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Register a new userShear Viscosity and Oscillations of Neutron Star Crusts
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Added by
Andrey Chugunov Mr.
Publication date
2005
fields
Physics
and research's language is
English
Authors
A.I. Chugunov
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We calculate the electron shear viscosity (determined by Coulomb electron collisions) for a dense matter in a wide range of parameters typical for white dwarf cores and neutron star crusts. In the density range from ~10^3 g cm^-3 to 10^7-10^10 g cm^-3 we consider the matter composed of widely abundant astrophysical elements, from H to Fe. For higher densities, 10^10-10^14 g cm^-3, we employ the ground-state nuclear composition, taking into account finite sizes of atomic nuclei and the distribution of proton charge over the nucleus. Numerical values of the viscosity are approximated by an analytic expression convenient for applications. Using the approximation of plane-parallel layer we study eigenfrequencies, eigenmodes and viscous damping times of oscillations of high multipolarity, l~500-1000, localized in the outer crust of a neutron star. For instance, at l~500 oscillations have frequencies f >= 40 kHz and are localized not deeper than ~300 m from the surface. When the crust temperature decreases from 10^9 K to 10^7 K, the dissipation time of these oscillations (with a few radial nodes) decreases from ~1 year to 10-15 days.
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We calculate the shear viscosity $eta = eta_{emu}+eta_{n}$ in a neutron star core composed of nucleons, electrons and muons ($eta_{emu}$ being the electron-muon viscosity, mediated by collisions of electrons and muons with charged particles, and $eta_{n}$ the neutron viscosity, mediated by neutron-neutron and neutron-proton collisions). Deriving $eta_{emu}$, we take into account the Landau damping in collisions of electrons and muons with charged particles via the exchange of transverse plasmons. It lowers $eta_{emu}$ and leads to the non-standard temperature behavior $eta_{emu}propto T^{-5/3}$. The viscosity $eta_{n}$ is calculated taking into account that in-medium effects modify nucleon effective masses in dense matter. Both viscosities, $eta_{emu}$ and $eta_{n}$, can be important, and both are calculated including the effects of proton superfluidity. They are presented in the form valid for any equation of state of nucleon dense matter. We analyze the density and temperature dependence of $eta$ for different equations of state in neutron star cores, and compare $eta$ with the bulk viscosity in the core and with the shear viscosity in the crust.
In the solid crusts of neutron stars, the advection of the magnetic field by the current-carrying electrons, an effect known as Hall drift, should play a very important role as the ions remain essentially fixed (as long as the solid does not break). Although Hall drift preserves the magnetic field energy, it has been argued that it may drive a turbulent cascade to scales at which Ohmic dissipation becomes effective, allowing a much faster decay in objects with very strong fields. On the other hand, it has been found that there are Hall equilibria, i.e., field configurations that are unaffected by Hall drift. Here, we address the crucial question of the stability of these equilibria through axially symmetric (2D) numerical simulations of Hall drift and Ohmic diffusion, with the simplifying assumption of uniform electron density and conductivity. We demonstrate the 2D-stability of a purely poloidal equilibrium, for which Ohmic dissipation makes the field evolve towards an attractor state through adjacent stable configurations, around which damped oscillations occur. For this field, the decay scales with the Ohmic timescale. We also study the case of an unstable equilibrium consisting of both poloidal and toroidal field components that are confined within the crust. This field evolves into a stable configuration, which undergoes damped oscillations superimposed on a slow evolution towards an attractor, just as the purely poloidal one.
Magnetic field evolution in neutron-star crusts is driven by the Hall effect and Ohmic dissipation, for as long as the crust is sufficiently strong to absorb Maxwell stresses exerted by the field and thus make the momentum equation redundant. For the strongest neutron-star fields, however, stresses build to the point of crustal failure, at which point the standard evolution equations are no longer valid. Here, we study the evolution of the magnetic field of the crust up to and beyond crustal failure, whence the crust begins to flow plastically. We perform global axisymmetric evolutions, exploring different types of failure affecting a limited region of the crust. We find that a plastic flow does not simply suppress the Hall effect even in the regime of a low plastic viscosity, but it rather leads to non-trivial evolution -- in some cases even overreacting and enhancing the impact of the Hall effect. Its impact is more pronouced in the toroidal field, with the differences on the poloidal field being less substantial. We argue that both the nature of magnetar bursts and their spindown evolution will be affected by plastic flow, so that observations of these phenomena may help to constrain the way the crust fails.
Giant pulsar frequency glitches as detected in the emblematic Vela pulsar have long been thought to be the manifestation of a neutron superfluid permeating the inner crust of a neutron star. However, this superfluid has been recently found to be entrained by the crust, and as a consequence it does not carry enough angular momentum to explain giant glitches. The extent to which pulsar-timing observations can be reconciled with the standard vortex-mediated glitch theory is studied considering the current uncertainties on dense-matter properties. To this end, the crustal moment of inertia of glitching pulsars is calculated employing a series of different unified dense-matter equations of state.
Motivated by the narrow range of spin frequencies of nearly 20 accreting neutron stars, Bildsten (1998) conjectured that their spin-up had been halted by the emission of gravitational waves. He also pointed out that small nonaxisymmetric temperature variations in the accreted crust will lead to wavy electron capture layers, whose horizontal density variations naturally create a mass quadrupole moment. We present a full calculation of the crusts elastic adjustment to these density perturbations and find that the elastic response of the crust reduces Bildstens original estimate of the quadrupole moment in the thin outer crust by a factor of 20-50. However, this basic picture, when applied to capture layers in the deep inner crust, can generate quadrupoles in the necessary range as long as there are ~5% lateral temperature variations in the inner crust. By calculating the thermal flow throughout the core and the crust, we find that temperature gradients this large are easily maintained by asymmetric heat sources or lateral composition gradients in the crust. We also derive a general relation between the stresses and strains in the crust and the maximum quadrupole moment they can generate. We show under quite general conditions that maintaining a quadrupole of the magnitude necessary to balance the accretion torque requires dimensionless strains close to 0.01 at near-Eddington accretion rates, of order the breaking strain of conventional materials.
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