The Formation of IRIS Diagnostics. V. A Quintessential Model Atom of C II and General Formation Properties of the C II Lines at 133.5 nm

The C ii 133.5 {nm} lines are important observables for the NASA/SMEX mission Interface Region Imaging Spectrograph. To make three-dimensional (3D) non-LTE radiative transfer computationally feasible, it is crucial to have a model atom with as few levels as possible while retaining the main physical processes. We here develop such a model atom and we study the general formation properties of the C ii lines. We find that a nine-level model atom of C i-C iii with the transitions treated assuming complete frequency redistribution (CRD) suffices to describe the C ii 133.5 {nm} lines. 3D scattering effects are important for the intensity in the core of the line. The lines are formed in the optically thick regime. The core intensity is formed in layers where the temperature is about 10 kK at the base of the transition region. The lines are 1.2-4 times wider than the atomic absorption profile due to the formation in the optically thick regime. The smaller opacity broadening happens for single peak intensity profiles where the chromospheric temperature is low with a steep source function increase into the transition region, the larger broadening happens when there is a temperature increase from the photosphere to the low chromosphere leading to a local source function maximum and a double peak intensity profile with a central reversal. Assuming optically thin formation with the standard coronal approximation leads to several errors: neglecting photoionization severly underestimates the amount of C ii at temperatures below 16 kK, erroneously shifts the formation from 10 kK to 25 kK, and leads to too low intensities.