Force-free pulsar magnetosphere: instability and generation of magnetohydrodynamic waves

Abstract

Context. Magnetohydrodynamic (MHD) instabilities can play an important role in the structure and dynamics of the pulsar magnetosphere. Aims. We consider the instability caused by differential rotation that is suggested by many theoretical models. Methods. Stability is considered by means of a linear analysis within the frame of the force-free MHD. Results. We argue that differentially rotating magnetospheres are unstable for any particular geometry of the magnetic field and rotation law. The characteristic growth time of instability is of the order of the rotation period. The instability can lead to fluctuations of the emission and enhancement of diffusion in the magnetosphere.

Formation of filament-like structures in the pulsar magnetosphere and the short-term variability of pulsar emission

“…In the general case, the hydrodynamic and current velocities can be comparable in the electron-positron plasma. MHD equations governing the electron-positron plasma can be obtained from the partial momentum equations for the electrons and positrons in the standard way (see Urpin 2012). Assuming that plasma is non-relativistic, the momentum equation for particles of the sort α (α = e, p) reads…”

“…where σ = e 2 n p τ e /m e is the conductivity of plasma. It was shown by Urpin (2012) that Eqs. (6)- (7) are equivalent to two equations…”

“…Hence, the hydrodynamic velocity should be non-zero as well since the current is advective. Therefore, the force-free magnetosphere can only exist if hydrodynamic motions are non-vanishing (Urpin 2012).…”

“…The magnetospheric waves can exist in the force-free pulsar magnetosphere only if the wavevector k and the unperturbed magnetic field B 0 are almost (but not exactly) perpendicular and the scalar production (k·B 0 ) is small but non-vanishing (see Urpin 2011Urpin , 2012. The reason for this is clear from simple qualitative arguments.…”

“…Such strong differential rotation should lead to instability that also arises on a timescale of the order of a rotation period. Note that the magnetorotational instability in the pulsar magnetosphere differs essentially from the standard magnetorotational instability because of a non-vanishing charge density and the force-free condition (Urpin 2012).…”