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Determination of the 'diffusion coefficient'.

At first we shall estimate D, using eq. (6). In this equation all variables, except , are known (in principle). Their values taken from Lipunov (1992) are shown in table 1.

Nagase (1992) gives results of GINGA observations of the cyclotron lines in X-ray pulsars. For Vela X-1 and Her X-1 values of magnetic field, B, coincides with the values that we used when radii of NS's are and correspondently. The value for B obtained from observations for Vela X-1, , coincides quite well with the assumption that there is no stable accretion disk in this pulsar.

Characteristic time for the wind-accreting systems can be determined from the equation:

where - a fraction of the specific angular momentum of the Kepler orbit at the magnitospheric radius, A-noise level (see table 2) (de Kool Anzer 1993).

 
Table 2:

In eq.(6) for we must use minimum values. These times were calculated using equations for pure spin-up from Lipunov (1992), are shown in table 1.

We took From eq. (7) we can get for Vela X-1 and GX 301-2. For Her X-1 and Cen X-3, is determined from the graph in de Kool Anzer (1993) (see table 3). So we can write equation for D in the form:

Values of D for four systems are shown in table 3.

From the theory of diffusion we can write:

where is the characteristic length in the frequency space.

For characteristic time in this space we can write:

We can give a physical interpretation for for wind-fed pulsars as a characteristic time of the momentum transfer:

For we obtain and for we obtain . These velocities are close to obtained using estimates of the 'diffusion coefficient'.

These characteristic time scales are also shown in table 3.

 

Table 3: