Ruling Out Impostors

A moon-deep transit with a planet-mass dynamical companion admits a short list of mundane explanations. Each has a proposed discriminant — an observable that the genuine dark-primary configuration does not trip — one inside the detection pipeline itself, the rest with standard follow-up. As the adversarial test below shows, this closure is demonstrated rather than guaranteed.

Code

from lastmoon.vetting import vetting_table

vetting_table()

Table length=5

scenario	mimics	tier	discriminant	rejection
str38	str60	str9	str229	str201
White-dwarf companion	a dark, massive primary paired with a small transiting body	follow-up	a WD is luminous (UV/optical excess in the SED), and a transiting WD's depth-derived radius is Earth-scale (~6e6 m), not lunar	no UV excess and a depth-derived radius consistent with a lunar-size body
Iron/ultra-dense dark planet	a high-density transiting object with a large dynamical mass	pipeline	even a pure-iron world obeys a mass-radius relation; the dynamical mass implied at the transiting radius exceeds any condensed-matter composition	mass_size_mismatch > 3 (the live pipeline threshold) is unreachable for iron-world compositions
Blended eclipsing binary	a shallow moon-depth transit from a diluted deep eclipse	follow-up	centroid shift during events; chromatic depth; secondary eclipses	achromatic depth, no centroid motion, no secondary eclipses
Grazing stellar eclipse	a shallow transit from a stellar companion clipping the limb	follow-up	V-shaped profile; km/s-scale RV signal; depth-duration inconsistency	box-consistent shape and an RV amplitude at the m/s scale
Ordinary planet with a transiting moon	moon-only transits with planet-scale dynamical mass	follow-up	TTV morphology: the moon's aliased timing period, absence of synodic chopping, and TTV/TDV quadrature distinguish a moon bound to the dark primary from a planet-on-planet super-period; density gate bites once co-location is shown	separated by TTV-morphology classification in the fiducial regime; a residual-degeneracy slice (coinciding aliased periods) requires TDV and co-location/density follow-up; universal closure not claimed

The pipeline-tier rejection regenerates from the package on every build, so the threshold shown always matches the survey configuration.

The ordinary non-transiting-planet-with-transiting-moon case is separated by TTV morphology: the moon’s aliased timing period, the absence of synodic “chopping”, and the TTV/TDV quadrature distinguish a moon bound to the dark primary from a planet-on-planet super-period. The implied-density gate then bites once co-location is shown.

Code

from lastmoon.figures.ttv_morphology import fiducial_impostor_scan

# The same fiducial M3V scan the manuscript's TTV-morphology figure uses.
scan = fiducial_impostor_scan()
print(
    f"separable fraction: {scan.separable_fraction:.2f} of {scan.n_total} impostors; "
    f"residual: {len(scan.residual_slice)}"
)

separable fraction: 1.00 of 125 impostors; residual: 0

Separation is clean across this illustrative fiducial scan (the separable fraction is printed above). A residual-degeneracy slice — where the aliased moon period coincides with the planet-planet super-period — requires TDV quadrature plus co-location/density follow-up; universal closure is not claimed.

The gate is not tied to the fiducial moon orbit: rerunning the same scan with the moon at 0.35 R_Hill and at the Domingos stability cap (0.4895 R_Hill) again separates the full impostor grid. A dense sweep across the whole stable separation range does, however, find isolated long-alias pockets — at 13 of 117 separations (2-yr baseline) the moon’s aliased timing period runs to near or past the observing baseline and a few light, near-resonant impostors become residual (worst separable fraction 0.952). Those pockets are an alias/baseline effect, not a property of the moon’s separation, they shrink with a longer baseline, and every residual impostor still faces the TDV-quadrature and density follow-up gates.

A stronger, adversarial test backs this up — and marks its limits. The paper runs a formal three-template cross-fit — a dense transiter, a moon plus dark primary, and a perturbed planet — on synthetic data, and for each case searches for the worst-case planet-planet impostor that best mimics the moon rather than scoring an arbitrary one. For a bright, strong target (TRAPPIST-1) the moon template wins decisively; yet even there the adversarial impostor is left undistinguished in ~9% of noise realizations, and at the marginal candidacy threshold (an M5V at 20 pc) the comparison is honestly inconclusive in both directions. This is a template comparison over a declared, locally-convergent search — deliberately not a Bayes factor and not a calibrated false-positive rate, and a full false-positive-rate calibration is left to future work. Morphology is load-bearing, but not a global guarantee.

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