1 Introduction

Balmer line strengths are highly sensitive to the temperature in cool stars because of the 10.2 eV excitation of the n=2 level from which they arise. Figure 151 from Unsöld's (1955) classic text illustrates this for H$\gamma$ equivalent widths. We show the effect in a different way in Fig. 1, based on more recent line-broadening theory. The figure is for points on the H$\alpha$profile 4 Å from the line center, but is characteristic of much of the line profile.

Figure 1: H$\alpha$ wing strength vs. $T_{\rm eff}$ for several values of $\log~g$. The profiles are taken from the BP00K2NOVER grid available in http://kurucz.harvard.edu

An extensive investigation of Balmer lines in cool dwarfs (Fuhrmann et al. 1993; Fuhrmann et al. 1994) concluded these lines provide a more consistent guide to effective temperatures than broad-band colors or b - y. Nevertheless, Balmer line profiles are not regularly used to fix the effective temperature of cool stars. The reasons for this are numerous, but have not been explicitly addressed. Some insight may be gained from the papers by van't Veer-Menneret & Mégessier (1996) or Castelli et al. (1997, henceforth, CGK). A recent paper which does discuss use of H$\alpha$ in the determination of effective temperatures is by Peterson et al. (2001). In addition to the uncertainties in placing the continuum level, uncertainties, both in the theory of stellar atmospheres (l/H, convection) and line formation remain unresolved.

The absorption coefficient of neutral hydrogen takes into account the effects due to the natural absorption (natural broadening), the velocity of the absorbing hydrogen atoms (thermal Doppler and microturbulent broadening), the interactions with charged perturbers (linear Stark broadening), with neutral perturbers different from hydrogen (van der Waals broadening), and with neutral hydrogen perturbers (resonance and van der Waals broadening). Each effect is represented by a profile and the total effect requires a convolution. Thermal Doppler and microturbulent broadenings are described by Gaussian functions while natural, resonance, and van der Waals broadenings have Lorentz profiles. These two profiles are combined into a Voigt function. The convolution of the Voigt profile with the Stark profile or Stark plus thermal Doppler effect then gives the total absorption profile.

Most of the damping constants and Stark profiles are computed from complex theories based on several approximations, while the complete convolution of all the above profiles is a very time consuming algorithm.

In this paper we describe our attempts to evaluate several aspects of the calculations of Balmer line profiles.