Theoretical Modeling of Propagation of Magnetoacoustic Waves in Magnetic Regions Below Sunspots

Abstract

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 shortwavelength (eikonal) approximation, providing its validation. The frequency dependence of the travel times is in a good qualitative agreement with observations.

Sunspot seismic halos generated by fast MHD wave refraction

“…The eikonal solution for the fast mode wave (Cally 2006;Moradi & Cally 2008;Khomenko et al 2009) allows us to develop a more complete physical picture of the wave behavior at different frequencies. Figure 2 gives the wave paths of the fast mode waves launched from their lower turning point (that roughly coincides with the location of the source in the simulations).…”

“…The temporal behavior of the source is described by a Ricker wavelet Khomenko et al 2009) with a central frequency of 3.3 mHz. In the second set of experiments the source is placed at X 0 = 30 Mm and Z 0 = −450 km, and it is harmonic and continuous in time with three different frequencies ν = 10, 5 and 3.3 mHz.…”

3D Numerical Simulations of f-Mode Propagation Through Magnetic Flux Tubes

“…The approach is already yielding interesting results in the context of sunspots, see e.g. Cameron, Gizon, and Daiffallah (2007), Hanasoge (2008), Khomenko, Collados, and Fellipe (2008), Cameron, Gizon, and Duvall (2008), Khomenko et al (2009).…”

Inversion of Full Acoustic Wavefield in Local Helioseismology: A Study With Synthetic Data

“…However, variations in solar source density have been shown to influence the amplitude of the helioseismic signals (Cobden et al 2010). Further developments will be needed to apply wavefield tomography to real helioseismic data, including the use of equations that capture the physics of the magnetic field (Khomenko et al 2009). In conclusion, our study highlights the importance of further development in the inversion of helioseismic data as most recent research efforts in local helioseismic methods tend to focus on forward modeling techniques.…”

“…It relies on the measurement of the time taken for a wave packet to travel between two points on the solar surface, estimated from the cross-covariance of the observed seismic time series at the two points. The derived travel times are sensitive to the mass flows (e.g., Zhao et al 2001;Jackiewicz et al 2007), magnetic field (Khomenko et al 2009), and sound-speed structure (e.g., Jensen et al 2001) of the region which the wave traverses, and thus inversion of the travel times can be used to map the subphotospheric variations of these variables.…”