Angular Momentum Transfer in the Binary X-ray Pulsar GX 1+4
Greenhill J G , Galloway D K , Murray J R, PASA, 16 (3), 240.
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Discussion & Conclusions

Optical and X-ray spectroscopy indicate that a circumstellar cloud or thick disc extends to at least 3 x 10¹² cm from the neutron star. This has a mean density $\sim 7\times 10^{10}\,{\rm cm^{-3}}$ and temperature $\sim 20,000$ K in the emission line region. We describe a model, proposed by Kotani et al (1999), in which, during the low intensity state, accretion is controlled by X-ray heating leading to an unstable negative feedback mechanism. This maintains L_X at relatively low levels but highly variable on timescales of $\sim$ months. Physical conditions in the trapped matter region may be more conducive to formation of a contra-rotating disc and neutron star spin-down when this feedback mechanism is active. When the accretion rate is high, the mechanism fails and L_X is higher and more stable. The transition between states is presumably controlled by some instability in the giant companion.

The X-ray pulse profiles from GX 1+4 changed remarkably during an observation by the RXTE satellite over 1996 July 19-21. The profiles were asymmetric and 'leading edge bright' during the early part of the observations when L_X (20-60 keV) was $\sim 6 \times 10^{36}\,{\rm erg s^{-1}}$ (source distance 10 kpc). After an interval of $\sim 6$ hr. when L_X was $\sim 10$ times lower, the intensity increased towards the initial level but the profiles had changed to 'trailing edge bright'. The change in profile may be related to a transition from spin-down to spin-up which was detected by the BATSE experiment on CGRO at about the same time. According to Greenhill et al (1998) leading edge bright/trailing edge bright profiles are normally associated with neutron star spin-down/spin-up repectively.

The X-ray spectrum during the RXTE observations was best characterised by Comptonised thermal emission with iron line emission and photo-electric absorption by cold matter in the source region. The column density n_H doubled between the the early and late phases of the observation and showed significant variation on timescales as short as 2 h. This change is too short to be associated with the feedback mechanism discussed above. The extra absorbing matter in the line of sight must be situated much closer to the neutron star.

Two dimensional SPH simulations have been used to investigate the interactions of an existing accretion disc with incoming matter having opposite angular momentum. The simulations showed that a counter-rotating disc was formed outside the existing disc which quickly shrunk inside the circularisation radius of the outer disc. The inner disc was accreted on the viscous timescale. The torque did not change until this disc was fully consumed and torque reversal was accompanied by a minimum in L_X. If the external mass reversal timescale is significantly shorter than the viscous timescale at the circularisation radius, a number of concentric rings with alternating senses of rotation can co-exist. Changes at the inner boundary of the disc occur at the same timescale as that imposed at the outer boundary. Material torque reversals occur at a minimum in L_X.

The net torque on the neutron star depends also on magnetic torques due to linkage with disc matter both inside and outside the co-rotation radius (Ghosh & Lamb, 1979, Li & Wickramasinghe, 1997). The two transitions to spin-up reported by Chakrabarty et al (1997) occurred when L_X was increasing by more than an order of magnitude from very low levels. Conversely the transition to spin-down was associated with a similar magnitude decrease to a very low level. Such transitions could be caused by a disc having alternate zones with prograde and retrograde motion. The BATSE record (Chakrabarty et al, 1997) shows that, during intervals of monotonic spin-up or monotonic spin-down, GX 1+4 and several other wind fed sources make step like transitions from one value of $\dot{P}$ to another. Hence, if the disc velocity profile has abrupt changes switching the sense of rotation between different zones, as discussed in section 4, step like changes in the magnitude of $\dot{P}$ will occur as the matter is transported inwards. The analysis by Wang & Welter (1981) indicates that asymmetry in pulse profiles may be a consequence of an asymmetry in the accretion flow onto the polar cap region. Hence, the reversal in the asymmetry of the pulse profiles observed in the RXTE data could be a consequence of accretion flow changes as the direction of rotation of the inner edge of the disc reversed. This occurred at a minimum in L_X as predicted by the SPH modelling.

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