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Register a new userA distinct magnetic property of the inner penumbral boundary III. Analysis of simulated sunspots
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The analyses of sunspot observations revealed a fundamental magnetic property of the umbral boundary, the invariance of the vertical component of the magnetic field. We aim to analyse the magnetic properties of the umbra-penumbra boundary in simulated sunspots and thus assess their similarity to observed sunspots. Also, we aim to investigate the role of plasma $beta$ and the ratio of kinetic to magnetic energy in simulated sunspots on the convective motions. We use a set of non-grey simulation runs of sunspots with the MURaM code. These data are used to synthesise the Stokes profiles that are then degraded to the Hinode spectropolarimeter-like observations. Then, the data are treated like real Hinode observations of a sunspot and magnetic properties at the umbral boundaries are determined. Simulations with potential field extrapolation produce a realistic magnetic field configuration on their umbral boundaries. Two simulations with potential field upper boundary, but different subsurface magnetic field structures, differ significantly in the extent of their penumbrae. Increasing the penumbra width by forcing more horizontal magnetic fields at the upper boundary results in magnetic properties that are not consistent with observations. This implies that the size of the penumbra is given by the subsurface structure of the magnetic field. None of the sunspot simulations is consistent with observed properties of the magnetic field and direction of the Evershed flow at the same time. Strong outward directed Evershed flows are only found in setups with artificially enhanced horizontal component of the magnetic field at the top boundary that are not consistent with the observed magnetic field properties at the UP boundary. We want to stress out that the `photospheric boundary of simulated sunspots is defined by a magnetic field strength of equipartition field value.
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A sunspot emanates from a growing pore or protospot. In order to trigger the formation of a penumbra, large inclinations at the outskirts of the protospot are necessary. The penumbra develops and establishes by colonising both umbral areas and granulation. Evidence for a unique stable boundary value for the vertical component of the magnetic field strength, $B^{rm stable}_{rm ver}$, was found along the umbra-penumbra boundary of developed sunspots. We use broadband G-band images and spectropolarimetric GFPI/VTT data to study the evolution of and the vertical component of the magnetic field on a forming umbra-penumbra boundary. For comparison with stable sunspots, we also analyse the two maps observed by Hinode/SP on the same spot after the penumbra formed. The vertical component of the magnetic field, $B_{rm ver}$, at the umbra-penumbra boundary increases during penumbra formation owing to the incursion of the penumbra into umbral areas. After 2.5 hours, the penumbra reaches a stable state as shown by the GFPI data. At this stable stage, the simultaneous Hinode/SP observations show a $B_{rm ver}$ value comparable to that of umbra-penumbra boundaries of fully fledged sunspots. We confirm that the umbra-penumbra boundary, traditionally defined by an intensity threshold, is also characterised by a distinct canonical magnetic property, namely by $B^{rm stable}_{rm ver}$. During the penumbra formation process, the inner penumbra extends into regions where the umbra previously prevailed. Hence, in areas where $B_{rm ver} < B^{rm stable}_{rm ver}$, the magneto-convection mode operating in the umbra turns into a penumbral mode. Eventually, the inner penumbra boundary settles at $B^{rm stable}_{rm ver}$, which hints toward the role of $B_{rm ver}^{rm stable}$ as inhibitor of the penumbral mode of magneto-convection.
We recently presented evidence that stable umbra-penumbra boundaries are characterised by a distinct canonical value of the vertical component of the magnetic field, $B^{rm stable}_{rm ver}$. In order to trigger the formation of a penumbra, large inclinations in the magnetic field are necessary. In sunspots, the penumbra develops and establishes by colonising both umbral areas and granulation, that is, penumbral magneto-convection takes over in umbral regions with $B_{rm ver} < B^{rm stable}_{rm ver}$, as well as in granular convective areas. Eventually, a stable umbra-penumbra boundary settles at $B^{rm stable}_{rm ver}$. Here, we aim to study the development of a penumbra initiated at the boundary of a pore, where the penumbra colonises the entire pore ultimately. We have used Hinode/SOT G-band images to study the evolution of the penumbra. Hinode/SOT spectropolarimetric data were used to infer the magnetic field properties in the studied region. The penumbra forms at the boundary of a pore located close to the polarity inversion line of NOAA,10960. As the penumbral bright grains protrude into the pore, the magnetic flux in the forming penumbra increases at the expense of the pore magnetic flux. Consequently, the pore disappears completely giving rise to an orphan penumbra. At all times, the vertical component of the magnetic field in the pore is smaller than $B^{rm stable}_{rm ver} approx 1.8$~kG. Our findings are in an agreement with the need of $B^{rm stable}_{rm ver}$ for establishing a stable umbra-penumbra boundary: while $B_{rm ver}$ in the pore is smaller than $B^{rm stable}_{rm ver}$, the protrusion of penumbral grains into the pore area is not blocked, a stable pore-penumbra boundary does not establish, and the pore is fully overtaken by the penumbral magneto-convective mode. This scenario could also be one of the mechanisms giving rise to orphan penumbrae.
It was empirically determined that the umbra-penumbra boundaries of stable sunspots are characterized by a constant value of the vertical magnetic field. We analyzed the evolution of the photospheric magnetic field properties of a decaying sunspot belonging to NOAA 11277 between August 28 - September 3, 2011. The observations were acquired with the spectropolarimeter on-board of the Hinode satellite. We aim to proof the validity of the constant vertical magnetic-field boundary between the umbra and penumbra in decaying sunspots. A spectral-line inversion technique was used to infer the magnetic field vector from the full-Stokes profiles. In total, eight maps were inverted and the variation of the magnetic properties in time were quantified using linear or quadratic fits. We found a linear decay of the umbral vertical magnetic field, magnetic flux, and area. The penumbra showed a linear increase of the vertical magnetic field and a sharp decay of the magnetic flux. In addition, the penumbral area quadratically decayed. The vertical component of the magnetic field is weaker on the umbra-penumbra boundary of the studied decaying sunspot compared to stable sunspots. Its value seem to be steadily decreasing during the decay phase. Moreover, at any time of the shown sunspot decay, the inner penumbra boundary does not match with a constant value of the vertical magnetic field, contrary to what was seen in stable sunspots. During the decaying phase of the studied sunspot, the umbra does not have a sufficiently strong vertical component of the magnetic field and is thus unstable and prone to be disintegrated by convection or magnetic diffusion. No constant value of the vertical magnetic field was found for the inner penumbral boundary.
Sunspots are the longest-known manifestation of solar activity, and their magnetic nature has been known for more than a century. Despite this, the boundary between umbrae and penumbrae, the two fundamental sunspot regions, has hitherto been solely defined by an intensity threshold. Here, we aim at studying the magnetic nature of umbra-penumbra boundaries in sunspots of different sizes, morphologies, evolutionary stages, and phases of the solar cycle. We used a sample of 88 scans of the Hinode/SOT spectropolarimeter to infer the magnetic field properties in at the umbral boundaries. We defined these umbra-penumbra boundaries by an intensity threshold and performed a statistical analysis of the magnetic field properties on these boundaries. We statistically prove that the umbra-penumbra boundary in stable sunspots is characterised by an invariant value of the vertical magnetic field component: the vertical component of the magnetic field strength does not depend on the umbra size, its morphology, and phase of the solar cycle. With the statistical Bayesian inference, we find that the strength of the vertical magnetic field component is, with a likelihood of 99%, in the range of 1849-1885 G with the most probable value of 1867 G. In contrast, the magnetic field strength and inclination averaged along individual boundaries are found to be dependent on the umbral size: the larger the umbra, the stronger and more horizontal the magnetic field at its boundary. The umbra and penumbra of sunspots are separated by a boundary that has hitherto been defined by an intensity threshold. We now unveil the empirical law of the magnetic nature of the umbra-penumbra boundary in stable sunspots: it is an invariant vertical component of the magnetic field.
Observations of a relation between continuum intensity and magnetic field strength in sunspots have been made during nearly five decades. This work presents full-Stokes measurements of the full-split (g = 3) line Fe I 1564.85 nm with spatial resolution of 0.5 obtained with the GREGOR Infrared Spectrograph in three large sunspots. The continuum intensity is corrected for instrumental scattered light and the brightness temperature is calculated. Magnetic field strength and inclination are derived directly from the line split and the ratio of Stokes components. The continuum intensity (temperature) relations to the field strength are studied separately in the umbra, light bridges, and penumbra. The results are consistent with previous studies and it was found that the scatter of values in the relations increases with increasing spatial resolution thanks to resolved fine structures. The observed relations show trends common for the umbra, light bridges, and the inner penumbra, while the outer penumbra has a weaker magnetic field compared to the inner penumbra at equal continuum intensities. This fact can be interpreted in terms of the interlocking comb magnetic structure of the penumbra. A comparison with data obtained from numerical simulations was made. The simulated data have a generally stronger magnetic field and a weaker continuum intensity than the observations, which may be explained by stray light and limited spatial resolution of the observations and by photometric inaccuracies of the simulations.
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