On the mean profiles of radio pulsars. III. Identifying the mode

Radio pulsars emit in two orthogonal polarization modes---ordinary (O mode) and extraordinary (X mode). Earlier theoretical work predicted that these modes can be identified by comparing circular polarization with the swing of the linear polarization angle. Testing these ideas on large observational datasets allows us to evaluate the statistical imprint of each mode on pulsar populations. The study aims to determine which polarization mode dominates in different profile types, to examine how pulse width statistics depend on mode identification, and to explore how these properties relate to pulsar spin-down energy and the occurrence of flat polarization angle curves. We analyzed polarization data from seven partially overlapping surveys. The source lists contain over 1400 unique pulsars. We classified the dominant mode from the correlation between the signs of the circular polarization V and of the position-angle derivative, dPA/dϕ. We examined pulse width distributions and relationships with spin-down energy loss rates. We find that 70% of single-profile classifications are X-mode ones and 71% of double-profile classifications are O-mode ones. The association is significant in every survey. In the two largest classified samples, the normalized pulse-width distributions are systematically narrower for X-mode than for O-mode pulsars, with catalog-dependent peaks near 7 9^̧irc for X-mode pulsars and ∼12^̧irc for O-mode pulsars. X-mode single profiles become increasingly prevalent at higher spin-down energy rates (>10 -- 33 erg/s). We identify pulsars with flat position angle curves, predominantly with shorter periods. The mode--profile association, the beam-radius scales, and the trend are consistent with the propagation-theory picture in which the O mode is refracted away from the magnetic axis while the X mode propagates rectilinearly. While mode assignments remain statistical, sample limitations and complex mode mixing require further research. Multifrequency polarimetry will be the decisive next test.