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Modeling based on differentiable programming holds great promise for astronomy, as it can employ techniques such as Hamiltonian Monte Carlo, gradient-based optimization, and other machine learning techniques. This new programming paradigm has motivated us to develop the first auto-differentiable spectrum model of exoplanets and brown dwarfs, ExoJAX (Kawahara et al. 2022). ExoJAX is designed to directly calculate cross-sections as functions of temperature and pressure, rather than interpolating tabulated data, to minimize errors in high-dispersion spectra modeling. However, its application was primarily proof-of-concept and limited to narrowband high-dispersion emission spectroscopy. In this paper, we have enhanced the differentiable opacity calculation using a new fast and memory-efficient algorithm, and have developed differentiable radiative transfer schemes, including emission, transmission, and reflection spectroscopy. These enhancements significantly expand the range of applications, as demonstrated through actual atmospheric retrievals: high-dispersion emission spectra of the brown dwarf GL229 B, medium-dispersion transmission spectra of the hot Saturn WASP-39 b from JWST, and high-dispersion reflection spectra of Jupiter. We obtained a C/O ratio for GL229 B consistent with its host star, constrained WASP-39 b's radial velocity from molecular fine structures at original resolution ($R \sim 3,000$), and estimated Jupiter's metallicity consistent with previous studies., Comment: 32 pages, 12 figures, submitted. ExoJAX is available at https://github.com/HajimeKawahara/exojax. ExoJAX2 is scheduled to be released after the review process

Optical phase curves of hot Jupiters can reveal global scattering properties. We implement a Bayesian inference framework for optical phase curves with flux contributions from: reflected light from a potentially inhomogeneous atmosphere, thermal emission, ellipsoidal variations, Doppler beaming, and stellar rotation via a Gaussian process in the time domain. We probe for atmospheric homogeneity and time-variability using the reflected light inferences for highly precise Kepler light curves of five hot Jupiters. We also investigate the scattering properties which constrain the most likely condensates in the inhomogeneous atmospheres. Cross validation prefers inhomogeneous albedo distributions for Kepler-7 b and Kepler-41 b, and a weak preference for inhomogeneity for KOI-13 b. None of the five planets exhibit significant variations in geometric albedo on one-year timescales, in agreement with theoretical expectations. We show that analytic reflected light phase curves with isotropic multiple scattering are in excellent agreement with full Rayleigh multiple scattering calculations, allowing for accelerated and analytic inference. In a case study of Kepler-41 b, we identify perovskite, forsterite, and enstatite as possible scattering species consistent with the reflected light phase curves, with condensate particle radii in the range 0.01-0.1 micron., Comment: Accepted in A&A