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.
Using Hinode satellite data, we can give statistical proof of an empirical law governing the boundary between umbra and penumbra in stable sunspots: The vertical component of the magnetic field, Bver, is invariant.
Contours of intensity at 50% of the granular quiet-sun value and contours of Bver=1867 G match. This is illustrated in the Fig. 1, in which contours for intensity (white) and Bver (red) are displayed for some of the spots that where included in the sample. Deviations were studied and shown to be non-significant (Jurcak et al. 2018).
This empirical law applies for all sunspots of the sample with different sizes, morphologies, evolutionary stages, and phases of the solar cycle. Thereby we have unveiled the magnetic property that discriminates between the umbral and penumbral modes of magneto-convection. This discovery carries strong consequences for the understanding of the fundamental processes of energy transport occurring in the magnetic Sun.
The validity of this empirical law and the value of this new constant is now being examined for different wavelengths and data sources. Figure 2 shows intensity images of sunspots observed with the GRIS@GREGOR spectograph. The value of Bver=1843 Gauss is consistent with the results from Jurcak et al 2018 with Hinode data.
We also studied the temporal evolution of Bver at the umbral boundary, in this case using HMI/SDO data. During the first disc passage, NOAA AR 11591, Bver remains constant at 1693 G with a root-mean-square deviation of 15 G, whereas the magnetic field strength varies substantially (mean 2171 G, rms of 48 G) and shows a long-term variation as shown in the residual in Fig. 3 after daily variations due to the satellite orbit are corrected. Hence, during the disc passage of a stable sunspot its umbral boundary can equivalently be defined by using the continuum intensity Ic or the vertical magnetic field component Bver. Contours of fixed magnetic field strength fail to outline the umbral boundary (Schmassmann et al. 2018).
Now, since observations have shown that in stable sunspots the umbral boundary is outlined by a critical value of the vertical magnetic field component, the key question is: What is the nature of the distinct magnetoconvection regimes in the umbra and penumbra? This is still unclear. To follow up on this, we analysed a sunspot simulation in an effort to understand the origin of the convective instabilities giving rise to the penumbral and umbral distinct regimes. We applied the criterion from Gough & Tayler (1966, MNRAS, 133, 85), accounting for the stabilising effect of the vertical magnetic field to investigate the convective instabilities in a MURaM sunspot simulation. The result is shown in Fig. 4: The deep subphotospheric sunspot trunk is magneto-convectivly stable. Upwards from some -5 Mm, columns of instabilty characterise the umbra of the sunspot. The subsphotospheric penumbra exhibits filamentary instabilities that are almost parallel to the solar surface. Hence, the Gough and Tayler criterion as a diagnostic tool reveals the tripartite nature of sunspot structure with distinct regimes of magneto-convection in the umbra, penumbra, and granulation operating in realistic MHD simulations. (Schmassmann et al. 2021)
Jurčák, J., Rezaei, R., Bello González, N. Schlichenmaier, R., Vomlel, J., 2018, Astronomy & Astrophysics, Volume 611, L4
Schmassmann, M., Schlichenmaier, R. 2018, Astronomy & Astrophysics, Volume 620, A104
Lindner, P., Schlichenmaier, R., Bello González N., 2020, Astronomy & Astrophysics, Volume 638, A25
Schmassmann, M., Rempel, M., Bello González, N., Schlichenmaier, R., Jurčák, J., 2021, Astronomy & Astrophysics, Volume 656, A92