4 Abundance analyses

We determined the metal abundances from the equivalent widths with Program WIDTH9 (Kurucz 1995). The adopted metal line damping constants were the default semi-classical approximations except for those of neutral and singly-ionized Ca-Ni lines whose values are based on the data of Kurucz (1995), for lines of C II multiplet 6 and Mg II multiplet 4 where the adopted values for the Stark broadening were based on data of Sahal-Brechot (1969) and for Si II and Ca II where the damping constants are those of Lanz et al. (1988) and Chapelle & Sahal-Brechot (1970) respectively.

We calculated abundances from Fe I and Fe II lines for a range of possible microturbulent velocities ($\xi$). For the final values, (Table 2), the abundances are not dependent on the equivalent widths ($\xi_{1}$) or minimize the rms scatter of the abundances ($\xi_{2}$). Values for both species were derived using lines with gf values only from Martin et al. (1988) and also with gf-values from compatible sources, in this case Kurucz (1995). From these species a mean microturbulence of 2.4 km s^-1 is found for HD 133029. The Cr II lines give a value of 2.9 km s^-1 while the Ti II lines suggest 1.7 km s^-1. For HD 192913, the Fe I and Fe II lines indicate a mean microturbulence of 0.9 km s^-1 while Ti II and Cr II lines 1.2 km s^-1. No microturbulence is expected if the magnetic CP stars have quiescent atmospheres as required by various radiative diffusion scenarios (see, e.g. Michaud 1970). The derived microturbulence is most likely a manifestation of an organized weak magnetic field with each line having its own effective microturbulence due to the width and the distribution of its Zeeman components. Strong lines with wide patterns and many components will be desaturated more easily than strong lines with smaller patterns and fewer components. Following Adelman (1973) we equated the mean width of the Zeeman $\sigma$ components to the Doppler broadening to derive an effective microturbulence for each line which increases with the strength of the magnetic field and the width of the Zeeman pattern. Although this approximation is adequate for the current data, more refined modeling will be required for observations with somewhat greater signal-to-noise ratios.

By assuming that there is no microturbulence and requiring that the abundances be independent of the derived magnetic field (H₁) or that the scatter in the derived abundances be a minimum (H₂) we found that surface magnetic field of HD 133029 (Table 3) is about 3.2 kG from the Fe I and Fe II lines. The Cr II lines yield 4.9 kG and the Ti II lines 3.1 kG. For HD 192913 we found a surface magnetic field of about 1.3 kG from the Fe I and Fe II lines, while Ti II lines indicated 2.30 kG and Cr II lines 1.8 kG. As the rms values about the mean are similar for both methods, we present the final abundance results for the assumption of a uniform microturbulence of 2.4 km s^-1 for HD 133029 and 0.9 km s^-1 for HD 192913.

We calculate the He I profiles in LTE from the model atmospheres with the program SYNSPEC (Hubeny et al. 1994). Only He I $\lambda$4026 is present for HD 133029 and its equivalent width is about 13 m${\mbox \AA}$. Thus HD 133029 is very He poor. For HD 192913 no He I lines were seen, making it too a very He poor star.

In Table 4 we present the analyses of the line spectra. For each line we give the multiplet number (Moore 1945), the laboratory wavelength, the gf value and its source, the equivalent width in m${\mbox \AA}$, and the derived abundance log $N/N_{\rm T}$. We did not include seriously blended lines in the analyses. To give an idea of the sensitivity of our results to errors in effective temperature and surface gravity, we derived the abundances of HD 192913 also for models 500 K hotter and log g 0.5 dex greater. Table 5 shows the size of the resultant changes.

  

Table 2: Determination of microturbulent velocity assuming no magnetic field

  

Table 3: Magnetic field determinations

  

Table 5: Sensitivity of the derived abundances of HD 192913 to changes in temperature and surface gravity