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)[39].
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[147])
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 [117]);
, 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.