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tokens: model. This is partially caused by the inner region of the circumbinary disk ( ), which is thinned out by the gravitational forces of the two stars (e.g., Avramenko et al. 2017 ). However, this effect only occurs if the separation between the two stellar components is on the order of . A smaller separation would lead to a behavior that is similar to circumstellar disks around a single star. If the separation is significantly larger, the dust and gas around the binary can no longer be described with a single circumbinary disk. In circumstellar disks with a single star, the inner region has the highest density and usually the highest magnetic field strength (see Fig. 1 in Sect. 5.4 ; Flock et al. 2017 ). Therefore, as mentioned in Sect. 6.3 , circumbinary disks lack a significant fraction of circularly polarized emission if the inner high magnetic field region is missing. In addition, the different directions of circulation of the toroidal magnetic field decrease the circularly polarized emission from regions with similar velocities relative to the observer if not spatially resolved. Furthermore, the estimation of the LOS magnetic field strength from circumstellar disks with a single star is dominated by the inner region characterized by high magnetic field strength. In contrast, a Zeeman observation of a circumbinary disk is able to provide information about the magnetic field farther out in the disk if the requirements for such an observation are fulfilled. However, this requires that a significant part of its innermost region be depleted by the gravitational forces of both stellar components. 7. Conclusions We studied the requirements to observe the Zeeman splitting of the CN lines in circumstellar disks and their dependence on selected disk parameters. Such observations can be used to resolve degeneracies and obtain complementary information about the magnetic field if combined with polarimetric continuum observations. However, this is only applicable, if the polarimetric continuum observations are mainly caused by elongated aligned dust grains. In particular, we evaluated whether Zeeman observations of circumstellar disks should be performed spatially resolved or unresolved. With spatially resolved Zeeman observations, the strength and structure of the magnetic field in the LOS direction can be reconstructed for most regions in circumstellar disks. Only the region close to the star cannot be traced. However, the required sensitivity (, if ) is far beyond the capabilities of recent and upcoming instruments/observatories. For spatially unresolved Zeeman observations, we obtained different results. Under the assumption of Keplerian rotation and a toroidal structure of the magnetic field, two independent average magnetic field strengths can be obtained from the circularly polarized fraction. These average values are sensitive to changes in the strength and structure of the magnetic field inside the disk. In addition, they can be used to