4. Spectrum synthesis
It was intended that the spectral analysis methods adopted should follow closely the line-by-line analysis of LSE 78 described by Jeffery (1993). However two major obstacles were encountered. First, the stars in the present sample are sufficiently cool that lines due to twice-ionized atoms of carbon, nitrogen and sulphur are weak and difficult to measure from the current spectra, excluding the possibility of measuring the ionization equilibria for these species. Second, at low surface gravities, the ionization equilibria previously used become insensitive to effective temperature, and approach the locus in space defined by the neutral helium line profiles. Previously, the intersection of these two loci were used to fix the stellar parameters. Therefore new procedures were developed based on the synthesis of large sections of spectrum, which can now be carried out routinely, and which reduce errors associated with the selection, measurement and analysis of individual absorption lines.
The spectral synthesis is carried out using an improved version of the radiative transfer code SPECTRUM (Dufton, Lennon, Conlon & Jeffery, unpublished). This code reads a converged model atmosphere structure, such as that computed using STERNE , and integrates the source function to obtain the emergent flux at given frequency points. The source function is computed either by assuming a strict LTE approximation () or by including electron scattering in which case the formal solution of the transfer equation is obtained using Feautrier's method. In this study, electron scattering is always included. The continuum opacity sources are matched to those used in the calculation of the model atmosphere. The ion populations assume LTE and partition functions from Traving et al. (1966). Line opacities are calculated using atomic data, including wavelengths, oscillator strengths, electron and radiative collision lifetimes and excitation potentials, taken from the CCP7 atomic data utility LTE__LINES (Jeffery 1994), which is updated from time to time to reflect the best atomic data available for the analysis of B-type stars. Classical lifetimes are used when better data are not available. Thermal and Doppler broadening is included in the Voigt profile for each line. Pretabulated broadening data are used for selected neutral helium lines (Barnard et al. 1969, Shamey 1969, Barnard et al. 1974, 1975, Dimitrijevic & Sahal Bechot 1984). More recent tabulations for neutral helium (Beauchamp et al. 1997) do not include sufficiently low densities to be useful here, whilst ionized helium lines are not observed in the current spectra. Although detailed theory is used to model the hydrogen lines (Vidal et al. 1973, Lemke 1997), they are so weak in the current spectra that Stark broadening is not important.
A complete synthetic spectrum includes over 500 transitions and 11 000 wavelength points between 3850 and 4850Å. On a Digital Alphaserver 1000A/466, each synthesis takes minutes. Several iterations of the procedures outlined below were necessary, involving the calculation of over 40 model atmospheres and 600 synthetic spectra.
© European Southern Observatory (ESO) 1998
Online publication: November 9, 1998