Optical torque reversal in the slowest accreting pulsar 4U 1954+319

Abstract Wind-fed accretion onto magnetised neutron stars drives long-term spin variability that can be used to trace angular-momentum transfer in structured stellar outflows. We analyse five years of TESS optical timing to measure the spin evolution of the wind-fed X-ray pulsar 4U 1954+319, which hosts the slowest known accretion-powered pulsar. Coherent hour-scale pulsations are detected in all eight TESS sectors. The optical spin period evolves non-monotonically from 5.51 ± 0.06 h to 5.72 ± 0.06 h and then returns to 5.55 ± 0.05 h, consistent with a mid-2023 break and a torque reversal from spin-down to spin-up ( Ṗ 1 = +0.68 ± 0.08 s d −1 to Ṗ 2 = −2.16 ± 0.35 s d −1 ). The observed Ṗ corresponds to torques of N 1 = (−1.2 ± 0.1) × 10 32 dyn cm and N 2 = (+3.6 ± 0.6) × 10 32 dyn cm for a canonical moment of inertia I = 10 45 g cm 2 , while the associated spin-down power remains negligible compared with the X-ray luminosity. Within the quasi-spherical settling accretion regime, a change in mass accretion rate by a factor of ∼ 3.6 is sufficient, at the order-of-magnitude level, to account for the measured torque ratio. The inferred torque scale is compatible with a surface dipole field B ≈ (0.5 − 5) × 10 12 G, with the magnetospheric radius remaining well inside co-rotation and no requirement for a propeller transition at the inferred luminosities. No clear contemporaneous hard-X-ray brightening is apparent in the BAT monitoring, which is consistent with an origin of the optical pulsations in reprocessing of the pulsed high-energy emission. Overall, the data favour a picture in which 4U 1954+319 is a long-period, near-equilibrium wind-fed pulsar whose torque reversals can arise from moderate changes in settling accretion, without invoking magnetar-strength fields or persistent propeller transitions. They also show that long-baseline optical timing can provide useful constraints on torque balance in faint wind-fed pulsars.