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Context. It has been reported that the boundary between the umbra and thepenumbra of sunspots occurs at a canonical value of the strength of thevertical magnetic field, independently of the size of the spot. This criticalfield strength is interpreted as to be the threshold for the onset ofmagnetoconvection.  Aims. Here we investigate the reasons why this criterion, also called theJur\v{c}\'ak criterion in the literature, does not always identify the boundarybetween umbra and penumbra.  Methods. We perform a statistical analysis of 23 sunspots observed withHinode/SOT. We compare the properties of the continuum intensity and thevertical magnetic field between filaments and spines and how they vary betweenspots of different sizes.  Results. We find that the inner boundary of the penumbra is not related to auniversal value of the vertical magnetic field. The properties of spines andfilaments vary between spots of different sizes. Both components are darker inlarger spots and the spines exhibit stronger vertical magnetic field. Thesevariations of the properties of filaments and spines with spot size are alsothe reason for the reported invariance of the averaged vertical magnetic fieldat 50% of the mean continuum intensity.  Conclusions. The formation of filaments and the onset of magnetoconvectionare not related to a canonical value of the strength of the vertical magneticfield. Such a seemingly unique magnetic field strength is rather an effect ofthe filling factor of spines and penumbral filaments.

No universal connection between the vertical magnetic field and the umbra-penumbra boundary in sunspots