Johannes Löhner-Böttcher, Nazaret Bello González & Wolfgang Schmidt
Kiepenheuer-Institut für Sonnenphysik, Freiburg, Germany

Sunspot waves are one of the most prominent and dynamical phenomena in the solar atmosphere. In the sunspot chromosphere, umbral flashes and running penumbral waves appear unceasingly as brightness and velocity oscillations. Observational studies^1,2,3 have confirmed that these phenomena are magnetoacoustic waves which are guided along the magnetic field lines toward higher atmospheric layers. Despite the fact that umbral and penumbral waves share the same wave character, their periodicities differ significantly².

To investigate the wave characteristics in sunspots, we observed the circular sunspot NOAA11823 (see Fig.1) close to disk center with the Interferometric BIdimensional Spectro-polarimeter (IBIS) at the Dunn Solar Telescope in a spectroscopic setup, performed a wavelet power analysis on the 1h-time series, and combined the results with the analysis of HMI and AIA data¹. We were thus able to confirm the proposed⁴ influence of the magnetic field orientation on the periodicity of sunspot waves. With increasing zenith inclination of the magnetic field lines from the umbra to the penumbra, the acoustic cut-off period of the solar atmosphere increases. This allows the propagation of wave modes with longer periods toward the upper solar atmosphere. The distribution of dominating wave periods in the chromosphere is shown in Fig. 1 (panel d), in comparison with the continuum intensity (panel a), magnetic field strength (panel b), and photospheric magnetic field inclination (panel c). The chromospheric umbra with the strongest and vertical magnetic field yields dominant 2.5–3 min waves. In the surrounding penumbra, the peak periods increase as a function of radial distance up to 8 min at the outer penumbra with a more inclined magnetic field^1,5.

Figure 1 | Time-averaged physical quantities of sunspot NOAA11823 on August 21st 2013. The distributions show the sunspot in a) normalized HMI continuum intensity, b) absolute magnetic field strengths, c) photospheric magnetic field inclination against the line-of-sight from HMI inversions, and d) dominant wave periods of chromospheric intensity oscillations (CaII 854.21nm) observed with IBIS at the Dunn Solar Telescope. The black contours mark the umbral and penumbral boundaries from continuum intensity. The arrow is pointing toward disk center.

In reverse, we were able to make use of the direct connection between the orientation of the magnetic waveguides and the dominant period in the power spectrum in order to reconstruct the zenith inclination of the sunspot in the chromosphere and upper photosphere. On the left of Fig. 2, the sunspot is shown in spectral intensity from the bottom photosphere to the middle chromosphere. The results of the magnetic field reconstruction based on intensity oscillations at the sampled layers are shown on the right. In the chromosphere, the inclination of the sunspot’s magnetic field increases from vertical (0&#176) in the umbra to around 60&#176 in the outer penumbra. With increasing altitude in the sunspot atmosphere, the magnetic field of the penumbra becomes less inclined. Moreover, the reconstruction in the upper sunspot photosphere is in very good agreement with the HMI magnetic field inversion. The discrepancy in the lower photosphere is caused by the mix of wave modes. The acoustic cut-off period starts to define the waves propagation only higher up in the photosphere.

Figure 2 | Three-dimensional distribution of spectral intensities (left-hand side) and reconstructed zenith inclinations ΦB of the magnetic field (right-hand side) from photospheric to chromospheric heights. The sunspot atmosphere at 15:00:06UTC is sampled by several line core and wing positions of FeI 630.15 nm, NaI 589.6 nm, and CaII 854.2nm. A bright umbral flash is present in the central umbra. The sunspot boundaries from continuum intensity are contoured in black. The photospheric line-of-sight inclination from HMI inversions is added at the bottom right.

The relations between the different sunspot parameters are best described in Fig. 3. The very circular and symmetrical shape of the sunspot allowed the computation of the azimuthal averages as a function of radial distance from the sunspot center. The decrease in magnetic field inclination from the photosphere to the chromosphere is in line with a magnetic field configuration that fans out toward the less dense upper chromosphere and corona.

Figure 3 | Azimuthally averaged sunspot parameters as a function of radial distance from the sunspot center: a) normalized HMI continuum intensity, b) absolute (black) and line-of-sight (blue) magnetic field strengths from HMI inversions, c) zenith inclinations ΦB of the magnetic field in the lower photosphere (black) and chromosphere (blue), d) dominant wave periods in the photosphere (black) and chromosphere (blue). The vertical dashed lines mark the average boundaries between umbra (U), penumbra (PU) and quiet Sun (QS). Error bars indicate the azimuthal standard deviations.

We conclude that the reconstruction of the magnetic field topology on the basis of sunspot oscillations from spectroscopic observations yields consistent and conclusive results. The novel technique opens up a new possibility to infer the magnetic field inclination in the solar chromosphere⁵.

References

[1] Löhner-Böttcher, J, 2016, PhD thesis, dx.doi.org/10.6094/UNIFR/10748
[2] Jess, D., Reznikova, V., Van Doorsselaere, T., Keys, P., & Mackay, D., 2013, ApJ, 779, 168
[3] Madsen, C. A., Tian, H., & DeLuca, E. E. 2015, ApJ, 800, 129
[4] Bel, N. & Leroy, B. 1977, A&A, 55, 239
[5] Löhner-Böttcher, J., Bello González, N. & Schmidt, W., 2016, arXiv eprint