a complicated way on the temperature, density, and the time history of the atmosphere owing to the non-equilibrium ionization of hydrogen. @2012ApJ...749..136L investigated the formation of [H$\alpha$]{} in a radiation-MHD simulation of the quiet Sun and found that in those circumstances the line can be reasonably accurately modeled assuming statistical equilibrium. In that simulation they also found that the line opacity weakly depended on temperature and mainly depended on mass density. investigated the ionization of , , and , and found that at temperatures above 15 kK, the fraction of  is much larger than the fractions of  and . and argued similarly, albeit based on LTE, that [H$\alpha$]{} can have an appreciable opacity at temperatures well above 20 kK.

Studies of the formation heights of the line cores based on the quiet-Sun-like simulation of indicate that [H$\alpha$]{} forms 300–1000 km below [K]{} and [k]{}  [@2013ApJ...772...90L]. The similarity of the line-core images in Fig. \[fig:observations\]a,b casts doubt on the validity of this result in active regions. We therefore investigated the formation heights in the MURaM simulation.

We measured the formation heights at optical depth unity in the corresponding line cores of [H$\alpha$]{}, [k]{}, [K]{}, and 8542 Å. Figure \[fig:formation\_height\] shows differences 