Astrophysical evidence for a weak new force?

Discrepancies between measurements of and theoretical predictions for the orbital precession in binary-star systems are reexamined assuming the existence of a hitherto undiscovered, very weak long-range force. The binary-star data are consistent with the existence of such a force only if the internal density parameter $k_2$, computed using stellar models, is uncertain to 80% for some of the stars involved. If so, the observations are compatible with a repulsive force that couples to electrically neutral bulk matter through a linear combination of neutron and proton number with ${10}^{\mathrm{-}5}$–${10}^{\mathrm{-}4}$ the strength of gravity and a range of (3–6)×${10}^6$ km. Surprisingly, such a force is consistent with the binary pulsar and extraterrestrial solar-system tests of general relativity. It is ruled out only by very recent tests of the principle of equivalence on Earth. Such binary-star systems are extremely sensitive to, and so furnish strong constraints on, new forces.