Introduction

One type of pulsed X-ray binary consists of an accreting neutron star and a companion which either transfers matter through Roche-lobe overflow or a strong stellar wind. These accreting pulsars radiate predominantly in the X-ray band, and the radiation is modulated by the stellar rotation. The intrinsic stellar magnetic field is typically G ( Tesla) and is generally strong enough to truncate the accretion flow at a certain distance, resulting in field channelled flow onto the surface of the neutron star where a shock is formed and X-rays are emitted. The central star is subject to a Lorentz torque from the magnetic star-disc interaction and also from the matter inflow (which may be much smaller). Over the years, observations of various systems have provided details of the spin-up and spin-down of the X-ray pulsars, and led to the advancement of the standard theory (Ghosh and Lamb 1979a,b; Wang 1987 and many others), which appeared to provide a general explanation of these observations. The small moment of inertia of a neutron star implies that its rotation rate is more sensitive to external torques in comparison to, for instance, a white dwarf. The pulsing X-ray binaries have thus provided an excellent laboratory for probing the details of the accretion flow and the magnetosphere-star interaction.

Observations in the past twenty years have shown that most of these systems exhibit oscillations in the stellar spin rate, indicating perhaps that these systems are in rotational equilibrium. Disc fed accretion was suggested for some of these systems because the disc magnetic dragging can provide an efficient spin-down torque on the star. The earlier work of Ghosh and Lamb (1979a,b) was intended to explain the state of rotational equilibrium. In this model, the part of the accretion disc which rotates faster than the star (within the corotation radius) tends to spin up the star, while the region of slower rotation outside the corotation radius tends to spin down the star. In addition to these magnetospheric torques, the accreting matter always contributes a significant spin-up torque. The sum of these three components yield the torque-accretion rate relation (cf. Fig. 1 ):

where we have introduced the fastness parameter and a dimensionless function which represents the net torque compared to , Subscript ``k'' denotes Keplerian rotation and ``0'' denotes the characteristic distance, normally called the inner edge of the accretion disc. Stellar rotational equilibrium corresponds to N=0.

  
Figure 1: An illustration of an axisymmetry star-disc magnetic system. Geometrical quantities are: , the true inner disc radius, (which may be interpreted as used in the standard model as defined at a radius that Keplerian motion is significantly altered); , the corotation radius which divides the inner magnetosphere () and the outer magnetosphere (); finally , the radius corresponding to the last closed field line, beyond which the magnetosphere is no longer stable and the field is open. In the standard model, . The outer magnetosphere has two states: the first one corresponds to a larger magnetosphere (spin-up) and the second corresponds to a smaller one (spin-down).

The recent high time resolution X-ray observations from BATSE, however, disclosed a quite unexpected picture. The stellar torque appears to alternate in sign frequently with a transition time much shorter than the instrument could resolve ( < 1 day). The positive and negative torques have similar magnitudes but are surprisingly much larger than the mean torque deduced from the pre-BATSE data. As argued by Nelson et al. (1997), the discovery is difficult to explain in terms of the standard model, according to which the torque changes with mass accretion rate in proportion . The observations would require a finely tuned change of by about a factor three on a very short time scale in a random manner, which seems implausible.

The difficulty in invoking the variation of mass accretion rate to explain the torque reversal has led Li & Wickramasinghe (1998) to suggest a semi-quantitative model which attributes the torque-reversal entirely to variation of magnetospheric coupling. Such a picture would naturally explain the observations, and we reported our exploratory work in the ANUATC workshop. This paper is meant to be a summary of our work. We first introduce the background, then the basic idea, and finally highlight the problems and future work in this direction.

© Copyright Astronomical Society of Australia 1997