How Temperature And Magnetic Field Are Related In Sunspots?

Our Sun is an enormous laboratory for studying the interaction between moving plasma and magnetic fields. All phenomena connected with the solar activity like flares, prominences, coronal loops, faculae, and sunspots are manifestations of this interaction.

Of them, sunspots (Fig. 1) were the first to be discovered and are in fact the first astrophysical objects where magnetic fields have been found.

Fig. 1 – A sunspot with an umbra, penumbra, and light bridges, observed with the telescope GREGOR, which is capable to resolve features of 70 km on the solar surface. Credit: Michal Sobotka

Sunspots are darker than their surroundings because a strong magnetic field inhibits subsurface convection that transfers heat to the solar surface. The magnetic field is nearly vertical in the central darkest part of a sunspot, umbra, while it is inclined in the outer filamentary part, penumbra. A relation between the magnetic field and brightness (or temperature) in sunspots was first predicted by theory: Regions with stronger magnetic field should be darker and cooler than those with a weaker field. This problem was extensively investigated theoretically as well as through observations.

The largest European solar telescope GREGOR (Schmidt et al., 2012), located on Tenerife, was recently used to measure the temperature – magnetic field relation in three large sunspots, taking advantage of excellent spatial resolution and high magnetic sensitivity in the infrared spectral region around λ = 1565 nm. It was possible to measure this relation separately for umbrae, penumbrae, and light bridges (bright features with a reduced magnetic field, embedded inside umbrae).

Fig. 2 – Scatter plot of magnetic field strength vs. continuum intensity/temperature in the umbra (green), light bridges (red), and penumbra (black). Solid lines show average values in the umbra (black), light bridges (yellow), and penumbra (purple), together with dashed lines representing the standard deviation. Credit: Michal Sobotka

 The results shown in Fig. 2 are in the form of a scatter plot of magnetic field strength versus intensity (temperature) at all locations inside the three sunspots. Fluctuations of temperature and magnetic field in small-scale structures cause a large scatter of points, however, average values show trends in the temperature – magnetic field relation that are very similar in the umbra, light bridges, and inner parts of the penumbra. This indicates that the interaction between moving plasma and magnetic field, a cause of sunspot cooling, has the same character in those parts of sunspots where the magnetic field is not far from the vertical.

The trend is different in the outer penumbra, where the magnetic field decreases quite rapidly. This points to a complex structure of the magnetic field in the penumbra, consisting of two different systems of magnetic field lines – a so-called interlocking comb structure (Thomas & Weiss, 2008). The first system has a stronger and more vertical field and it is common for the umbra, light bridges, and the inner penumbra. The outer penumbra is dominated by the second, weaker and more horizontal field system, which explains the drop of the magnetic field strength.

Fig. 3 – Scatter-plot densities of magnetic field strength vs. continuum intensity/temperature for the umbra (left) and penumbra (right). The contours represent observed data, while the grey-scale clouds depict results of numerical simulations. Credit: Michal Sobotka

Modern methods of numerical simulations based on radiative magnetohydrodynamic codes are capable to create a synthetic sunspot (Rempel, 2012) very similar to observed spots and free of instrumental effects that degrade the observations. A comparison of the observed temperature – magnetic field relation with that derived from the synthetic sunspot is shown in Fig. 3. The scatter-plot densities obtained from observations are depicted by contours, while grey-scale clouds represent the corresponding synthetic data. It can be seen that both in the umbra and penumbra, the observed magnetic field is weaker and the temperature is higher.

The high temperature can be explained by light scattered in the Earth’s atmosphere, which spuriously increases the observed intensity. On the other hand, also the simulations may underestimate the synthetic intensity and temperature. The reason why we observe a weaker magnetic field is the spatial resolution, which is by the factor of 30 worse than in the simulations. Features with an extremely strong magnetic field that appear in the synthetic data are too small to be observed.

A relatively simple study of the temperature – magnetic field relation is complementary to the sophisticated methods of spectropolarimetric analysis and numerical simulations that are currently used to study sunspots. Nevertheless, it can serve to verify their results and even to add some new details.

References:

• Rempel, M.: 2012, Numerical sunspot models: Robustness of photospheric velocity and magnetic field structure. The Astrophysical Journal, 750, 62.
• Schmidt, W., von der Lühe, O., Volkmer, R., et al.: 2012, The 1.5 meter solar telescope GREGOR, Astronomische Nachrichten, 333, 796.
• Thomas, J.H. & Weiss, N.O.: 2008, Sunspots and Starspots. Cambridge University Press, Cambridge.

These findings are described in the article entitled The Temperature – Magnetic Field Relation in Observed and Simulated Sunspots, published in the journal Solar Physics, vol. 292, article 188 (December 2017). This work was led by Michal Sobotka from Astronomical Institute of the Czech Academy of Sciences together with Reza Rezaei from Instituto de Astrofísica de Canarias.