Magnetohydrodynamics of neutron star interiors

Abstract

The dynamics of the charged particles in the fluid interior of rotating magnetized neutron stars (pulsars) is investigated. It is shown that a magnetohydrodynamic approach is valid under a wide variety of conditions. The small amplitude waves that can propagate in the "charged" <-4 fluid are sound waves (period ^> 10 sec), inertial waves (-1 sec) and hydromagnetic-inertial waves (£ months). Generally, the most effective damping mechanism is viscosity. Viscous damping times for hydromagneticinertial waves can be as long as hundreds of years. Several normal sound mode and normal inertial mode calculations are performed. The motion of the charged fluid over the time scales of inertial waves and hydromagnetic-inertial waves is simulated on a computer. Mode-mode coupling, boundary layers, and the acceleration of the crust due to charged fluid motion are also studied. The most important conclusion in this thesis is that the time the charged fluid as a whole takes to respond to a sudden disturbance such as a change in the angular velocity or acceleration of the crust is the time for a long wavelength hydromagnetic-inertial wave to cross the star. Contrary to an assumption which has been made in models of pulsar postglitch behaviour, the charged fluid response time is not necessarily small compared to post-glitch relaxation times. In view of this, models of post-glitch behaviour which assume that the charged fluid response time is small compared to post-glitch relaxation times should be reexamined .

Two-fluid models of superfluid neutron star cores

“…Electrons and muons are transformed into each other via the lepton‐modified Urca processes where X is either a nucleon or a lepton (the direct process is kinematically forbidden). The relaxation time associated with electromagnetic processes, of the order of 10 −22 s (Easson & Pethick 1979), is much smaller than the characteristic time‐scales of the neutron star phenomena considered here, so that the matter can be treated as electrically neutral. This condition reads …”

Ultrahigh energy cosmic ray acceleration in newly born magnetars and their associated gravitational wave signatures

“…[19] find that the value of β can range between 1 − 10 for perfectly conducting interiors (normal matter), 10−100 for type I superconductors and can reach 100 for type II superconductors. The relation above might not stand however when the interior magnetic field is dominated by the toroidal component [22], and the magnetar internal field being already close to or exceeding the critical field value (of order 10 15 G [38]), it is possible that no significant enhancement of the magnetar deformation happens beyond ε ∼ 10 −4 − 10 −3 . In the following, we will rely on this relation for simplicity.…”

Type I and two-gap superconductivity in neutron star magnetism

“…Easson & Pethick (1979) have given the transport relaxation time for electrons charge neutralized by normal protons, number densities N e = N p . It is In this expression, α is the fine structure constant; k Fe and ε Fp are the electron Fermi wave number and proton Fermi energy.…”

“…In this frame, it has the familiar dipole form, with components ( v l ) s =− U a 2 cos θ/ s 2 and ( v l ) θ =− U a 2 sin θ/ s 2 , for filament velocity U perpendicular to its axis. By integration of the expression for the dissipation rate per unit volume given in terms of the stress tensor (see Landau & Lifshitz 1959), we find that the electronic viscous force per unit length acting on a filament is, in which the shear viscosity is, (Easson & Pethick 1979) and is of the order of 10 20 g cm −1 s −1 at 10 8 K. It is worth noting that the same calculation, made for a sphere of radius a , gives a force −12πη e a U which is twice the Stokes force, an example of the minimum dissipation theorem (see Batchelor 1967, p. 227). is independent of a provided a ≫ c τ e μ and so can be significant for thin filaments.…”