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The Stopping Radius in the Supercritical Case


The estimates presented above for the stopping radius were obtained under the assumption that the energy released during accretion does not exceed the Eddington limit,  so we neglected the reverse action of radiation on the accretion flux parameters.

Now, we turn to the situation where one cannot neglect the radiation pressure. Consider this effect after Lipunov (1982b)[99]. Suppose that the accretion  rate of matter captured by the magnetic rotator is such that the luminosity at the stopping radius  exceeds the Eddington limit


We shall assume (after Shakura and Sunyaev, 1973)[177] that the radiation sweeps away exactly that amount of matter which is needed for the accretion luminosity  of the remaining flux to be of the order of the Eddington luminosity  at any radius:


This gives


where tex2html_wrap_inline9504 is a spherization radius  (where the accretion luminosity first reaches the Eddington limit),  and tex2html_wrap_inline9506 designates the specific opacity of matter. Using the continuity equation, the ram pressure of the accreting plasma is now obtained as another function of the radial distance (see Figure 4)


in contrast to the subcritical regime when tex2html_wrap_inline9508 .

Matching tex2html_wrap_inline9471 and tex2html_wrap_inline9469 (see the previous section) for the supercritical case gives (see inequality (4.4.6))


The critical accretion rate tex2html_wrap_inline9514 is defined by the boundary of the inequality


and, correspondingly, is


The dependence of the Alfven radius  on the accretion rate is such that the Alfven radius (beyond the capture radius) slightly decreases with increasing accretion rate as tex2html_wrap_inline9516 , while it decerases below the capture radius as tex2html_wrap_inline9518 and attains its lowest value (4.4.5) for the critical accretion rate tex2html_wrap_inline9520 , beyond which it is independent of the external conditions.

We also note that in the supercritical regime, the pressure of the accreting plasma increases more slowly (as tex2html_wrap_inline9522 ) when approaching the magnetic rotator than the pressure of the relativistic wind (as tex2html_wrap_inline9524 ) ejected by it. This means that in the supercritical case a cavern  may exist even below the capture radius. 

The estimates presented here, of course, are most suitable for the case of disk accretion.   In fact, the supercritical regime seems to emerge most frequently under these conditions. This can be simply understood. Indeed, the accretion rate is proportional to the square of the capture radius tex2html_wrap_inline9526 . At the same time, the angular momentum of the captured matter is also proportional to tex2html_wrap_inline9528 . Hence, at high accretion rates the formation of the disk looks natural. 

next up previous contents index
Next: Effect of the Magnetic Up: ``Ecology'' of Magnetic Rotators Previous: The Stopping Radius

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