The magnetic field in umbral dots

The magnetic topology in umbral dots has been studied by means of the inversion of spectropolarimetric data recorded with the Hinode satellite and the GREGOR solar telescope. The SP instrument attached to the 0.5-meter SOT telescope on-board the Hinode satellite records spectropolarimetric data of two Fe I lines at 630 nm, which are formed about 60-80 km higher than the three Fe I lines at 1565 nm observed with the GRIS instrument attached to the 1.5-meter ground solar telescope GREGOR.

Central region of the Sunspot NOAA AR 12581 observed on August 29th, 2016. All maps have been rotated and re-scaled to a common scale. {\it Left columns}: results obtained from the inversion of three Fe I spectral lines at 1565 nm observed with the GRIS instrument attached to the ground 1.5-meter GREGOR telescope. {\it Right columns}: results obtained from the inversion of two Fe I spectral lines at 630 nm observed with the SP instrument attached to the 0.5-meter SOT telescope on-board the Hinode satellite. First row: continuum intensities normalized to the quiet Sun. Dashed-white contour encircles the dark umbral region, while the solid-white contours denote the location of several umbral dots. Second row: temperature at tau_5=1 obtained from a Milne-Eddington-like inversion using the SIR code. Third row: magnetic field obtained from a Milne-Eddington-like inversion using the SIR code. Bottom-left panel: scatter plot of the temperature at tau_5=1 obtained from the inversion of GREGOR data (x-axis) and Hinode (y-axis) for pixels inside the dark umbral region (red crosses) and umbral dots (blue crosses). Bottom-right panel: same as on the bottom-left panel but for the magnetic field.

The same region (Sunspot NOAA AR 12581) was observed quasi-simultaneously with both instruments in August 29th, 2016. The magnetic field in the umbral core (see dashed-white contours in attached figures) increases with depth. This is inferred by the fact that the values obtained from Hinode are lower than those inferred from GREGOR (see red crosses in bottom-right panel). A similar situation is seen in umbral dots since (see blue crosses in bottom-right panel). In the dark umbral core this is an expected result, as it is consistent with a flux tube that expands with height. However in the case of umbral dots our results are at odd with the predictions made by three-dimensional magnetohydrodynamic simulations of sunspot structure. We are looking to confirm these unexpected results with further observations and more detailed analysis.