Variation of the Mn I 539.4 nm line with the solar cycle

Context. As a part of the long-term program at Kitt Peak National Observatory (KPNO), the Mn I 539.4 nm line has been observed for nearly three solar cycles using the McMath telescope and the 13.5 m spectrograph in double-pass mode. These full-disk spectrophotometric observations revealed an unusually strong change of this line's parameters over the solar cycle. Aims. Optical pumping by the Mg II k line was originally proposed to explain these variations. More recent studies have proposed that this is not required and that the magnetic variability (i.e., the changes in solar atmospheric structure due to faculae) might explain these changes. Magnetic variability is also the mechanism that drives the changes in total solar irradiance variations (TSI). With this work we investigate this proposition quantitatively by using the same model that was earlier successfully employed to reconstruct the irradiance. Methods. We reconstructed the changes in the line parameters using the model SATIRE-S, which takes only variations of the daily surface distribution of the magnetic field into account. We applied exactly the same model atmospheres and value of the free parameter as were used in previous solar irradiance reconstructions to now model the variation in the Mn I 539.4 nm line profile and in neighboring Fe I lines. We compared the results of the theoretical model with KPNO observations. Results. The changes in the Mn I 539.4 nm line and a neighbouring Fe I 539.52 nm line over approximately three solar cycles are reproduced well by the model without additionally tweaking the model parameters, if changes made to the instrument setup are taken into account. The model slightly overestimates the change for the strong Fe I 539.32 nm line. Conclusions. Our result confirms that optical pumping of the Mn II 539.4 nm line by Mg II k is not the main cause of its solar cycle change. It also provides independent confirmation of solar irradiance models which are based on the assumption that irradiance variations are caused by the evolution of the solar surface magnetic flux. The result obtained here also supports the spectral irradiance variations computed by these models.