Rotational Mapping and Regional Atmospheric Retrievals of Variable Brown Dwarfs: Application to Luhman 16B and SIMP 0136

We present a Bayesian framework for converting time-resolved spectroscopy into rotation-inferred regional spectra and atmospheric constraints for variable brown dwarfs. We derive an analytic mapping framework with evidence-optimized regularization and uncertainty propagation by marginalizing over physical parameters and model complexities. We provide methods for selecting characteristic spectral end-members from the inferred surface maps, and highlight the advantage of analyzing these rotation-inferred regional spectra over the disk-integrated time-resolved observations, while explicitly accounting for the geometric degeneracies inherent to rotational mapping. We apply this framework to published JWST/NIRSpec rotational monitoring of Luhman 16B and SIMP 0136. For both objects, we identify dominant spectral regions and retrieve regional variations in cloud structure, thermal gradients, and chemistry that are consistent with cloud radiative feedback. In addition, we demonstrate the importance of limb darkening in deriving surface maps. These results establish a statistically controlled method for linking rotational spectral variability to atmospheric heterogeneity and enable future rotational mapping and regional atmospheric studies of giant planet atmospheres.