Slide 9 of 59
Notes:
Pulsars are observed to slow down, ie dP/dtɬ thus they are losing rotational energy. So can the energy lost via this process account for the observed levels of emission? Or is some other process required to meet observed levels?
Rotational energy is given by half of the moment of inertia (I) multiplied by the square of the angular velocity (then just substitute to put equation in terms of P).
Differentiating, d/dt = d/dP x dP/dt
So differentiating with respect to P; d(P^-2)/dP = -2.P^-3 then substituting, which leaves a factor of dP/dt.