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The vertical component of the magnetic field ($B_\perp$) was found to reach aconstant value at the umbra-penumbra boundary of stable sunspots in a recentstatistical study of Hinode/SP data. The objective of this work is to verifythe existence of a constant value for $B_\perp$ at the umbra-penumbra boundaryfrom ground-based data in the near-infrared wavelengths and to determine itsvalue for GREGOR Infrared Spectrograph (GRIS) data. This is the firststatistical study on the Jurcak criterion with ground-based data, and wecompare it with the results from Hinode and HMI data. Elevenspectropolarimetric data sets from the GRIS slit-spectograph containing stablesunspots were selected from the GRIS archive (sdc.leibniz-kis.de). SIRinversions including a polarimetric straylight correction are used to producemaps of the magnetic field vector using the Fe 1564.8 and 1566.2 nm lines.Averages of $B_\perp$ along umbra-penumbra boundaries are analyzed for the 11data sets. Geometric differences between contours at the resulting$B_\perp^{\rm const}$ value and contours in intensity, $\Delta P$, arecalculated. Averaged over the 11 sunspots, we find a value of$B_\perp=1787\pm100$ gauss. Contours at $B_\perp=B_\perp^{\rm const}$ andcontours calculated in intensity maps match from a visual inspection and thegeometric distance $\Delta P$ was found to be on the order of 2 pixels.Furthermore, the standard deviation between different data sets of averagesalong umbra--penumbra contours is smaller for $B_\perp$ than for $B_\parallel$by a factor of 2.4. Our results provide further support to the Jurcak criterionwith the existence of an invariable value $B_\perp^{\rm const}$ at theumbra--penumbra boundary. We also found that the geometric difference, $\DeltaP$, between intensity contours and contours at $B_\perp=B_\perp^{\rm const}$acts as an index of stability for sunspots.

astronomy and astrophysics

Characterization of the umbra-penumbra boundary by the vertical  component of the magnetic field -- Analysis of ground-based data from the  GREGOR Infrared Spectrograph