Two-body gravitational spin-orbit interaction at linear order in the mass ratio

We analytically compute, to linear order in the mass ratio, the ``geodetic'' spin-precession frequency of a small spinning body orbiting a large (nonspinning) body to the eight-and-a-half post-Newtonian order, thereby extending previous analytical knowledge which was limited to the third post-Newtonian level. These results are obtained applying analytical gravitational self-force theory to the first-derivative level generalization of Detweiler's gauge-invariant redshift variable. We compare our analytic results with strong-field numerical data recently obtained by Dolan et al. Phys. Rev. D 89, 064011 (2014). Our new, high-post-Newtonian-order results capture the strong-field features exhibited by the numerical data. We argue that the spin precession will diverge as -0. 14/ (1-3y) as the light ring is approached. We transcribe our kinematical spin-precession results into a corresponding improved analytic knowledge of one of the two (gauge-invariant) effective gyrogravitomagnetic ratios characterizing spin-orbit couplings within the effective-one-body formalism. We provide simple, accurate analytic fits both for spin precession and the effective gyrogravitomagnetic ratio. The latter fit predicts that the linear-in-mass-ratio correction to the gyrogravitomagnetic ratio changes sign before reaching the light ring. This strong-field prediction might be important for improving the analytic modeling of coalescing spinning binaries.