Validity regime of the local plane-parallel approximation

Quantify the regime in which the local plane-parallel Thomson-scattering approximation remains valid for aspherical photospheres, particularly by determining when non-local radiative-transfer effects and photospheric curvature can no longer be neglected.

Background

The study treats each surface element independently using the plane-parallel Chandrasekhar atmosphere solution. This treatment is justified when the optical-depth scale height is sufficiently small compared with the photospheric size, so that photons escape locally and curvature and non-local transport are negligible.

The paper warns that the approximation can fail in tenuous envelopes where photons travel distances comparable to the photospheric size. In that regime, more sophisticated methods such as Monte Carlo radiative-transfer calculations are required, and the boundary of validity of the local approximation remains unresolved.

References

However, the approximation may break down in more tenuous envelopes, where photons can travel over distances comparable to the size of the photosphere before escaping. In such cases, more sophisticated approaches, such as Monte Carlo radiative-transfer calculations, are required. Quantifying the regime in which the local plane-parallel approximation remains valid is left for future work.

— Polarization Properties of Thomson-Scattering Triaxial Ellipsoids  (2610.21499 - Hachisu et al., 15 Oct 2026) in Section 4, Summary, caveats associated with the plane-parallel atmosphere approximation