Pulsar braking and the P–$\dot{P}$ diagram

The location of radio pulsars in the period–period derivative (P–P˙) plane has been a key diagnostic tool since the early days of pulsar astronomy. Of particular importance is how pulsars evolve through the P–P˙ diagram with time. Here we show that the decay of the inclination angle (α˙) between the magnetic and rotation axes plays a critical role. In particular, α˙ strongly impacts on the braking torque, an effect that has been largely ignored in previous work. We carry out simulations that include a negative α˙ term, and show that it is possible to reproduce the observational P–P˙ diagram without the need for either pulsars with long birth periods or magnetic field decay. Our best model indicates a birth rate of one radio pulsar per century and a total Galactic population of ∼20 000 pulsars beaming towards Earth.

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