Geometry of ray paths in spherical PHOENIX atmosphere models (not to scale). Dashed arcs above R_* represent the modeled extended atmosphere grid. The PHOENIX spherical model grid runs from the center of the star with 15 rays intersecting an optically thick core and includes a modeled atmosphere (64 layers) out to low ∼nbar pressures at the top, r_top. The thick red arc illustrates the effective stellar radius at the photosphere, R_*(τ = 1). For limb darkening, ﹩\mu =\cos (\theta )﹩ needs to be renormalized so that μ = 0 corresponds to R_*(τ = 1).