The problem of external boundary condition in acoustic mode calculation

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Sun: Oscillations

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As for any other problem in physics, the calculation of solar acoustic modes implies the resolution of differential equations under certain boundary conditions. In the frame of linear adiabatic oscillations, the set of equations is very well known and the Isothermal Atmosphere Approximation (IsAtAp) is generally used for external boundary conditions. The resulting eigenfrequencies obtained by numerical codes are in very good agreement with observational ones in the range 800-2500 μHz. But at larger frequencies, the discrepancies become more and more important to reach tens or hundreds of microHz, respectively for low or high-degree modes. Those disagreements are commonly supposed to come from problems in the near surface layers, but numerous attempts to introduce alternative physics at the surface do not succeed to really explain them. In this work, I first point out the drawbacks of the IsAtAp or any similar type of approximation using a specific atmosphere. Then, I propose to use a new boundary condition based on the relative importance of wavelength vs. pressure-height. This method allows to better characterize the near surface layers while it cancels the disagreement at large frequencies, even for high-degree modes.

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