EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

An Introduction to the Study of Stellar Structure

Observations of magnetars and some of the high magnetic field pulsars have shown that their thermal luminosity is systematically higher than that of classical radiopulsars, thus confirming the idea that magnetic fields are involved in their X-ray emission. Here we present the results of 2D simulations of the fully-coupled evolution of temperature and magnetic field in neutron stars, including the state-of-the-art kinetic coefficients and, for the first time, the important effect of the Hall term. After gathering and thoroughly re-analysing in a consistent way all the best available data on isolated, thermally emitting neutron stars, we compare our theoretical models to a data sample of 40 sources. We find that our evolutionary models can explain the phenomenological diversity of magnetars, high-B radio-pulsars, and isolated nearby neutron stars by only varying their initial magnetic field, mass and envelope composition. Nearly all sources appear to follow the expectations of the standard theoretical models. Finally, we discuss the expected outburst rates and the evolutionary links between different classes. Our results constitute a major step towards the grand unification of the isolated neutron star zoo.

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Unifying the observational diversity of isolated neutron stars via magneto-thermal evolution models.

Magnetars are the strongest magnets in the present universe and the combination of extreme magnetic field, gravity and density makes them unique laboratories to probe current physical theories (from quantum electrodynamics to general relativity) in the strong field limit. Magnetars are observed as peculiar, burst-active x-ray pulsars, the anomalous x-ray pulsars (AXPs) and the soft gamma repeaters (SGRs); the latter emitted also three 'giant flares', extremely powerful events during which luminosities can reach up to 10(47) erg s(-1) for about one second. The last five years have witnessed an explosion in magnetar research which has led, among other things, to the discovery of transient, or 'outbursting', and 'low-field' magnetars. Substantial progress has been made also on the theoretical side. Quite detailed models for explaining the magnetars' persistent x-ray emission, the properties of the bursts, the flux evolution in transient sources have been developed and confronted with observations. New insight on neutron star asteroseismology has been gained through improved models of magnetar oscillations. The long-debated issue of magnetic field decay in neutron stars has been addressed, and its importance recognized in relation to the evolution of magnetars and to the links among magnetars and other families of isolated neutron stars. The aim of this paper is to present a comprehensive overview in which the observational results are discussed in the light of the most up-to-date theoretical models and their implications. This addresses not only the particular case of magnetar sources, but the more fundamental issue of how physics in strong magnetic fields can be constrained by the observations of these unique sources.

http://iopscience.iop.org/article/10.1088/0034-4885/78/11/116901/pdf

Magnetars: the physics behind observations. A review.

Magnetars are the strongest magnets in the present universe and the combination of extreme magnetic field, gravity and density makes them unique laboratories to probe current physical theories (from quantum electrodynamics to general relativity) in the strong field limit. Magnetars are observed as peculiar, burst--active X-ray pulsars, the Anomalous X-ray Pulsars (AXPs) and the Soft Gamma Repeaters (SGRs); the latter emitted also three "giant flares," extremely powerful events during which luminosities can reach up to 10^47 erg/s for about one second. The last five years have witnessed an explosion in magnetar research which has led, among other things, to the discovery of transient, or "outbursting," and "low-field" magnetars. Substantial progress has been made also on the theoretical side. Quite detailed models for explaining the magnetars' persistent X-ray emission, the properties of the bursts, the flux evolution in transient sources have been developed and confronted with observations. New insight on neutron star asteroseismology has been gained through improved models of magnetar oscillations. The long-debated issue of magnetic field decay in neutron stars has been addressed, and its importance recognized in relation to the evolution of magnetars and to the links among magnetars and other families of isolated neutron stars. The aim of this paper is to present a comprehensive overview in which the observational results are discussed in the light of the most up-to-date theoretical models and their implications. This addresses not only the particular case of magnetar sources, but the more fundamental issue of how physics in strong magnetic fields can be constrained by the observations of these unique sources.

Magnetars: the physics behind observations

Hydrodynamic and hydromagnetic stability

We derive general equations for axisymmetric Newtonian magnetohydrodynamics and use these as the basis of a code for calculating equilibrium configurations of rotating magnetized neutron stars in a stationary state. We investigate the field configurations that result from our formalism, which include purely poloidal, purely toroidal and mixed fields. For the mixed-field formalism, the toroidal component appears to be bounded at less than 7 per cent. We calculate distortions induced both by magnetic fields and by rotation. From our non-linear work, we are able to look at the realm of validity of perturbative work: we find for our results that perturbative-regime formulae for magnetic distortions agree to within 10 per cent of the non-linear results if the ellipticity is less than 0.15 or the average field strength is less than 10^17 G. We also consider how magnetized equilibrium structures vary for different polytropic indices.

Magnetic fields in axisymmetric neutron stars

Crustquake events may be connected with both rapid spin-up ‘glitches’ within the regular slowdown of neutron stars, and high-energy magnetar flares. We argue that magnetic-field decay builds up stresses in a neutron star's crust, as the elastic shear force resists the Lorentz force's desire to rearrange the global magnetic-field equilibrium. We derive a criterion for crust-breaking induced by a changing magnetic-field configuration, and use this to investigate strain patterns in a neutron star's crust for a variety of different magnetic-field models. Universally, we find that the crust is most liable to break if the magnetic field has a strong toroidal component, in which case the epicentre of the crustquake is around the equator. We calculate the energy released in a crustquake as a function of the fracture depth, finding that it is independent of field strength. Crust-breaking is, however, associated with a characteristic local field strength of 2.4 × 1014 G for a breaking strain of 0.001, or 2.4 × 1015 G at a breaking strain of 0.1. We find that even the most luminous magnetar giant flare could have been powered by crustal energy release alone.

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Magnetically driven crustquakes in neutron stars

The presence of superconducting and superfluid components in the core of mature neutron stars calls for the rethinking of a number of key magnetohydrodynamical notions like resistivity, the induction equation, magnetic energy and flux-freezing. Using a multi-fluid magnetohydrodynamics formalism, we investigate how the magnetic field evolution is modified when neutron star matter is composed of superfluid neutrons, type-II superconducting protons and relativistic electrons. As an application of this framework, we derive an induction equation where the resistive coupling originates from the mutual friction between the electrons and the vortex/fluxtube arrays of the neutron and proton condensates. The resulting induction equation allows the identification of two timescales that are significantly different from those of standard magnetohydrodynamics. The astrophysical implications of these results are briefly discussed.

Magnetic Field Evolution in Superconducting Neutron Stars

The interior of a neutron star is likely to be predominantly a mixture of superfluid neutrons and superconducting protons. This results in the quantization of the star's magnetic field into an array of thin flux tubes, producing a macroscopic force very different from the Lorentz force of normal matter. We show that in an axisymmetric superconducting equilibrium the behavior of a magnetic field is governed by a single differential equation. Solving this, we present the first self-consistent superconducting neutron star equilibria with poloidal and mixed poloidal-toroidal fields and also give the first quantitative results for the corresponding magnetically induced distortions to the star. The poloidal component is dominant in all our configurations. We suggest that the transition from normal to superconducting matter in a young neutron star may cause a large-scale field rearrangement.

Magnetic fields in superconducting neutron stars.

We construct barotropic stellar equilibria, containing magnetic fields with both poloidal and toroidal field components. We extend earlier results by exploring the effect of different magnetic field and current distributions. Our results suggest that the boundary treatment plays a major role in determining whether the poloidal or toroidal field component is globally dominant. Using time evolutions we provide the first stability test for mixed poloidal–toroidal fields in barotropic stars, finding that all these fields suffer instabilities due to one of the field components: these are localized around the pole for toroidal-dominated equilibria and in the closed-field line region for poloidal-dominated equilibria. Rotation provides only partial stabilization. There appears to be very limited scope for the existence of stable magnetic fields in barotropic stars. We discuss what additional physics from real stars may allow for stable fields

S. K. Lander

Papers

Magnetic fields in axisymmetric neutron stars

Magnetically driven crustquakes in neutron stars

Magnetic Field Evolution in Superconducting Neutron Stars

Magnetic fields in superconducting neutron stars.

Are there any stable magnetic fields in barotropic stars