--- title: Sonora Flame Skimmer Models in Exoplanet Imaging url: https://www.emergentmind.com/topics/sonora-flame-skimmer-models type: topic --- # Sonora Flame Skimmer Models in Exoplanet Imaging 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 [2602.23423]. ## 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 ${\rm [M/H]} \in \{-1.0,-0.5,0.0,+0.5,+1.0,+1.5,+2.0\}$ dex. For the paper’s alternate-mass scenario, the adopted subset is solar metallicity ${\rm [M/H]}=0$, chemical equilibrium, and $M_p=\{0.524,0.786,1.048\}\,M_{\rm Jup}$ at age $t=1.1\pm0.1$ Gyr [2602.23423]. The boundary conditions are cloud-free Sonora FS atmospheric $T(\tau)$ and $P(\tau)$ 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 $T$–$P$ regimes, no helium rain is included. Thermal evolution is set by the internal-energy equation $$ L=-\frac{dU}{dt}, $$ where $U$ is internal energy. At fixed $(M_p,{\rm [M/H]})$ and $t=1.1$ Gyr, each track yields $T_{\rm eff}$, radius $R_p$, surface gravity $$ g=\frac{GM_p}{R_p^2}, $$ and bolometric luminosity $$ L_{\rm bol}=4\pi R_p^2\,\sigma\,T_{\rm eff}^4. $$ These quantities form the bridge from bulk planetary parameters to emergent spectra and direct-imaging observables. | Quantity | Sonora FS specification | |---|---| | Mass range | $15\,M_\oplus \ldots 83\,M_{\rm Jup}$ | | Core prescription | $15\,M_\oplus$ cores for $M_p<3\,M_{\rm Jup}$ | | Metallicity grid | ${\rm [M/H]}=-1.0$ to $+2.0$ dex | | Boundary condition | Cloud-free atmospheric $T(\tau),P(\tau)$ profiles | | Alternate-mass subset | $0.524,0.786,1.048\,M_{\rm Jup}$ at $1.1\pm0.1$ 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 $\mathrm{H_2O}$, $\mathrm{CH_4}$, $\mathrm{NH_3}$, $\mathrm{CO}$, and $\mathrm{CO_2}$; collision-induced absorption from $\mathrm{H_2}$–$\mathrm{H_2}$ and $\mathrm{H_2}$–He; and Rayleigh scattering from $\mathrm{H_2}$ and He [2602.23423]. Radiative–convective equilibrium is imposed through net-flux conservation, $$ \nabla\!\cdot F=\nabla\!\cdot(F_{\rm rad}+F_{\rm conv})=0. $$ The radiative transfer equation is written in plane-parallel 1D form as $$ \mu\,\frac{dI_{\nu}(\tau,\mu)}{d\tau_\nu}= I_{\nu}-S_{\nu}, $$ where $\tau_\nu$ is optical depth, $\mu=\cos\theta$, $I_\nu$ is specific intensity, and $S_\nu$ is the source function, usually $S_\nu=B_\nu$ in LTE. Convection is included through mixing-length theory when $\nabla_{\rm rad}>\nabla_{\rm ad}$. 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 $\mu$m region. ## 3. Synthetic spectra, scaling laws, and photometric observables The emergent model flux density at the top of the atmosphere is $$ F_{\nu}(\lambda)=2\pi\int_{0}^{1} \mu\,I_{\nu}(\mu,\tau=0,\lambda)\,d\mu. $$ To obtain the observed flux at Earth for distance $D$ and planetary radius $R_p$, Sanghi et al. use $$ F_{\nu,\oplus}=\left(\frac{R_p}{D}\right)^2 F_{\nu}. $$ This scaling makes the evolutionary outputs $R_p$ and $T_{\rm eff}$ 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: $$ F_X=\frac{\int F_{\lambda}(\lambda)\,T(\lambda)\,d\lambda}{\int T(\lambda)\,d\lambda}. $$ The corresponding Vega-based magnitude is $$ m_X=-2.5\,\log_{10}\!\left(\frac{F_X}{F_{0,X}}\right). $$ Planet–star contrast in a filter is the ratio of planet to stellar flux, and the associated magnitude difference is $\Delta m = m_{\rm star}-m_{\rm planet}$. In the $\epsilon$ Eri b application, this chain—evolutionary state $\rightarrow$ atmospheric structure $\rightarrow$ spectrum $\rightarrow$ band-integrated flux $\rightarrow$ 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 $$ n_i \propto 10^{\rm [M/H]}. $$ Higher ${\rm [M/H]}$ strengthens $\mathrm{CO_2}$ bands around $4.2$–$4.4\,\mu$m and $\mathrm{CO}$ bands at $4.5$–$4.8\,\mu$m, thereby suppressing the 4–5 $\mu$m flux. This is the central spectral mechanism by which metal enrichment can reconcile an intrinsically cold Jupiter-analog with a stringent F444W non-detection [2602.23423]. The summary also states that disequilibrium chemistry via vertical mixing $K_{zz}$ boosts $\mathrm{CO}$ and $\mathrm{CO_2}$ further. In practice, this strengthens the same opacity channels that reduce F444W-band flux. The model comparisons therefore depend not only on ${\rm [M/H]}$, but on the coupled set $(T_{\rm eff}, g, {\rm [M/H]}, K_{zz})$. Water-ice clouds are introduced through an additional absorption-plus-scattering opacity $\kappa_{\rm cloud}(\lambda,P)$ computed with Mie theory and parameterized by particle size and sedimentation parameter $f_{\rm sed}$. In the patchy-cloud model, with clear fraction $h$, the total flux is $$ F_{\nu,\rm tot}=h\,F_{\nu,\rm clear}+(1-h)\,F_{\nu,\rm cloudy}. $$ Cloud optical depth is $$ \tau_{\rm cloud}(\lambda)=\int \kappa_{\rm cloud}(\lambda,P)\,\rho\,ds. $$ The summary specifies that clouds form where $$ T17.95$ mag (Vega). For each model in $(T_{\rm eff},g,{\rm [M/H]},K_{zz})$, the procedure is to compute $F_p/F_\star$, convert to $m_p$, and compare against this limit. The cloud-free FS comparison yields a sharply structured set of constraints. All ${\rm [M/H]}<0$ models are ruled out. Solar metallicity, ${\rm [M/H]}=0$, is only marginally allowed, and only if $T_{\rm eff}\approx150$ K, corresponding to the lowest-temperature track. For $T_{\rm eff}\ge175$ K, ${\rm [M/H]}\ge+0.5$ dex is required; if ${\rm [M/H]}=+0.5$, strong mixing with $\log K_{zz}\ge4$ is needed to match the limit. When patchy water clouds are added with $h=0.25$ and $f_{\rm sed}=8$, the 4–5 $\mu$m flux is further suppressed, but ${\rm [M/H]}\ge+0.5$ remains preferred for $T_{\rm eff}\ge175$ K. | Model regime | Relation to the F444W limit | |---|---| | ${\rm [M/H]}<0$ | Ruled out | | ${\rm [M/H]}=0$ | Marginally allowed only at $T_{\rm eff}\approx150$ K | | ${\rm [M/H]}\ge+0.5$, $T_{\rm eff}\ge175$ K | Required | | ${\rm [M/H]}=+0.5$ | Needs $\log K_{zz}\ge4$ | | Patchy water clouds, $h=0.25$, $f_{\rm sed}=8$ | Further suppression; ${\rm [M/H]}\ge+0.5$ still preferred | The paper therefore concludes that the non-detection can be explained by a metal-enriched atmosphere and/or an atmosphere containing water ice clouds. It further states that both possibilities suggest that $\epsilon$ Eri b’s atmosphere is strikingly similar to that of Jupiter in the Solar System. The fundamental parameter link remains $$ L_{\rm bol}=4\pi R_p^2 \sigma T_{\rm eff}^4, $$ with the $R_p/D$ scaling setting the absolute 4.4 $\mu$m flux. ## 6. Alternative mass interpretation and observational implications A distinct interpretation emerges when the dynamical mass constraint, $0.98\pm0.09\,M_{\rm Jup}$, is not enforced. In that case, Sanghi et al. use solar-metallicity, cloud-free Sonora FS evolutionary tracks at $t=1.1\pm0.1$ Gyr for $M_p=\{0.524,0.786,1.048\}\,M_{\rm Jup}$ and compute the predicted $m_{\rm F444W}(M_p)$ [2602.23423]. Interpolating those tracks, the F444W limit is reached at $M_p=0.81\pm0.05\,M_{\rm Jup}$. The stated consequence is specific: if one does not enforce the dynamical mass, then a solar-metallicity, cloud-free planet with $M_p\lesssim0.81\,M_{\rm Jup}$ 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 $\epsilon$ Eri b with additional JWST observations, the Roman Coronagraph Instrument, the ExtraSolar Coronagraph on the Lazuli Observatory, and EELT/METIS. Source: https://www.emergentmind.com/topics/sonora-flame-skimmer-models