X-ray timing studies of the persistent, Galactic, accretion-powered pulsar 4U 1626$-$67 reveal torque reversals, during which the pulse frequency $\nu(t)$ alternates between multiyear episodes of secular acceleration and deceleration, separated by transitions lasting $\lesssim 150 \, \rm{ days}$. Here an unscented Kalman filter is applied to track the $\nu(t)$ fluctuations observed in 22.7 years (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 maximum a posteriori log likelihood ratio equal to 2.5. The mass accretion rate $Q(t)$ and magnetocentrifugal fastness $\omega(t)$ transition smoothly between episodes of deceleration and acceleration; $Q(t)$ shifts by $\leq 0.34 \, { \rm dex}$ across the reversal, and one measures $\omega(t) \approx 0.25$ and $\omega(t) \approx 0.30$ during deceleration and acceleration, respectively. The angular acceleration $\dot{ \Omega}(t)$ satisfies $-9 \lesssim \dot{ \Omega}(t)/(10^{ -12} \, \rm{ rad \, s^{ -2}}) \lesssim -5$ and $2 \lesssim \dot{ \Omega}(t)/(10^{ -12} \, \rm{ rad \, s^{ -2}}) \lesssim 9$ before and after the 2008 reversal, respectively, compared to $\dot{ \Omega} \approx -3.0 \times 10^{ -12} \, \rm{ rad \, s^{ -2}}$ before reversal and $\dot{ \Omega} \approx 2.5 \times 10^{ -12} \, \rm{ rad \, s^{ -2}}$ after reversal, as inferred from previous long-term X-ray timing and spectral analysis of 4U 1626$-$67.
Categories: astro-ph.HE hep-ph