A figure of merit for kinematic limitation of binary-pulsar tests of orbital decay

The observed orbital period derivative ˙Pb of a binary pulsar contains kinematic contri- butions — the Shklovskii term and the differential Galactic acceleration — that must be subtracted before comparison with the general-relativistic (GR) prediction for gravitational- wave emission. We ask whether the radiative test of GR is limited by the precision of the ˙Pb measurement or by the uncertainty in the kinematic correction, and which measure- ment would most improve it. We define a dimensionless figure of merit F , the ratio of the uncertainty in the kinematic correction (the distance error propagated jointly through the Shklovskii and Galactic terms, the proper-motion error, and the difference between two Galactic potential models, evaluated by Monte Carlo and split into components) to the measurement uncertainty in ˙Pobs b . We compute F for sixteen binary pulsars from the timing literature and for 28 field binaries in the ATNF Pulsar Catalogue (v2.8.1), and use a smoothed-bootstrap synthetic population of 2 × 105 systems to test the stability of the classification. Six of the sixteen literature systems are distance-limited (F ≥ 1), six border- line, and four measurement-limited; omitting the Galactic term understates the kinematic limitation for six systems, including B1913+16. Systems reach F ≥ 1 through large proper motion at small distance (the Shklovskii term) or large distance at low Galactic latitude (the Galactic term); for most the dominant uncertainty is the distance, but for J1909−3744 it is the Galactic potential model. Eleven of the 28 catalogue systems are distance-limited. F does not predict the achieved test precision. In the synthetic population, 7.9% of systems change class under realistic measurement noise (4.0% with parallax distances, 14.9% with DM distances), and the distribution of F is consistent with a single log-normal component, so the thresholds F = 0.3 and 1 are conventions. F is a per-system diagnostic of which lim- itation dominates, not a predictor of test quality; where the Galactic-model term dominates, ˙Pb is more informative as a probe of the Galactic potential than as a test of GR.