Relativistic Alfv\'en Waves Entering Charge Starvation in the Magnetospheres of Neutron Stars

TL;DR

This paper investigates how relativistic Alfvén waves in neutron star magnetospheres can sustain large currents despite charge starvation, using analytic models and kinetic simulations to assess their dissipation and implications for fast radio bursts.

Contribution

It provides a combined analytic and simulation study of charge-starved Alfvén waves, revealing their ability to propagate and dissipate energy in neutron star magnetospheres.

Findings

Alfvén waves can sustain large currents even when exceeding plasma support.

Wave dissipation power is estimated to be around 10^{35} erg/s.

Charge starvation dissipation is insufficient to power fast radio bursts.

Abstract

Instabilities in a neutron star can generate Alfv\'en waves in its magnetosphere. Propagation along the curved magnetic field lines strongly shears the wave, boosting its electric current $j_{\rm A}$. We derive an analytic expression for the evolution of the wave vector $\boldsymbol{k}$ and the growth of $j_{\rm A}$. In the strongly sheared regime, $j_{\rm A}$ 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 Alfv\'en wave continues to propagate successfully even when $\kappa \equiv j_{\rm A}/j_{0} \gg 1$. It sustains $j_{\rm A}$ 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 $L_{\rm diss}\sim 10^{35}(\kappa/100)^{1/2} (B_w/10^{11}\,{\rm G})\,\mathrm{erg/s}$, 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.