tokens: X1, the most well known of these systems, periodic occultation of the source due to the precession of the warped inner disc results in a luminosity not proportional to the accretion rate and as a consequence the torque luminosity correlation is not good (Klochkov etal. 2009 ). We have seen that the dimensionless torque near the equilibrium is qualitatively different from the predictions of the existing models. Across the torque equilibrium the torque is concave-up in its dependence on the fastness parameter, whereas the existing models (Ghosh Lamb 1979b ; Li Wang 1996 ) predict concave-down (convex) relation. The torque has a cubic dependence near the torque equilibrium and the general qualitative behaviour can be represented by superposition of two hyperbolic functions and is shown to be very different from the existing analytical models. These qualitative differences indicate either that an important ingredient of the discmagnetosphere interaction is not captured in these models or that one or more of our assumptions in constructing the torque are not justified. An assumption implicit in our construction of the torque is the proportionality of the inner radius with the Alfvn radius, R in R A , yet it is possible that is not a constant but depends on the fastness parameter. This condition will be relaxed in a future study, but we would like to mention that our comparison of the dimensionless torque with the existing torque models of Ghosh Lamb ( 1979b ) and Li Wang ( 1996 ) is self-consistent in the sense that these authors also find to be constant, independent of the fastness parameter. Another assumption that can be questioned is the proportionality of luminosity, and hence the flux received, to the accretion rate. There could be two ways this assumption may fail: it is possible that the inner disc is warped and obscures some of the X-ray flux as is the case in Her X1. This possibility is recently suggested by Beri, Paul Dewangan ( 2015 ) relying on the pulse-phase dependence of the emission lines. Yet we note that the object shows a very smooth torque evolution near the torque equilibrium with a very satisfactory torqueflux correlation (Camero-Arranz etal. 2010 , 2012 ) as opposed to the case in Her X-1. This is probably because we are seeing the system face on: we do not see the Doppler modulations, yet we do know the orbital period through optical modulation of the companion (Chakrabarty 1998 ). There is another way the linear relation between the accretion rate and the luminosity could break down. Yi, Wheeler Vishniac ( 1997 ) suggested that the torque reversals from spin-up to spin-down could be a consequence of transition of the flow in the disc from a Keplerian flow to a sub-Keplerian flow. A torque reversal from spin-up to spin-down is then associated with a spectral transition from soft- to hard-state (Vaughan Kitamoto 1997 ; Yi Vishniac 1999 ). Such spectral transitions, in the case of black holes, are associated with transition
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