2026ApJ...997..130O

X-ray timing studies of the persistent, Galactic, accretion-powered pulsar 4U 1626-67 reveal torque reversals, during which the pulse frequency ν(t) alternates between multiyear episodes of secular acceleration and deceleration, separated by transitions lasting ≲150 days. Here an unscented Kalman filter is applied to track the ν(t) fluctuations observed in 22.7 yr (3340 samples) of publicly available Compton Gamma-Ray Observatory and Fermi Gamma-Ray Space Telescope data to test the canonical picture of magnetocentrifugal accretion for consistency with prograde-prograde and retrograde-prograde accretion disk configurations on either side of the 2008 torque reversal. It is found that the retrograde-prograde model is preferred, with a log Bayes factor equal to 0.44 and a maximum a posteriori log likelihood ratio equal to 2.5. The mass accretion rate Q(t) and magnetocentrifugal fastness ω(t) transition smoothly between episodes of deceleration and acceleration: Q(t) shifts by ≤0.34 dex across the reversal, and one measures ω(t) ≈ 0.25 and ω(t) ≈ 0.30 during deceleration and acceleration, respectively. The angular acceleration $\dot{{\rm{\Omega }}}(t)$ satisfies $-9\,\lesssim \,\dot{{\rm{\Omega }}}(t)/(1{0}^{-12}\,{\rm{rad}}\,{{\rm{s}}}^{-2})\,\lesssim \,-5$ and $2\,\lesssim \,\dot{{\rm{\Omega }}}(t)/(1{0}^{-12}\,{\rm{rad}}\,{{\rm{s}}}^{-2})\,\lesssim \,9$ before and after the 2008 reversal, respectively, compared to $\dot{{\rm{\Omega }}}\approx -3.0\,\times 1{0}^{-12}\,{\rm{rad}}\,{{\rm{s}}}^{-2}$ before reversal and $\dot{{\rm{\Omega }}}\approx 2.5\times 1{0}^{-12}\,{\rm{rad}}\,{{\rm{s}}}^{-2}$ after reversal, as inferred from previous long-term X-ray timing and spectral analysis of 4U 1626-67.