surface magnetic field. The energy injected into the pairs all comes from the spin-down and the surface magnetic field is assumed to be constant. In the CZ01 model, $$\label{eq:Emean}
{\overline{E}}\simeq 44 {\rm GeV} \left(\frac{P}{0.1 {\rm s}}\right)^{-3.6}\left(\frac{B}{10^{12} {\rm G}}\right)^{0.27}\,$$ where $P$ is the period of the pulsar at the time of emission and one of the parameters of the CZ01 model, the fraction of pairs escaping from the light cylinder, is set to 0.01.

The CZ01 model converts a fraction of the available spin-down power for pulsar ages $>10^5~ {\rm yr}$ to pairs. To set the scale we note that in this model, for $P=0.5~ {\rm s}$ and $B=10^{12}~ {\rm  G}$, the differential $e^+ e^-$ emission rate is $10^{35} /{\rm GeV}/{\rm s}$, with mean energy $1 ~{\rm
  GeV}$. Only the gamma-ray pulsars are assumed to produce $e^+ e^-$ pairs in this model and this introduces a $B$ dependent upper-limit on the period ($P < 0.25 (B/10^{12} {\rm G})^{6/13} {\rm  s}$).

To predict the properties of the pulsar today, we need the initial period and magnetic field, and also the initial kick that the nascent neutron star received when the supernova occurred. The CZ01 study includes a Monte Carlo of these and 