Relativistic Alfvén Waves Entering Charge Starvation in the Magnetospheres of Neutron Stars

Abstract

Instabilities in a neutron star can generate Alfvén waves in its magnetosphere. Propagation along the curved magnetic field lines strongly shears the wave, boosting its electric current $j_{\mathrm{A}}$. We derive an analytic expression for the evolution of the wave vector $\mathbf{k}$ and the growth of $j_{\mathrm{A}}$. In the strongly sheared regime, $j_{\mathrm{A}}$ may exceed the maximum current $j_0$ that can be supported by the background $e^{\pm }$ plasma. We investigate these "charge-starved" waves, first using a simplified two-fluid analytic model, then with first-principles kinetic simulations. We find that the Alfvén wave continues to propagate successfully even when $\kappa \equiv j_{\mathrm{A}}/j_0\gg 1$. It sustains $j_{\mathrm{A}}$ by compressing and advecting the plasma along the magnetic field lines with particle Lorentz factors $\sim {\kappa }^{1/2}$. The simulations show how plasma instabilities lead to gradual dissipation of the wave energy, giving a dissipation power $L_{\mathrm{diss}}\sim 10^{35}(\kappa /100{)}^{1/2}(B_w/10^{11}\mathrm{G})erg/s$, where $B_w$ is the wave amplitude. Our results imply that dissipation due to charge starvation is not sufficient to power observed fast radio bursts (FRBs), in contrast to recent proposals.

9 pages, 5 figures, submitted to ApJ