Differentiable Modeling of Planet and Substellar Atmosphere: High-resolution Emission, Transmission, and Reflection Spectroscopy with ExoJAX2

Abstract Modeling based on differentiable programming holds great promise for astronomy, enabling advanced techniques such as gradient-based posterior sampling and optimization. This paradigm motivated us to develop ExoJAX , the first auto-differentiable spectrum model of exoplanets and brown dwarfs. ExoJAX directly calculates cross-sections as functions of temperature and pressure to minimize interpolation errors in high-dispersion spectra, although initial work focused on narrowband emission spectroscopy. Here, we introduce a fast, memory-efficient opacity algorithm and differentiable radiative transfer for emission, transmission, and reflection spectroscopy. In the era of data-rich JWST observations, retrieval analyses are often forced to bin high-resolution spectra due to computational bottlenecks. The new algorithm efficiently handles native-resolution data, preserving the full information content and dynamic range. The advances proposed in this paper enable broader applications, demonstrated by retrievals of GL 229B’s high-dispersion emission, WASP-39 b’s JWST mid-resolution transmission at original resolution ( R ∼ 2700), and Jupiter’s reflection spectrum. We derive a C/O ratio for GL 229B consistent with its host star, constrain WASP-39 b’s radial velocity from molecular line structures, and infer Jupiter’s metallicity in line with previous estimates.