TY - JOUR
T1 - Acoustic wave propagation through solar granulation
T2 - Validity of effective-medium theories, coda waves
AU - Poulier, P. L.
AU - Fournier, D.
AU - Gizon, L.
AU - Duvall, T. L.
N1 - Funding Information:
We thank Aaron C. Birch for useful discussions and comments. PLP is a member of the International Max Planck Research School (IMPRS) for Solar System Science at the University of Göttingen. The computational resources were provided by the German Data Center for SDO through grant 50OL1701 from the German Aerospace Center (DLR).
Publisher Copyright:
© P.-L. Poulier et al. 2020.
PY - 2020/11/1
Y1 - 2020/11/1
N2 - Context. The frequencies, lifetimes, and eigenfunctions of solar acoustic waves are affected by turbulent convection, which is random in space and in time. Since the correlation time of solar granulation and the periods of acoustic waves (∼5 min) are similar, the medium in which the waves propagate cannot a priori be assumed to be time independent. Aims. We compare various effective-medium solutions with numerical solutions in order to identify the approximations that can be used in helioseismology. For the sake of simplicity, the medium is one dimensional. Methods. We consider the Keller approximation, the second-order Born approximation, and spatial homogenization to obtain theoretical values for the effective wave speed and attenuation (averaged over the realizations of the medium). Numerically, we computed the first and second statistical moments of the wave field over many thousands of realizations of the medium (finite-amplitude sound-speed perturbations are limited to a 30 Mm band and have a zero mean). Results. The effective wave speed is reduced for both the theories and the simulations. The attenuation of the coherent wave field and the wave speed are best described by the Keller theory. The numerical simulations reveal the presence of coda waves, trailing the ballistic wave packet. These late arrival waves are due to multiple scattering and are easily seen in the second moment of the wave field. Conclusions. We find that the effective wave speed can be calculated, numerically and theoretically, using a single snapshot of the random medium (frozen medium); however, the attenuation is underestimated in the frozen medium compared to the time-dependent medium. Multiple scattering cannot be ignored when modeling acoustic wave propagation through solar granulation.
AB - Context. The frequencies, lifetimes, and eigenfunctions of solar acoustic waves are affected by turbulent convection, which is random in space and in time. Since the correlation time of solar granulation and the periods of acoustic waves (∼5 min) are similar, the medium in which the waves propagate cannot a priori be assumed to be time independent. Aims. We compare various effective-medium solutions with numerical solutions in order to identify the approximations that can be used in helioseismology. For the sake of simplicity, the medium is one dimensional. Methods. We consider the Keller approximation, the second-order Born approximation, and spatial homogenization to obtain theoretical values for the effective wave speed and attenuation (averaged over the realizations of the medium). Numerically, we computed the first and second statistical moments of the wave field over many thousands of realizations of the medium (finite-amplitude sound-speed perturbations are limited to a 30 Mm band and have a zero mean). Results. The effective wave speed is reduced for both the theories and the simulations. The attenuation of the coherent wave field and the wave speed are best described by the Keller theory. The numerical simulations reveal the presence of coda waves, trailing the ballistic wave packet. These late arrival waves are due to multiple scattering and are easily seen in the second moment of the wave field. Conclusions. We find that the effective wave speed can be calculated, numerically and theoretically, using a single snapshot of the random medium (frozen medium); however, the attenuation is underestimated in the frozen medium compared to the time-dependent medium. Multiple scattering cannot be ignored when modeling acoustic wave propagation through solar granulation.
KW - Scattering
KW - Sun: granulation
KW - Sun: helioseismology
KW - Sun: oscillations
KW - Waves
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U2 - 10.1051/0004-6361/202039201
DO - 10.1051/0004-6361/202039201
M3 - Article
AN - SCOPUS:85096773551
SN - 0004-6361
VL - 643
JO - Astronomy and Astrophysics
JF - Astronomy and Astrophysics
M1 - A168
ER -