3 Spectrum synthesis and line identification

For the purpose of line identification and determination of the mean stellar RV we computed a synthetic spectrum of $\gamma$ Equ in the 6140-6166 Å spectral region. Model atmosphere parameters, an approximate model of the magnetic geometry, and elemental abundances were adopted from Ryabchikova et al. (1997). All relevant atomic parameters were extracted from the VALD database (Kupka et al. 1999). The oscillator strengths of Ca I 6162.17, 6163.76 Å lines and Si I 6142.48, 6145.02, 6155.13 Å lines were further tuned by fitting the solar atlas of Kurucz et al. (1994). For the spectral lines of Pr III oscillator strengths were kindly provided to us by D. Bord (private communication). Synthetic spectra were calculated with the Synthmag magnetic spectrum synthesis code (Piskunov 1999), which makes it possible to obtain an accurate numerical solution of the polarised vector radiative transfer equation, and evaluate local Stokes profiles for a number of limb angles. Then an external IDL subroutine was used to obtain disk-integrated normalized spectra for a given macroturbulent and rotation velocity under the assumption of a homogeneous surface magnetic distribution. Although the latter simplification is generally not adequate for the explanation of the polarisation properties and variability of the radiation from Ap stars, it still provides a robust estimate of the Zeeman effect in the unpolarised line profiles of the slowly rotating Ap stars.

The line identification in 6140-6166 Å region is fairly complete. The only relatively strong unidentified spectral feature is located at $\lambda$ 6148.86 Å and probably belongs to the singly or doubly ionized REE (see Savanov et al. 1999 and Sect. 4). The Nd III 6145.07 Å line is blended with the line of Si I 6145.02 Å and the latter may contribute up to 25% to the total intensity of the observed feature.

A comparison between the spectrum synthesis and the average observed spectrum of $\gamma$ Equ ( $S/N\simeq 700$) is illustrated in Fig. 1. In the calculations we assumed that the atmosphere of the star is locally stabilized by the magnetic field, and therefore no micro or macroturbulent broadening was introduced into the spectrum synthesis. Similarly, rotational broadening of the $\gamma$ Equ spectra should be negligible due to the very long rotation period of the star. Thus, the only broadening effects that we expect are due to the magnetic field and the finite instrumental resolution. Nevertheless, the upper panel of Fig. 1 shows that the synthetic spectrum, convolved with a Gaussian profile ( ${\it FWHM}=37$ mÅ) to account for the instrumental broadening, still possesses much sharper spectral features than those seen in the observed spectrum. This excessive broadening cannot be ascribed to real macroturbulent or microturbulent motions, or to spurious instrumental smearing. In fact, we did not find any combination of these effects that could simultaneously fit wide wings of the strong lines (such as Ba II 6141.71 Å, Nd III 6145.07 Å, and Ca I 6162.17 Å) and not wipe out the partially resolved Zeeman structure of the weaker lines (La II 6146.52 Å, Cr II 6147.14 Å, and Fe I 6151.62Å). On the other hand, the separation of the Zeeman components of Fe II 6149.26Å is well reproduced in our calculations. This suggests that the discrepancy between observations and spectrum synthesis cannot be explained by an underestimate of the mean field modulus in our model of the magnetic topology.

Stratification of chemical elements in the stellar atmosphere is one of the effects that may be responsible for the peculiar shape of the line profiles in the spectrum of $\gamma$ Equ. Diffusion theory (Michaud 1970), which is the leading theoretical framework for the explanation of the abundance anomalies of Ap and related stars, predicts that in stellar atmospheres, stabilized by kilogauss magnetic fields, radiation pressure and gravitational settling will gradually build up a superficial layer with a peculiar chemical composition. Detailed diffusion calculations by Babel (1992) suggested that strong vertical abundance gradients can be expected within the line forming regions. In particular, elemental concentrations of Ca and iron-peak elements feature similar vertical distributions consisting of the layer with enhanced abundance, located at the bottom of the atmosphere, and the layer with solar (or even less than solar) abundance above optical depth $\log\tau_{5000}=-1$. In this scheme the spectral lines of stratified chemical elements will tend to have weaker cores and wider wings relative to line profiles calculated under the assumption of an homogeneous vertical distribution.

Numerical tests confirmed that introducing vertical stratification can in principle improve the fit to the observed line profiles. It also allows us to achieve consistency in the abundances, derived from the spectral lines of different ionization stages of the same elements as well as weaker and stronger lines of the same ions. However, in our preliminary calculations we could not find a unique vertical chemical abundance distribution that can account for both abnormal profiles and strength of doubly ionized REE lines. This has to be confirmed by detailed quantitative investigation of the vertical stratification in $\gamma$ Equ which is outside the scope of the present paper.

An effect of stellar pulsation on line broadening will be discussed in Sect. 6.

From the shift between the synthetic and average observed spectrum we found that the mean radial velocity of $\gamma$ Equ is -16.87 kms^-1, which is in good agreement with other recent determinations (Mkrtichian et al. 1998).