Electromagnetic multipole fields of neutron stars

There is now indisputable evidence that some pulsars possess space velocities so high that internal asymmetries in the dynamics of their formation are strongly implied. We develop in this paper a complete formalism for the calculation of the only such mechanism that has yet been subjected to quantitative analysis: electromagnetic recoil radiation. To make the general problem tractable without doing violence to the physics, we have made the following simplifying assumptions: (1) the magnetic induction B in athin shell enclosing the surface can be satisfactorily approximated by a sum of vacuum multipole fields; (2) the star is spherical, and all parts are in good electrical contact; (3) vertical-bar Ω X r vertical-barvery-much-less-thanc everywhere within the star; and (4) the star is surrounded by a vacuum. Our qualitative conclusions hold even if these assumptions are violated, but corrections to our quantitative results required by a relaxation of our assumptions are not easily computed.Given this simple electrodynamic model of a neutron star, we solve the following problems: (1) What electric multipoles are induced by each magnetic multipole. (2) What is the general formula for the recoil produced by the projection on the rotational axis of a net linear momentum flux produced by the rotation of any two magnetic multipoles. (3) What is the set of centered multipoles that represents the field of an arbitrary off-centered multipole. We use these general results go perform a detailed analysis of the linear momentum radiated by an off-centered dipole. We find a force larger by a factor 6 than that obtained for the special case treated in the best previous calculation. In spite of this considerable increase in the computed strengrh of the effect, we still believe it to be too weak to produce the large space velocities observed for pulsars. For the mechanism to be effective, the pulsar must be born rotating near the breakup velocity