Plane-parallel validity from pressure scale height ($H/R\ll 1$)

A plane-parallel atmosphere is geometrically accurate only if the relevant line-forming region is thin relative to the stellar radius. An isothermal estimate gives $H=k_{B}T/(\mu m_u{g}_{\mathrm{eff}})$. Radiative acceleration reduces the effective gravity and increases extension. A small photospheric $H/R$ does not justify a plane-parallel description of wind lines formed far above that photosphere.