Transit light curves
light_curves() turns a simulated spectrum
into the time domain: one white-light curve, or several split by wavelength
band.
obs = lazuli_exo.observe("WASP-39 b", scenario="clear", n_transits=1)
lc = obs.light_curves(n_groups=1, seed=0) # white light
lcb = obs.light_curves(n_groups=5, seed=0) # five wavelength bands
n_groups splits the binned spectrum into contiguous, equal-count groups,
inverse-variance combined. The geometry is shared across bands; the depth and
limb darkening are not.
The observation window
Sampling spans \(\pm t_{14}\) around mid-transit, the equal
out-of-transit baseline the noise tables assume (see The noise model), at the
instrument’s native integration time t_obs_s. If that would exceed
max_points samples (default 2000), the cadence is coarsened; it is never
made finer than the real integration time.
The occultation model
transit_flux() computes the normalized flux of a
quadratically limb-darkened star occulted by an opaque disk of radius ratio
\(k\) at projected separations \(z\) in stellar radii.
It is a numpy-only numerical disk integration: per separation, quadrature over the occulted radial band \([|z|-k,\, |z|+k]\) of the analytic overlap-arc weight times the intensity profile. A Chebyshev-type substitution \(r = c - h\cos\psi\) absorbs the square-root behaviour at both band edges, the planet edge and the stellar limb.
It is validated, not asserted. Against the analytic uniform-source solution (\(u_1 = u_2 = 0\)), the maximum absolute flux error at the default resolution is \(\sim 3 \times 10^{-7}\) for \(k = 0.15\), about 13 ppm of the transit depth, and the fractional error is independent of \(k\). Notebook 4. Transit light curves runs that comparison in full.
Geometry
For planets in the frozen registry (see Tables and targets), the geometry is real rather than assumed:
\(b\) from \(a/R_\star\) and \(\cos i\), with an eccentricity factor \(f_e = (1 + e\sin\omega)/\sqrt{1-e^2}\).
\(z(t)\) is the exact sky-projected separation of the Keplerian orbit (Kepler’s equation solved by Newton iteration), with mid-transit at inferior conjunction so \(z(0) = b\) exactly.
The registry \(t_{14}\) is the measured archive duration and sets the noise and the window; the geometric duration from \((P, a/R_\star, k, i, e, \omega)\) can differ (HAT-P-11 b: 7184 s vs 8480 s), so the orbit clock is scaled by their ratio and the model’s first-to-fourth-contact duration equals \(t_{14}\) (
meta["t14_geom_s"],meta["time_stretch"]).
Limb-darkening coefficients come from per-planet tables computed with exotic-ld (PHOENIX grid, trilinear interpolation, 48 wavelength chunks), interpolated to each band’s bin centres. They vary strongly across the band (for WASP-39 b, \(u_1\) runs from 0.78 in the blue to 0.18 in the near-IR), which is why banded curves change shape as well as depth.
The trapezoid fallback
A planet with no registry entry, missing orbital parameters, or no limb-darkening table falls back to a \(b = 0\) trapezoid with no limb darkening and ingress \(t_{14}\,k/(1+k)\), where \(k = \sqrt{\mathrm{depth}}\).
meta["shape"] always records which model was used, and u1/u2 are
None on the fallback path:
lc.meta["shape"] # 'quadratic-ld' or 'trapezoid'
lc.meta["b"] # present only for 'quadratic-ld'
lc.u1 # None on the fallback
Per-point noise
The per-sample scatter is derived from the band’s depth precision, not computed independently:
for cadence \(c\). This keeps the light curves consistent with the same equal out-of-transit baseline the spectra assume, so the two views of an observation cannot silently disagree about how much signal there was.
It also means the light curves inherit every caveat from The noise model, including the unbounded \(1/\sqrt{N}\) scaling.
Fields on LightCurveSet
Field |
Meaning |
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Sample times, hours from mid-transit. |
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Sampling cadence and transit duration, seconds. |
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Planet, scenario, |