similarity between the hole moving in the $S=1/2$ and the $S=1$ antiferromagnet would not be achieved in the classical double exchange picture [@Zener1951], for the latter one would not allow for the existence of the $|1, 0 \rangle$ states on any site.

Conclusions. {#sec:conclusions}
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In this work we showed how a relatively simple spin $S=1$ $t$–$J$ model, that was mapped onto an $S=1$ spin polaron model, can qualitatively reproduce the high-binding energy part of the observed Ca$_2$RuO$_4$ photoemission spectrum. In particular, we were able to explain the observed incoherent and almost momentum-independent photoemission spectrum by linking these peculiar features of the spectrum to two anisotropies present in the employed spin polaron model—the spin anisotropy [@Kunkemoeller2017] and the hopping anisotropy [@Harris2004; @Sutter2017].

Interestingly, the differences between the spectral functions of the ‘standard’ spin polaron model well-known from the cuprates (i.e. spin $S=1/2$) and the model for Ca$_2$RuO$_4$ should not be regarded as being intrinsic to the $S=1$ spin polaron model: They are all solely related to the above-mentioned strong anisotropies present in the model suggested for Ca$_2$RuO$_4$ and [*not*]{} to the potential differences between the hole moving in the $S=1/2$ and the $S=1$ antiferromagnet. These turn out to be basically 