An unbiased independent 0.10 m/s BERV calibration meets a 10% annual coefficient error limit in 13 of 151 HARPS designs with formal white noise

A residual velocity correction that follows the barycentric Earth radial velocity (BERV) can reduce precision near an annual planet period. We calculated the independent calibration precision needed to limit this effect in 151 public HARPS observation designs. The sample has 27,250 night bins from 88,594 exposures. Each fit has two circular signal coefficients at 365.25 days, instrument-era offsets, a slope, and a residual BERV coefficient. Calibration errors are in m/s of the equivalent annual amplitude of that residual template, not errors in Earth's known velocity. An exact block covariance gives the largest standard-error ratio over all linear contrasts of the two signal coefficients. With formal independent Gaussian night errors and an unbiased independent calibration, the median calibration standard error limit for a 10% coefficient error increase is 0.04427 m/s. A 0.10 m/s calibration passes in 13 of 151 designs. Adding independent 1 or 2 m/s night noise gives medians of 0.07380 and 0.12280 m/s. At each target's 10% variance limit, an imposed 0.10 m/s calibration mean error raises the median largest root-mean-square-error ratio to 1.510 in the formal model. Direct fits, 500,000 simulations, and a fresh full run check the calculations. The package gives per-target budgets, code, figures, the exact source extract, and source hashes. These are conditional precision requirements for fixed-period signal coefficients. They do not establish planet detections or the precision of an existing instrument calibration. Correlated stellar noise and template errors are outside the tested models.

HARPS · radial velocity · BERV · annual signals · independent calibration · precision budget · linear estimation · calibration bias · public data