We use 2D numerical simulations and eikonal approximation, to study properties of MHD waves traveling below the solar surface through the magnetic structure of sunspots. We consider a series of magnetostatic models of sunspots of different magnetic field strengths, from 10 Mm below the photosphere to the low chromosphere. The purpose of these studies is to quantify the effect of the magnetic field on local helioseismology measurements by modeling waves excited by sub-photospheric sources. Time-distance propagation diagrams and wave travel times are calculated for models of various field strength and compared to the non-magnetic case. The results clearly indicate that the observed time-distance helioseismology signals in sunspot regions correspond to fast MHD waves. The slow MHD waves form a distinctly different pattern in the time-distance diagram, which has not been detected in observations. The numerical results are in good agreement with the solution in the short-wavelength (eikonal) approximation, providing its validation. The frequency dependence of the travel times is in a good qualitative agreement with observations.
By analyzing numerically simulated solar oscillation data, we study the influence of non-uniform distribution of acoustic wave amplitude, acoustic source strength, and perturbations of the sound speed on the shifts of acoustic travel times measured by the time-distance helioseismology method. It is found that for short distances, the contribution to the mean travel time shift caused by non-uniform distribution of acoustic sources in sunspots may be comparable to (but smaller than) the contribution from the sound speed perturbation in sunspots, and that it has the opposite sign to the sound-spe…
At the surface of the Sun, acoustic waves appear to be affected by the presence of strong magnetic fields in active regions. We explore the possibility that the inclined magnetic field in sunspot penumbrae may convert primarily vertically propagating acoustic waves into elliptical motion. We use helioseismic holography to measure the modulus and phase of the correlation between incoming acoustic waves and the local surface motion within two sunspots. These correlations are modeled assuming the surface motion is elliptical, and we explore the properties of the elliptical motion on the magnetic …
Five-minute oscillations on the Sun (acoustic and surface gravity waves) are excited by subsurface turbulent convection. However, in sunspots the excitation is suppressed because strong magnetic field inhibits convection. We use 3D simulations to investigate how the suppression of excitation sources affects the distribution of the oscillation power in sunspot regions. The amplitude of random acoustic sources was reduced in circular-shaped regions to simulate the suppression in sunspots. The simulation results show that the amplitude of the oscillations can be approximately 2-4 times lower in t…
Results from a realistic simulation of 3D radiative magneto-convection in a strong background magnetic field corresponding to the conditions in sunspot umbrae are shown. The convective energy transport is dominated by narrow upflow plumes with adjacent downflows, which become almost field-free near the surface layers. The strong external magnetic field forces the plumes to assume a cusp-like shape in their top parts, where the upflowing plasma loses its buoyancy. The resulting bright features in intensity images correspond well (in terms of brightness, size, and lifetime) to the observed umbra…
We report on the spatial distribution of magnetogram oscillatory power and phase angles between velocity and magnetogram signals as observed with the Michelson Doppler Imager. The dataset is 151.25 arcsec times 151.25 arcsec containing sunspot from Dec 2, 1997 with a temporal sampling interval of 60 seconds and spatial sampling of 0.605 arcsec. Simultaneously observed continuum intensity and surface velocity accompany the magnetic information. We focus on three frequency regimes: 0.5-1.0, 3.0-3.5 and 5.5-6.0 mHz corresponding roughly to timescales of magnetic evolution, p-modes and the 3 minut…
In order to understand the influence of magnetic fields on the propagation properties of waves, as derived from different local helioseismology techniques, forward modeling of waves is required. Such calculations need a model in magnetohydrostatic equilibrium as initial atmosphere to propagate oscillations through it. We provide a method to construct such a model in equilibrium for a wide range of parameters to be used for simulations of artificial helioseismologic data. The method combine the advantages of self-similar solutions and current-distributed models. A set of models is developed by …
We present a comparative seismic study of conditions around and beneath isolated sunspots. Using the European Grid of Solar Observations' Solar Feature Catalogue of sunspots derived from SOHO/MDI continuum and magnetogram data, 1996-2005, we identify a set of isolated sunspots by checking that within a Carrington Rotation there were no other spots detected in the vicinity. We then use level-2 tracked MDI Dopplergrams available from SOHO website to investigate wave-speed perturbations of such sunspots using time-distance helioseismology.
The penumbra of a sunspot is a fascinating phenomenon featuring complex velocity and magnetic fields. It challenges both our understanding of radiative magneto-convection and our means to measure and derive the actual geometry of the magnetic and velocity fields. In this contribution we attempt to summarize the present state-of-the-art from an observational and a theoretical perspective.
The structure of the surface layers of the Sun is changed by magnetic activity which, in turn, changes the eigenfrequencies of the acoustic modes. These frequency shifts have been observed both in low- and high-degree data, and are found to be correlated with the solar cycle. Time-distance helioseismology has shown that waves travelling through sunspots suffer time delays. Also it is known that sunspots induce phase shifts between inwardly and outwardly propagating waves. In the present work we show how these phase shifts are related to the observed time delays by treating the scattering of ac…
We employ a 3-dimensional magnetohydrostatic model of a horizontal flux tube, embedded in a magnetic surrounding atmosphere, to successfully reproduce the azimuthal and center-to-limb variations of the Net Circular Polarization observed in sunspot penumbrae. This success is partly due to the realistic modeling of the interaction between the flux tube and the surrounding magnetic field.
We investigate p-mode absorption in a sunspot using SOHO/MDI high-resolution Doppler images. The Doppler power computed from a three and a half hour data set is used for studying the absorption in a sunspot. The result shows an enhancement in absorption near the umbral-penumbral boundary of the sunspot. We attempt to relate the observed absorption with the magnetic field structure of the sunspot. The transverse component of the potential field is computed using the observed SOHO/MDI line-of-sight magnetograms. A comparison of the power map and the computed potential field shows enhanced absorp…
A multi-wavelength photometric analysis was performed in order to study the sub-structure of a sunspot light bridge in the photosphere and the chromosphere. Active region NOAA 8350 was observed on 1998 October 8. The data consist of a 100 min time series of 2D spectral scans of the lines FeI 5576, H-alpha 6563, FeI 6302.5, and continuum images at 5571. We recorded line-of-sight magnetograms in 6302.5. The observations were taken at the Dunn Solar Telescope at U. S. National Solar Observatory, Sacramento Peak. We find evidence for plasma ejection from a light bridge followed by Ellerman bombs. …
Velocity oscillations in sunspot umbrae have been measured simultaneously in two spectral lines: the photospheric Silicon I 10827 A line and the chromospheric Helium I 10830 A multiplet. From the full Stokes inversion of temporal series of spectropolarimetric observations we retrieved, among other parameters, the line of sight velocity temporal variations at photospheric and chromospheric heights. Chromospheric velocity oscillations show a three minute period with a clear sawtooth shape typical of propagating shock wave fronts. Photospheric velocity oscillations have basically a five minute pe…
Based on observations obtained with the Solar and Heliospheric Observatory - SOHO joint observing program for velocity fields in sunspot regions, we have detected 3 min transition region umbral oscillations in NOAA 8156. Simultaneous recordings of O V $λ$629 and N V $λ$1238, $λ$1242 with the SUMER instrument give the spatial distribution of power in the 3 min oscillations, both in intensity and line-of-sight velocity. Comparing loci with the same phase we find that the entire umbral transition region oscillates. The observed maxima in peak line intensity are nearly in phase with the maxima in …
The propagation of solar waves through the sunspot of AR 9787 is observed using temporal cross-correlations of SOHO/MDI Dopplergrams. We then use three-dimensional MHD numerical simulations to compute the propagation of wave packets through self-similar magneto-hydrostatic sunspot models. The simulations are set up in such a way as to allow a comparison with observed cross-covariances (except in the immediate vicinity of the sunspot). We find that the simulation and the f-mode observations are in good agreement when the model sunspot has a peak field strength of 3 kG at the photosphere, less s…
Recent observations of helioseismic holography revealed that magnetic fields inclined to the line-of-sight direction could cause systematic variations in measured acoustic phase shifts, and that the surface magnetic field may shift the phases and impair the coherence of acoustic waves (known as "showerglass effect"). We examine how these affect time-distance helioseismology measurements. It is confirmed that the inclined magnetic field could cause variations in acoustic travel times inside sunspot penumbra, however, inversions of the measured times show that this effect only slightly shifts th…
Sunspot penumbrae show a fine structure in continuum intensity that displays considerable dynamics. The magnetic field, in contrast, although also highly structured, has appeared to be relatively static. Here we report the discovery of inward moving magnetic enhancements in the penumbrae of two regular sunspots based on time series of SOHO/MDI magnetograms. Local enhancements of the LOS component of the magnetic field in the inner part of the penumbral region move inward to the umbra-penumbra boundary with a radial speed of about 0.3 km s$^{-1}$. These local inward-moving enhancements of the L…
The relation between the Evershed flow and moving magnetic features (MMFs) is studied using high-cadence, simultaneous spectropolarimetric measurements of a sunspot in visible (630.2 nm) and near-infrared (1565 nm) lines. Doppler velocities, magnetograms, and total linear polarization maps are calculated from the observed Stokes profiles. We follow the temporal evolution of two Evershed clouds that move radially outward along the same penumbral filament. Eventually, the clouds cross the visible border of the spot and enter the moat region, where they become MMFs. The flux patch farther from th…
It is well known that the observed amplitude of solar oscillations is lower in sunspots than in quiet regions of the Sun. We show that this local reduction in oscillation amplitudes combined with the phase-speed filtering procedure in time-distance helioseismic analyses could be a source of systematic errors in the range of 5 - 40% in the measured travel-time anomalies of acoustic waves around sunspots. Removing these travel time artifacts is important for correctly inferring the subsurface structure of sunspots. We suggest an empirical correction procedure and illustrate its usage for a small…
The acoustic spectra in sunspots are known to be richer in higher frequency power. We have attempted a generalized study of the effect of magnetic fields on the shape of the acoustic spectrum using GONG+ bread-board data (spatial scale of ~ 2 arc-sec per pixel) of 11 May, 2000 and 12 June, 2000. The mean power spectra of the velocity oscillations were obtained by averaging over several spectra for different values of the magnetic field. With increasing magnetic field, the acoustic power increases at higher frequencies and decreases at lower frequencies with a transition at ~= 5 mHz. This behav…
One of the main uncertainties associated with time-distance measurements is how to interpret observations made in regions of strong magnetic field as isolating the effects of the magnetic field from thermal or sound-speed perturbations has proved to be quite complex. One possible way to decouple these effects is by using a 3D sunspot model, with a surrounding stratified, quiet-Sun atmosphere to model the magneto-acoustic ray propagation, and analyze the resulting ray travel-time perturbations that will directly account for the magnetic field. These artificial travel-time perturbation profiles …
Some observations suggest that solar spicules show small amplitude and high frequency oscillations of magneto-acoustic waves, which arise from photospheric granular forcing. We apply the method of MHD seismology to determine the period of kink waves. For this purposes, the oscillations of a magnetic cylinder embedded in a field-free environment is investigated. Finally, diagnostic diagrams displaying the oscillatory period in terms of some equilibrium parameters are provided to allow a comparison between theoretical results and those coming from observations.
We study the evolution of the flows and horizontal proper motions in and around a decaying follower sunspot based on time sequences of two-dimensional spectroscopic observations in the visible and white light imaging data obtained over six days from June~7 to~12, 2005. During this time period the sunspot decayed gradually to a pore. The spectroscopic observations were obtained with the Fabry-Pérot based Visible-Light Imaging Magnetograph (VIM) in conjunction with the high-order adaptive optics (AO) system operated at the 65 cm vacuum reflector of the Big Bear Solar Observatory (BBSO). We apply…
We study the magnetohydrostatic equilibrium of magnetic flux tubes with circular cross sections embedded in a magnetic surrounding atmosphere. We solve the static momentum equation in 2.5D to obtain the thermodynamics that are consistent with a prescribed velocity and magnetic fields. We show that force balance is roughly satisfied if the flux tube's magnetic field is aligned with its axis. Equilibrium is guaranteed if this magnetic field possesses a transverse component. Several forms of this transverse field are investigated. The resulting magnetic field configurations are critically reviewe…
