On the physics of cold MHD winds from oblique rotators

TL;DR

This paper demonstrates that the physics of cold MHD winds from oblique rotators can be understood through axisymmetric models, showing that their properties are similar and that all pulsars are likely slow rotators emitting Poynting flux-dominated winds.

Contribution

It extends axisymmetric MHD wind solutions to oblique rotators, revealing their properties are equivalent and providing an analytical approximation for slow rotators.

Findings

Rotational losses are inclination angle independent.

Oblique rotator flows are similar to axisymmetric cases.

All radio pulsars are likely slow rotators with Poynting-dominated winds.

Abstract

I show that the self-consistent solution of the problem of MHD plasma flow in magnetosphere of an oblique rotator with an initially split-monopole magnetic field is reduced to the solution of the similar problem for the axisymmetric rotator. All properties of the MHD cold plasma flows from the axisymmetric rotators with the initially split-monopole magnetic field are valid for the oblique rotators as well. Rotational losses of the oblique rotator do not depend on the inclination angle and there is no temporal evolution of this angle. Self-consistent analytical and numerical solutions for the axisymmetric plasma flows obtained earlier show that the rotators can be divided on fast rotators ($\sigma_0/U_0^2 > 1$) and slow rotators ($\sigma_0/U_0^2 < 1$), where $\sigma_0$ is the ratio of the Poynting flux to the matter energy flux in the flow at the equator on the surface of the star, $U_0 = \gamma_0v_0/c$, $v_0$ and $\gamma_0$ are the initial velocity and Lorentz-factor of the plasma. The self-consistent approximate analytical solution for the plasma flow from the oblique rotator is obtained under the condition $\sigma_0/U_0^2 \ll 1$. Implications of these results for radio pulsars are discussed. In particular, I argue that all radio pulsars are apparently the slow rotators ejecting the Poynting dominated relativistic wind.