The geometry of radio pulsar magnetospheres

Data on the profiles and polarization of the 10- and 20-cm emission of radio pulsars are used to calculate the angle β between the rotational axis of the neutron star and its magnetic moment. It is shown that, for these calculations, it is sufficient to use catalog values of the pulse width at the 10% level W ₁₀, since the broadening of the observed pulses due to the transition to the full width W ₀ and narrowing of the pulses associated with the emission of radiation along tangents to the field lines approximately cancel each other out. The angles β ₁ are calculated for 283 pulsars at 20 cm and 132 pulsars at 10 cm, assuming that the line of sight passes through the center of the emission cone. The mean values of these angles are small and similar for the two wavelengths (〈β ₁〉 = 18° at λ = 10 cm and 〈β ₁〉 = 14° at λ = 20 cm). The angle β ₂ is estimated for several dozen pulsars for the case when the orientation of the angle to the line of sight is arbitrary. The mean value of β ₂ at 10 cm is found to be 〈β ₂〉 = 33.9° if the maximum derivative of the polarization position angle C is positive and 〈β ₂〉 = 52.1° ifC < 0. We find at 20 cm 〈β ₂〉 = 33.9° ifC > 0 and 〈β2〉 = 54.1° ifC < 0. The values at the two wavelengths are equal within the errors, and close to the β ₂ value obtained earlier at 30 cm (〈β ₂〉 = 36.4° if C >0 and 〈β2〉 = 49.1° if C < 0). The mean 〈β ₂〉 for the entire set of data can be taken to be 43.5°. The period dependence of the pulse width W(P) √ P ^−0.25 differs from the relation that is usually used in the polar-cap model, W(P) √ P ^−0.5. This difference could be associated with the rate of development of plasma instabilities near the surface of the neutron star (in the region where high-frequency radiation is generated). The role of the quadrupole component of the magnetic field is not important here. There is no dependence of the angle β on the pulsar age (z distance, luminosity L, or characteristic age τ = P/(2dP/dt)) for the studied sample.