Jan Jurcak

Context . Granular light bridges in sunspots are a manifestation of magnetoconvection in an approximately vertical magnetic field that is weaker than the field of the umbra. Aims . We studied the relationships between the observed properties of granules and the magnetic field in five strong granular light bridges located in a complex sunspot. Methods . Thermal parameters, the magnetic field vector, and line-of-sight velocity were obtained from an inversion of the GREGOR spectropolarimetric scan in the lines Si I 1082.71 nm and Ca I 1083.90 nm. Sizes and lifetimes of granules were measured in a simultaneous sequence of images in the TiO band. Results . The light bridges under study are comprised of granules spanning 0.″ 2–1.″ 4 with lifetimes of approximately 6 minutes. The largest granular structures (>1″) are spatially correlated with 1 km s ⁻¹ upflows and weak, inclined magnetic fields (≃300 G) near the equipartition threshold. Statistical comparisons demonstrated an inverse relationship between magnetic field strength and continuum intensities, line-of-sight velocity dispersions, and effective granular diameters. These relationships vary among individual light bridges, depending on the large-scale magnetic field topology. Conclusions . Large expanding granules similar to the photospheric ones appear in light bridges only when the local magnetic field strength approaches the equipartition value.

Context. Existing sunspot simulations fail to reproduce the observed magnetic field distribution due to an artificially increased B _hor at the upper boundary. Aims. We explore alternative ways to better reproduce the magnetic and dynamic properties of observed sunspots. Methods. We used the MURaM radiative magnetohydrodynamic code. As the initial conditions, we placed a potential magnetic field into small-scale dynamo simulations and used potential field extrapolation as the top boundary conditions. Results. We find that (1) simulations with increasing initial magnetic field strengths (20 kG, 40 kG, 80 kG, and 160 kG) show increasing spot, umbral, and penumbral sizes; (2) penumbral-to-spot sizes are smaller than those measured in observed sunspots; (3) none of the runs show pure Evershed (radially outwards) flows and, instead, bi-directional flows with inflows in the inner penumbra and outflows in the outer penumbra were measured, consistent with observations of early stages of penumbra formation for runs with 80 kG or more and 96/32 km resolution, whereas runs with ≤40 kG showed pure inflows; (4) simulations with 160 kG and an increased resolution of 32/16 km contain filaments with bi-directional and Evershed flows; (5) simulations with fluxes > 10 ²² Mx show unrealistically strong fields in the umbra; and (6) best runs with 160 kG and 10 ²² Mx give realistic profiles of B _z and B _r with radius, albeit with stronger fields than those typically observed. Finally, (7) increasing the width of the box and reducing the overall flux by subtracting a uniform opposing vertical field have little influence on internal spot dynamics and fields. Nonetheless, these choices affect the average vertical field beyond the spot. Conclusions. Simulations of small (10 ²² Mx) sunspots with an initial potential field and intensified magnetic field strength at the bottom of the box seem to best reproduce observational results of the initial stages of sunspot formation. Our findings also suggest that increased numerical resolution could be critical for achieving fully developed penumbrae.

Context. A recent case study of a long-lived sunspot confirmed earlier observational indications that the outer boundary of sunspots is defined by an invariant value of the magnetic field strength. This property is also found in magnetohydrodynamic sunspot simulations, which show that this invariant value corresponds to the equipartition field strength. Aims. We investigated a large sample of sunspots throughout their evolution to statistically assess the magnetic field strength at their outer boundaries, determine whether it systematically reaches an invariant value, and evaluate possible dependences on sunspot size and evolutionary phase. Methods. We automatically processed nearly 1000 active regions observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory and identified and tracked 312 unique sunspots. The outer boundary of each sunspot was defined using a continuum-intensity threshold. For all evolutionary stages, we computed the mean magnetic field strength along this boundary and its standard deviation. Results. Across the sample, the mean magnetic field along the boundary decreases during formation, reaches a minimum during the stable phase, and increases again during decay. For sunspots with a fully developed penumbra, this minimum is remarkably consistent, with a value of 605 ± 27 G. The standard deviation of the magnetic field exhibits a similar temporal evolution, and its minimum provides an additional diagnostic of penumbral maturity: fully developed penumbrae correspond to σ _B ⪅ 200 G, whereas higher values indicate either forming or decaying structures. For sunspots with fully developed penumbrae, the mean B value at their boundaries varies weakly with sunspot size; larger sunspots tend to have stronger B . Conclusions. The results demonstrate that fully developed sunspots systematically reach an invariant magnetic field strength value, namely the equipartition field strength, at their outer boundary. The temporal evolution of the mean field and its spatial variability along the boundary provides a robust diagnostic of sunspot formation, stability, and decay.

Solar granulation consists of dynamic convective plasma cells that rise from the solar interior to the surface. The interaction between these plasma cells and the Sun's magnetic field provides valuable insights into plasma dynamics near the solar surface and how they evolve in the presence of magnetic fields. This study analyses the morphological characteristics of solar convective cells, investigating the relationship between magnetic field properties and granule dynamics - specifically how granule area, shape, and brightness vary under different magnetic field conditions. Observations of the active region NOAA 11768 were taken with the Swedish 1-m Solar Telescope (SST). A segmentation algorithm was applied to continuum intensity images to identify individual granules and determine their sizes, shapes, and mean brightness. The magnetic field vector and line-of-sight velocity were derived from CRISP spectropolarimetric data to investigate their role in shaping granule properties. We find that granular area decreases systematically with increasing magnetic field strength, with the largest granules occurring in non-magnetic regions and a mean granule area of approximately 1.58 arcsec$^2$ (effective diameter of 1.42 arcseconds). Both mean continuum intensity and granule size decrease with stronger fields, confirming the suppression of convective energy transport in magnetised regions. No correlation was found between mean granule brightness and mean up-flow velocity. Highly elongated granules appear in both magnetic and non-magnetic regions, while near-circular granules are exclusive to non-magnetic areas. An alignment between granule major axes and magnetic field azimuth is observed where the horizontal field component is strong, confirming that granules are highly sensitive to magnetic fields, which inhibit the lateral expansion of convective cells.

Context. Sunspot boundaries are commonly outlined by contours of the continuum intensity. However, their magnetic nature has not yet been fully characterised. Aims. We investigate the properties of the outer boundary of a long-lived sunspot, aiming to identify the magnetic property that defines it. Methods. We analysed the magnetic properties of AR NOAA 11591 spot during its two passages across the solar disc. To this end, we used SDO/HMI continuum intensity and magnetic field parameters and determined the contours of these parameters to outline the outer boundary. Results. During the first disc passage, in which the sunspot is in its stable phase, we find that the intensity contours at 0.9 of the mean intensity of the vicinity of the spot and isocontours of the magnetic field strength of 625 G provide an almost perfect match between the two contours. With these thresholds, the time-averaged area of mismatch is minimised, yielding an average distance between the contours of 0.58 pixel, corresponding to less than 0.26 arcsec. During the second disc passage, the spot shows clear signs of decay, and we find that the 0.9 intensity and 625 G magnetic isocontours detach from each other, coupled to the disappearance of penumbra. In this super-equipartition area, granulation still operates. Conclusions. Based on a comparison with simulation data from our previous work, and in agreement with findings of other authors, we conclude that the outer boundary of stable sunspots is defined by an invariant magnetic field: the equipartition field. From the discrepancy between intensity and magnetic contours during the decaying phase of the sunspot, we surmise that alongside the well-established (magneto-)convective regimes of the photosphere – granular, penumbral, and umbral – a super-equipartition granular regime can be identified. In this regime, bright, but smaller granules occur where the magnetic field exceeds equipartition but remains subcritical for convection suppression.

Context. Although sunspots have been extensively studied, the mechanism behind the formation of penumbrae is still not fully understood. Aims. In this work, we investigate the process of sunspot penumbrae formation from a novel approach based on the analysis of magnetic fields from non-linear force-free field (NLFFF) extrapolations aiming to identifying the key parameters driving this process. Methods. We calculate NLFFF extrapolations from HMI/SDO data sampling the development of the active region NOAA 12757 before, during, and after penumbra formation. We analyse the resulting magnetic field inclination, magnetic field tension, and the current density evolution in the leading spot. The analysis focuses on the stable part of the sunspot, away from the AR opposite polarity. Results. The analysis of the extrapolations has revealed that: (1) the magnetic field inclination measured at the footpoints of the extrapolated field lines agrees with the results inferred from inversions, confirming the consistency of the methodology. (2) Penumbra formation is preceded by the continuous emergence of magnetic flux as outlined by serpentine fields observed in the low layers. After emerging, these fields further rise shaping the active region field topology formed by high-lying loops. (3) The emergence of local patches of new flux is characterised by high magnetic tension and significant current densities, primarily concentrated at the protospot boundary. Both the magnetic tension and current densities gradually dissipate as the magnetic loops continue to rise. This flux emergence occurs in regions where the penumbra is not yet formed and the magnetic canopy is not yet developed. (4) With the increase of emerged flux, a magnetic canopy develops and gradually expands around the spot in unison with the forming underlying penumbra. (5) As the penumbra and canopy expand, the surrounding network field, initially present close to the spot boundary, gradually migrates outward, reaching a maximum distance of about 9 Mm. This and the rise of serpentine fields, footpointed by migrating moving magnetic features provide evidence of the connectivity between the sunspot’s core magnetic field and the surrounding network field. Conclusions. This case study provides clear evidence that the formation of stable penumbra results from a bottom-up approach: the continuous emergence and upward rise of serpentine field lines into the corona during which a sunspot magnetic canopy develops.

Context. The SDO/HMI instrument provides continuous full-disk observations with a high temporal cadence but moderate spatial resolution. In contrast, Hinode/SOT-SP observes the Sun with high spatial resolution but at a low temporal cadence and within a limited field of view. Aims. This study seeks to enhance SDO/HMI observations by applying deconvolution techniques, specifically to the continuum intensity and full vector magnetic field in a local reference frame. Hinode datum, used as a training set, helps the model improve the resolution of HMI data to a Hinode-like level. Methods. We use deep residual convolutional neural networks trained on HMI-like and SOT-SP observations. The HMI-like observations utilise the SOT-SP observations and the exact HMI point-spread function and noise realisation. Results. The trained model successfully deconvolves both the intensity and the vector magnetic field. The model predictions and SOT-SP observations show the same level of detail. The root mean square difference between the two is 0.02 quiet-Sun level for intensity and between 40 and 45 G for vector magnetic field that is below the disambiguation noise level. Conclusions. Our model effectively addresses disambiguation noise and enables the deconvolution of the full vector magnetic field. Additionally, the modelled deconvolution provides enhanced results compared to the standard HMI pipeline products.

Context. In recent years, the magnetic properties of the umbra-penumbra boundary of sunspots and the boundary of pores at various evolutionary stages have been characterised using datasets from different instruments. Aims. We aim to study the intrinsic differences between the intensity and vector magnetic field properties derived from Hinode/SP and SDO/HMI observations of a decaying sunspot. Methods. We analysed the sunspot embedded in active region NOAA 12797 during six days in 30 SP/Hinode scans and 704 HMI/SDO for both regular maps and maps corrected for scattered light, HMI_dcon. We studied the correlation of the magnetic properties and continuum intensity in the datasets within the spot, and we investigated the differences at the umbra-penumbra boundary. We examined the decaying process in detail using the full temporal resolution of the HMI_dcon maps. Results. We find a good one-to-one correspondence between the magnetic properties in the SP and HMI_dcon maps, but the continuum intensity of the spots in the SP maps is found to be 0.04 I_QS brighter than in the HMI_dcon maps. The considerable influence of scattered light in the HMI maps makes it the least ideal dataset for studying the boundary of spots without a penumbra. The properties at the umbra-penumbra boundary evolve slowly during the sunspot decay stage, while the penumbra still provides some stability. In contrast, they respond more abruptly to areal changes in the naked-spot stage. During the sunspot decay, we find linear decay in the area and in the magnetic flux. Moreover, the umbra shows two characteristic decaying processes: a slow decay during the first three days, and a sudden fast decay during the final dissipation of the penumbra. We find indications of a 3.5 h lag between the dissipation of the vertical fields in the umbral region and the photometric decay of the umbral area. Conclusions. The differences found in the continuum intensity and in the vertical component of the magnetic field, B_ver, between the analysed datasets explain the discrepancies among the B_ver values found at the boundaries of umbrae in previous studies.

Context. Fully fledged penumbrae have been widely studied both observationally and theoretically. Yet the relatively fast process of penumbra formation has not been studied closely with high spatial resolution. Aims. We investigate the stages previous to and during the formation of penumbral filaments in a developing sunspot. Methods. We analysed Milne-Eddington inversions from spectro-polarimetric data of the leading sunspot of NOAA 11024 during the development of its penumbra. We focused on selected areas of this protospot in which segments of penumbra develop. Results. We find that few types of distinctive flow patterns develop at the protospot limb and centre sides previous to penumbra formation. The flow in the centre side is often characterised by a persistent (> 20 min) inflow-outflow pattern extending radially over 4 arcsec at the direct periphery of the protospot umbra. This inflow-outflow system often correlates with elongated granules, as seen in continuum intensity maps, and is also coupled with magnetic bipolar patches at its edges, as seen in magnetograms. The field is close to horizontal between the bipolar patches, which is indicative of its possible loop configuration. All of these aspects are analogous to observations of magnetic flux emergence. In the protospot limb side, however, we observed a mostly regular pattern associated with small granules located near the protospot intensity boundary. Locally, an inflow develops adjacent to an existing penumbral segment, and this inflow is correlated with a single bright penumbral filament that is brighter than filaments containing the Evershed flow. All investigated areas at the centre and limb side eventually develop penumbral filaments with an actual Evershed flow that starts at the umbral boundary and grows outwards radially as the penumbral filaments become longer in time.

Context.The bright heads of penumbral filaments, penumbral grains (PGs), show apparent horizontal motions inward, toward the umbra, or outward, away from the umbra.Aims.We aim to ascertain statistically whether the direction of PGs’ apparent motion is related to the inclination of the surrounding magnetic field.Methods.We used spectropolarimetric observations of five sunspot penumbrae to compare magnetic inclinations inside PGs with those in their surroundings. The data were taken by three observatories: the Hinode satellite, the Swedish Solar Telescope, and the GREGOR solar telescope. The direction of PGs’ motion was determined by feature tracking. The atmospheric conditions in PGs and their surroundings, including magnetic field information, were retrieved by means of height-stratified spectropolarimetric inversions.Results.Out of a sample of 444 inward-moving PGs and 269 outward-moving ones, we show that 43% of the inward-moving PGs have a magnetic inclination larger by 8° ±4° than the inclination in their surroundings and 51% of the outward-moving PGs have an inclination smaller by 13° ±7° than the surrounding one. The opposite relation of inclinations is observed in only one fifth of the inward- and outward-moving PGs.Conclusions.Rising hot plasma in PGs surrounded by a less inclined magnetic field may adapt its trajectory to be more vertical, causing an inward apparent motion of PGs. Conversely, it may be dragged by a more horizontal surrounding magnetic field such that an outward apparent motion is observed.