2 Symmetric features of the model

It has been argued in many studies of radio properties of pulsars (e.g. Blaskiewicz et al. 1991; Gangadhara & Gupta 2001) that a rigidly rotating static-like dipole can be used as a good approximation of dipolar magnetic field as long as only most important rotation effects, of the order of $\beta = v/c$ (where v is the local corotation velocity and c is the speed of light), are to be considered. According to order-of-magnitude estimates, small distortions of the dipolar magnetosphere induced by rotationally-driven currents can be neglected: longitudinal currents suspected to flow within the open field line region cannot modify $\vec B$ by a factor exceeding $\beta^{3/2}$ whereas toroidal currents due to plasma corotation change $\vec B$ barely by a value of the order of $\beta^2$. A more comprehensive discussion of the influence of currents on the magnetospheric structure can be found in Beskin (1999) and references therein.

Below we follow the approximation of a rigidly rotating static-like dipole: at any instant the magnetic field has the shape of a static dipole in the frame which corotates with a neutron star. Moreover, the magnetosphere is assumed to be filled out everywhere with the Goldreich-Julian charge density, so that a rotation-induced electric field $\vec E = -\vec\beta\times\vec B$is present in the OF, whereas $\vec E^\prime = 0$in the frame corotating with the star. We neglect deviations from this corotational electric field which are present in the charge-deficient polar gap region - they do not exceed a factor of $\beta^{3/2}$.

In our Monte Carlo simulations (Sect. 4) development of gamma-ray radiation is based on the model of Daugherty & Harding (1982), with primary electrons being injected along magnetic field lines at an altitude of a few neutron star radii, at the magnetic colatitude corresponding to the last open magnetic field lines, and uniformly in the magnetic azimuth. The electrons are assumed to accelerate instantly to the energy $E_0 \sim 10^7$ MeV and subsequently to cool down emitting curvature photons. Some of the photons induce in turn electromagnetic cascades which propagate outwards in a form of a hollow cone beam (see Dyks & Rudak 2000 for detailed description of directionality aspects of the casades as well as viewing geometry).