Magnetic field decay in isolated neutron stars

Abstract

We investigate three mechanisms that promote the loss of magnetic flux from an isolated neutron star. Ohmic decay produces a diffusion of the magnetic field with respect to the charged particles. It proceeds at a rate that is inversely proportional to the electric conductivity and independent of the magnetic field strength. Ohmic decay occurs in both the fluid core and solid crust of a neutron star, but it is too slow to directly affect magnetic fields of stellar scale. Ambipolar diffusion involves a drift of the magnetic field and charged particles relative to the neutrons. The drift speed is proportional to the second power of the magnetic field strength if the protons form a normal fluid. Variants of ambipolar diffusion include both the buoyant rise and the dragging by superfluid neutron vortices of magnetic flux tubes. Ambipolar diffusion operates in the outer part of the fluid core where the charged particle composition is homogeneous, protons and electrons being the only species. The charged particle flux associated with ambipolar diffusion decomposes into a solenoidal and an irrotational component. Both components are opposed by frictional drag. The irrotational component perturbs the chemical equilibrium between neutrons, protons, and electrons, thus generating pressure gradients that effectively choke it. The solenoidal component is capable of transporting magnetic flux from the outer core to the crust on a short time scale. Magnetic flux that threads the inner core, where the charged particle composition is inhomogeneous, would be permanently trapped unless particle interactions could rapidly smooth departures from chemical equilibrium. Magnetic fields undergo a Hall drift related to the Hall component of the electric field. The drift speed is proportional to the magnetic field strength. Hall drift occurs throughout a neutron star. Unlike ohmic decay and ambipolar diffusion which are dissipative, Hall drift conserves magnetic energy. Thus, it cannot by itself be responsible for magnetic field decay. However, it can enhance the rate of ohmic dissipation. In the solid crust, only the electrons are mobile and the tangent of the Hall angle is large. There, the evolution of the magnetic field resembles that of vorticity in an incompressible fluid at large Reynolds number. This leads us to speculate that the magnetic field undergoes a turbulent cascade terminated by ohmic dissipation at small scales. The small-scale components of the magnetic field are also transported by Hall drift waves from the inner crust where ohmic dissipation is slow to the outer crust where it is rapid. The diffusion of magnetic flux through the crust takes-5 x 10 8 /B 12 yr, where B 12 is the crustal magnetic field strength measured in units of 10 12 G.

The Magnetic Decoupling Stage of Star Formation

“…Goldreich & Reisenegger (1992) also adopt this approach ; they assert that ohmic dissipation should be independent of the magnetic Ðeld B. Hence, the ohmic resistivity should be isotropic ; i.e., The g MOD \ g AOD .…”

“…Thus, is equal to the increase g MAD in above the value Summarizing, then, Nakano & g M g A . Umebayashi (1986aUmebayashi ( , 1986b and Goldreich & Reisenegger (1992) separate ambipolar di †usion and ohmic dissipation as follows :…”

Magnetic field evolution in superconducting neutron stars

“…Hence, the coupling timescale is increased further, making this dissipation mechanism irrelevant. Additionally, ambipolar diffusion, describing the motion of charged particles and magnetic field lines relative to the neutrons, could cause magnetic field decay and drive the flux from the core to the crust (Goldreich & Reisenegger 1992). This mechanism was originally considered by Thompson & Duncan (1995) to explain the magnetar activity.…”

Magnetic Field Evolution in Accreting White Dwarfs

“…This effect, studied extensively in neutron stars (in particular by Goldreich & Reisenegger 1992), arises when the conducting electrons move in a fixed background of ions, and is described by the Hall term in Ohm's law, E = -(ve/c)xB, where v e = J/n e ec is the electron velocity. Physically, the field moves with the electrons, so that for example an initial poloidal field spontaneously twists under the action of its toroidal current (e.g., see Cumming & Arras 2003).…”

“…Physically, the field moves with the electrons, so that for example an initial poloidal field spontaneously twists under the action of its toroidal current (e.g., see Cumming & Arras 2003). The relevant timescale is the shearing time of the electron flow « L/v e , giving inaii w n e ecL/J sa Aim e eL 2 /cB (Goldreich & Reisenegger 1992). Evaluating the Hall time for a white dwarf gives…”