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The equilibrium period


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[38]; Lipunov and Shakura, 1976[109]). 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: 


  where tex2html_wrap_inline9892  s yr tex2html_wrap_inline8853 , and
tex2html_wrap_inline9896  s yr tex2html_wrap_inline8853 , tex2html_wrap_inline9900 , tex2html_wrap_inline9902  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 tex2html_wrap_inline9739 through a dimensionless factor:


The parameters tex2html_wrap_inline9479 and tex2html_wrap_inline9908 must be such that tex2html_wrap_inline9910 . Since tex2html_wrap_inline9912 , the equilibrium period in the case of disk accretion is close to the critical period, tex2html_wrap_inline9739 , 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[99])


Mike E. Prokhorov
Sat Feb 22 18:38:13 MSK 1997