As mentioned earlier, the transition of the rotator from the ejector state to the propeller state is not symmetrical. Here we consider this effect in more detail. In terms of our approach, we must study the dependence of on . To find , we must match the ram pressure of the accreting plasma with that caused by the relativistic wind or by the magnetosphere of the rotator (see Section 4.3). This dependence will be substantially different for rapidly ( ) and slowly ( ) rotating stars (see Figure 12). One can see that in the case of a fast rotator, an interval of appears where three different values of are possible, the upper value corresponding to the ejector state and the bottom value to the propeller state; the intermediate value is unstable. This means that the rotator's state is not determined solely by the value of , but also depends on previous behavior of .
Figure 12: Dependence of the stopping radius on the modified gravimagnetic radius for two possible relations between the light cylinder radius and the gravitation capture radius : (left-hand panel) and (right-hand panel; here the ejector-propeller hysteresis becomes possible).
Now consider a periodic changing of caused, for example, by the rotator's motion along an eccentric orbit, and large enough for the rotator to transit from the ejector state to the propeller state and vice versa. Initially, the rotator is in the ejector state. By approaching the normal star, the accretion rate increases and reaches a critical value , where the equilibrium points (stable point corresponding to the ejector state) and (unstable) approach (upper kink), where they merge (see Figure 12). After that only one equilibrium point remains in the system, the stopping radius jumps from down to , and the rotator changes to the propeller state.
As decreases further along the orbit and reaches the critical value once again, the reverse transition from propeller to ejector does not occur. The transition only occurs when reaches another critical value, where the unstable point meets the stable propeller point , and the stopping radius jumps from up to .
It should be noted that for fast enough rotators, a situation is possible when the step down from the ejector state occurs in such a manner that the stopping radius and the rotator passes directly to the accretion state. The reverse transition always passes through the propeller stage: . In principle, transitions from the ejector state to supercritical states SP or SA are also possible (Prokhorov, 1987a; Osminkin and Prokhorov, 1995)[166, 147]. In the case of slow rotators ( ), the ``E-P'' hysteresis is not possible, and transitions between these states are symmetrical.