Geometry of giant star model atmospheres: A consistency test

We investigate the effect of a geometric inconsistency in the calculation of synthetic spectra of giant stars. Spectra computed with model atmospheres calculated in spherical geometry while using the plane-parallel approximation for line formation calculations (s_p), as well as the fully plane-parallel case (p_p), are compared to the consistently spherical case (s_s). We present abundance differences for solar metallicity models with Teff ranging from 4000 to 6500 K and logg from 0.5 to 3.0 [cgs]. The effects are smaller for s_p calculations (-0.1 dex in the worst case) than for the p_p case (up to +0.35 dex for minority species and at most -0.04 dex for majority species), both with respect to the s_s case. In the s_p case the differences increase slightly with temperature, while in the p_p case they show a more complex behaviour. In both cases the effects decrease with increasing logg and increase with equivalent width. Thus, within the parameter range of F, G and K giants, consistency seems to be less important than using a spherical model atmosphere. The abundance differences due to sphericity effects presented here can be used for error estimation in abundance studies relying on plane-parallel modelling.