Compressible Fluid Model for the Seismic Waves Generated by A Sunquake |
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| Authors: | J J Podesta |
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| Institution: | (1) Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, U.S.A. |
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| Abstract: | The solar convection zone is modeled as a horizontally stratified atmosphere with a constant gravitational field and an adiabatic
temperature gradient (a neutrally stratified polytrope). At equilibrium, the gas pressure and density decreases to zero at
the solar surface so that the solar surface is treated as a free surface which is bounded by vacuum. The evolution of small
amplitude perturbations about the equilibrium state is described by the linearized Euler equations for an inviscid compressible
fluid with an adiabatic equation of state. A sunquake is initiated at time zero by means of an initial perturbation with a
Gaussian velocity profile and the exact solution of the initial value problem is obtained in terms of a Fourier integral.
Comparisons between theory and observations indicate that this highly simplified model is able to predict the propagation
of sunquake waves across the solar surface with an error of approximately 10% or 20%. |
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