Plasma flow in force-free magnetospheres: two-fluid model near pulsars and black holes

Abstract

Force-free electrodynamics describes the electromagnetic field of the magnetically dominated plasma found near pulsars and active black holes, but gives no information about the underlying particles that ultimately produce the observable emission. Working in the two-fluid approximation, we show how particles can be "painted on" to a force-free solution as a function of boundary conditions that encode the particle output of "gap regions" where the force-free approximation does not hold. These boundary conditions also determine the leading parallel electric field in the entire magnetosphere. Our treatment holds in a general (possibly curved) spacetime and is phrased in language intrinsic to the 1+1 dimensional "field sheet spacetimes" experienced by particles stuck to magnetic field lines. Besides the new results, this provides an elegant formulation of some standard equations; for example, we show that the zero-gyroradius guiding center approximation is just the Lorentz force law on the field sheet. We derive a general perturbative method and apply it to pulsar and black hole magnetospheres with radial magnetic fields to produce fully analytic models that capture key features of the full problem. When applied to more realistic magnetic field configurations together with simulation-informed boundary conditions for the gap regions, this approach has the potential to provide global magnetosphere models without the need for global particle-in-cell simulations.

Figures (7)

• Figure 1:
• Figure 2:
• Figure 4: Light cylinder acceleration in a finely tuned region of parameter space. Centrifugal acceleration of the low-velocity positrons causes extreme acceleration of the modest-velocity to electrons (see text for details). The setup and parameters are the same as Fig. \ref{['fig: Michel r velocity e p']} except where indicated.
• Figure 5: The parallel electric field of the flow in Fig. \ref{['fig: Michel r velocity e p']}. The sign of $\delta E_{0}$ is positive at the star and becomes negative before reaching the LC. The strength of the electric field is larger for the flow that has a larger separation in the velocity of electrons and positrons. Notice that even at the turning points, the electric field does not diverge.
• Figure 6: The parallel electric field for the flow of Fig. \ref{['fig: Michel r velocity e p SA']}, where features light cylinder acceleration. Our analytic estimates (\ref{['eq:location SA']}) and (\ref{['eq: strongest E at LC']}) for location and value (respectively) of the strongest electric field are shown as gray lines in the inset.