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By expecting the expression for the stopping radius in the subcritical regime ( ), one can note that the magnetic dipole moment and the accretion rate always appear in the same combination,
as was first noticed by Davis and Pringle (1981). The parameter y characterizes the ratio between the gravitational and magnetic ``properties'' of a star and will, therefore, be called the gravimagnetic parameter. Two magnetic rotators having quite different magnetic fields, subjected to different external conditions but with identical gravimagnetic parameters, have similar magnetospheres, as long as the accretion rate is quite low ( ). Otherwise, the flux of matter near the stopping radius no longer depends on the accretion rate at a large distance.
In fact, the number of independent parameters can be further reduced (see Osminkin and Prokhorov, 1995) by introducing the parameter
Plotting the rotator's period p versus the Y-parameter we can draw a somewhat less obvious but more general classification diagram than the `` '' diagram discussed above. This permits us to show on a single plot the rotators with key parameters , and spanning a very wide range (Figure 9).
Figure: The observed magnetic rotators on the universal period - gravimagnetic parameter `` '' diagram: ``+'', isolated WD (Lipunov and Nazin, 1992 ); , intermediate polars; , accreting NS; , radiopulsars. For isolated rotators, the accretion rate yr is assumed. The horizontal bar shows the orbital eccentricity-induced accretion rate change in binary pulsar PSR B1259-63.
In the case of supercritical accretion, another characteristic combination is found in all the expressions:
Analoguous to the subcritical `` '' diagram, a supercritical `` '' diagram can be drawn.