Sonora Flame Skimmer Models in Exoplanet Imaging

• Sonora Flame Skimmer models are a coupled framework combining evolutionary tracks and cloud-free atmospheric profiles to translate planetary mass, metallicity, and age into observable properties.
• They enable detailed interpretation of JWST direct-imaging limits by linking T_eff, radius, and luminosity with complex atmospheric chemistry including metallicity enhancements and the presence of water ice clouds.
• The models provide alternative interpretations for non-detections by comparing enhanced-metallicity and patchy-cloud scenarios with a lower-mass, solar-metallicity solution.

Sonora Flame Skimmer models, as used by Sanghi et al., denote a coupled framework of evolutionary tracks and cloud-free atmospheric models that map planetary mass, metallicity, age, and thermodynamic structure onto observables such as $T_{\rm eff}$, $R_p$, $g$, $L_{\rm bol}$, synthetic spectra, and filter-dependent photometry. In the direct-imaging analysis of the nearest Jupiter-analog exoplanet, $\epsilon$ Eri b, these models were combined with custom PICASO patchy cloud models to interpret a JWST/NIRCam F444W non-detection. Within that application, the models support two main explanations for the suppressed 4–5 $\mu$m flux: enhanced atmospheric metallicity and/or the presence of water ice clouds; if the dynamical mass is not enforced, a lower-mass solar-metallicity cloud-free planet also remains consistent with the data (Sanghi et al., 26 Feb 2026).

1. Evolutionary-grid definition

The Sonora Flame Skimmer evolutionary model grid summarized by Sanghi et al. spans masses from $15\,M_\oplus$ to $83\,M_{\rm Jup}$, with $15\,M_\oplus$ cores for $M_p<3\,M_{\rm Jup}$. The metallicity grid is discrete, with $R_p$0 dex. For the paper’s alternate-mass scenario, the adopted subset is solar metallicity $R_p$1, chemical equilibrium, and $R_p$2 at age $R_p$3 Gyr (Sanghi et al., 26 Feb 2026).

The boundary conditions are cloud-free Sonora FS atmospheric $R_p$4 and $R_p$5 profiles. The interior physics uses the H–He equation of state from Chabrier & Potekhin (2019) and Chabrier et al. (2021), and the water EOS from Mazevet et al. (2019). For the relevant $R_p$6–$R_p$7 regimes, no helium rain is included. Thermal evolution is set by the internal-energy equation

$R_p$8

where $R_p$9 is internal energy.

At fixed $g$0 and $g$1 Gyr, each track yields $g$2, radius $g$3, surface gravity

$g$4

and bolometric luminosity

$g$5

These quantities form the bridge from bulk planetary parameters to emergent spectra and direct-imaging observables.

Quantity	Sonora FS specification
Mass range	$g$6
Core prescription	$g$7 cores for $g$8
Metallicity grid	$g$9 to $L_{\rm bol}$0 dex
Boundary condition	Cloud-free atmospheric $L_{\rm bol}$1 profiles
Alternate-mass subset	$L_{\rm bol}$2 at $L_{\rm bol}$3 Gyr

2. Atmospheric structure and radiative–convective closure

The cloud-free Sonora FS atmospheres are 1D and plane-parallel. Their opacity budget includes molecular line absorption from $L_{\rm bol}$4, $L_{\rm bol}$5, $L_{\rm bol}$6, $L_{\rm bol}$7, and $L_{\rm bol}$8; collision-induced absorption from $L_{\rm bol}$9–$\epsilon$0 and $\epsilon$1–He; and Rayleigh scattering from $\epsilon$2 and He (Sanghi et al., 26 Feb 2026).

Radiative–convective equilibrium is imposed through net-flux conservation,

$\epsilon$3

The radiative transfer equation is written in plane-parallel 1D form as

$\epsilon$4

where $\epsilon$5 is optical depth, $\epsilon$6, $\epsilon$7 is specific intensity, and $\epsilon$8 is the source function, usually $\epsilon$9 in LTE.

Convection is included through mixing-length theory when $\mu$0. The chemistry is treated with rainout, so condensable species are removed from the gas phase below their condensation points, depleting gas-phase abundances self-consistently. In this formulation, the atmospheric structure is not merely a post-processing step: it is the boundary condition that closes the evolutionary calculation and sets the spectral morphology in the 4–5 $\mu$1m region.

3. Synthetic spectra, scaling laws, and photometric observables

The emergent model flux density at the top of the atmosphere is

$\mu$2

To obtain the observed flux at Earth for distance $\mu$3 and planetary radius $\mu$4, Sanghi et al. use

$\mu$5

This scaling makes the evolutionary outputs $\mu$6 and $\mu$7 directly relevant to imaging detectability, since the absolute flux depends on both the atmospheric spectrum and the geometric dilution factor.

Filter photometry is defined by transmission-weighted integration over the bandpass:

$\mu$8

The corresponding Vega-based magnitude is

$\mu$9

Planet–star contrast in a filter is the ratio of planet to stellar flux, and the associated magnitude difference is $15\,M_\oplus$0. In the $15\,M_\oplus$1 Eri b application, this chain—evolutionary state $15\,M_\oplus$2 atmospheric structure $15\,M_\oplus$3 spectrum $15\,M_\oplus$4 band-integrated flux $15\,M_\oplus$5 contrast—is the operational definition of how Sonora Flame Skimmer models are confronted with coronagraphic upper limits.

4. Metallicity enhancement, disequilibrium chemistry, and water-ice clouds

Within the Sonora FS framework, metallicity rescales bulk abundances according to

$15\,M_\oplus$6

Higher $15\,M_\oplus$7 strengthens $15\,M_\oplus$8 bands around $15\,M_\oplus$9–$83\,M_{\rm Jup}$0m and $83\,M_{\rm Jup}$1 bands at $83\,M_{\rm Jup}$2–$83\,M_{\rm Jup}$3m, thereby suppressing the 4–5 $83\,M_{\rm Jup}$4m flux. This is the central spectral mechanism by which metal enrichment can reconcile an intrinsically cold Jupiter-analog with a stringent F444W non-detection (Sanghi et al., 26 Feb 2026).

The summary also states that disequilibrium chemistry via vertical mixing $83\,M_{\rm Jup}$5 boosts $83\,M_{\rm Jup}$6 and $83\,M_{\rm Jup}$7 further. In practice, this strengthens the same opacity channels that reduce F444W-band flux. The model comparisons therefore depend not only on $83\,M_{\rm Jup}$8, but on the coupled set $83\,M_{\rm Jup}$9.

Water-ice clouds are introduced through an additional absorption-plus-scattering opacity $15\,M_\oplus$0 computed with Mie theory and parameterized by particle size and sedimentation parameter $15\,M_\oplus$1. In the patchy-cloud model, with clear fraction $15\,M_\oplus$2, the total flux is

$15\,M_\oplus$3

Cloud optical depth is

$15\,M_\oplus$4

The summary specifies that clouds form where

$15\,M_\oplus$5

Within the paper’s application, patchiness does not replace metallicity as an explanatory variable; rather, it provides further flux suppression in conjunction with metal enrichment.

5. Interpretation of the JWST/NIRCam F444W non-detection of $15\,M_\oplus$6 Eri b

Sanghi et al. present a JWST/NIRCam coronagraphic search for $15\,M_\oplus$7 Eri b between 4–5 $15\,M_\oplus$8m in F444W. The target is the nearest Jupiter-analog exoplanet at $15\,M_\oplus$9 pc. At the expected planet separation of approximately $M_p<3\,M_{\rm Jup}$0, the observations reach a $M_p<3\,M_{\rm Jup}$1 contrast sensitivity of approximately $M_p<3\,M_{\rm Jup}$2, corresponding to $M_p<3\,M_{\rm Jup}$3 mag. The paper states that this is the deepest 4–5 $M_p<3\,M_{\rm Jup}$4m contrast performance achieved for any JWST/NIRCam observation to date at these separations, and more than $M_p<3\,M_{\rm Jup}$5 better than ground-based limits, yet the planet remains undetected (Sanghi et al., 26 Feb 2026).

The stellar age is updated to $M_p<3\,M_{\rm Jup}$6 Gyr using the latest gyrochronology relations, older than previous age estimates. This revision materially changes the planetary thermal expectation: for a $M_p<3\,M_{\rm Jup}$7 planet, evolutionary models now place $M_p<3\,M_{\rm Jup}$8 between 150 and 200 K. The F444W $M_p<3\,M_{\rm Jup}$9 limit at $R_p$00 implies

$R_p$01

with $R_p$02 mag (Vega). For each model in $R_p$03, the procedure is to compute $R_p$04, convert to $R_p$05, and compare against this limit.

The cloud-free FS comparison yields a sharply structured set of constraints. All $R_p$06 models are ruled out. Solar metallicity, $R_p$07, is only marginally allowed, and only if $R_p$08 K, corresponding to the lowest-temperature track. For $R_p$09 K, $R_p$10 dex is required; if $R_p$11, strong mixing with $R_p$12 is needed to match the limit. When patchy water clouds are added with $R_p$13 and $R_p$14, the 4–5 $R_p$15m flux is further suppressed, but $R_p$16 remains preferred for $R_p$17 K.

Model regime	Relation to the F444W limit
$R_p$18	Ruled out
$R_p$19	Marginally allowed only at $R_p$20 K
$R_p$21, $R_p$22 K	Required
$R_p$23	Needs $R_p$24
Patchy water clouds, $R_p$25, $R_p$26	Further suppression; $R_p$27 still preferred

The paper therefore concludes that the non-detection can be explained by a metal-enriched atmosphere and/or an atmosphere containing water ice clouds. It further states that both possibilities suggest that $R_p$28 Eri b’s atmosphere is strikingly similar to that of Jupiter in the Solar System. The fundamental parameter link remains

$R_p$29

with the $R_p$30 scaling setting the absolute 4.4 $R_p$31m flux.

6. Alternative mass interpretation and observational implications

A distinct interpretation emerges when the dynamical mass constraint, $R_p$32, is not enforced. In that case, Sanghi et al. use solar-metallicity, cloud-free Sonora FS evolutionary tracks at $R_p$33 Gyr for $R_p$34 and compute the predicted $R_p$35 (Sanghi et al., 26 Feb 2026).

Interpolating those tracks, the F444W limit is reached at $R_p$36. The stated consequence is specific: if one does not enforce the dynamical mass, then a solar-metallicity, cloud-free planet with $R_p$37 would remain consistent with the NIRCam non-detection. This is the principal alternative to the enhanced-metallicity and/or water-cloud interpretation.

This distinction clarifies a common misunderstanding of non-detections in direct imaging. The absence of an F444W detection does not uniquely imply either atmospheric cloud opacity or high metallicity; it does so only under the adopted mass prior. Conversely, relaxing the dynamical-mass prior restores consistency with a lower-mass, solar-metallicity, cloud-free solution. The paper also places limits on the size of a potential ring system using NIRCam/F210M data and discusses the opportunity to directly image $R_p$38 Eri b with additional JWST observations, the Roman Coronagraph Instrument, the ExtraSolar Coronagraph on the Lazuli Observatory, and EELT/METIS.