Atmospheric radiation boundary conditions for high frequency waves in time-distance helioseismology

TL;DR

This paper develops and tests radiative boundary conditions for modeling high-frequency waves in the solar atmosphere, improving the accuracy of time-distance helioseismology measurements above the acoustic cut-off frequency.

Contribution

It implements and evaluates radiative boundary conditions for high-frequency wave propagation in the solar atmosphere using finite element methods.

Findings

A boundary condition 500 km above the photosphere accurately reproduces infinite atmosphere solutions.

Applying the boundary 2 Mm above the photosphere shows the influence of atmospheric models on wave diagnostics.

Different atmospheric models can produce distinct features like double-ridge structures in the time-distance diagram.

Abstract

The temporal covariance between seismic waves measured at two locations on the solar surface is the fundamental observable in time-distance helioseismology. Above the acoustic cut-off frequency ($\sim$5.3~mHz), waves are not trapped in the solar interior and the covariance function can be used to probe the upper atmosphere. We wish to implement appropriate radiative boundary conditions for computing the propagation of high-frequency waves in the solar atmosphere. We consider the radiative boundary conditions recently developed by Barucq et al. (2017) for atmospheres in which sound-speed is constant and density decreases exponentially with radius. We compute the cross-covariance function using a finite element method in spherical geometry and in the frequency domain. The ratio between first- and second-skip amplitudes in the time-distance diagram is used as a diagnostic to compare boundary conditions and to compare with observations. We find that a boundary condition applied 500 km above the photosphere and derived under the approximation of small angles of incidence accurately reproduces the `infinite atmosphere' solution for high-frequency waves. When the radiative boundary condition is applied 2 Mm above the photosphere, we find that the choice of atmospheric model affects the time-distance diagram. In particular, the time-distance diagram exhibits double-ridge structure when using a VAL atmospheric model.