Constraints on Torque‐reversing Accretion‐powered X‐Ray Pulsars

Abstract

The observed abrupt torque reversals in X-ray pulsars, 4U 1626-67, GX 1+4, and OAO 1657—415, can be explained by a transition in accretion-flow rotation from Keplerian to sub-Keplerian, which takes place at a critical accretion rate, ~1016-1017gs-1. When a pulsar system spins up near equilibrium spin before the transition, the system goes into spin-down after transition to sub-Keplerian. If a system is well into the spin-up regime, the transition can cause a sharp decrease in spin-up rate but not a sudden spin-down. These observable types of abrupt torque change are distinguished from the smooth torque variation caused by a change of in the Keplerian flow. The observed abrupt torque reversal is expected when the pulsar magnetic field B* ~5 × 1011b−1/2p L P1/2*,10 G, where the magnetic pitch parameter bp is of the order of a few, Lx,36 is the X-ray luminosity in 1036 ergs s-1, and P*,10 is the pulsar spin period in 10 s. Observed quasi-periodic oscillation (QPO) periods tightly constrain the model. For 4U 1626-67, ≈ 2.7 × 1016 g s-1 with b1/2p B* ≈ 2 × 1012 G. We estimate ~6 × 1016 g s-1 and b1/2p B* ~5 × 1013 G for GX 1+4, and ~1 × 1017 g s-1 and b1/2p B* ~2 × 1013G for OAO 1657-415. Reliable detection of QPOs before and after torque reversal could directly test the model. We discuss some outstanding uncertainties and difficulties in the present model.