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 lines parameters over the solar cycle. 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 might explain it. 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 using the model SATIRE-S. 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. Our result confirms that optical pumping of the Mn I 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.
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