic spectrum and the instrumental spread function $P(\Delta \lambda)$:

$$F(\lambda) = P(\Delta\lambda) \otimes \left\{ F_{\rm c}(\lamb... ...rod_i \exp[-\tau_i(\lambda,\lambda_{\rm c},N,b)] \right\}\cdot$$ (2)

If the program fails to converge on a reasonable model, the parameters can be adjusted by hand. In this way the fit can be modified to be acceptable by eye and then re-minimized. In some exceptional cases this procedure is the only chance to free a converged solution from a local chi-square minimum.

After line identification the parameters of the test lines can be transformed to the actual redshift and oscillator strength. However, the contribution of unknown profile components can still be considered using the test line results. A final Voigt profile fit with all identified components includes the simultaneous multiplet treatment, keeping the redshift, column density, and line width the same during the chi-square minimization. The upper limit of the column densities of non-detected lines is estimated assuming a $5\,\sigma$significance level for the equivalent width.