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

Context. The vertical component of the magnetic field was found to reach a constant value at the boundary between penumbra and umbra of stable sunspots in a recent statistical study of Hinode/SP data. This finding has profound implications as it can serve as a criterion to distinguish between fundamentally different magneto-convective modes operating in the sun.Aims. The objective of this work is to verify the existence of a constant value for the vertical component of the magnetic field (B) at the boundary between umbra and penumbra from ground-based data in the near-infrared wavelengths and to determine its value for the GREGOR Infrared Spectrograph (GRIS@GREGOR) data. This is the first statistical study on the Jurak criterion with ground-based data, and we compare it with the results from space-based data (Hinode/SP and SDO/HMI).Methods. Eleven spectropolarimetric data sets from the GRIS@GREGOR slit-spectograph containing fully-fledged stable sunspots were selected from the GRIS archive. SIR inversions including a polarimetric straylight correction are used to produce maps of the magnetic field vector using the Fe I 15648 angstrom and 15662 angstrom lines. Averages of B along the contours between penumbra and umbra are analyzed for the 11 data sets. In addition, contours at the resulting B-perpendicular to(const) B perpendicular to const are drawn onto maps and compared to intensity contours. The geometric difference between these contours, Delta P, is calculated for each data set.Results. Averaged over the 11 sunspots, we find a value of B-perpendicular to(const) = (1787 +/- 100) gauss B perpendicular to const =(1787 +/- 100)gauss . The difference from the values previously derived from Hinode/SP and SDO/HMI data is explained by instrumental differences and by the formation characteristics of the respective lines that were used. Contours at B-perpendicular to = B-perpendicular to(const) B perpendicular to = B perpendicular to const and contours calculated in intensity maps match from a visual inspection and the geometric distance Delta P was found to be on the order of 2 pixels. Furthermore, the standard deviation between different data sets of averages along umbra-penumbra contours is smaller for B-perpendicular to than for B-parallel to by a factor of 2.4.Conclusions. Our results provide further support to the Jurak criterion with the existence of an invariable value B-perpendicular to(const) B perpendicular to const at the umbra-penumbra boundary. This fundamental property of sunspots can act as a constraining parameter in the calibration of analysis techniques that calculate magnetic fields. It also serves as a requirement for numerical simulations to be realistic. Furthermore, it is found that the geometric difference, Delta P, between intensity contours and contours at B-perpendicular to = B-perpendicular to(const) B perpendicular to = B perpendicular to const acts as an index of stability for sunspots.