Ca ii λ854.2 nm in an enhanced network region simulated with MURaM-ChE

The ̧aefft line is widely used to study the chromosphere of the Sun. In the quiet Sun, the spatially averaged line profile shows a red asymmetry and a redshift of the line center. It is known that the effect of isotopic splitting must be taken into account in the forward modeling to reproduce the observed asymmetry. So far, no numerical model has been able to match an average observed line profile in terms of the line width and asymmetry. Our goal is to investigate how well a simulation computed with the chromospheric extension of the MURaM code (MURaM-ChE) reproduces the spatially averaged ̧aefft line profile. We aim to determine the contributions from the isotopic splitting versus the dynamics in the atmosphere to the resulting line width and asymmetry. For this purpose, we forward-modeled the line based on a simulated enhanced network region, representing a region of the quiet Sun network with stronger-than-average magnetic flux. Our study builds on forward modeling of the ̧aefft line in a series of MURaM-ChE simulation snapshots representing an enhanced network region. We solved the radiative transfer problem three times, once considering only the most abundant isotope of calcium in the atmosphere, once taking six calcium isotopes into account, and finally using a single ``composite'' atom model, which mimics the presence of all six isotopes. We find the forward-modeled, spatially and temporally averaged spectra to be in good agreement with the Hamburg Fourier-Transform-Spectrograph atlas observation of the quiet Sun. In order to match the observed line width, the simulated atmosphere must be sufficiently dynamic. The typical red asymmetry can only be reproduced by taking the isotopic splitting effect into account, as suggested in the literature. The closer match between the new model and the observations compared to earlier numerical models is a result of the higher rms velocity in the MURaM-ChE chromosphere. The center of the spatially averaged line profile tends to be slightly redshifted, which is a result of a net downflow velocity at the formation height of the line center intensity. This does not, however, imply an average mass downflow. We find the composite atom model is a good approximation of the full isotope computation but shows some differences in the line core and asymmetry. We show that forward modeling of the ̧aefft line from a MURaM-ChE simulation can result in a close match to the line shape of an average quiet-Sun observation. The atmosphere must be sufficiently dynamic to match the observed line width. Our results confirm that it is important to include the isotopic splitting effect of calcium when modeling the ̧aefft line.