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The impact of eccentricity on the observed properties of X-ray pulsars has been considered in many papers (Guseinov, 1971; Shakura and Sunyaev, 1973; Pacini and Shapiro, 1975; Lipunov and Shakura, 1976). The most important consequence of orbital eccentricity for the evolution of rotators can be understood without detailed calculations, and suggests the existence of two different types of binary systems separated by a critical eccentricity, (Gnusareva and Lipunov, 1985)).
Consider an ideal situation when a rotator enters a binary system with some eccentricity. The normal star (no matter how) supplies matter to the compact magnetized rotator. We assume that all the parameters of the binary system (binary separation, eccentricity, masses, accretion rate, etc.) are stationary and unchanged. Then a critical eccentricity appears such that at the rotator is not able to reach the accretion state in principle. Let the rotator be rapid enough initially to be at the ejector (E) state. With other parameters constant, the evolution of such a star is determined only by its spindown. The star will gradually spindown to such a state that when passing close to the periastron where the density of the surrounding matter is higher, the pulsar will ``choke'' with plasma and pass into the propeller regime. Therefore, for a small part of its life the rotator will be in a mixed EP-state, being in the propeller state at periastron and at the ejector state close to apastron. The subsequent spindown of the rotator leads most probably to the propeller state along the entire orbit. This is due to the fact that the pressure of matter penetrating the light cylinder increases faster than that caused by relativistic wind and radiation, as first noted by Schwartzman (1971). So it proves to be much harder for the rotator to pass from the P state to the E state than from E to P state (see the following section).
The rotator will spindown ultimately to some period, , at which accretion will be possible during the periastron passage. Accretion, in contrast, will lead to a spin-up of the rotator, so that it reaches some average equilibrium state characterized by an equilibrium period defined by the balance of accelerating and decelerating torques averaged over the orbital period. If the eccentricity were zero, the rotator would be in the accretion state all the time. By increasing the eccentricity and keeping the periastron separation between the stars unchanged, we increase the contribution of the decelerating torque over the orbital period and thus decrease . At some ultimate large enough eccentricity the equilibrium period will be less than the critical period permitting the transition from the propeller state to the accretion state at apastron to occur. The rotational torque applied to the rotator, averaged over orbital period, vanishes, and in this sense the equilibrium state is achieved, but the rotator periodically passes from the propeller state to the accretion state.
Thus, X-ray pulsars with unreachable full-orbit accretion state must exist. This means that from the observational point of view such binaries will be observed as transient X-ray sources with stationary parameters for the normal component.
Typically, the evolutionary track of a rotator in an eccentric binary is
this may be a principal means of transient X-ray source formation.