X-ray light curves of three X-ray pulsars , SMC X-1 , LMC X-4 and Her X-1 , folded with their respective super-orbital periods , are shown to be well reproduced by a model in which X-rays from a compact object towards us are periodically obscured by a precessing ring at the outermost part of an accretion disk around the central object .
A situation is considered in which matter from a companion star flows into a gravitational field of a compact star carrying a certain amount of specific angular momentum and first forms a geometrically thick ring-tube along the Keplerian circular orbit .
For the model to well fit to the observations , it is necessary that the optical depth of the ring-tube for Compton scattering , \tau \simeq 1 \sim 2 , the ring matter temperature , T \simeq 10 ^ { 5 } \sim 10 ^ { 6 } K and the ionization parameter , \xi \simeq 10 ^ { 2 } erg cm s ^ { -1 } due to X-ray heating from the central X-ray source .
From simple energetics- and perturbation-arguments , we find that a precession of such a ring is rather stable and possible to be excited in the T and \xi ranges .
The time during which matter accumulates in the ring is estimated to be \sim 10 ^ { 6 } s , and is shown to be comparable to the time for an accretion disk to extend from the ring .
It is discussed that in the above T and \xi ranges , the ring-tube matter could become thermally unstable .
Then , relatively high density regions in the ring-tube further cools down and tends to shrink to the tube center .
The flow across the ring circulating flow should excite turbulent motions , and angular momenta of the matter would be effectively transferred across the tube .
Finally , a steady flow should be established from the companion star through the accretion ring to the accretion disk towards the central compact star .