SPHEREx Ultracool Dwarf spectral Atlas (SUDA): Atmospheric and Fundamental Parameters of Ultracool Dwarfs

Abstract: We present the SPHEREx Ultracool Dwarf spectral Atlas (SUDA), a homogeneous sample of 1675 ultracool dwarfs with continuous 0.75--5 $μ$m spectroscopy from SPHEREx QR2. Using the SAND and ATMO2020++ atmospheric model grids, we derive atmospheric parameters and calculate bolometric luminosities ($L_{\rm bol}$). We combine the inferred $T_{\mathrm{eff}}$ and radii with evolutionary tracks to estimate masses and ages for the full sample. Evolutionary surface gravities ($\log g$) are also reported for sources with parallaxes. In the 1700--2500~K range, the atmospheric $\log g$ from spectral fitting are systematically lower than the evolutionary $\log g$, with a median offset of about 1.1~dex, likely reflecting residual degeneracy between $\log g$ and metallicity in low resolution SPHEREx spectra. We also construct an empirical spectral atlas by grouping the spectra in the adopted parameter space, using the $T_{\mathrm{eff}}$ and the evolutionary $\log g$. The resulting atlas contains 52 parameter bins and spans $T_{\mathrm{eff}}\simeq 700$--$3000$~K. Molecular indices reveal a coherent atmospheric sequence across the sample. H$2$O and CH$_4$ strengthen toward lower $T{\mathrm{eff}}$, whereas CO and CO$2$ rise below $\sim$1500~K and turn over near $\sim$1000~K. Comparison with model sequences shows that the CO$_2$ index is a useful empirical metallicity tracer at $T{\mathrm{eff}}\sim 800$--1300~K. Together, these results establish SUDA as a reference sample for linking observed 0.75--5~$μ$m spectral morphology to atmospheric and evolutionary trends in ultracool dwarfs.

• The paper introduces a homogeneous infrared spectral atlas of 1675 ultracool dwarfs using continuous 0.75–5 μm coverage from SPHEREx, breaking degeneracies in atmospheric modeling.
• It employs a two-tier approach combining grid-based χ² minimization with Bayesian nested sampling to estimate atmospheric parameters, bolometric luminosities, and evolutionary tracks.
• The study validates SPHEREx spectra against JWST data, providing precise calibrations for metallicity diagnostics and insights into substellar evolutionary trends.

The SPHEREx Ultracool Dwarf spectral Atlas (SUDA): Homogeneous Atmospheric and Evolutionary Characterization of Ultracool Dwarfs

Overview and Motivation

The SPHEREx Ultracool Dwarf spectral Atlas (SUDA) introduces a comprehensive, homogeneous dataset of 1675 ultracool dwarfs, leveraging the unprecedented 0.75–5 μm spectral coverage provided by SPHEREx Quick Release 2 (QR2). The continuous wavelength domain is key to robust atmospheric characterization and breakage of long-standing degeneracies in the modeling of low-mass stellar and substellar objects, providing direct bolometric flux measurements unattainable in prior, non-uniform samples. The study combines spectral fitting (SAND, ATMO2020++ grids), accurate bolometric luminosity determinations, and evolutionary tracks (C23) to derive radii, masses, ages, and empirical gravity estimates for this population, delivering a high-precision reference for population-level atmospheric and evolutionary studies.

Data Acquisition, Assembly, and Validation

The SUDA sample derives from an astrometrically matched cross-referencing of the UltracoolSheet catalog with SPHEREx QR2 spectral products, resulting in 1675 sources after rigorous S/N, photometric consistency, and contamination filtering. Crucially, SPHEREx spectra's absolute and relative flux scales were validated via direct comparison with JWST NIRSpec observations for three representative brown dwarfs, revealing flux consistency to within 1.4–4.0% (Figure 1).

Figure 1: Comparison between SPHEREx and JWST spectra of three representative brown dwarfs, confirming the fidelity and flux calibration of SPHEREx QR2 data over 1–5 μm.

This agreement establishes the reliability of SPHEREx for broad, empirical characterization, justifying downstream atmospheric and physical parameter inference on this large population.

Spectral Modeling Methodology

A two-tier methodology is employed for atmospheric parameter estimation:

• Grid-based χ² minimization: Initial parameter estimation utilizes the SAND and ATMO2020++ atmospheric model grids, both spectrally convolved to match device resolution ($R=40$–130), with optimization for low-$T_{\rm eff}$ sources (ATMO2020++ preferred for $T_{\rm eff} \leq 1300$ K).
• Bayesian Nested Sampling: These solutions are refined by UltraNest, delivering robust posteriors and uncertainties on $T_{\rm eff}$, $\log g$, [M/H], and flux scale, with priors tightly constrained by the grid-fit.

Bolometric Flux and Luminosity Determination

Bolometric fluxes are computed by direct integration of the observed spectrum augmented by best-fit model extensions beyond observed coverage. For sources with reliable parallax data, bolometric luminosity ($L_{\rm bol}$) is derived via the standard distance-luminosity relation; for those lacking parallax, $L_{\rm bol}$ is inferred from atmospheric parameters using an XGBoost regressor trained on the parallax sample. A crossmatch analysis with the literature benchmark catalog [2023ApJSanghi] demonstrates an extremely low mean offset (0.014 dex for parallax-based, 0.080 dex for ML-based) and tight MADs, affirming the method's fidelity.

Evolutionary Parameter Estimation

Mass, age, and evolutionary gravity are interpolated from the C23 substellar cooling models, using the observed $T_{\rm eff}$ and inferred radii. Radii are derived directly from the flux scaling and parallax for the parallax subset. The SUDA objects populate the appropriate evolutionary loci in the $T_{\rm eff}$–$R$ space (Figure 2), validating the consistency of the sample with theoretical expectations across the brown dwarf and ultracool regime.

Figure 2: Radius vs. $T_{\rm eff}$0 for SUDA sources, illustrating evolutionary trends and model congruence across the sample as compared to C23 evolutionary tracks.

A systematic offset is found between atmospheric and evolutionary $T_{\rm eff}$1 in the 1700–2500 K regime (median $T_{\rm eff}$21.1 dex lower for atmospheric fits), attributed to degeneracy between surface gravity and metallicity at SPHEREx spectral resolution (Figure 3).

Figure 3: Direct comparison between atmospheric and evolutionary $T_{\rm eff}$3 for objects with parallaxes, highlighting systematic gravity offsets in the L-dwarf temperature range.

Empirical Spectral Atlas

The empirical atlas is constructed by binning spectra in $T_{\rm eff}$4–$T_{\rm eff}$5 space (using atmospheric and evolutionary estimates, respectively), with each bin containing the normalized median spectrum of at least five sources. The atlas contains 52 bins and spans $T_{\rm eff}$6–3000 K, with gravity dependence only weakly manifest except at the lowest temperatures. This resource enables direct, data-driven mapping of observed spectral morphology to physical parameter space and serves as a future reference for model validation and spectral classification.

Figure 4: Empirical SUDA spectral atlas showing median normalized spectra ordered by $T_{\rm eff}$7 and $T_{\rm eff}$8, encapsulating the morphological diversity across ultracool dwarfs.

Molecular Index Trends

Four major molecular indices (H$T_{\rm eff}$9O, CH$T_{\rm eff} \leq 1300$0, CO, CO$T_{\rm eff} \leq 1300$1) are computed for the sample, serving as diagnostics for $T_{\rm eff} \leq 1300$2, chemistry, and metallicity. H$T_{\rm eff} \leq 1300$3O and CH$T_{\rm eff} \leq 1300$4 indices track cooling and the L/T transition, showing steep enhancements between 1300–1100 K. CO and CO$T_{\rm eff} \leq 1300$5 rise below 1500 K, peaking near 1000 K, with CO$T_{\rm eff} \leq 1300$6 displaying strong sensitivity to [M/H] in the 800–1300 K range. Comparing observations with SAND and ATMO2020++ models demonstrates that dispersion in CO/CO$T_{\rm eff} \leq 1300$7 indices is largely explained by metallicity, and ATMO2020++ models reproduce the observed index behavior more faithfully in the carbon-bearing domains (Figure 5).

Figure 5: Molecular index trends for H$T_{\rm eff} \leq 1300$8O, CH$T_{\rm eff} \leq 1300$9, CO, and CO$T_{\rm eff}$0 as a function of $T_{\rm eff}$1, with model tracks overlaid and metallicity dependencies illustrated.

These index behaviors empirically validate trends expected from atmospheric chemistry and mixing, reinforcing the dataset's suitability for metallicity and chemical diagnostics.

Machine Learning Luminosity Regression

For parallax-free objects, an XGBoost regressor is trained to map $T_{\rm eff}$2 to $T_{\rm eff}$3 using the parallax sample as ground truth, achieving an out-of-fold MAE $T_{\rm eff}$4 dex. This approach generalizes previous empirical magnitude relations, is robust to multimodal parameter dependencies, and preserves the accuracy required for evolutionary modeling.

Figure 6: Prediction performance and error distribution of the XGBoost regressor for $T_{\rm eff}$5 estimation from atmospheric parameters, confirming high fidelity for the no-parallax subset.

Implications and Future Applications

SUDA establishes a new baseline for ultracool dwarf atmospheric and evolutionary analysis, providing a statistically powerful, homogeneously derived set of parameters that can serve multiple research lines:

• Model Calibration: The empirical atlas enables testing and refinement of atmospheric forward models and retrievals across the L, T, and Y sequence, particularly in the mid-infrared regime where model–data tension has persisted.
• Metallicity Diagnostics: The CO$T_{\rm eff}$6 index trend establishes a scalable spectroscopic proxy for metallicity in brown dwarfs, supporting population synthesis and galactic archaeology.
• Substellar Evolution: Cohesive mass-age determinations from uniform cooling tracks advance studies of the brown dwarf mass function, formation environments, and the star/brown dwarf boundary.
• Exoplanetary Benchmarking: The dataset interfaces with interpretations of directly imaged exoplanets, particularly for comparative atmospheric science in the low-mass, cool regime.

The systematic offset in atmospheric vs. evolutionary gravity parameters underscores the need for higher-resolution or longer-wavelength spectral inputs to fully disentangle $T_{\rm eff}$7 and [M/H]. Nevertheless, SUDA will inform the selection, calibration, and validation of future high-sensitivity infrared surveys (e.g., Roman, Rubin, and other JWST-class data streams) for population-scale substellar astrophysics.

Conclusion

The SUDA sample constructed from SPHEREx QR2 data constitutes the most homogeneous and comprehensive infrared spectral atlas for ultracool dwarfs to date, enabling robust physical parameter estimation, evolutionary modeling, and empirical atmospheric diagnostics across 0.75–5 μm. The methodology demonstrates that high-fidelity population studies are now practical due to all-sky low-resolution spectroscopy with continuous spectral coverage. SUDA's empirical and model-derived resources will remain a foundational dataset for substellar astrophysics, model calibration, and comparative atmospheric studies, bridging the gap between targeted deep observations (e.g., JWST) and wide-field survey science.