Plasma Modes Along the Open Field Lines of a Neutron Star

TL;DR

This paper investigates electrostatic plasma modes along open magnetic field lines of a rotating neutron star within a general relativistic framework, revealing how charge density and plasma oscillations behave near the star and Schwarzschild radius.

Contribution

It derives a second order differential equation for nonlinear plasma modes in curved spacetime and analyzes the growth of plasma modes near the Schwarzschild radius.

Findings

Charge density peaks at the polar cap and remains stable in an extended region.

Plasma frequency is affected by gravitational redshift near the Schwarzschild radius.

Plasma modes can propagate with minimal damping along open field lines.

Abstract

We consider electrostatic plasma modes along the open field lines of a rotating neutron star. Goldreich-Julian charge density in general relativity is analyzed for the neutron star with zero inclination. It is found that the charge density is maximum at the polar cap and it remains almost same in certain extended region of the pole. For a steady state Goldreich-Julian charge density we found the usual plasma oscillation along the field lines; plasma frequency resembles to the gravitational redshift close to the Schwarzschild radius. We study the nonlinear plasma mode along the field lines. From the system of equations under general relativity, a second order differential equation is derived. The equation contains a term which describes the growing plasma modes near Schwarzschild radius in a black hole environment. The term vanishes with the distance far away from the gravitating object. For initially zero potential and field on the surface of a neutron star, Goldreich-Julian charge density is found to create the plasma mode, which is enhanced and propagates almost without damping along the open field lines. We briefly outline our plan to extend the work for studying soliton propagation along the open field lines of strongly gravitating objects.