The parametric model

lazuli_exo.simulate() builds a transmission spectrum for any transiting planet. The showcase tables froze one POSEIDON run per planet and scenario; the parametric model runs POSEIDON once, offline, on a grid that every planet shares, and applies everything planet-specific analytically at request time (about 20 ms, numpy only). The noise then comes from a live slicersim run on a PHOENIX stellar SED.

Inputs

Parameter	Meaning
`T_eq_K`, `R_p_RJ`, `M_p_MJ`, `R_s_RSun`	Planet temperature, band-median transit radius, mass; stellar radius. Gravity is evaluated at \(R_p\).
`log_met` (−1…3), `c_to_o` (0.3…1.0)	Atmospheric metallicity (log, solar = 0) and C/O for the equilibrium chemistry.
`mu`	Mean molecular weight [amu]; `None` takes the equilibrium-chemistry value stored with the grid.
`log_P_cloud_bar`	Gray cloud-deck top pressure; `None` = clear.
`log_a_haze`, `haze_slope`	POSEIDON MacMad17 haze: enhancement over H2 Rayleigh at 0.35 µm (log) and power-law slope \(\gamma\); `log_a_haze=None` = no haze.
`teff_K`, `logg`, `feh`	Star for the PHOENIX SED (solar metallicity only, 2000–12000 K, log g 3.5–5.5; out-of-range T_eff, log g and any non-zero [Fe/H] clamp to the nearest node and are reported in `info["clamped"]`).
`f_spot`, `T_spot_K`, `f_fac`, `T_fac_K`	Unocculted spots and faculae (transit light source effect, Rackham et al. 2018 eq. 2): the model depth is multiplied by \(\epsilon(\lambda)\) from PHOENIX fluxes at the three temperatures. Default off (`f_spot = f_fac = 0`); `star.TLSE_PRESETS` holds literature covering fractions.
`mag`, `band` (J/H/Ks/V), `mag_system` (`"vega"` default, `"ab"`)	Normalisation magnitude. slicersim normalises in AB; archive magnitudes are Vega and are converted through sncosmo.
`t14_s`	Transit duration; the noise assumes an equal out-of-transit baseline.

Physics

For an isothermal, well-mixed atmosphere the photospheric pressure at each wavelength, written as \(\zeta(\lambda) = -\ln[P_{\tau=1}(\lambda)/1\,\mathrm{bar}]\), depends on the gas opacity, that is on (T, [M/H], C/O), and only weakly on the planet. It is tabulated for two fiducial planets (1 R_J at 10 m s^-2 and 0.3 R_J at 30 m s^-2) at the model’s native R = 10,000 and interpolated trilinearly in (T, [M/H], C/O). Everything else is analytic:

\[\begin{split}x_p &= \tfrac{1}{2}\ln\frac{R_p H}{R_{p,0} H_0} - \ln\frac{T_\mathrm{eq}}{T_\mathrm{chem}} \qquad\text{(slant-column variable)}\\ \zeta_p &= \zeta_0 + s(\lambda)\,(x_p - x_0) \qquad s = \frac{\zeta_1 - \zeta_0}{x_1 - x_0} \approx \frac{1}{1+a}\ \text{for}\ \tau\propto P^{1+a}\\ \zeta_g &= \mathrm{logaddexp}(\zeta_p,\ \zeta_\mathrm{haze}),\qquad P_\mathrm{haze}(\lambda) = \frac{k T_\mathrm{eq}}{\kappa_\mathrm{haze}\sqrt{2\pi R_p H}}\\ \zeta &= \zeta_d + s\,\mathrm{Ein}\!\left(e^{(\zeta_g - \zeta_d)/s - \gamma_E}\right), \qquad \zeta_d = -\ln P_\mathrm{cloud}\\ R(\lambda) &= \frac{R_p}{1 - (H/R_p)\,[\zeta - \tilde\zeta]},\qquad \mathrm{depth} = \left(\frac{R(\lambda)}{R_s}\right)^2\end{split}\]

with \(H = kT_\mathrm{eq}/(\mu m_H g)\), \(g\) at \(R_p\), and \(\tilde\zeta\) the band median (0.40–1.70 µm) so that \(R_p\) is the band-median transit radius. The last line is the exact isothermal hydrostatic solution for \(g\propto r^{-2}\). The deck line is the exact effective radius of an exponential optical-depth profile above an opaque deck (POSEIDON integrates \(1-e^{-\tau}\) over impact parameter, so gas whose \(\tau=1\) level lies just below the deck still absorbs); it tends to \(\max(\zeta_g,\zeta_d)\) in both limits. Ein is the entire exponential integral.

Conventions worth knowing

Radius. The showcase tables put the archive radius at the 10 bar reference level; the parametric model puts it at the transit photosphere, roughly ten scale heights higher. The validation therefore feeds the model each table’s own band-median radius. For a user the archive radius is the transit radius, so no correction is needed.
Temperature floor. The chemistry grid starts at 300 K. Colder planets use 300 K chemistry but the true \(T_\mathrm{eq}\) for \(H\); info["T_clamped"] records it.
Deck discretisation. POSEIDON applies a deck to layers strictly deeper than \(P_\mathrm{cloud}\), so on its 100-layer grid a nominal 1 mbar deck is realised at 1.38 mbar. The model keeps the user’s value literal.
Flat preset. presets.showcase(planet, "flat") uses a deck at 10 nbar.

Validation

precompute/validate_zeta_grid.py compares the model with the 14 × 5 POSEIDON tables in precompute/tables/ (plus a set of off-registry holdout runs) at R = 100, after removing a constant offset, against the single-transit per-bin uncertainty. The gates are: worst bin within 1 sigma (G2), the error spectrum’s own template S/N below 3 (G5), and the template S/N within 10 % of the table’s (G3); flat is gated on its absolute amplitude. Expected failures are waivers in the script, each naming the gate and the GitHub issue that would remove it, and a waiver that no longer fails is itself an error. CI runs the gate on every push. The notebook 6. The parametric model shows the grid and the comparison.

What it cannot do

Non-isothermal profiles, disequilibrium chemistry, patchy clouds, red noise, and light curves for custom stars (no limb-darkening tables). Stellar contamination is a user-supplied covering fraction, not a prediction of the host’s activity. Changing mu by hand does not change the opacities, which stay at the chemistry implied by log_met and c_to_o.