Effects of Strong Magnetic Fields on the Equation of State of Cold Non-Accreting Neutron-Star Crusts (original) (raw)
Inner Crusts of Neutron Stars in Strongly Quantizing Magnetic Fields
The Astrophysical Journal, 2011
We study the properties and stability of nuclei in the inner crust of neutron stars in the presence of strong magnetic fields ∼ 10 17 G. Nuclei coexist with a neutron gas and reside in a uniform gas of electrons in the inner crust. This problem is investigated within the Thomas-Fermi model. We extract the properties of nuclei based on the subtraction procedure of Bonche, Levit and Vautherin. The phase space modification of electrons due to Landau quantisation in the presence of strong magnetic fields leads to the enhancement of electron as well as proton fractions at lower densities ∼ 0.001 fm −3. We find the equilibrium nucleus at each average baryon density by minimising the free energy and show that ,in the presence of strong magnetic fields, it is lower than that in the field free case. The size of the spherical cell that encloses a nucleus along with the neutron and electron gases becomes smaller in strong magnetic fields compared with the zero field case. Nuclei with larger mass and atomic numbers are obtained in the presence of strong magnetic fields as compared with cases of zero field.
We have investigated some of the properties of dense sub-nuclear matter at the crustal region (both the outer crust and the inner crust region) of a magnetar. The relativistic version of Thomas-Fermi (TF) model is used in presence of strong quantizing magnetic field for the outer crust matter. The compressed matter in the outer crust, which is a crystal of metallic iron, is replaced by a regular array of spherically symmetric Wigner-Seitz (WS) cells. In the inner crust region, a mixture of iron and heavier neutron rich nuclei along with electrons and free neutrons has been considered. Conventional Harrison-Wheeler (HW) and Bethe-Baym-Pethick (BBP) equation of states are used for the nuclear mass formula. A lot of significant changes in the characteristic properties of dense crustal matter, both at the outer crust and the inner crust, have been observed. Comment: 20 pages, 11 .eps figures, to appear in EPJA
Physical Review C, 2012
The equilibrium properties of the outer crust of cold nonaccreting magnetars (i.e. neutron stars endowed with very strong magnetic fields) are studied using the latest experimental atomic mass data complemented with a microscopic atomic mass model based on the Hartree-Fock-Bogoliubov method. The Landau quantization of electron motion caused by the strong magnetic field is found to have a significant impact on the composition and the equation of state of crustal matter. It is also shown that the outer crust of magnetars could be much more massive than that of ordinary neutron stars.
Effect of strong magnetic fields on the crust-core transition and inner crust of neutron stars
Physical Review C
The Vlasov equation is used to determine the dispersion relation for the eigenmodes of magnetized nuclear and neutral stellar matter, taking into account the anomalous magnetic moment of nucleons. The formalism is applied to the determination of the dynamical spinodal section, a quantity that gives a good estimation of the crust-core transition in neutron stars. We study the effect of strong magnetic fields, of the order of 10 15 -10 17 G, on the extension of the crust of magnetized neutron stars. The dynamical instability region of neutron-proton-electron (npe) matter at subsaturation densities is determined within a relativistic mean field model. It is shown that a strong magnetic field has a large effect on the instability region, defining the crust-core transition as a succession of stable and unstable regions due to the opening of new Landau levels. The effect of the anomalous magnetic moment is non-negligible for fields larger than 10 15 G. The complexity of the crust at the transition to the core and the increase of the crust thickness may have direct impact on the properties of neutrons stars related with the crust.
Effect of the Landau quantization of electrons on the inner crusts of hot neutron stars
Physical Review C, 2021
In the present work we study the effects of strongly quantizing magnetic fields and finite temperature on the properties of inner crusts of hot neutron stars. The inner crust of a neutron star contains neutron-rich nuclei arranged in a lattice and embedded in gases of free neutrons and electrons. We describe the system within the Wigner-Seitz (WS) cell approximation. The nuclear energy is calculated using Skyrme model with SkM* interaction. To isolate the properties of nuclei we follow the subtraction procedure presented by Bonche, Levit and Vautherin, within the Thomas-Fermi approximation. We obtain the equilibrium properties of inner crust for various density, temperatures and magnetic fields by minimizing the free energy of the WS cell satisfying the charge neutrality and β−equilibrium conditions. We infer that at a fixed baryon density and temperature, strong quantizing magnetic field reduces the cell radii, neutron and proton numbers in the cell compared with the field free case. However, the nucleon number in the nucleus increases in presence of magnetic field. The free energy per nucleon also decreases in magnetized inner crust. On the other hand, we find that finite temperature tends to smear out the effects of magnetic field. Our results can be important in the context of r−process nucleosynthesis in the binary neutron star mergers.
We investigate the thermal, magnetic and rotational evolution of isolated neutron stars assuming that the dipolar magnetic field is confined to the crust. Our treatment, for the first time, uses a fully general relativistic formalism not only for the thermal but also for the magnetic part, and includes partial general relativistic effects in the rotational part. Due to the fact that the combined evolution depends crucially upon the compactness of the star, three different equations of state have been employed in the calculations. In the absence of general relativistic effects, while upon increasing compactness a decrease of the crust thickness takes place leading into an accelerating field decay, the inclusion of general relativistic effects intend to "decelerate this acceleration". As a consequence we find that, within the crustal field hypothesis, a given equation of state is compatible with the observed distribution of pulsar periods P and period derivativeṖ provided the initial field strength and current location as well as the magnitude of the impurity content are appropriately constrained.
Temperature distribution in magnetized neutron star crusts
We investigate the influence of different magnetic field configurations on the temperature distribution in neutron star crusts. We consider axisymmetric dipolar fields which are either restricted to the stellar crust, "crustal fields", or allowed to penetrate the core, "core fields". By integrating the two-dimensional heat transport equation in the crust, taking into account the classical (Larmor) anisotropy of the heat conductivity, we obtain the crustal temperature distribution, assuming an isothermal core. Including classical and quantum magnetic field effects in the envelope as a boundary condition, we deduce the corresponding surface temperature distributions. We find that core fields result in practically isothermal crusts unless the surface field strength is well above 10 15 G while for crustal fields with surface strength above a few times 10 12 G significant deviations from crustal isothermality occur at core temperatures inferior or equal to 10 8 K. At the stellar surface, the cold equatorial region produced by the suppression of heat transport perpendicular to the field by the Larmor rotation of the electrons in the envelope, present for both core and crustal fields, is significantly extended by that classical suppression at higher densities in the case of crustal fields. This can result, for crustal fields, in two small warm polar regions which will have observational consequences: the neutron star has a small effective thermally emitting area and the X-ray pulse profiles are expected to have a distinctively different shape compared to the case of a neutron star with a core field. These features, when compared with X-ray data on thermal emission of young cooling neutron stars, would provide a first step toward a new way of studying the magnetic flux distribution within a neutron star.
Thermodynamics of neutrons in a magnetic field and its implications for neutron stars
Physical Review C, 2019
We investigate the effects of a magnetic field on the thermodynamics of a neutron system at finite density and temperature. Our main motivation is to deepen the understanding of the physics of a class of neutron stars known as magnetars, which exhibit extremely strong magnetic fields. Taking into account two facts: (i) the existence of a pressure anisotropy in the presence of a magnetic field and (ii) that the quantum field theory contribution to the pressure is non-negligible, we show that the maximum value that the inner magnetic field of a star can reach while being in agreement with the magneto-hydrostatic equilibrium between the gravitational and matter pressures becomes 10 17 G, an order of magnitude smaller than the previous value obtained through the scalar virial theorem; that the magnetic field has a negligible effect on the neutron system's equation of state; that the system's magnetic susceptibility increases with the temperature and that the specific heat CV does not significantly change with the magnetic field in the range of temperatures characteristic of proto neutron stars.
Many Aspects of Magnetic Fields in Neutron Stars
Universe, 2018
In this work, we explore different aspects in which strong magnetic fields play a role in the composition, structure and evolution of neutron stars. More specifically, we discuss (i) how strong magnetic fields change the equation of state of dense matter, alter its composition, and create anisotropies, (ii) how they change the structure of neutron stars (such mass and radius) and the formalism necessary to calculate those changes, and (iii) how they can affect neutron stars' evolution. In particular, we focus on how a time-dependent magnetic field modifies the cooling of a special group known as X-ray dim neutron stars.
On the structure of the crust of neutron stars
We calculate the mass and the thickness of neutron star crust s corresponding for different neutron star core mass-radius relations. The system of equilibrium equations, taking into account quantum statistics, electro-weak, and strong interactions, is for mulated within the framework of general relativity in the non-rotating spherically symmetric case . The core is assumed to be composed of interacting degenerate neutrons, protons and electrons in beta equilibrium. The strong interaction between nucleons is modeled through sigma-omega-rho meson exchange in the context of the extended Walecka model.
Crust‐Core Interactions and the Magnetic Dipole Orientation in Neutron Stars
The Astrophysical Journal, 1998
We develop an effective model for a neutron star with a magnetosphere. It takes into account the electromagnetic torques acting on the magnetic dipole, the friction forces between the crust and the core, and the gravitational corrections. Anomalous electromagnetic torques, usually neglected in a rigid star model, play here a crucial role for the alignement of the magnetic dipole. The crust-core coupling time implied by the model is consistent with the observational data and other theoretical estimations. This model describes the main features of the behavior of the magnetic dipole during the life of the star, and in particular gives a natural explanation for the n < 3 value of the breaking index in a young neutron star.
Studies of the neutron star crust
Journal of Physics: Conference Series, 2017
The physics of the neutron star crust is highly relevant for many observable phenomena like the temperature evolution of accreting neutron stars or the evolution of supernovae. In order to investigate the structure and dynamics of the crust we perform extensive molecular-dynamics-type simulations of the nucleons in the crust including the neutralizing effect of the electron background. Simulations for a range of densities, temperatures and proton-toneutron ratios have been performed. Results for the isospin dependence of the energy per particle and nucleonic correlation functions as obtained from the simulation runs are discussed.
Equation of state and thickness of the inner crust of neutron stars
Physical Review C, 2014
The cell structure of β-stable clusters in the inner crust of cold and warm neutron stars is studied within the Thomas-Fermi approach using relativistic mean field nuclear models. The relative size of the inner crust and the pasta phase of neutron stars is calculated, and the effect of the symmetry energy slope parameter, L, on the profile of the neutron star crust is discussed. It is shown that while the size of the total crust is mainly determined by the incompressibility modulus, the relative size of the inner crust depends on L. It is found that the inner crust represents a larger fraction of the total crust for smaller values of L. Finally, it is shown that at finite temperature the pasta phase in β-equilibrium matter essentially melts above 5 − 6 MeV, and that the onset density of the rodlike and slablike structures does not depend on the temperature.
The Impact of Magnetic Field on the Thermal Evolution of Neutron Stars
Astrophysical Journal, 2008
The impact of strong magnetic fields B>1013 G on the thermal evolution of neutron stars is investigated, including crustal heating by magnetic field decay. For this purpose, we perform 2D cooling simulations with anisotropic thermal conductivity considering all relevant neutrino emission processes for realistic neutron stars. The standard cooling models of neutron stars are called into question by showing that the magnetic field has relevant (and in many cases dominant) effects on the thermal evolution. The presence of the magnetic field significantly affects the thermal surface distribution and the cooling history of these objects during both the early neutrino cooling era and the late photon cooling era. The minimal cooling scenario is thus more complex than generally assumed. A consistent magnetothermal evolution of magnetized neutron stars is needed to explain the observations.
The influence of magnetic field geometry in neutron stars' crustal oscillations
Astronomische Nachrichten, 2019
In this work, we have studied oscillations in the crust of a neutron star which magnetic field has both dipolar and toroidal components, the former extends from the stellar interior to the outer space and the later is confined inside the star radius. Our study is based on the solutions we have got for perturbations in the star fluid, confined to the crust thickness. Our results are compared to the frequencies observed in the Soft Gamma Repeaters signals.
arXiv (Cornell University), 2023
We investigate outer crust compositions for a wide range of magnetic field strengths, up to B ≃ 4 × 10 18 G, employing the latest experimental nuclear masses supplemented with various mass models. The essential effects of the magnetic field are twoholds: 1) Enhancement of electron fraction, which is connected to that of protons via the charge neutrality condition, due to the Landau-Rabi quantization of electron motion perpendicular to the field, namely, neutron-richness is supressed for a given pressure. As a result, 2) nuclei can exist at higher pressures without dripping out neutrons. By exploring optimal outer-crust compositions from all possible nuclei predicted by theoretical models, we find that neutron-rich heavy nuclei with neutron magic numbers 50, 82, 126, as well as 184, with various proton numbers emerge for B 10 17 G. Moreover, we show that superheavy nuclei with proton numbers Z ≥ 104, including unknown elements such as Z = 119, 120, 122, and/or 124, depending on mass models, may emerge as an equilibrium composition at bottom layers of the outer crust for B 10 18 G, which are extremely neutron-rich (N ≈ 260-287, i.e., N/Z ≈ 2.2-2.4). We point out that those extremely neutron-rich superheavy nuclei locate around the next neutron magic number N = 258 after N = 184, underlining importance of nuclear structure calculations under such really exotic, extreme conditions. We demonstrate how the superstrong magnetic field substantially alters crustal properties of neutron stars, which may have detectable consequences.
The Astrophysical Journal, 1998
We present numerical calculations of the equation of state for dense matter in high magnetic fields, using a temperature dependent Thomas-Fermi theory with a magnetic field that takes all Landau levels into account. Free energies for atoms and matter are also calculated as well as profiles of the electron density as a function of distance from the atomic nucleus for representative values of the magnetic field strength, total matter density, and temperature. The Landau shell structure, which is so prominent in cold dense matter in high magnetic fields, is still clearly present at finite temperature as long as it is less than approximately one tenth of the cyclotron energy. This structure is reflected in an oscillatory behaviour of the equation of state and other thermodynamic properties of dense matter and hence also in profiles of the density and pressure as functions of depth in the surface layers of magnetic neutron stars. These oscillations are completely smoothed out by thermal effects at temperatures of the order of the cyclotron energy or higher.