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The evolution equation presented above indicates that an accreting compact star must endeavor to attain an equilibrium state in which the resultant torque vanishes (Davidson and Ostriker, 1973; Lipunov and Shakura, 1976). This hypothesis is confirmed by observations of X-ray pulsars.
By equating the right-hand side of equation (4.10.2) to zero, we obtain the equilibrium period:
s yr , , days.
Let us turn to the case of disk accretion. The above model of the spin-up and spin-down torques possesses an unexpected property. The equilibrium period obtained by setting the torque to zero is connected with the critical period through a dimensionless factor:
The parameters and must be such that . Since , the equilibrium period in the case of disk accretion is close to the critical period, , separating accretion stage A and the propeller stage P. In the case of the supercritical accretion the equilibrium period is determined by formula (Lipunov, 1982b)