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Next: The
Scenario Machine: Operational Up: Evolution
of Magnetic Rotators Previous: Ejector-propeller
hysteresis
Orbital motion of the rotator around the normal companion in an eccentric
binary draws a horizontal line on the 
diagram, with the beginning at a point corresponding to 
, and the end at a point corresponding to 
(here 
and 
are the periasrton and apastron distances, respectively). The length of
this segment is determined by the eccentricity. Since 
, the rotator moves along this segment from left to right and back as it
revolves from the apastron to the periastron. At each successive orbital
period, this line slowly drifts up to larger periods. The evolution of
this system is thus determined by the order the critical lines on the diagram
are crossed by this ``line''. It is seen from the
diagram that the regions with and without hysteresis are separated by a
certain value of the parameter 
. Since 
, four different situations are possible depending on the relationship
of the binary orbital separation a with critical value 
, corresponding to 
(Osminkin and Prokhorov, 1995[147];
see Figure 13 and corresponding cases
(a)-(d) below).
Figure 13: Possible variants of the ejector-propeller transitions
of a NS in an eccentric binary system. The NS rotational period spins down
from left to right. Four cases (a-d) correspond to different parameters
of binary systems: eccentricity, semi-axis and stellar wind
parameters as defined in the text. The hatched parts of the ellipses correspond
to propeller regime.
In this case no hysteresis occurs and transitions E--P and
the reverse take place in symmetrical points of the orbit. The rotator
passes the following sequence of stages: 
. Here EP means a mixed state of the rotator at which it is in the
ejector state during one part of the orbit, and in the propeller state
during the rest of the orbital cycle.
In this case, the hysteresis occurs at the beginning of the mixed EP-state
(state 
), but as the rotator slows down the hysteresis gradually decays and disappears.
E-P transition for this system is 
. The hysteresis is possible in principle, but the shape of the transition
depends on the eccentricity. Suppose a pulsar has spun down so much that
the first transition from the ejector to the propeller occurred at the
periastron. If the eccentricity were small 
, (do not confuse this 
with the critical eccentricity introduced in the previous section)
the reverse transition to the ejector state would not occur even at the
apastron, and the evolutionary path would be 
.
, the track is 
. It should be noted that just after the first EP transition (as
well as before the last), the system spends a finite time in the E
and P states at every revolution. The value of
can be expressed through the orbital parameters as
To conclude, we note that the hysteresis during the ejector-propeller
transition may be possible for single radiopulsars also.
For example, when the pulsar moves through a dense cloud of interstellar
plasma, the pulses can be absorbed. The radiopulsar turns on again when
it comes out from the cloud. The hysteresis amplitude for single pulsars
can be high enough because of small relative velocities of the interstellar
gas and the pulsar, so that 
