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Sunspots host a large variety of oscillatory phenomena, whose properties depend on the nature of the wave modes and the magnetic and thermodynamic structure of the spot. Umbral chromospheric oscillations exhibit significant differences compared to their photospheric counterparts. They show an enhanced power and a shorter dominant period, from waves with an amplitude of a few hundred meters per second in the five-minute band at the photosphere, to amplitudes of several kilometers per second in the three-minute band at the chromosphere. Various models have been proposed to explain this behaviour, including the presence of a chromospheric resonance cavity between the photosphere and the transition region. Jess et al. (2020, Nature Astronomy, 4, 220) claimed the detection of observational evidence supporting this model, obtained from the comparison of spectropolarimetric observations and numerical simulations. Here, it is shown that the observational insight reported by Jess et al. is not a common property of sunspots. More importantly, numerical modelling also shows that it is not an unequivocal signature of an acoustic resonator., Comment: Matters Arising published in Nature Astronomy. The publisher's final edited version of this article is available at https://rdcu.be/b5JCS

We study the evolution of the decaying active region NOAA 12708, from the photosphere up to the corona using high resolution, multi-wavelength GREGOR observations taken on May 9, 2018. We utilize spectropolarimetric scans of the 10830 Å spectral range by the GREGOR Infrared Spectrograph (GRIS), spectral imaging time-series in the Na ID2 spectral line by the GREGOR Fabry-Pérot Interferometer (GFPI) and context imaging in the Ca IIH and blue continuum by the High-resolution Fast Imager (HiFI). Context imaging in the UV/EUV from the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) complements our dataset. The region under study contains one pore with a light-bridge, a few micro-pores and extended clusters of magnetic bright points. We study the magnetic structure from the photosphere up to the upper chromosphere through the spectropolarimetric observations in He II and Si I and through the magnetograms provided by the Helioseismic and Magnetic Imager (HMI). The high-resolution photospheric images reveal the complex interaction between granular-scale convective motions and a range of scales of magnetic field concentrations in unprecedented detail. The pore itself shows a strong interaction with the convective motions, which eventually leads to its decay, while, under the influence of the photospheric flow field, micro-pores appear and disappear. Compressible waves are generated, which are guided towards the upper atmosphere along the magnetic field lines of the various magnetic structures within the field-of-view. Modelling of the He i absorption profiles reveals high velocity components, mostly associated with magnetic bright points at the periphery of the active region, many of which correspond to asymmetric Si I Stokes-V profiles revealing a coupling between upper photospheric and upper chromospheric dynamics. Time-series of Na ID2 spectral images reveal episodic high velocity components at the same locations. State-of-the-art multi-wavelength GREGOR observations allow us to track and understand the mechanisms at work during the decay phase of the active region.

The spectral window, containing Fraunhofer lines formed in the solar photosphere, around the magnetically sensitive Cr I lines at 5780.9, 5781.1, 5781.7, 5783.0, and 5783.8 \r{A}, with Land\'e g-factors between 1.6 and 2.5, is explored. The goal is to analyze simultaneously 15 spectral lines, which comprise Cr I, Cu I, Fe I, Mn I, and Si I lines, without polarimetry to infer the thermodynamic and magnetic properties in strongly magnetized plasmas using an inversion code. The study is based on a new setup at the Vacuum Tower Telescope (VTT, Tenerife) which includes fast spectroscopic scans in the wavelength range around the Cr I 5781.75 \r{A} line. The snapshot 385 of the Enhanced Network simulation from the Bifrost code serves to synthesize all the lines, which are in turn inverted simultaneously with SIR to establish the best inversion strategy. This strategy is then applied to VTT observations of a sunspot belonging to NOAA 12723 on 2018 September 30 and the results are compared to full-disk vector-field data obtained with the Helioseismic and Magnetic Imager (HMI). The 15 simultaneously inverted intensity profiles (Stokes I) delivered accurate temperatures and Doppler velocities when compared against the simulations. The derived magnetic fields and inclinations are most accurate when the fields are oriented along the line-of-sight (LOS) and less accurate when the fields are transverse to the LOS. In general, the results appear similar to the HMI vector-field data, although some discrepancies exist. The analyzed spectral range has the potential to deliver thermal, dynamic, and magnetic information in strongly magnetized features on the Sun, such as pores and sunspots, even without polarimetry. The highest sensitivity of the lines is found in the lower photosphere, on average around $\log \tau = -1$. The multiple-line inversions provide smooth results across the whole field-of-view., Comment: Accepted for publication in Astronomy & Astrophysics, 12 pages, 12 figures

Context. Far-side helioseismology is a technique used to infer the presence of active regions in the far hemisphere of the Sun based on the interpretation of oscillations measured in the near hemisphere. A neural network has been recently developed to improve the sensitivity of the seismic maps to the presence of far-side active regions. Aims. Our aim is to evaluate the performance of the new neural network approach and to thoroughly compare it with the standard method commonly applied to predict far-side active regions from seismic measurements. Methods. We have computed the predictions of active regions using the neural network and the standard approach from five years of far-side seismic maps as a function of the selected threshold in the signatures of the detections. The results have been compared with direct extreme ultraviolet observations of the far hemisphere acquired with the Solar Terrestrial Relations Observatory (STEREO). Results. We have confirmed the improved sensitivity of the neural network to the presence of far-side active regions. Approximately 96% of the active regions identified by the standard method with a strength above the threshold commonly employed by previous analyses are related to locations with enhanced extreme ultraviolet emission. For this threshold, the false positive ratio is 3.75%. For an equivalent false positive ratio, the neural network produces 47% more true detections. Weaker active regions can be detected by relaxing the threshold in their seismic signature. Conclusions. The neural network is a promising approach to improve the interpretation of the seismic maps provided by local helioseismic techniques., Comment: Accepted for publication in Astronomy and Astrophysics. Abridged abstract

In stratified atmospheres, acoustic waves can only propagate if their frequency is above the cutoff value. Different theories provide different cutoff values. We developed an alternative method to derive the cutoff frequency in several standard solar models, including various quiet-Sun and umbral atmospheres. We performed numerical simulations of wave propagation in the solar atmosphere. The cutoff frequency is determined from the inspection of phase difference spectra computed between the velocity signal at two atmospheric heights. The process is performed by choosing pairs of heights across all the layers between the photosphere and the chromosphere, to derive the vertical stratification of the cutoff in the solar models. The cutoff frequency predicted by the theoretical calculations departs significantly from our measurements. In quiet-Sun atmospheres, the cutoff shows a strong dependence on the magnetic field for adiabatic wave propagation. When radiative losses are taken into account, the cutoff frequency is greatly reduced and the variation of the cutoff with the strength of the magnetic field is lower. The effect of the radiative losses in the cutoff is necessary to understand recent quiet-Sun and sunspot observations. In the presence of inclined magnetic fields, our numerical calculations confirm the reduction of the cutoff frequency due to the reduced gravity experienced by waves propagating along field lines. An additional reduction is also found in regions with significant changes in the temperature, due to the lower temperature gradient along the path of field-guided waves. Our results show that the cutoff values are not correctly captured by theoretical estimates. In addition, most of the widely-used analytical cutoff formulae neglect the impact of magnetic fields and radiative losses, whose role is critical to determine the evanescent or propagating nature of the waves., Accepted for publication in A&A. Abstract has been modified to fit arXiv limit

Sunspot umbrae show a change in the dominant period of their oscillations from five minutes in the photosphere to three minutes in the chromosphere. In this paper, we explore the two most popular models proposed to explain the three-minute oscillations: the chromospheric acoustic resonator and the propagation of waves with frequency above the cutoff value directly from lower layers. We employ numerical simulations of wave propagation from the solar interior to the corona. Waves are driven by a piston at the bottom boundary. We have performed a parametric study of the measured chromospheric power spectra in a large number of numerical simulations with differences in the driving method, the height of the transition region (or absence of transition region), the strength of the vertical magnetic field, and the value of the radiative cooling time. We find that both mechanisms require the presence of waves with period in the three-minute band at the photosphere. These waves propagate upward and their amplitude increases due to the drop of the density. Their amplification is stronger than that of evanescent low-frequency waves. This effect is enough to explain the dominant period observed in chromospheric spectral lines. However, waves are partially trapped between the photosphere and the transition region, forming an acoustic resonator. This chromospheric resonant cavity strongly enhances the power in the three-minute band. The chromospheric acoustic resonator model and the propagation of waves in the three-minute band directly from the photosphere can explain the observed chromospheric three-minute oscillations. They are both important in different scenarios. Resonances are produced by waves trapped between the temperature minimum and the transition region. Strong magnetic fields and radiative losses remove energy from the waves inside the cavity, resulting in weaker amplitude resonances., Accepted for publication in A&A

Chromospheric umbral oscillations produce periodic brightenings in the core of some spectral lines, known as umbral flashes. They are also accompanied by fluctuations in velocity, temperature, and, according to several recent works, magnetic field. In this study, we aim to ascertain the accuracy of the magnetic field determined from inversions of the Ca II 8542 \AA\ line. We have developed numerical simulations of wave propagation in a sunspot umbra. Synthetic Stokes profiles emerging from the simulated atmosphere were computed and then inverted using the NICOLE code. The atmospheres inferred from the inversions have been compared with the original parameters from the simulations. Our results show that the inferred chromospheric fluctuations in velocity and temperature match the known oscillations from the numerical simulation. In contrast, the vertical magnetic field obtained from the inversions exhibits an oscillatory pattern with a $\sim$300 G peak-to-peak amplitude which is absent in the simulation. We have assessed the error in the inferred parameters by performing numerous inversions with slightly different configurations of the same Stokes profiles. We find that when the atmosphere is approximately at rest, the inversion tends to favor solutions that underestimate the vertical magnetic field strength. On the contrary, during umbral flashes, the values inferred from most of the inversions are concentrated at stronger fields than those from the simulation. Our analysis provides a quantification of the errors associated with the inversions of the Ca II 8542 \AA\ line and suggests caution with the interpretation of the inferred magnetic field fluctuations., Comment: Accepted for publication in The Astrophysical Journal

Umbral flashes are sudden brightenings commonly visible in the core of chromospheric lines. Theoretical and numerical modeling suggest that they are produced by the propagation of shock waves. According to these models and early observations, umbral flashes are associated with upflows. However, recent studies have reported umbral flashes in downflowing atmospheres. We aim to understand the origin of downflowing umbral flashes. We explore how the existence of standing waves in the umbral chromosphere impacts the generation of flashed profiles. We performed numerical simulations of wave propagation in a sunspot umbra with the code MANCHA. The Stokes profiles of the Ca II 8542 \AA\ line were synthesized with NICOLE. For freely-propagating waves, the chromospheric temperature enhancements of the oscillations are in phase with velocity upflows. In this case, the intensity core of the Ca II 8542 \AA\ atmosphere is heated during the upflowing stage of the oscillation. If we consider a different scenario with a resonant cavity, the wave reflections at the sharp temperature gradient of the transition region lead to standing oscillations. In this situation, temperature fluctuations are shifted backward and temperature enhancements partially coincide with the downflowing stage of the oscillation. In umbral flashes produced by standing oscillations, the reversal of the emission feature is produced when the oscillation is downflowing. The chromospheric temperature keeps increasing while the atmosphere is changing from a downflow to an upflow. During the appearance of flashed Ca II 8542 \AA\ cores, the atmosphere is upflowing most of the time, and only 38\% of the flashed profiles are associated with downflows. We find a scenario that remarkably explains the recent empirical findings of downflowing umbral flashes as a natural consequence of the presence of standing oscillations above sunspot umbrae., Comment: Letter accepted for publication in A&A

Oscillations in sunspot umbrae exhibit remarkable differences between the photosphere and chromosphere. We evaluate two competing scenarios proposed for explaining those observations: a chromospheric resonant cavity and waves traveling from the photosphere to upper atmospheric layers. We have employed numerical simulations to analyze the oscillations in both models. They have been compared with observations in the low (Na I D2) and high (He I 10830 \AA) chromosphere. The nodes of the resonant cavity can be detected as phase jumps or power dips, although the identification of the latter is not sufficient to claim the existence of resonances. In contrast, phase differences between velocity and temperature fluctuations reveal standing waves and unequivocally prove the presence of an acoustic resonator above umbrae. Our findings offer a new seismic method to probe active region chromospheres through the detection of resonant nodes., Comment: Accepted for publication in The Astrophysical Journal Letters

In the solar atmosphere, the acoustic cutoff frequency is a local quantity which depends on the atmospheric height. It separates the low-frequency evanescent waves from the high-frequency propagating waves. We measure the cutoff frequency of slow magnetoacoustic waves at various heights of a sunspot umbra and compare the results with the estimations from several analytical formulae. We analyzed the oscillations in the umbra of a sunspot belonging to active region NOAA 12662 observed in the 10830 \AA\ spectral region with the GREGOR Infrared Spectrograph and in the Fe I 5435 \AA\ line with the GREGOR Fabry-P\'erot Interferometer. Both instrumets are attached to the GREGOR telescope at the Observatorio del Teide, Tenerife, Spain. We have computed the phase and amplification spectra between the velocity measured from different pairs of lines that sample various heights of the solar atmosphere. The cutoff frequency and its height variation have been estimated from the inspection of the spectra. At the deep umbral photosphere the cutoff frequency is around 5 mHz and it increases to 6 mHz at higher photospheric layers. At the chromosphere the cutoff is $\sim 3.1$ mHz. The comparison of the observationally determined cutoff with the theoretically predicted values reveals an agreement in the general trend and a reasonable match at the chromosphere, but also significant quantitative differences at the photosphere. Our analyses show strong evidence of the variation of the cutoff frequency with height in a sunspot umbra, which is not fully accounted for by current analytical estimations. This result has implications for our understanding of wave propagation, the seismology of active regions, and the evaluation of heating mechanisms based on compressible waves., Comment: Accepted for publication in A&A

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., Accepted for publication in A&A

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 towards inversions for sunspot structure., Comment: Accepted for publication in The Astrophysical Journal

Solar active regions show a wide variety of oscillatory phenomena. The presence of the magnetic field leads to the appearance of several wave modes, whose behavior is determined by the sunspot thermal and magnetic structure. We aim to study the relation between the umbral and penumbral waves observed at the high photosphere and the magnetic field topology of the sunspot. Observations of the sunspot in active region NOAA 12662 obtained with the GREGOR telescope (Observatorio del Teide, Spain) were acquired on 2017 June 17. The data set includes a temporal series in the Fe I 5435 \AA\ line obtained with the imaging spectrograph GREGOR Fabry-P\'erot Interferometer (GFPI) and a spectropolarimetric raster map acquired with the GREGOR Infrared Spectrograph (GRIS) in the 10830 \AA\ spectral region. The Doppler velocity deduced from the restored Fe I 5435 \AA\ line has been determined, and the magnetic field vector of the sunspot has been inferred from spectropolarimetric inversions of the Ca I 10839 \AA\ and the Si I 10827 \AA\ lines. A two-armed spiral wavefront has been identified in the evolution of the two-dimensional velocity maps from the Fe I 5435 \AA\ line. The wavefronts initially move counterclockwise in the interior of the umbra, and develop into radially outward propagating running penumbral waves when they reach the umbra-penumbra boundary. The horizontal propagation of the wavefronts approximately follows the direction of the magnetic field, which shows changes in the magnetic twist with height and horizontal position. The spiral wavefronts are interpreted as the visual pattern of slow magnetoacoustic waves which propagate upward along magnetic field lines. Their apparent horizontal propagation is due to their sequential arrival to different horizontal positions at the formation height of the Fe I 5435 \AA\ line, as given by the inclination and orientation of the magnetic field., Comment: Accepted for publication in A&A

Context. Determining empirical atmospheric models for the solar chromosphere is difficult since it requires the observation and analysis of spectral lines that are affected by non-local thermodynamic equilibrium (NLTE) effects. This task is especially difficult in sunspot umbrae because of lower continuum intensity values in these regions with respect to the surrounding brighter granulation. Umbral data is therefore more strongly affected by the noise and by the so-called scattered light, among other effects. Aims. The purpose of this study is to analyze spectropolarimetric sunspot umbra observations taken in the near-infrared Si I 1082.7 nm line taking NLTE effects into account. Interestingly, we detected emission features at the line core of the Si I 1082.7 nm line in the sunspot umbra. Here we analyze the data in detail and offer a possible explanation for the Si I 1082.7 nm line emission. Methods. Full Stokes measurements of a sunspot near disk center in the near-infrared spectral range were obtained with the GRIS instrument installed at the German GREGOR telescope. A point spread function (PSF) including the effects of the telescope, the Earth's atmospheric seeing, and the scattered light was constructed using prior Mercury observations with GRIS and the information provided by the adaptive optics system of the GREGOR telescope during the observations. The data were then deconvolved from the PSF using a principal component analysis deconvolution method and were analyzed via the NICOLE inversion code, which accounts for NLTE effects in the Si I 1082.7 nm line. The information of the vector magnetic field was included in the inversion process. Results. The Si I 1082.7 nm line seems to be in emission in the umbra of the observed sunspot after the effects of scattered light (stray light coming from wide angles) are removed. We show how the spectral line shape of umbral profiles changes dramatically with the amount of scattered light. Indeed, the continuum levels range, on average, from 44% of the quiet Sun continuum intensity to about 20%. Although very low, the inferred levels are in line with current model predictions and empirical umbral models. The Si I 1082.7 nm line is in emission after adding more that 30% of scattered light so that it is very sensitive to a proper determination of the PSF. Additionally, we have thoroughly investigated whether the emission is a byproduct of the particular deconvolution technique but have not found any evidence to the contrary. Only the circular polarization signals seem to be more sensitive to the deconvolution strategy because of the larger amount of noise in the umbra. Interestingly, current umbral empirical models are not able to reproduce the emission in the deconvolved umbral Stokes profiles. The results of the NLTE inversions suggests that to obtain the emission in the Si I 1082.7 nm line, the temperature stratification should first have a hump located at about log τ = -2 and start rising at lower heights when moving into the transition region. Conclusions. This is, to our knowledge, the first time the Si I 1082.7 nm line is seen in emission in sunspot umbrae. The results show that the temperature stratification of current umbral models may be more complex than expected with the transition region located at lower heights above sunspot umbrae. Our finding might provide insights into understanding why the sunspot umbra emission in the millimeter spectral range is less than that predicted by current empirical umbral models.© 2017 ESO., This work was partly supported by the BK21 plus program through the National Research Foundation (NRF) funded by the Ministry of Education of Korea. This study is supported by the European Commissions FP7 Capacities Programme under the Grant Agreement number 312495. The GRIS instrument was developed thanks to the support by the Spanish Ministry of Economy and Competitiveness through the project AYA2010-18029 (Solar Magnetism and Astrophysical Spectropolarimetry) and AYA2014-60476-P. This work has also been supported by Spanish Ministry of Economy and Competitiveness through projects ESP2014-56169-C6-1-R and ESP-2016-77548-C5-1-R.

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 $p-$modes excited around 5 Mm beneath the sunspot. Using numerical simulations, we have performed a parametric study of the waves observed at the photosphere and higher layers produced by sources located at different depths. The observational measurements are consistent with waves driven between approximately 1 Mm and 5 Mm below the sunspot surface., Accepted for publication in A&A

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.

The use of instruments that record narrow band images at selected wavelengths is a common approach in solar observations. They allow the scanning of a spectral line by sampling the Stokes profiles with 2D images at each line position, but require a compromise between spectral resolution and temporal cadence. We evaluate the impact of the time-dependent acquisition of different wavelengths on the inversion of spectropolarimetric profiles from chromospheric lines during umbral flashes. Simulations of non-linear wave propagation in a sunspot were performed with the code MANCHA. Synthetic Stokes parameters in the Ca II 8542 A line in NLTE were computed for an umbral flash using the code NICOLE. Artificial profiles with the same wavelength coverage and temporal cadence from reported observations were constructed and inverted. The inferred atmospheric stratifications were compared with the original models. The inferred atmospheres provide a reasonable characterization of the thermodynamic properties of the atmosphere during most of the phases of the umbral flash. Only at the early stages of the flash, when the shock wave reaches the formation height of the line, the Stokes profiles present apparent wavelength shifts and other spurious deformations. These features are misinterpreted by the inversion code, which can return unrealistic atmospheric models from a good fit of the Stokes profiles. The misguided results include flashed atmospheres with strong downflows, even though the simulation exhibits upflows during the umbral flash, and large variations in the magnetic field strength. Our analyses validate the inversion of Stokes profiles acquired by sequentially scanning certain selected wavelengths of a line profile, even in the case of rapidly-changing events such as umbral flashes. However, the inversions are unreliable during a short period at the development phase of the flash., Accepted for publication in A&A

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., Comment: Accepted for publication in MNRAS

Spectropolarimetric temporal series from Fe I $\lambda$ 6301.5 \AA\ and Ca II infrared triplet lines are obtained by applying the Stokes synthesis code NICOLE to a numerical simulation of wave propagation in a sunspot umbra from MANCHA code. The analysis of the phase difference between Doppler velocity and intensity core oscillations of the Fe I $\lambda$ 6301.5 \AA\ line reveals that variations in the intensity are produced by opacity fluctuations rather than intrinsic temperature oscillations, except for frequencies between 5 and 6.5 mHz. On the other hand, the photospheric magnetic field retrieved from the weak field approximation provides the intrinsic magnetic field oscillations associated to wave propagation. Our results suggest that this is due to the low magnetic field gradient of our sunspot model. The Stokes parameters of the chromospheric Ca II infrared triplet lines show striking variations as shock waves travel through the formation height of the lines, including emission self-reversals in the line core and highly abnormal Stokes V profiles. Magnetic field oscillations inferred from the Ca II infrared lines using the weak field approximation appear to be related with the magnetic field strength variation between the photosphere and the chromosphere., Comment: Accepted for publication in The Astrophysical Journal

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 an 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., Accepted for publication in The Astrophysical Journal

We use numerial 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 with 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., Accepted for publication in The Astrophysical Journal

Atmosphere above sunspots is abundant with different types of waves. Among these waves are running penumbral waves in the chromosphere, quasi-periodic oscillations in the lower coronal loops, and recently reported running waves in sunspots' photosphere, all of which were interpreted as magnetoacoustic waves by some authors. Are these waves in different atmospheric layers related to each other, what is the nature of these waves, and where are the ultimate sources of these waves? Applying a time–distance helioseismic analysis over a suite of multi-wavelength observations above a sunspot, we demonstrate that the helioseismic p-mode waves are able to channel up from the photosphere through the chromosphere and transition region into the corona, and that the magnetoacoustic waves observed in different atmospheric layers are a same wave originating from the photosphere but exhibiting differently under different physical conditions. We also show waves of different frequencies travel along different paths, which can be used to derive the physical properties of the atmosphere above sunspots. Our numerical simulation of traveling of waves from a subphotospheric source qualitatively resembles the observed properties of the waves and offers an interpretation of the shapes of the wavefronts above the photosphere.

The conversion of fast waves to the Alfven mode in a realistic sunspot atmosphere is studied through three-dimensional numerical simulations. An upward propagating fast acoustic wave is excited in the high-beta region of the model. The new wave modes generated at the conversion layer are analyzed from the projections of the velocity and magnetic field in their characteristic directions, and the computation of their wave energy and fluxes. The analysis reveals that the maximum efficiency of the conversion to the slow mode is obtained for inclinations of 25 degrees and low azimuths, while the Alfven wave conversions peaks at high inclinations and azimuths between 50 and 120 degrees. Downward propagating Alfven waves appear at the regions of the sunspot where the orientation of the magnetic field is in the direction opposite to the wave propagation, since at these locations the Alfven wave couples better with the downgoing fast magnetic wave which are reflected due to the gradients of the Alfven speed. The simulations shows that the Alfven energy at the chromosphere is comparable to the acoustic energy of the slow mode, being even higher at high inclined magnetic fields., Accepted for publication in The Astrophysical Journal

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 which 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 emsemble 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., Comment: Accepted for publication in The Astrophysical Journal

We aim at reproducing the height dependence of sunspot wave signatures obtained from spectropolarimetric observations through 3D MHD numerical simulations. A magneto-static sunspot model based on the properties of the observed sunspot is constructed and perturbed at the photosphere introducing the fluctuations measured with the \SiI\ $\lambda$ 10827 \AA\ line. The results of the simulations are compared with the oscillations observed simultaneously at different heights from the \HeI\ $\lambda$ 10830 \AA\ line, the \CaIIH\ core and the \FeI\ blends in the wings of the \CaIIH\ line. The simulations show a remarkable agreement with the observations. They reproduce the velocity maps and power spectra at the formation heights of the observed lines, as well as the phase and amplification spectra between several pair of lines. We find that the stronger shocks at the chromosphere are accompanied with a delay between the observed signal and the simulated one at the corresponding height, indicating that shocks shift the formation height of the chromospheric lines to higher layers. Since the simulated wave propagation matches very well the properties of the observed one, we are able to use the numerical calculations to quantify the energy contribution of the magneto-acoustic waves to the chromospheric heating in sunspots. Our findings indicate that the energy supplied by these waves is too low to balance the chromospheric radiative losses. The energy contained at the formation height of the lowermost \SiI\ $\lambda$ 10827 \AA\ line in the form of slow magneto-acoustic waves is already insufficient to heat the higher layers, and the acoustic energy which reaches the chromosphere is around 3-9 times lower than the required amount of energy. The contribution of the magnetic energy is even lower., Comment: Accepted for publication in The Astrophysical Journal

We study the propagation of waves from the photosphere to the chromosphere of sunspots. From time series of cospatial Ca II H (including its line blends) intensity spectra and polarimetric spectra of Si I 1082.7 nm and He I 1083.0 nm we retrieve the line-of-sight velocity at several heights. The analysis of the phase difference and amplification spectra shows standing waves for frequencies below 4 mHz and propagating waves for higher frequencies, and allows us to infer the temperature and height where the lines are formed. Using these observational data, we have constructed a model of sunspot, and we have introduced the velocity measured with the photospheric Si I 1082.7 nm line as a driver. The numerically propagated wave pattern fits reasonably well with the observed using the lines formed at higher layers, and the simulations reproduce many of the observed features. The observed waves are slow MHD waves propagating longitudinally along field lines., proceedings of GONG 2010/SOHO 24 meeting, June 27 - July 2, 2010, Aix-en-Provence, France

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 Newton's 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., Comment: Accepted by The Astrophysical Journal

We present results of non-linear, 2D, numerical simulations of magneto-acoustic wave propagation in the photosphere and chromosphere of small-scale flux tubes with internal structure. Waves with realistic periods of three to five minutes are studied, after applying horizontal and vertical oscillatory perturbations to the equilibrium model. Spurious reflections of shock waves from the upper boundary are minimized thanks to a special boundary condition. This has allowed us to increase the duration of the simulations and to make it long enough to perform a statistical analysis of oscillations. The simulations show that deep horizontal motions of the flux tube generate a slow (magnetic) mode and a surface mode. These modes are efficiently transformed into a slow (acoustic) mode in the vA < cS atmosphere. The slow (acoustic) mode propagates vertically along the field lines, forms shocks and remains always within the flux tube. It might deposit effectively the energy of the driver into the chromosphere. When the driver oscillates with a high frequency, above the cut-off, non-linear wave propagation occurs with the same dominant driver period at all heights. At low frequencies, below the cut-off, the dominant period of oscillations changes with height from that of the driver in the photosphere to its first harmonic (half period) in the chromosphere. Depending on the period and on the type of the driver, different shock patterns are observed., 22 pages 6 color figures, submitted to Solar Physics, proceeding of SOHO 19/ GONG 2007 meeting, Melbourne, Australia

We investigate the properties of a sunspot light-bridge, focusing on the changes produced by the impact of a plasma blob ejected from a C-class flare. We observed a sunspot in active region NOAA 12544 using spectropolarimetric raster maps of the four Fe I lines around 15655 \AA\ with the GREGOR Infrared Spectrograph (GRIS), narrow-band intensity images sampling the Fe I 6173 \AA\ line with the GREGOR Fabry-P\'erot Interferometer (GFPI), and intensity broad band images in G-band and Ca II H band with the High-resolution Fast Imager (HiFI). All these instruments are located at the GREGOR telescope at the Observatorio del Teide, Tenerife, Spain. The data cover the time before, during, and after the flare event. The analysis is complemented with Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) data from the Solar Dynamics Observatory (SDO). The physical parameters of the atmosphere at differents heights were inferred using spectral-line inversion techniques. We identify photospheric and chromospheric brightenings, heating events, and changes in the Stokes profiles associated to the flare eruption and the subsequent arrival of the plasma blob to the light bridge, after traveling along an active region loop. The measurements suggest that these phenomena are the result of reconnection events driven by the interaction of the plasma blob with the magnetic field topology of the light bridge., Comment: Accepted for publication in A&A