Two K2-18 HARPS reductions do not resolve the free four-term co-orbital diagnostic under 85 fixed noise models

Can public HARPS velocities resolve the co-orbital phase diagnostic of K2-18 b without a bound on the first-order eccentricity terms? We fit all four Fourier terms at the transit-anchored orbit period and its second harmonic. We use all 100 LBL rows and all 106 NAIRA rows. The reductions share spectra and are tested separately. For Q = A + 2C, the primary fixed correlated-noise model gives -0.444 +/- 1.299 m/s for LBL and -0.267 +/- 1.566 m/s for NAIRA. Errors are one standard error. All 85 specified noise cases keep the complete-table estimates within 0.69 standard error of zero. The 99 matched exposures also stay within one standard error. Circular and small-eccentricity restrictions shift the best Q to positive values, but give little fit improvement over Q = 0. Exact Keplerian controls, changed inner periods, and omitted data give no strong contrary result. The primary model has only 3.25% and 2.06% power to detect a true Q of 1.5 m/s at a two-sided three-standard-error threshold. Thus, the null result does not exclude a weak companion. This HARPS-only study does not reproduce the combined-instrument TROY analysis. The new products are joint coefficient likelihoods for every tested noise setting and a reproducible sensitivity audit. The package includes code, derived data, figures, source hashes, and download instructions. The free Fourier mean is a diagnostic, not a physical model of an orbit with large eccentricity. All statistical results are conditional on the fixed mean and noise models.

K2-18 · HARPS · co-orbital planets · radial velocities · Fourier coefficients · stellar noise · conditional likelihood · sensitivity analysis · public data