5. Photospheric parameters and abundances
The object of analysing the spectra of the program stars is to deduce the effective temperature, surface gravity, microturbulent velocity, rotational velocity and photospheric abundances. These are evaluated by establishing equilibria for successive ionization stages of selected atoms, by fitting the profiles of Stark-broadened neutral helium lines, by constraining the abundance derived from each line of a given ion to be independent of its equivalent width, and by fitting individual line profiles. It was clear from attempts to follow previous practise that the surface gravities of all three programme stars were very low and that !! the effective temperatures were .
Microturbulent and radial velocities were determined from O ii lines. Synthetic spectra for O ii were computed on a grid of oxygen abundances, microturbulent and rotational velocities (). The mean-square differences between observed and synthetic spectra were formed to establish, approximately, the oxygen abundance and more precisely the microturbulent and rotational velocities for each star (Table 1). The minima in the mean-square difference surfaces are shallow, and errors of are indicated. The microturbulent velocities of km/s are 50% higer than the sound speed in the line-forming region (10 km/s). As in previous studies (e.g. Drilling et al. 1998), this is a reminder that the notion of microturbulnece is useful in accounting for well-known discrepancies between theoretical and observed stellar atmospheres, but has a limited physical significance.
From this point it was possible to refine individual stellar parameters by selecting appropriate diagnostics and carrying out a mean-square residual minimization, operated as follows. In most cases, a limited grid of synthetic spectra is calculated. The difference between the observed and synthetic spectrum, normalized and velocity-shifted as described, is constructed. Where appropriate, this difference spectrum may be edited to remove unwanted information. For example, only regions of spectrum containing silicon lines would be retained to evaluate the silicon ionization equilibrium. The mean square residual is then calculated. Comparing this residual for several synthetic spectra from the grid enables a local minimum to be established. Since the location of this minimum depends on several quantities (e.g. rotation velocity, microturbulence, carbon abundance in the model grid), it is often necessary to repeat each derivation until a fully self-consistent solution is achieved.
To measure effective temperatures and surface gravities a synthetic spectrum was calculated for each model atmosphere in the grid over the interval 3900-4800 Å. A surface defined by the mean square residual with respect to the observed spectra was constructed, and a global miniumum located. In practise this minimum was constrained by the lowest gravity for which model atmospheres could be constructed. With a grid interval of 1 000 K, the effective temperature is accurate to within 500 K for a given surface gravity. However a 0.2 dex reduction in gravity could reduce the effective temperature by up to 1 000 K, with severe consequences for the remainder of the analysis. The results are given in Table 1.
The effective temperatures may in principle be cross-checked by comparing the observed ultraviolet and optical flux distribution for each star with that predicted by the model atmosphere. However previous studies have shown that this procedure gives, principally, a measurement of interstellar reddening as a function of and adds nothing to the measurement obtained from the optical spectrum.
The gravities indicate luminosity to mass ratios for the programme stars (solar units), substantially lower than the critical value of 4.6 above which Heber et al. (1986) suggested that the assumption of plane-parallel geometry might be doubtful.
Once a model atmosphere has been adopted for each star, appropriate to the parameters determined in the previous section, the abundances of individual species were determined by minimizing the mean square residuals, as before, to obtain the results presented in Table 2.
Table 2. Atmospheric abundances of three low-gravity EHes compared with other EHe and R CrB stars. Abundances are given (i) as , normalised to and (ii) as , where the values adopted for [Fe] is shown in the final column.
Errors in photospheric abundances were previously obtained from the variance in line abundances. With synthesis methods, confidence is provided by the shape of the minima obtained in the fitting procedure. For species with many lines, a dex abundance change leads to an increase in the fit statistic by . To be more specific, especially for species with few lines, the statistic will have to be refined to exclude invariant fluxes from the fit. However, the figure of dex is comparable with random errors obtained in previous line-by-line analyses. Systematic errors are discussed in detail by Drilling et al. (1998). The most important source of error here arises from the poor constraint on surface gravity, and hence on effective temperature.
In local spectral regions and considering the S/N ratio in the original spectra, a comparison between the observed and final synthetic spectra are highly satisfactory (Fig. 1). Principally because of calibration errors already described, a global comparison between the observed and synthetic spectra is less auspicious - especially in the vicinity of diffuse helium lines.
Several comments are appropriate. The calcium abundance is measured from the H and K lines. Care was taken to remove the interstellar component before fitting the line profiles. Several lines were used to measure the magnesium abundance, and not just Mg II 4482 Å. The iron abundance measurement was unsatisfactory, being due to three lines for which we have little confidence in the current atomic data. Consequently, in comparing the overall abundance patterns in Table 2 we have adopted a value which is more consistent with the argon and calcium measurements.
In the spectral region shown (Fig. 1), the following features attract remark. First, the diffuse singlet He I 4388 Å and the majority of lines in this region of the spectrum are reproduced well in all three cases. For individual line identifications, the atlas by Leuenhagen et al. (1994) should be consulted. Second, a few lines are either too strong or too weak in the model. Since the abundance for each atomic species is defined in most cases by a large ensemble of absorption lines, this probably indicates local errors in the atomic data or contamination by photon shot noise. It is noted that line-by-line analyses have yielded total variations of over 2 dex in the abundance of some species (e.g. O ii in LSE 78: Jeffery 1993). One example of poor atomic data in the present case may be for C II 4368.3 Å, which was also rejected as an abundance indicator in a recent analysis of helium star LSS 3184 (Drilling et al. 1998). Finally, a few lines simply do not appear in the model, either because reliable atomic data is not available or because they have not yet been identified. A good example is a line at 4329.9Å, also recognised but unidentified in the spectra of helium stars DY Cen, LSE 78, V348 Sgr, BD2179 (Leuenhagen et al. 1994) and LSS 3184 (Drilling et al. 1998).
© European Southern Observatory (ESO) 1998
Online publication: November 9, 1998