A possible discrimination between two luminosity laws for radio pulsars

In order to discriminate between two different luminosity laws for radio pulsars (L₁ ∝ B² and L₂ ∝ P^-1P^0.35) their expected influence on the correlation between the magnetic field strengths and transverse velocities and on the distribution in the magnetic field versus period diagram is investigated. It is shown that both laws lead to a predicted correlation between the field strengths and the velocities, that is consistent with the observations for decay times of the magnetic field ranging from two to nine million years. However, the distributions of observable pulsars in the B vs P diagram, predicted by both laws, are very different. It is shown that the relation L ∝ B² leads to distributions that are similar to the one observed for decay times of the field between two and five million years. The other relation for the luminosity produces distributions that are inconsistent with the observed one.