Magnetized Neutron Star Crust Research Articles

Magnetized neutron star crust within effective relativistic mean-field model

Even though the crystallize nature of the neutron star crust plays a pivotal role in describing various fascinating astrophysical observations, its microscopic structure is not fully understood in the presence of a colossal magnetic field. In the present work, we study the crustal properties of a neutron star within an effective relativistic mean field framework in the presence of magnetic field strength $\sim 10^{17}$G. We calculate the equilibrium composition of the outer crust by minimizing the Gibbs free energy using the most recent atomic mass evaluations. The magnetic field significantly affects the equation of state (EoS) and the properties of the outer crust, such as neutron drip density, pressure, and melting temperature. For the inner crust, we use the compressible liquid drop model for the first time to study the crustal properties in a magnetic environment. The inner crust properties, such as mass and charge number distribution, isospin asymmetry, cluster density, etc., show typical quantum oscillations (De Haas-van Alphen effect) sensitive to the magnetic field's strength. The density-dependent symmetry energy influences the magnetic inner crust like the field-free case. We study the probable modifications in the pasta structures and it is observed that their mass and thickness changes by $\sim 10-15 \%$ depending upon the magnetic field strength. The fundamental torsional oscillation mode frequency is investigated for the magnetized crust in the context of quasiperiodic oscillations (QPO) in soft gamma repeaters. The magnetic field strengths considered in this work influences only the EoS of outer and shallow regions of the inner crust, which results in no significant change in global neutron star properties. However, the outer crust mass and its moment of inertia increase considerably with increase in magnetic field strength.

Magneto-elastic equilibrium of a neutron star crust

ABSTRACT We examine the equilibrium of a magnetized neutron star crust. We calculate axially symmetric models in which an elastic force balances solenoidal motion driven by a Lorentz force. A large variety of equilibrium models are allowed by incorporating the elastic shear deformation; in addition, toroidal-magnetic-field-dominated models are available. These results remarkably differ from those in barotropic fluid stars. We demonstrate some models wherein the magnetic energy exceeds the elastic energy. The excess comes from the fact that a large amount of magnetic energy is associated with the irrotational part of the magnetic force, which is balanced with gravity and pressure. It is sufficient for equilibrium models that the minor solenoidal part is balanced by a weak elastic force. We find that the elasticity in the crust plays an important role on the magnetic field confinement. Further, we present the spatial distribution of the shear stress at the elastic limit, by which the crust-fracture location can be identified. The result has useful implications for realistic crust-quake models.

Asymmetric accretion and thermal ‘mountains’ in magnetized neutron star crusts

ABSTRACT Accreting neutron stars (NSs) are one of the main targets for continuous gravitational wave searches, as asymmetric accretion may lead to quadrupolar deformations, or ‘mountains’, on the crust of the star, which source gravitational wave (GW) emission at twice the rotation frequency. The GW torque may also impact on the spin evolution of the star, possibly dictating the currently observed spin periods of NSs in low-mass X-ray binaries and leading to the increased spin-down rate observed during accretion in PSR J1023+0038. Previous studies have shown that deformed reaction layers in the crust of the NS lead to thermal and compositional gradients that can lead to GW emission. However, there are no realistic constraints on the level of asymmetry that is expected. In this paper, we consider a natural source of asymmetry, namely the magnetic field, and calculate the density and pressure perturbations that are expected in the crust of accreting NSs. In general, we find that only the outermost reaction layers of the NS are strongly perturbed. The mass quadrupole that we estimate is generally small and cannot explain the increase of spin-down rate of PSR J1023+0038. However, if strong shallow heating sources are present at low densities in the crust, as cooling observations suggest, these layers will be strongly perturbed and the resulting quadrupole could explain the observed spin-down of PSR J1023+0038, and lead to observable GW signals from systems with higher accretion rates.

Numerical simulation of an anisotropic heat transfer in magnetized neutron stars with 3D basic operators method

We have solved numerically a three dimensional boundary-value problem for a heat transfer equation in a magnetized neutron star crust with an updated tensorial heat conductivity coefficient. The temperature distribution in a neutron star crust in presence of a magnetic field was simulated. To calculate the surface temperature distribution, we have constructed a local one-dimensional plane-parallel model of a magnetized outer envelope of the neutron star and used it as an outer boundary condition for 3D problem to find a self-consistent solution.This problem was solved with our extension of a basic (support) operators numerical method on a tetrahedral mesh. The idea of operator approach consists of inclusion the boundary conditions into difference form of the solving problem and its formulation as one operator equation. The finite difference operators are constructed in the way to fulfill corresponding relations between continuous operators (for example, div(curl)=0, div is conjugated to -grad so div(grad) is self-conjugated etc.). Such approach allows to obtain completely conservative implicit finite difference schemes. Efficient iterative methods can be used to find the solution because constructed matrixes have good properties, such as symmetry and positive definiteness.

Application of 3D basic operators method extension to astrophysical problems

Basic (support) operators method (Samarskii’s method, operator-difference method) has proven itself well in 2D numerical simulations of the astrophysical problems. An idea of the operator approach consists of the inclusion of boundary conditions in a finite difference form into the grid analogue of solving problem and formulation of the finite difference problem as an operator equation. The finite difference operators are constructed in the way to fulfill corresponding relations between continuous operators (for instance, div(rot)=0, div is conjugated to -grad; -div(grad) is self-conjugated etc.). The approach allows obtaining completely conservative finite difference schemes. The matrix which corresponds to the self-conjugated operator is symmetrical and can be inversed efficiently by modern iteration methods. In the paper a 3D generalization of 2D grid analogues for continuous differential operators using a cell-node approximation on triangular grid was realized for tetrahedral mesh. For testing we calculated a 3D Newtonian gravitational potential, and a stationary heat transfer equation in spherical layer with the first type boundary condition on the inner surface and the third type boundary condition on the outer one was calculated. The method was applied to simulation of anisotropic heat transfer in magnetized neutron star crust.

Resonant nuclear reaction 23Mg (p,γ) 24Al in strongly screening magnetized neutron star crust**Supported by National Natural Science Foundation of China (11565020), the Counterpart Foundation of Sanya (2016PT43), the Special Foundation of Science and Technology Cooperation for Advanced Academy and Regional of Sanya (2016YD28), the Scientific Research Starting Foundation for 515 Talented Project of Hainan Tropical Ocean University (RHDRC201701) and the

Based on the relativistic theory of superstrong magnetic fields (SMF), by using three models those of Lai (LD), Fushiki (FGP), and our own (LJ), we investigate the influence of SMFs due to strong electron screening (SES) on the nuclear reaction 23Mg (p,γ) 24Al in magnetars. In a relatively low density environment (e.g., ρ7<0.01) and 1<B12<102, our screening rates are in good agreement with those of LD and FGP. However, in relatively high magnetic fields (e.g., B12>102), our reaction rates can be 1.58 times and about three orders of magnitude larger than those of FGP and LD, respectively (B12, ρ7 are in units of 1012G, 107g cm−3). The significant increase of strong screening rate can imply that more 23Mg will escape from the Ne-Na cycle due to SES in a SMF. As a consequence, the next reaction, 24Al (β+, ν) 24Mg, will produce more 24Mg to participate in the Mg-Al cycle. Thus, it may lead to synthesis of a large amount of A>20 nuclides in magnetars.

Shear viscosity in magnetized neutron star crust

The electron shear viscosity due to Coulomb scattering of degenerate electrons by atomic nuclei throughout a magnetized neutron star crust is calculated. The theory is based on the shear viscosity coefficient calculated neglecting magnetic fields but taking into account gaseous, liquid and solid states of atomic nuclei, multiphonon scattering processes, and finite sizes of the nuclei albeit neglecting the effects of electron band structure. The effects of strong magnetic fields are included in the relaxation time approximation with the effective electron relaxation time taken from the field-free theory. The viscosity in a magnetized matter is described by five shear viscosity coefficients. They are calculated and their dependence on the magnetic field and other parameters of dense matter is analyzed. Possible applications and open problems are outlined.

Thermodynamic functions of magnetized Coulomb crystals

Free energy, internal energy, and specific heat for each of the three phonon spectrum branches of a magnetized Coulomb crystal with body-centered cubic lattice are calculated by numerical integration over the Brillouin zone in the range of magnetic fields $B$ and temperatures $T$, such that $0 \le \omega_{\rm B}/\omega_{\rm p}\le 10^3$ and $10^{-4} \le T/T_{\rm p} \le 10^4$. In this case, $\omega_{\rm B}$ is the ion cyclotron frequency, $\omega_{\rm p}$ and $T_{\rm p}$ are the ion plasma frequency and plasma temperature, respectively. The results of numerical calculations are approximated by simple analytical formulas. For illustration, these formulas are used to analyze the behavior of the heat capacity in the crust of a neutron star with strong magnetic field. Thermodynamic functions of magnetized neutron star crust are needed for modeling various observational phenomena in magnetars and high magnetic field pulsars.

Magnetised Neutron Star Crusts and Torsional Shear Modes of Magnetars

We discuss outer and inner crusts of neutron stars in strong magnetic fields. Here, we demonstrate the effect of Landau quantization of electrons on the ground state properties of matter in outer and inner crusts in magnetars. This effect leads to the enhancement of the electron number density in strong magnetic fields with respect to the zero field case. For the outer crust, we adopt the magnetic Baym-Pethick-Sutherland model and obtain the sequence of nuclei and equation of state (EoS). The properties of nuclei in the inner crust in the presence of strong magnetic fields are investigated using the Thomas-Fermi model. The coexistence of two phases of nuclear matter – liquid and gas, is assumed in this case. The proton number density in the Wigner-Seitz cell is affected in strong magnetic fields through the charge neutrality. We perform this calculation using the Skyrme nucleon-nucleon interaction with different parameterisations. We find nuclei with larger mass and atomic numbers in the inner crust in the presence of strong magnetic fields than those of the zero field case for all those parameter sets. Further we investigate torsional shear mode frequencies using the results of magnetised neutron star crusts and compare those with observations.

On the dynamics of mechanical failures in magnetized neutron star crusts

We consider the dynamics of a mechanical failure induced by a shear stress in a strongly magnetized neutron-star crust. We show that even if the elastic properties of the crust allow the creation of a shear crack, the strongly sheared magnetic field around the crack leads to a back-reaction from the Lorentz force which does not allow large relative displacement of the crack surfaces. Instead, the global evolution of the crack proceeds on a slow resistive time scale, and is unable to release any substantial mechanical energy. Our calculations demostrate that for {\it some} magnetic-field configurations, the magnetic forces cause, effectively, a plastic deformation of the crust when the resulting elastic shear stress exceeds the critical value for mechanical failure.

Coulomb crystals in the magnetic field

The body-centered-cubic Coulomb crystal of ions in the presence of a uniform magnetic field is studied using the rigid electron background approximation. The phonon mode spectra are calculated for a wide range of magnetic-field strengths and for several orientations of the field in the crystal. The phonon spectra are used to calculate the phonon contribution to the crystal energy, entropy, specific heat, Debye-Waller factor of ions, and the rms ion displacements from the lattice nodes for a broad range of densities, temperatures, chemical compositions, and magnetic fields. Strong magnetic field dramatically alters the properties of quantum crystals. The phonon specific heat increases by many orders of magnitude. The ion displacements from their equilibrium positions become strongly anisotropic. The results can be relevant for dusty plasmas, ion plasmas in Penning traps, and especially for the crust of magnetars (neutron stars with superstrong magnetic fields B > or approximately equal 10(14) G ). The effect of the magnetic field on ion displacements in a strongly magnetized neutron star crust can suppress the nuclear reaction rates and make them extremely sensitive to the magnetic-field direction.

Temperature distribution in magnetized neutron star crusts

We continue the study of the effects of a strong magnetic field on the temperature distribution in the crust of a magnetized neutron star (NS) and its impact on the observable surface temperature. Extending the approach initiated in Geppert et al. (2004), we consider more complex and, hence, more realistic, magnetic field structures but still restrict ourselves to axisymmetric configurations. We put special emphasis on the heat blanketing effect of a toroidal field component. We show that asymmetric temperature distributions can occur and a crustal field consisting of dipolar poloidal and toroidal components will cause one polar spot to be larger than the opposing one. These two warm regions can be separated by an extended cold equatorial belt. As an example we present an internal magnetic field structure which can explain, assuming local blackbody emission, both the X-ray and optical spectra of the isolated NS RXJ 1856-3754, the hot polar regions dominating the X-ray flux and the equatorial belt contributing predominantly to the optical emission. We investigate the effects of the resulting surface temperature profiles on the observable lightcurve which an isolated thermally emitting NS would produce for different field geometries. The lightcurves will be both qualitatively (deviations from sinusoidal shape) and quantitatively (larger pulsed fraction for the same observational geometry) different from those of a NS with an isothermal crust. This opens the possibility to determine the internal magnetic field strengths and structures in NSs by modeling their X-ray lightcurves and spectra. The striking similarities of our model calculations with the observed spectra and pulse profiles of isolated thermally emitting NSs is an indication for the existence of strong magnetic field components maintained by crustal currents.