On the Nature of Pulsars. I. Theory

We present in this paper the initial installment of a quantitative exploration of one particular pulsar model. We first make plausible and then assume that the seat of the pulsar phenomenon is a rotating neutron star having a dipolar magnetic field which is not parallel to the rotation axis. We then show that such stars may be expected to emit large amounts (1050₁052 ergs) of magnetic-dipole and gravitational- quadrupole radiation, that these energy losses are inevitably associated with losses of angular momentum and increases in the rotation periods, and that the emitted low-frequency magnetic-dipole radiation is extremely efficient at accelerating charged particles to relativistic energies. An explicit expression for the period as a function of time allows us to calculate the age of the Crab Nebula (with 20 percent accuracy) and to predict the so far unobserved second derivative of the period (d2P/dt2). We also de- termine the luminosity of the nebula and the highest-energy electrons presently being injected into it- both numbers found to be in good agreement with independent observations. In extreme cases the ac- celeration mechanism can produce protons with energies up to m~c2 (e2/Gm~) '/3 or 1021 eV, which is somewhat in excess of the most energetic cosmic rays yet observed. The theory predicts a relation be- tween period, F, and rate of change of period, dP/dt 3 X 10'5/P (sec), which is well observed, in the mean, for pulsars. Finally, after determining the magnetic decay time to be about 4 million years, we predict that few pulsars should be found with periods in excess of 1. 5 seconds, also in good accord with observations. We do not discuss the origin of the pulses themselves