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تسجيل مستخدم جديدNo universal connection between the vertical magnetic field and the umbra-penumbra boundary in sunspots
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Context. It has been reported that the boundary between the umbra and the penumbra of sunspots occurs at a canonical value of the strength of the vertical magnetic field, independently of the size of the spot. This critical field strength is interpreted as to be the threshold for the onset of magnetoconvection. Aims. Here we investigate the reasons why this criterion, also called the Jurv{c}ak criterion in the literature, does not always identify the boundary between umbra and penumbra. Methods. We perform a statistical analysis of 23 sunspots observed with Hinode/SOT. We compare the properties of the continuum intensity and the vertical magnetic field between filaments and spines and how they vary between spots of different sizes. Results. We find that the inner boundary of the penumbra is not related to a universal value of the vertical magnetic field. The properties of spines and filaments vary between spots of different sizes. Both components are darker in larger spots and the spines exhibit stronger vertical magnetic field. These variations of the properties of filaments and spines with spot size are also the reason for the reported invariance of the averaged vertical magnetic field at 50% of the mean continuum intensity. Conclusions. The formation of filaments and the onset of magnetoconvection are not related to a canonical value of the strength of the vertical magnetic field. Such a seemingly unique magnetic field strength is rather an effect of the filling factor of spines and penumbral filaments.
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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 d
efined 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.
We investigate the vertical gradient of the magnetic field of sunspots in the photospheric layer. Independent observations were obtained with the SOT/SP onboard the Hinode spacecraft and with the TIP-2 mounted at the VTT. We apply state-of-the-art in
version techniques to both data sets to retrieve the magnetic field and the corresponding vertical gradient. In the sunspot penumbrae we detected patches of negative vertical gradients of the magnetic field strength, i.e.,the magnetic field strength decreases with optical depth in the photosphere. The negative gradient patches are located in the inner and partly in the middle penumbrae in both data sets. From the SOT/SP observations, we found that the negative gradient patches are restricted mainly to the deep photospheric layers and are concentrated near the edges of the penumbral filaments. MHD simulations also show negative gradients in the inner penumbrae, also at the locations of filaments. Both in the observations and simulation negative gradients of the magnetic field vs. optical depth dominate at some radial distances in the penumbra. The negative gradient with respect to optical depth in the inner penumbrae persists even after averaging in the azimuthal direction, both in the observations and, to a lesser extent, also in MHD simulations. We interpret the observed localized presence of the negative vertical gradient of the magnetic field strength in the observations as a consequence of stronger field from spines expanding with height and closing above the weaker field inter-spines. The presence of the negative gradients with respect to optical depth after azimuthal averaging can be explained by two different mechanisms: the high corrugation of equal optical depth surfaces and the cancellation of polarized signal due to the presence of unresolved opposite polarity patches in the deeper layers of the penumbra.
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 resoluti
on 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.
Context: In sunspots, the geometric height of continuum optical depth unity is depressed compared to the quiet Sun. This so-called Wilson depression is caused by the Lorentz force of the strong magnetic field inside the spots. However, it is not unde
rstood in detail yet, how the Wilson depression is related to the strength and geometry of the magnetic field or to other properties of the sunspot. Aims: We aim to study the dependence of the Wilson depression on the properties of the magnetic field of the sunspots and how exactly the magnetic field contributes to balancing the Wilson depression with respect to the gas pressure of the surroundings of the spots. Methods: Our study is based on 24 spectropolarimetric scans of 12 individual sunspots performed with Hinode. We derived the Wilson depression for each spot using both, a recently developed method that is based on minimizing the divergence of the magnetic field, and an approach developed earlier that enforces an equilibrium between the gas pressure and the magnetic pressure inside the spot and the gas pressure in the quiet Sun, thus neglecting the influence of the curvature force. We then performed a statistical analysis by comparing the Wilson depression resulting from the two techniques with each other and by relating them to various parameters of the sunspots, such as their size or the strength of the magnetic field. Results: We find that the Wilson depression becomes larger for spots with a stronger magnetic field, but not as much as one would expect from the increased magnetic pressure. This suggests that the curvature integral provides an important contribution to the Wilson depression, particularly for spots with a weak magnetic field. Our results indicate that the geometry of the magnetic field in the penumbra is different between spots with different strengths of the average umbral magnetic field.
In this study, we investigate magnetic properties of umbra of magneto-conjugate leading and following sunspots, i.e. connected through magnetic field lines. We established dependences between individual sunspot umbra field characteristics, and betwee
n these characteristics on the umbra area ($S$) separately for sunspot pairs, for which the minimal angle between the umbra magnetic field line of the leading ($L$) sunspot and the positive normal line to the Sun surface is smaller, than that in the following ($F$) sunspot ($alpha_{min-L}<alpha_{min-F}$; such sunspot pairs are the bulk) and, on the contrary, when $alpha_{min-L}>alpha_{min-F}$. The $alpha_{min-L}(S_L)$, $alpha_{min-F}(S_F)$, $B_{max-L}(S_L)$ and $B_{max-F}(S_F)$ dependences are shown to have similar behavior features, and are quantitatively close for two sunspot groups with a different asymmetry of the sunspot magnetic field connecting them (here, $B_{max-L,F}(S_L)$ is the magnetic induction maximum induction in umbrae of the leading and the following sunspots). The dependence of mean values of angles within umbra $<alpha_{L,F}>$ on the sunspot umbra area $S_{L,F}$ and on the mean value of magnetic induction in umbra $<B_{L,F}>$ appeared different for two cases. Also, in the bulk of the investigated sunspot pairs, the leading sunspot was shown to appear closer to the polarity inversion line between the sunspots, than the following one. This result and the conclusion that, in the bulk of the investigated pairs of the magnetically conjugate sunspots, $alpha_{min-L}<alpha_{min-F}$ are closely coupled.
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