Tempawral: 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 dataset. 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 JWST/NIRISS-SOSS time-series observations of a highly variable T2.5 brown dwarf. The observed variability is best explained by a $\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.

Figures (21)

• Figure 1: Simplified physical picture for modeling time-variable brown dwarf atmospheres. Multiple surface regions with distinct chemical compositions, cloud properties, or thermal structures may coexist, evolve, and interact dynamically. When these heterogeneous atmospheric structures are superimposed on a more homogeneous background and rotate in and out of view, the resulting disk-averaged atmospheric properties can exhibit approximately sinusoidal temporal behavior, which is also the assumption used in Tempawral. However, such atmospheric variability evolution pattern can be more complex (see detailed discussion in Section \ref{['sec:Sinusoidal']}).
• Figure 2: Schematic overview of the Tempawral framework. Starting from a time-series spectroscopic dataset, a baseline atmospheric retrieval is performed on the time-averaged spectrum to obtain reference values on model parameters. Time-variable parameters (temperature, chemical abundances, and cloud properties) are perturbed sinusoidally to generate the time-evolution model parameters; which is fed into the time-series forward model to produce simulated spectra. PCA is then applied to both observed and simulated time-series spectra to extract eigen-spectra, capturing the dominant modes of wavelength-dependent variability. The Bayesian retrieval module compares these eigen-spectra, inferring posterior distributions for the perturbation amplitudes and phase shifts of the atmospheric parameters.
• Figure 3: Flowchart of the Tempawral's time-series forward model. The baseline model provides a reference matrix, $\mathbf{M}_{\rm ref}$, derived from the best-fit solution to the time-averaged spectrum of the observed object. Periodic modulations from rotating atmospheric features are captured through variability amplitude and phase-shift terms, yielding the perturbation and phase-shift matrices, $\mathbf{M}_{\rm var}$ and $\mathbf{M}_{\rm shift}$, which are sampled at each retrieval iteration. The resulting matrix, $\mathbf{L}$, encodes the full time evolution of all model parameters, with each column representing a complete parameter set at a given time step. These parameter sets are passed to the snapshot forward model to generate the simulated time-series spectra, $\mathbf{S}$.
• Figure 4: Eigen-spectra sensitivity test on the variance of each model parameters. Starting from a baseline set of atmospheric parameters, time-series spectra are simulated by allowing cloud properties, chemical abundances, and the temperature structure to vary sinusoidally over a full rotation. Each time-variable parameter is perturbed by 10% from its reference value. In each subplot, we only assign variance on the selected parameter while fixing all others to their reference values, and use this to generate synthetic time-series spectra. The first principal component is then extracted from the resulting time-series. While the parameters $\log p_{\rm ref}$ and $\log dp$, which define the location and extent of temperature perturbations, are modeled as single values and are not treated as time-variable parameters with associated amplitudes and phase shifts.
• Figure 5: Simulated light curves for a SIMP 0136-like brown dwarf using our time series forward model. The retrieved median values for each model parameter, as listed in Table \ref{['tab1']} from real SIMP 0136 time-averaged data, are used as the reference values. The variance for each model parameter follows Table \ref{['tab2']}, with phase shifts set to zero for all time variables.