Chroma+ model stellar surface intensities: Spherical formal solution

Abstract: We announce V. 2025-08-08 of the Chroma+ suite of stellar atmosphere and spectrum modelling codes for fast, approximate, effectively platform-independent stellar spectrum synthesis, written in a number of free well-supported programming languages. The Chroma+ suite now computes the emergent surface intensity and flux distributions and the hydrostatic pressure structure assuming a spherical atmosphere rather than local flatness by implementing the analytic formal solution of the 1D spherical radiative transfer equation of Chapman (1966} based on an integration factor. We present our adaptation and discretization of the solution and demonstrate the resulting impact of our sphericity treatment on a number of computed observables, including exo-planet transit light-curves. All codes are available from the OpenStars www site: www.ap.smu.ca/OpenStars.