Context. Synthetic spectra from 3D models of the solar atmosphere have become increasingly successful at reproducing observations, but there are still some outstanding discrepancies for chromospheric spectral lines, such as Ca II and Mg II, particularly regarding the width of the line cores. It has been demonstrated that using sufficiently high spatial resolution in the simulations significantly diminishes the differences in width between the mean spectra in observations and simulations, but a detailed investigation into how this impacts subgroups of individual profiles is currently lacking.

Aims. We compare and contrast the typical shapes of synthetic Ca II 854.2 nm spectra found in Bifrost simulations having different magnetic activity with the spectral shapes found in a quiet-Sun observation from the Swedish 1-m Solar Telescope (SST).

Methods. We used clustering techniques to extract the typical Ca II 854.2 nm profile shapes synthesized from Bifrost simulations with varying amounts of magnetic activity. We degraded the synthetic profiles to observational conditions and repeated the clustering, and we compared our synthetic results with actual observations. Subsequently, we examined the atmospheric structures in our models for some select sets of clusters, with the intention of uncovering why they do or do not resemble actual observations.

Results. While the mean spectra for our high resolution simulations compare reasonably well with the observations, we find that there are considerable differences between the clusters of observed and synthetic intensity profiles, even after the synthetic profiles have been degraded to match observational conditions. The typical absorption profiles from the simulations are both narrower and display a steeper transition from the inner wings to the line core. Furthermore, even in our most quiescent simulation, we find a far larger fraction of profiles with local emission around the core, or other exotic profile shapes, than in the quiet-Sun observations. Looking into the atmospheric structure for a selected set of synthetic clusters, we find distinct differences in the temperature stratification for the clusters most and least similar to the observations. The narrow and steep profiles are associated with either weak gradients in temperature or temperatures rising to a local maximum in the line wing forming region before sinking to a minimum in the line core forming region. The profiles that display less steep transitions show extended temperature gradients that are steeper in the range−3 ≲ log τ₅₀₀₀ ≲ −1.