Effect of suppressed excitation on the amplitude distribution of 5-min oscillations in sunspots

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 the sunspot regions in comparison to the quiet Sun, just because of the suppressed sources. Using SOHO/MDI data we measured the amplitude ratio for the same frequency bands outside and inside sunspots, and found that this ratio is approximately 3-4. Hence, the absence of excitation sources inside sunspots makes a significant contribution (about 50% or higher) to the observed amplitude ratio and must be taken into account in sunspot seismology.Comment: 12 pages, 5 figures, accepted to ApJ

Theoretical modeling of propagation of magneto-acoustic waves in magnetic regions below sunspots

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.Comment: accepted by Ap

Influence of Non-Uniform Distribution of Acoustic Wavefield Strength on Time-Distance Helioseismology Measurements

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-speed effect. This effect may cause some underestimation of the negative sound-speed perturbations in sunspots just below the surface, that was found in previous time-distance helioseismology inferences. This effect cannot be corrected by artificially increasing the amplitude of oscillations in sunspots. For large time-distance annuli, the non-uniform distribution of wavefields does not have significant effects on the mean travel times, and thus the sound-speed inversion results. The measured travel time differences, which are used to determine the mass flows beneath sunspots, can also be systematically shifted by this effect, but only in an insignificant magnitude.Comment: 16 pages, 6 figures, accepted for publication in Ap

Numerical simulation of excitation and propagation of helioseismic MHD waves: Effects of inclined magnetic field

Investigation of propagation, conversion, and scattering of MHD waves in the Sun is very important for understanding the mechanisms of observed oscillations and waves in sunspots and active regions. We have developed 3D linear MHD numerical model to investigate influence of the magnetic field on excitation and properties of the MHD waves. The results show that the magnetic field can substantially change the properties of the surface gravity waves (f-mode), but their influence on the acoustic-type waves (p-modes) is rather moderate. Comparison our simulations with the time-distance helioseismology results from SOHO/MDI shows that the travel time variations caused by the inclined magnetic field do not exceed 25% of the observed amplitude even for strong fields of 1400-1900 G. This can be an indication that other effects (e.g. background flows and non-uniform distribution of magnetic field) can contribute to the observed travel time variations. The travel time variations caused by the wave interaction with magnetic field are in phase with the observations for strong fields of 1400-1900 G if Doppler velocities are taken at the height of 300 km above the photosphere where plasma parameter beta<<1. The simulations show that the travel times only weakly depend on the height of velocity observation. For the photospheric level the travel times are systematically smaller on approximately 0.12 min then for the hight of 300 km above the photosphere for all studied ranges of the magnetic field strength and inclination angles. The numerical MHD wave modeling and new data from the HMI instrument of the Solar Dynamics Observatory will substantially advance our knowledge of the wave interaction with strong magnetic fields on the Sun and improve the local helioseismology diagnostics.Comment: 24 pages, 10 figures, submitted to Ap

Travel Time Shifts due to Amplitude Modulation in Time-Distance Helioseismology

Correct interpretation of acoustic travel times measured by time-distance helioseismology is essential to get an accurate understanding of the solar properties that are inferred from them. It has long been observed that sunspots suppress p-mode amplitude, but its implications on travel times has not been fully investigated so far. It has been found in test measurements using a 'masking' procedure, in which the solar Doppler signal in a localized quiet region of the Sun is artificially suppressed by a spatial function, and using numerical simulations that the amplitude modulations in combination with the phase-speed filtering may cause systematic shifts of acoustic travel times. To understand the properties of this procedure, we derive an analytical expression for the cross-covariance of a signal that has been modulated locally by a spatial function that has azimuthal symmetry, and then filtered by a phase speed filter typically used in time-distance helioseismology. Comparing this expression to the Gabor wavelet fitting formula without this effect, we find that there is a shift in the travel times, that is introduced by the amplitude modulation. The analytical model presented in this paper can be useful also for interpretation of travel time measurements for non-uniform distribution of oscillation amplitude due to observational effects.Comment: 17 pages, 1 figure, accepted for publication in Ap

Excitation of acoustic waves by vortices in the quiet Sun

Five-minutes oscillations is one of the basic properties of solar convection. Observations show mixture of a large number of acoustic wave fronts propagating from their sources. We investigate the process of acoustic waves excitation from the point of view of individual events, by using realistic 3D radiative hydrodynamic simulation of the quiet Sun. The results show that the excitation events are related to dynamics vortex tubes (or swirls) in the intergranular lanes. These whirlpool-like flows are characterized by very strong horizontal velocities (7 - 11 km/s) and downflows (~ 7 km/s), and are accompanied by strong decreases of the temperature, density and pressure at the surface and in a ~ 0.5-1 Mm deep layer below the surface. High-speed whirlpool flows can attract and capture other vortices. According to our simulation results, the processes of the vortex interaction, such as vortex annihilation, can cause the excitation of acoustic waves.Comment: 10 pages, 5 figure, submitted to ApJ

Magneto-acoustic waves in sunspots: first results from a new 3D 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 non-linear 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 non-linear 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 subphotospheric level, from short periods, introduced for academic purposes, to longer and realistic periods of three and five minutes. We present a detailed description of the three-dimensional mode transformation in a non-trivial sunspot-like magnetic field configuration, including the conversion between fast and slow magneto-acoustic waves and the Alfv\'en wave, by calculation of the wave energy fluxes. Our main findings are the following: (1) the conversion from acoustic to the Alfv\'en mode is only observed if the the driving pulse is located out of the sunspot axis, but this conversion is energetically inefficient; (2) as a consequence of the cut-off 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 beta=1; (3) waves with frequencies above the cut-off propagate field-aligned to the chromosphere and their power becomes dominating over that of evanescent 5-minute oscillations, in agreement with observations