Greenhill J G , Galloway D K , Murray J R, PASA, 16 (3), 240.
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Title/Abstract Page: Angular Momentum Transfer in
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SPH modelling of a counter rotating disc
The new continuous monitoring data obtained by BATSE (Bildsten et al. 1997, Nelson et al. 1997, Chakrabarty et al. 1997) have yielded values for the mass accretion rate (X-ray luminosity) and the accretion torque (change in spin frequency) on a regular basis for a large number of X-ray pulsars. This data set has allowed a detailed comparison of the observed relation between accretion rate and torque, and that predicted by theoretical models.
The observations are not consistent with the standard Ghosh & Lamb (1979) model, since this predicts a clear correlation between spin-up and an increase in X-ray luminosity, whereas the observations show a variety of behaviour, with spin-up or spin-down occurring at the same apparent luminosity.
Numerical simulations (see Ruffert, 1997 and references therein) have shown that it is possible to form temporary accretion discs with alternating senses of rotation in wind-accreting systems. Nelson et al. (1997) made the ad hoc suggestion that many observational features of some systems that are normally thought to contain discs (GX 1+4, 4U 1626-67) would be explained if they were accreting from discs with alternately prograde and retrograde senses of rotation. Previously, Makishima et al. (1988), Dotani et al. (1989) and Greenhill et al. (1993) had also sought to explain the rapid spin-down of GX 1+4 in terms of accretion from a retrograde disc.
If the secondary star is feeding the accretion disc via Roche lobe overflow, as is almost certainly the case in 4U 1626-67, it is hard to conceive how a retrograde disc could ever come about. However, in the case of GX 1+4, the suggestion is not unreasonable. This X-ray pulsar is unique in the sense that it is accreting from a red giant or AGB star wind (Chakrabarty & Roche 1997), and is in a very wide orbit. Estimating the timescale of disc reversal for accretion from such a wind, one obtains a timescale of the order of years, and the disc would form at a large radius (
cm) so that the inner part of the accretion flow is expected to be like a normal accretion disc. A timescale of years corresponds well with the timescale on which the accretion behaviour in GX 1+4 is observed to change, with a negative correlation between accretion rate and spin-up in some phases while the disc would be retrograde, and a positive one at other times when it is prograde (Chakrabarty et al. 1997). Thus, this system is ideally suited to study the possibility of forming retrograde discs, since the timescale for disc reversal would be much longer than that of the torque fluctuations on a timescale of one day or less that are common in all types of X-ray pulsars. In the systems that accrete from a fast wind, the two timescales are comparable, and the effects will be difficult to separate.
Two dimensional smoothed particle hydrodynamics (SPH) simulations were used to investigate the interactions of an existing accretion disc with material coming in with opposite angular momentum. See Murray, de Kool & Li, 1999 for more details of the calculations. Ideally we should like to simulate the entire accretion disc. However, for GX 1+4, this would require resolution over several decades in radius. Instead we completed two separate simulations: the first being of the inner, viscously dominated region which for GX 1+4 we expect to extend from the neutron star magnetosphere out to a radius
cm; and the second being of the outer disc in which the dynamical mixing of material with opposite angular momentum dominates.
We found that in the inner disc, once the sense of rotation of inflowing material was reversed (figure 3), the existing disc was rapidly driven inside the circularisation radius of the new counter-rotating matter. Further evolution occurred on the viscous time scale, with the initial disc slowly being accreted at the same time as a second counter-rotating disc formed outside it. We found that the rate of angular-momentum accretion (i.e. the material torque, shown in figure 5) was proportional to the mass accretion rate. The material torque did not change sign until the initial disc had been entirely consumed. The change in sign of the torque was accompanied by a minimum in the accretion luminosity.
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The second calculation (figure 4) began with two counter-rotating rings with Gaussian density profiles. New material, with the same sense of rotation as the inner ring, was then added at a constant rate at the outer boundary. As with the first calculation we found the initial rings were rapidly driven in until they lay within the circularisation radius of the newly added material. We had anticipated a catastrophic cancellation of angular momentum followed by radial inflow once the rings interacted. This did not happen. Instead the rings remained cohesive with a well defined gap between them. The newly added material then formed a third, outer ring. We concluded that, 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 could be present between the circularisation radius and the radius at which the viscous timescale is comparable to the reversal timescale.
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Next Section: Discussion & Conclusions
Title/Abstract Page: Angular Momentum Transfer in
Previous Section: Spectral characteristics of GX
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