A stated Gaussian model gives 4.6% power at the worst phase for a 0.35 m/s, 636.13-day circular signal in 136 Tau Ceti nights

We test the power to detect four circular velocity signals in 136 public ESPRESSO nights of Tau Ceti. All four periods are fixed at the central values reported in 2017. The test fits their sine and cosine terms together with two instrument offsets and a polynomial trend. We calculate exact power across phase under fixed Gaussian covariance models. A central model has correlated amplitude 0.50 m/s, jitter 0.45 m/s, rotation period 42 days, lifetime 105 days, and shape parameter 1. With a quadratic trend, a 0.35 m/s signal at 636.13 days has detection power of 4.60% at the worst phase and 10.86% at the best phase. The family false alarm limit is 1% across the four tests. An amplitude of 1.118 m/s is required for 95% power at the worst phase. The full stress grid has 29 noise cases and three trend choices. Its simultaneous upper-bound envelope is 0.566, 0.527, 0.656, and 1.048 m/s at 20.00, 49.41, 162.87, and 636.13 days. Some stress cases have poor residual scatter and are reported with diagnostics. The bounds have conditional coverage only if an included model is correct. Simulations at the actual observing times check the power and coverage. Seven related velocity reductions and nearby periods provide sensitivity tests. The package preserves input data, hashes, code, figures, results, and reproduction instructions. The result does not establish the true stellar noise or the presence or absence of a planet.

Tau Ceti · HD 10700 · ESPRESSO · radial velocity · detection power · circular signals · Gaussian noise · phase sensitivity · reproducible research