Results and Conclusion

We find from the analytic expression derived above that for

,

, and thus that a moderate-sized wedge of enhanced mildly relativistic electron number density develops for parameters applicable to V417 Tau. If the mildly-relativistic electrons drift very slowly, or radiate all their energy very swiftly, they would not drift far from the white dwarf, but pile up in a thin wedge of very small opening angle. At the other extreme, if the mildly-relativistic electrons drift very fast or radiate their energy very slowly, then they would drift many times around the star and smear out any azimuthal structure in the number density of the mildly-relativistic electrons. Our calculations show that the middle ground of a moderate-sized wedge of enhanced mildly-relativistic electron number density forms.

In our numerical work (Nicholls and Storey 1998) we use various models for the azimuthal distribution of the mildly-relativistic electrons in the region of enhanced density, to simulate the loss of energy of the electrons through synchrotron radiation. Such models include linear and power law decreases of electron density with azimuthal angle. Those models with an opening angle for the wedge of

, regardless of the way the electron number density decreases with azimuthal angle, best reproduce the orbital phases of the peaks and troughs of the observed data. This range of angles agrees closely with the estimates from the analytical work above.

In summary, for mildly relativistic electrons we have calculated analytically the bounce-average drift velocity and the bounce-average lifetime, t_f, in a dipolar magnetic field, and used these expressions to find the average angle through which such electrons drift during time t_f. We have applied this analytic expression to the model for V471 Tau and shown that the numerical results are consistent with the analytic approximation.

© Copyright Astronomical Society of Australia 1997