2 Stark profiles

Most work on stellar atmospheres makes use of codes provided by Kurucz (http://kurucz.harvard.edu). For computing hydrogen lines the codes are either BALMER9 (Kurucz 1993a) which produces profiles for H$_{\alpha }$, H$_{\beta}$, H$_{\gamma}$, and H$_{\delta}$ or the SYNTHE code (Kurucz 1993b) which produces profiles for any hydrogen line. In the first case Stark profiles are interpolated in the Vidal et al. (1973, henceforth VCS) tables, while in the second case the Stark profiles are based on the quasi-static Griem theory with parameters adjusted in such a way that profiles from Griem theory fit the VCS profiles of the first members of the Lyman and Balmer series.

Only the most recent work on the Balmer lines (e.g. Barklem et al. 2000, henceforth, BPO) has included the new Stark profiles of Chantal Stehlé (henceforth CS) and her coworkers. They are available from a link on her website: http://dasgal.obspm.fr/stehle/. A recent reference is Stehlé & Hutcheon (1999).

A problem arises when a given Stark profile is interpolated either in the VCS or in the CS tables by using the interpolation method taken from the BALMER9 code. This is a bilinear interpolation in $\log(T)$ and $\log(N_{\rm e})$, followed by a linear interpolation in the parameter $\Delta\alpha = \Delta\lambda[{\rm\AA}]/F^0$. Here, F⁰ is the normal field strength in Gaussian cgs units, $F^0 = 1.25 N_{\rm e}^{2/3}$, so the interpolation in $\Delta\alpha$ is not independent of the previous one which involves the electron density $N_{\rm e}$. We find this introduces a small error that shows up as an oscillation in a plot of the Stark profile $S(\Delta\alpha)$ vs. depth in the solar atmosphere for a small range of displacements from the line center as shown in Fig. 2.

Figure 2: Normalized Stark width at $\Delta \lambda = 0.5$Å for H$\alpha$ vs. 137 depths in an Holweger-Müller (1974) solar model. Each depth step is 0.05 in $\log(\tau_{\lambda 5000})$. The vertical lines mark depths corresponding to boundaries of the tables giving $S(\alpha )$ for a fixed value of the electron density.

We were able to remove the oscillations by rewriting the CS tables with $\Delta\lambda$ as the third (independent) variable, and using essentially the same interpolation scheme as BALMER9. Fortunately, it has resulted that the improved interpolation leads to no perceptible changes in the resulting line profiles.