tokens: polarization fraction. Note also that the magnetic pole and equator are the two main contributors to the surface emissions in the current configuration (see the explanations given later). We next discuss the phase-averaged quantities. The semi-amplitudes and polarization fractions are shown in the upper and lower panels of Figure 6 , respectively. Note that, rigorously speaking, the semi-amplitude is not a phase-averaged quantity, but we consider it here just for comparison. In this paper, the semi-amplitude is defined as the quantity related to the total variation of the polarization angle during the rotational period divided by four, which is expressed aswhere the supremum is taken over all possible partitions of the range for ψ . This definition coincides with that given in Taverna et al. ( 2015 ) in most cases but not always (see below). The photon energy is set to following Taverna et al. ( 2015 ). In the left column, the mode conversion is neglected on purpose for comparison with the previous work, whereas it is incorporated in the right column. The results without mode conversion are consistent with those in Taverna et al. ( 2015 ). The discontinuous suppression of the semi-amplitude on the diagonal line observed in our result (see the top left panel of Figure 6 ) but absent in their result is mainly due to the fact that our definition of the semi-amplitude is not completely the same as theirs. Figure 6. Semi-amplitudes of the polarization angle (upper panels) and phase-averaged polarization fractions (lower panels) for different configurations of a rotating neutron star. The left and right columns correspond to the cases without and with the mode conversion, respectively. The photon energy is set to . We explain this in more detail using Figure 7 , which shows how the polarization angle changes with the rotational phase for different combinations of η and γ . Figure 7. (a) Top views of the observed patches (orange circles) on the polarization-limiting surface in the middle row and the polarization directions (red arrows) at different rotational phases in the bottom row for (left), (center), and (right). The trajectories of the (extended) magnetic north pole are drawn in green. Blue arrows and black crosses in the bottom panels indicate the directions of the average magnetic fields at the different rotational phases and the position of the coordinate origin, respectively. (b) Polarization angles as functions of the rotational phase. The angle η is fixed to , whereas the angle γ is changed: . In the middle panels of Figure 7 (a), we schematically draw the top views of the observed patch on the polarization-limiting surface for , , and . The green circles indicate the trajectories of the (extended) magnetic north pole on this surface. Note that they are not exact circles in general. In the bottom panels, we give the corresponding average magnetic fields (blue arrows) and polarization directions (red arrows), which are estimated from the
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