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Acoustic wave propagation in the solar sub-photosphere with localised magnetic field concentration: effect of magnetic tension  

Sergiy Shelyag   Submitted: 2009-01-23 06:50

Aims. In this paper we analyse numerically the propagation and dispersion of acoustic waves in the solar-like sub-photosphere with localised non-uniform magnetic field concentrations, mimicking sunspots with various representative magnetic field configurations. Methods. Numerical simulations of wave propagation through the solar sub-photosphere with a localised magnetic field concentration are carried out using SAC, which solves the MHD equations for gravitationally stratified plasma. The initial equilibrium density and pressure stratifications are derived from a standard solar model. Acoustic waves are generated by a source located at the height approximately corresponding to the visible surface of the Sun. We analyse the response of vertical velocity to changes in the interior due to magnetic field at the level corresponding to the visible solar surface, by the means of local time-distance helioseismology. Results. The results of numerical simulations of acoustic wave propagation and dispersion in the solar sub-photosphere with localised magnetic field concentrations of various types are presented. Time-distance diagrams of the vertical velocity perturbation at the level corresponding to the visible solar surface show that the magnetic field perturbs and scatters acoustic waves and absorbs the acoustic power of the wave packet. For the weakly magnetised case the effect of magnetic field is mainly thermodynamic, since the magnetic field changes the temperature stratification. However, we observe the signature of slow magnetoacoustic mode, propagating downwards, for the strong magnetic field cases.

Authors: S. Shelyag, S. Zharkov, V. Fedun, R. Erdelyi, M.J. Thompson
Projects: None

Publication Status: submitted
Last Modified: 2009-01-23 09:36
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Subject will be restored when possible  

Sergiy Shelyag   Submitted: 2008-05-12 05:49

In this paper we describe a newly developed magnetohydrodynamic (MHD) code with the capacity to simulate the interaction of any arbitrary perturbation (i.e. not necessarily limited to the linearised limit) with a magnetohydrostatic equilibrium background. By rearranging the terms in the system of MHD equations and explicitly taking into account the magnetohydrostatic equilibrium condition, the equations governing the perturbations that describe the deviations from the background state of plasma for the density, internal energy and magnetic field are defined. It was found to be advantageous to use this modified form of the MHD equations for numerical simulations of physical processes taking place in a stable gravitationally stratified plasma. The governing equations are implemented in a novel way in the code. Sub-grid diffusion and resistivity are applied in order to ensure numerical stability of the computed solution of the MHD equations. A fourth-order central difference scheme is applied to calculate the spatial derivatives, and an arbitrary Runge-Kutta scheme is implemented to advance the solution in time. We have built in the proposed method, suitable for strongly stratified magnetised plasma, in the well-documented VAC MHD code and performed a number of one- and multi-dimensional hydrodynamic and MHD tests in order to demonstrate the feasibility and robustness of the code for applications to astrophysical plasmas.

Authors: S. Shelyag, V. Fedun, R. Erdélyi
Projects: None

Publication Status: Accepted
Last Modified: 2008-05-12 07:01
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Subject will be restored when possible  

Sergiy Shelyag   Submitted: 2008-05-12 05:49

In this paper we describe a newly developed magnetohydrodynamic (MHD) code with the capacity to simulate the interaction of any arbitrary perturbation (i.e. not necessarily limited to the linearised limit) with a magnetohydrostatic equilibrium background. By rearranging the terms in the system of MHD equations and explicitly taking into account the magnetohydrostatic equilibrium condition, the equations governing the perturbations that describe the deviations from the background state of plasma for the density, internal energy and magnetic field are defined. It was found to be advantageous to use this modified form of the MHD equations for numerical simulations of physical processes taking place in a stable gravitationally stratified plasma. The governing equations are implemented in a novel way in the code. Sub-grid diffusion and resistivity are applied in order to ensure numerical stability of the computed solution of the MHD equations. A fourth-order central difference scheme is applied to calculate the spatial derivatives, and an arbitrary Runge-Kutta scheme is implemented to advance the solution in time. We have built in the proposed method, suitable for strongly stratified magnetised plasma, in the well-documented VAC MHD code and performed a number of one- and multi-dimensional hydrodynamic and MHD tests in order to demonstrate the feasibility and robustness of the code for applications to astrophysical plasmas.

Authors: S. Shelyag, V. Fedun, R. Erdélyi
Projects:

Publication Status: Accepted
Last Modified: 2008-09-23 21:01
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Stokes diagnostics of simulated solar magneto-convection  

Sergiy Shelyag   Submitted: 2007-03-21 07:12

We present results of synthetic spectro-polarimetric diagnostics of radiative MHD simulations of solar surface convection with magnetic fields. Stokes profiles of Zeeman-sensitive lines of neutral iron in the visible and infrared spectral ranges emerging from the simulated atmosphere have been calculated in order to study their relation to the relevant physical quantities and compare with observational results. We have analyzed the dependence of the Stokes-I line strength and width as well as of the Stokes-V signal and asymmetries on the magnetic field strength. Furthermore, we have evaluated the correspondence between the actual velocities in the simulation with values determined from the Stokes-I (Doppler shift of the centre of gravity) and Stokes-V profiles (zero-crossing shift). We confirm that the line weakening in strong magnetic fields results from a higher temperature (at equal optical depth) in the magnetic flux concentrations. We also confirm that considerable Stokes-V asymmetries originate in the peripheral parts of strong magnetic flux concentrations, where the line of sight cuts through the magnetopause of the expanding flux concentration into the surrounding convective donwflow.

Authors: S. Shelyag, M. Schuessler, S.K. Solanki, A. Voegler
Projects: None

Publication Status: accepted to A&A
Last Modified: 2007-03-21 10:48
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Forward modelling of sub-photospheric flows for time-distance helioseismology  

Sergiy Shelyag   Submitted: 2007-03-06 04:39

Results of forward modelling of acoustic wave propagation in a realistic solar sub-photosphere with two cases of steady horizontal flows are presented and analysed by the means of local helioseismology. The simulations are based on fully compressible ideal hydrodynamical modelling in a Cartesian grid. The initial model is characterised by solar density and pressure stratifications taken from the standard Model S and is adjusted in order to suppress convective instability. Acoustic waves are excited by a non-harmonic source located below the depth corresponding to the visible surface of the Sun. Numerical experiments with coherent horizontal flows of linear and Gaussian dependences of flow speed on depth are carried out. These flow fields may mimic horizontal motions of plasma surrounding a sunspot, differential rotation or meridional circulation. An inversion of the velocity profiles from the simulated travel time differences is carried out. The inversion is based on the ray approximation. The results of inversion are then compared with the original velocity profiles. The influence of steady flow on the propagation of sound waves through the solar interior is analysed. Further, we propose a method of obtaining the travel-time differences for the waves propagating in sub-photospheric solar regions with horizontal flows. The method employs directly the difference between travel-time diagrams of waves propagating with and against the background flow. The analysis shows that the flow speed profiles obtained from inversion based on the ray approximation differ from the original ones. The difference between them is caused by the fact that the wave packets propagate along the ray bundle, which has a finite extent, and thus reach deeper regions of the sub-photosphere in comparison with ray theory.

Authors: S. Shelyag, R. Erdelyi, M. J. Thompson
Projects: None

Publication Status: A&A (submitted)
Last Modified: 2007-03-06 13:53
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Forward Modeling of Acoustic Wave Propagation in the Quiet Solar Subphotosphere  

Sergiy Shelyag   Submitted: 2007-03-05 08:33

The results of numerical simulations of acoustic wave propagation and dispersion in the nonmagnetic solar subphotosphere are presented. Initial equilibrium density and pressure stratifications are taken from a standard solar model but modified to suppress convective instabilities in fully compressible two-dimensional ideal hydrodynamical modeling. Acoustic waves are generated by sources located below the height corresponding to the visible solar surface. The dynamic response of the solar interior to two acoustic source types, namely a harmonic source and one representing downward-propagating photospheric plumes, is studied. A large number of randomly distributed localized cooling sources with random amplitudes is also introduced. The methods used to analyze the simulation data are similar to ones used in observational studies in local helioseismology. Time-distance diagrams of the pressure and vertical velocity perturbations at the level corresponding to the solar surface show the appearance of wave packets propagating with different speeds, which are reflected at different depths beneath the subphotosphere. The (ω, kh) power spectra, derived from the vertical velocity data, show the existence of g-, f-, and p-modes; p-mode ridges are identifiable up to high radial orders of n~11; g-modes appear in the simulations, unlike in the real Sun, where they cannot propagate in the convectively unstable solar subphotosphere. Cross-correlation analysis of vertical velocity perturbations shows a good correspondence with the observed time-distance helioseismic data for quiet Sun. Thus, the ability of the implemented approach of forward modeling to investigate propagation of acoustic, internal, and surface gravity waves in a realistic solar interior model is shown.

Authors: S. Shelyag , R. Erdelyi , and M. J. Thompson
Projects: None

Publication Status: ApJ, published
Last Modified: 2007-03-06 14:00
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Abstracts by Author
Acoustic wave propagation in the solar sub-photosphere with localised magnetic field concentration: effect of magnetic tension
Subject will be restored when possible
Subject will be restored when possible
Stokes diagnostics of simulated solar magneto-convection
Forward modelling of sub-photospheric flows for time-distance helioseismology
Forward Modeling of Acoustic Wave Propagation in the Quiet Solar Subphotosphere

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