The observed abrupt torque reversals in X-ray pulsars , 4U 1626-67 , GX 1+4 , and OAO 1657-415 , can be explained by transition in accretion flow rotation from Keplerian to sub-Keplerian , which takes place at a critical accretion rate , \sim 10 ^ { 16 } -10 ^ { 17 } g / s .
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 change of { \dot { M } } in the Keplerian flow .
The observed abrupt torque reversal is expected when the pulsar magnetic field B _ { * } \sim 5 \times 10 ^ { 11 } b _ { p } ^ { -1 / 2 } L _ { x, 36 } ^ { 1 / 2 } P _ { *, 10 } ^ { 1 / 2 } G where the magnetic pitch parameter b _ { p } \sim a few , L _ { x, 36 } is the X-ray luminosity in 10 ^ { 36 } erg / s , and P _ { *, 10 } is the pulsar spin period in 10s .
Observed quasi-periodic oscillation ( QPO ) periods tightly constrain the model .
For 4U 1626-67 , { \dot { M } } \approx 2.7 \times 10 ^ { 16 } g / s with b _ { p } ^ { 1 / 2 } B _ { * } \approx 2 \times 10 ^ { 12 } G .
We estimate { \dot { M } } \sim 6 \times 10 ^ { 16 } g / s and b _ { p } ^ { 1 / 2 } B _ { * } \sim 5 \times 10 ^ { 13 } G for GX 1+4 , and { \dot { M } } \sim 1 \times 10 ^ { 17 } g / s and b _ { p } ^ { 1 / 2 } B _ { * } \sim 2 \times 10 ^ { 13 } G for OAO 1657-415 .
Reliable detection of QPOs before and after torque reversal could directly test the model .