Multi-Fluid Simulation of the Magnetic Field Evolution in Neutron Stars

Abstract

Using a numerical simulation, we study the effects of ambipolar diffusion and ohmic diffusion on the magnetic field evolution in the interior of an isolated neutron star. We are interested in the behavior of the magnetic field on a long time scale, over which all Alfvén and sound waves have been damped. We model the stellar interior as an electrically neutral plasma composed of neutrons, protons and electrons, which can interact with each other through collisions and electromagnetic forces. Weak interactions convert neutrons and charged particles into each other, erasing chemical imbalances. As a first step, we assume that the magnetic field points in one fixed Cartesian direction but can vary along an orthogonal direction. We start with a uniformdensity background threaded by a homogeneous magnetic field and study the evolution of a magnetic perturbation as well as the density fluctuations it induces in the particles. We show that the system evolves through different quasi-equilibrium states and estimate the characteristic time scales on which these quasi-equilibria occur.

Noether currents for Eulerian variational principles in non-barotropic magnetohydrodynamics and topological conservations laws

“…It may be more efficient to incorporate the developed formalism in the framework of an existing code instead of developing a new code from scratch. Possible existing codes are described in Mignone et al (2010), Igumenshchev, Narayan & Abramowicz (2003) and Hoyos, Reisenegger & Valdivia (2007). Applications of this study may be useful to both linear and nonlinear stability analysis of known barotropic MHD configurations (Bernstein et al 1958;Almaguer et al 1988;Katz et al 1993;Yahalom, Katz & Inagaki 1994;Vladimirov, Moffatt & Ilin 1996, 1997, 1999Yahalom 2011).…”

Simplified variational principles for non-barotropic magnetohydrodynamics

“…Possible existing codes are described in Igumenshchev, Narayan & Abramowicz (2003), Miyoshi & Kusano (2005), Faber et al. (2006), Hoyos, Reisenegger & Valdivia (2007), Mignone et al. (2010).…”

“…It may be more efficient to incorporate the developed formalism in the frame work of an existing code instead of developing a new code from scratch. Possible existing codes are described in Igumenshchev, Narayan & Abramowicz (2003), Miyoshi & Kusano (2005), Faber et al (2006), Hoyos, Reisenegger & Valdivia (2007), Mignone et al (2010). I anticipate applications of this study both to linear and nonlinear stability analyses of known barotropic magnetohydrodynamic configurations (Bernstein et al 1958;Almaguer et al 1988;Vladimirov et al 1996Vladimirov et al , 1997Vladimirov et al , 1999.…”

“…It may be more efficient to incorporate the developed formalism in the frame work of an existing code instead of developing a new code from scratch. Possible existing codes are described in [15,16,17,18,19]. I anticipate applications of this study both to linear and non-linear stability analysis of known barotropic magnetohydrodynamic configurations [20,21,22].…”

A Three Function Variational Principle for Stationary Non-Barotropic Magnetohydrodynamics

“…We shall now show that a velocity field given by equation ( 19), such that the equations for α, β, χ, η, ν, σ, s satisfy the corresponding equations (16,21,25,27) must satisfy Euler's equations. Let us calculate the material derivative of ⃗ v:…”