T. Felipe

Multi-layer Study of Wave Propagation in Sunspots

We analyze the propagation of waves in sunspots from the photosphere to the chromosphere using time series of co-spatial Ca II H intensity spectra (including its line blends) and polarimetric spectra of Si I 10827 and the He I 10830 multiplet. From the Doppler shifts of these lines we retrieve the variation of the velocity along the line-of-sight at several heights. Phase spectra are used to obtain the relation between the oscillatory signals. Our analysis reveals standing waves at frequencies lower than 4 mHz and a continuous propagation of waves at higher frequencies, which steepen into shocks in the chromosphere when approaching the formation height of the Ca II H core. The observed non-linearities are weaker in Ca II H than in He I lines. Our analysis suggests that the Ca II H core forms at a lower height than the He I 10830 line: a time delay of about 20 s is measured between the Doppler signal detected at both wavelengths. We fit a model of linear slow magnetoacoustic wave propagation in a stratified atmosphere with radiative losses according to Newtons cooling law to the phase spectra and derive the difference in the formation height of the spectral lines. We show that the linear model describes well the wave propagation up to the formation height of Ca II H, where non-linearities start to become very important.

MAGNETO-ACOUSTIC WAVES IN SUNSPOTS: FIRST RESULTS FROM A NEW THREE-DIMENSIONAL NONLINEAR MAGNETOHYDRODYNAMIC CODE

Waves observed in the photosphere and chromosphere of sunspots show complex dynamics and spatial patterns. The interpretation of high-resolution sunspot wave observations requires modeling of three-dimensional (3D) nonlinear wave propagation and mode transformation in the sunspot upper layers in realistic spot model atmospheres. Here, we present the first results of such modeling. We have developed a 3D nonlinear numerical code specially designed to calculate the response of magnetic structures in equilibrium to an arbitrary perturbation. The code solves the 3D nonlinear MHD equations for perturbations; it is stabilized by hyper-diffusivity terms and is fully parallelized. The robustness of the code is demonstrated by a number of standard tests. We analyze several simulations of a sunspot perturbed by pulses of different periods at a subphotospheric level, from short periods, introduced for academic purposes, to longer and realistic periods of 3 and 5 minutes. We present a detailed description of the 3D mode transformation in a non-trivial sunspot-like magnetic field configuration, including the conversion between fast and slow magneto-acoustic waves and the Alfven wave, by calculation of the wave energy fluxes. Our main findings are as follows: (1) the conversion from acoustic to the Alfven mode is only observed if the driving pulse is located out of the sunspot axis, but this conversion is energetically inefficient; (2) as a consequence of the cutoff effects and refraction of the fast magneto-acoustic mode, the energy of the evanescent waves with periods around 5 minutes remains almost completely below the level β = 1; (3) waves with frequencies above the cutoff propagate field aligned to the chromosphere and their power becomes dominating over that of evanescent 5 minute oscillations, in agreement with observations.

NUMERICAL SIMULATIONS OF MULTIPLE SCATTERING OF THE f-MODE BY FLUX TUBES

We use numerical simulations to study the absorption and phase shift of surface-gravity waves caused by groups of magnetic flux tubes. The dependence of the scattering coefficients on the distance between the tubes and their positions is analyzed for several cases with two or three flux tubes embedded in a quiet Sun atmosphere. The results are compared with those obtained neglecting completely or partially multiple scattering effects. We show that multiple scattering has a significant impact on the absorption measurements and tends to reduce the phase shift. We also consider more general cases of ensembles of randomly distributed flux tubes, and we have evaluated the effects on the scattering measurements of changing the number of tubes included in the bundle and the average distance between flux tubes. We find that for the longest wavelength incoming waves, multiple scattering enhances the absorption, and its efficiency increases with the number of flux tubes and the reduction of the distance between them.

Scattering of the f-mode by Small Magnetic Flux Elements from Observations and Numerical Simulations

The scattering of f-modes by magnetic tubes is analyzed using three-dimensional numerical simulations. An f-mode wave packet is propagated through a solar atmosphere embedded with three different flux tube models that differ in radius and total magnetic flux. A quiet-Sun simulation without a tube present is also performed as a reference. Waves are excited inside the flux tube and propagate along the field lines, and jacket modes are generated in the surroundings of the flux tube, carrying 40% as much energy as the tube modes. The resulting scattered wave is mainly an f-mode composed of a mixture of m = 0 and m = ±1 modes. The amplitude of the scattered wave approximately scales with the magnetic flux. A small amount of power is scattered into the p 1-mode. We have evaluated the absorption and phase shift from a Fourier-Hankel decomposition of the photospheric vertical velocities. They are compared with the results obtained from the ensemble average of 3400 small magnetic elements observed in high-resolution MDI Doppler datacubes. The comparison shows that the observed dependence of the phase shift with wavenumber can be matched reasonably well with the simulated flux tube model. The observed variation of the phase shifts with the azimuthal order m appears to depend on details of the ensemble averaging, including possible motions of the magnetic elements and asymmetrically shaped elements.

Three-dimensional structure of a sunspot light bridge

Context. Active regions are the most prominent manifestations of solar magnetic fields; their generation and dissipation are fundamental problems in solar physics. Light bridges are commonly present during sunspot decay, but a comprehensive picture of their role in the removal of the photospheric magnetic field is still lacking. Aims. We study the three-dimensional configuration of a sunspot, and in particular, its light bridge, during one of the last stages of its decay. Methods. We present the magnetic and thermodynamical stratification inferred from full Stokes inversions of the photospheric Si i 10 827 A and Ca i 10 839 A lines obtained with the GREGOR Infrared Spectrograph of the GREGOR telescope at the Observatorio del Teide, Tenerife, Spain. The analysis is complemented by a study of continuum images covering the disk passage of the active region, which are provided by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. Results. The sunspot shows a light bridge with penumbral continuum intensity that separates the central umbra from a smaller umbra. We find that in this region the magnetic field lines form a canopy with lower magnetic field strength in the inner part. The photospheric light bridge is dominated by gas pressure (high- β ), as opposed to the surrounding umbra, where the magnetic pressure is higher. A convective flow is observed in the light bridge. This flow is able to bend the magnetic field lines and to produce field reversals. The field lines merge above the light bridge and become as vertical and strong as in the surrounding umbra. We conclude that this occurs because two highly magnetized regions approach each other during the sunspot evolution.

Helioseismic Holography of Simulated Sunspots: Magnetic and Thermal Contributions to Travel Times

Wave propagation through sunspots involves conversion between waves of acoustic and magnetic character. In addition, the thermal structure of sunspots is very different than that of the quiet Sun. As a consequence, the interpretation of local helioseismic measurements of sunspots has long been a challenge. With the aim of understanding these measurements, we carry out numerical simulations of wave propagation through sunspots. Helioseismic holography measurements made from the resulting simulated wavefields show qualitative agreement with observations of real sunspots. We use additional numerical experiments to determine, separately, the influence of the thermal structure of the sunspot and the direct effect of the sunspot magnetic field. We use the ray approximation to show that the travel-time shifts in the thermal (non-magnetic) sunspot model are primarily produced by changes in the wave path due to the Wilson depression rather than variations in the wave speed. This shows that inversions for the subsurface structure of sunspots must account for local changes in the density. In some ranges of horizontal phase speed and frequency there is agreement (within the noise level in the simulations) between the travel times measured in the full magnetic sunspot model and the thermal model. If this conclusion proves to be robust for a wide range of models, it would suggest a path toward inversions for sunspot structure.

Evaluation of the Capability of Local Helioseismology to Discern between Monolithic and Spaghetti Sunspot Models

The helioseismic properties of the wave scattering generated by monolithic and spaghetti sunspots are analyzed by means of numerical simulations. In these computations, an incident f- or p1-mode travels through the sunspot model, which produces absorption and phase shift of the waves. The scattering is studied by inspecting the wavefield, computing travel-time shifts, and performing Fourier-Hankel analysis. The comparison between the results obtained for both sunspot models reveals that the differences in the absorption coefficient can be detected above noise level. The spaghetti model produces a steep increase of the phase shift with the degree of the mode at short wavelengths, while mode mixing is more efficient for the monolithic model. These results provide a clue for what to look for in solar observations to discern the constitution of sunspots between the proposed monolithic and spaghetti models.

Helioseismic holography of simulated sunspots: dependence of the travel time on magnetic field strength and Wilson depression

Improving methods for determining the subsurface structure of sunspots from their seismic signature requires a better understanding of the interaction of waves with magnetic field concentrations. We aim to quantify the impact of changes in the internal structure of sunspots on local helioseismic signals. We have numerically simulated the propagation of a stochastic wave field through sunspot models with different properties, accounting for changes in the Wilson depression between 250 and 550 km and in the photospheric umbral magnetic field between 1500 and 3500 G. The results show that travel-time shifts at frequencies above approximately 3.50 mHz (depending on the phase-speed filter) are insensitive to the magnetic field strength. The travel time of these waves is determined exclusively by the Wilson depression and sound-speed perturbation. The travel time of waves with lower frequencies is affected by the direct effect of the magnetic field, although photospheric field strengths below 1500 G do not leave a significant trace on the travel-time measurements. These results could potentially be used to develop simplified travel-time inversion methods.

Synthetic polarimetric spectra from stellar prominences

Stellar prominences detected in rapidly rotating stars serve as probes of the magnetism in the corona of cool stars. We have synthesized the temporal evolution of the Stokes profiles generated in the He I 10830 and 5876 A triplets during the rotation of a prominence around a star. The synthesis was performed with the HAZEL code using a cloud model in which the prominence is characterized by a slab located at a fixed latitude and height. It accounts for the scattering polarization and Zeeman and Hanle effects. Several cases with different prominence magnetic field strengths and orientations have been analyzed. The results show an emission feature that drifts across the profile while the prominence is out of the stellar disk. When the prominence eclipses the star, the intensity profile shows an absorption. The scattering induced by the prominence generates linear polarization signals in Stokes Q and U profiles, which are modified by the Hanle effect when a magnetic field is present. Due to the Zeeman effect, Stokes V profiles show a signal with very low amplitude when the magnetic field along the line-of-sight is different from zero. The estimated linear polarization signals could potentially be detected with the future spectropolarimeter MIRADAS, to be attached to GTC telescope.

Dependence of sunspot photospheric waves on the depth of the source of solar p-modes

Photospheric waves in sunspots moving radially outwards at speeds faster than the characteristic wave velocities have been recently detected. It has been suggested that they are the visual pattern of