<tt>Tempawral</tt> : a time-resolved retrieval framework for variable brown dwarfs and exoplanets

ABSTRACT Brown dwarfs and exoplanets are thought to host complex atmospheric phenomena such as clouds, storms, and chemical heterogeneity, akin to weather patterns on Earth. These features can produce pronounced spectral variability. Time-variability monitoring provides a unique window into surface inhomogeneities that cannot be directly resolved with foreseeable imaging technology. Current time-series analysis techniques have provided qualitative constraints on variability mechanisms but lack the ability to quantitatively estimate the extent of variation on atmospheric properties. We present Tempawral, the first data-driven time-resolved atmospheric retrieval framework that quantitatively retrieving variability in atmospheric parameters via an eigen-spectra inversion technique, leveraging the full spectra data set. We validate this method on simulated time-series spectra of a variable brown dwarf, demonstrating that it successfully recovers key variability drivers, including inhomogeneous cloud coverage, evolving chemical abundances, and changes in temperature structure. We further showcase the utility of Tempawral by applying it to James Web Space Telescope (JWST)/Near Infrared Imager and Slitless Spectrograph in the Single Object Slitless Spectroscopy mode time-series observations of a highly variable T2.5 brown dwarf. The observed variability is best explained by an $\sim$300 K temperature perturbation near the 1-bar, accompanied by variations in the abundances of $\rm H_{2}O$, $\rm CO$, $\rm FeH$, as well as changes in the thickness of the iron cloud deck. This work provides a generalized framework for time-resolved atmospheric retrievals in the JWST era, enabling comprehensive interpretations of dynamic atmospheric processes in substellar objects.