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The evolution of NS in binaries must be studied in conjunction with the evolution of normal stars. This problem was discussed qualitatively by Bisnovatyi-Kogan and Komberg (1974), van den Heuvel (1977) and Lipunov (1982a), etc. We begin with the qualitative analysis presented in the latter of these paper.
The most convenient method of analysis of NS evolution is using the diagram. It should be recalled that L is just the potential accretion luminosity of the NS. This quantity is equal to the real luminosity only at the accretion stage.
Figure: Tracks of NS on the period (p) -
gravimagnetic parameter (Y) diagram:
track of a single NS (vertical line) and of a NS in a binary system (looped
line). For the second track, possible observational appearances of the
NS are indicated.
In Figure 10 we show the evolutionary tracks of a NS. As a rule, a NS in a binary is born when the companion star belongs to the main sequence (loop-like track). During the first - years, the NS is at the ejector stage, and usually it is not seen as a radiopulsar since its pulse radiation is absorbed in the stellar wind of the normal star. The period of the NS increases in accordance with the magnetic dipole losses. After this, the matter penetrates into the light cylinder and the NS passes first into the propeller stage and then into the accretor stage. By this time, the normal star leaves the main sequence and the stellar wind strongly increases. This results in the emergence of a bright X-ray pulsar. The period of the NS stabilizes around its equilibrium value. Finally, the normal star fills the Roche lobe and the accretion rate suddenly increases; the NS moves first to the right and then vertically downward in the diagram. In other words, the NS enters the supercritical stage SA (superaccretor) and its spin period tends to a new equilibrium value (see equation (4.10.6)).
After the mass exchange, only the helium core of the normal star is left (a WR star in the case of massive stars), the system becomes detached and the NS returns back to the propeller or ejector state. Accretion is still hampered by rapid NS rotation. This is probably the reason underlying the absence of X-ray pulsars in pairs with Wolf-Rayet stars (Lipunov, 1982e). Since the helium star evolves on a rather short time-scale ( yr), the NS does not have time to spindown considerably: after explosion of the normal star, the system can be disrupted leaving the old NS as an ejector, i.e. as a high-velocity radiopulsar.
The ``loop-shaped'' track discussed above can be written in the form:
Another version of the evolutionary track of a NS formed in the process of mass exchange within a binary system is:
The overall lifetime of a NS in a binary system depends on the lifetime of the normal star and on the parameters of the binary system. However, the number of transitions from one stage to another during the time the NS is in the binary is proportional to the magnetic field strength of the NS.
Figure 11 demonstrates the effect of NS magnetic field decay (track (a) with and (b) without magnetic field decay). The first track illustrates the common path which results in the production of a typical millisecond pulsar.
Figure 11: The period-gravimagnetic parameter diagram for NS
in binary systems. (a) with NS magnetic field decay
(the oblique part of the track corresponds to ``movement'' of the accreting
NS along the so-called ``spin-up'' line), (b) a typical
track of a NS without field decay in a massive binary system.