Left panel: density distribution by colour at time t = 5.8 × 10⁴ s in the (quasi)-steady state. The star is located at (r_∗,z_∗) = (0,4.8 × 10¹²) cm and the pulsar wind is injected at a distance of 2.4 × 10¹¹ cm with respect the pulsar centre at (r_p,z_p) = (0,4 × 10¹¹) cm. The grey lines show the obtained streamlines describing the trajectories of the pulsar wind fluid cells; the grey scale and the numbers are only for visualization purposes. Centre panel: distribution by colour of the module of the three-velocity at time t = 5.8 × 10⁴ s in the (quasi)-steady state. Right panel: distribution by colour of the Doppler boosting enhancement (δ⁴) for the emission produced in the shocked pulsar wind, as seen from 45° (top) and 135° (bottom) from the pulsar-star axis, at time t = 5.8 × 10⁴ s in the (quasi)-steady state.