Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information they might yield about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on equilibrium properties and on nonaxisymmetric oscillations and instabilities in $f$-modes and $r$-modes have been updated. Several new sections have been added on equilibria in modified theories of gravity, approximate universal relationships, the one-arm spiral instability, on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity including both hydrodynamic and magnetohydrodynamic studies of these objects.

Rotating Stars in Relativity

Context. The photospheres of about 5–10% of the upper main sequence stars exhibit remarkable chemical anomalies. Many of these chemically peculiar (CP) stars have a global magnetic field, the origin of which is still a matter of debate. Aims. We present a comprehensive statistical investigation of the evolution of magnetic CP stars, aimed at providing constraints to the theories that deal with the origin of the magnetic field in these stars. Methods. We have collected from the literature data for 150 magnetic CP stars with accurate Hipparcos parallaxes. We have retrieved from the ESO archive 142 FORS1 observations of circularly polarized spectra for 100 stars. From these spectra we have measured the mean longitudinal magnetic field, and discovered 48 new magnetic CP stars (five of which belonging to the rare class of rapidly oscillating Ap stars). We have determined effective temperature and luminosity, then mass and position in the H-R diagram for a final sample of 194 magnetic CP stars. Results. We found that magnetic stars with $M > 3 ~M_\odot$ are homogeneously distributed along the main sequence. Instead, there are statistical indications that lower mass stars (especially those with $M \le 2~M_\odot$) tend to concentrate in the centre of the main sequence band. We show that this inhomogeneous age distribution cannot be attributed to the effects of random errors and small number statistics. Our data suggest also that the surface magnetic flux of CP stars increases with stellar age and mass, and correlates with the rotation period. For stars with $M > 3~M_\odot$, rotation periods decrease with age in a way consistent with the conservation of the angular momentum, while for less massive magnetic CP stars an angular momentum loss cannot be ruled out. Conclusions. The mechanism that originates and sustains the magnetic field in the upper main sequence stars may be different in CP stars of different mass.

https://www.aanda.org/articles/aa/pdf/2006/17/aa4596-05.pdf

Evolutionary state of magnetic chemically peculiar stars

Context. We study the physics of the solar tachocline (i.e. the thin transition layer between differential rotation in the convection zone and quasi uniform rotation in the radiative interior), and related MHD instabilities. Aims. We have performed 3D MHD simulations of the solar radiative interior to check whether a fossil magnetic field is able to prevent the spread of the tachocline. Methods. Starting with a purely poloidal magnetic field and a latitudinal shear meant to be imposed by the convection zone at the top of the radiation zone, we have investigated the interactions between magnetic fields, rotation and shear, using the spectral code ASH on massively parallel supercomputers. Results. In all cases we have explored, the fossil field diffuses outward and ends up connecting with the convection zone, whose differential rotation is then imprinted at latitudes above ≈40 ◦ throughout the radiative interior, according to Ferraro’s law of isorotation. Rotation remains uniform in the lower latitude region which is contained within closed field lines. We find that the meridional flow cannot stop the inward progression of the differential rotation. Further, we observe the development of non-axisymmetric magnetohydrodynamic instabilities, first due to the initial poloidal configuration of the fossil field, and later to the toroidal field produced by shearing the poloidal field through the differential rotation. We do not find dynamo action as such in the radiative interior, since the mean poloidal field is not regenerated. But the instability persists during the whole evolution, while slowly decaying with the mean poloidal field; it is probably sustained by small departures from isorotation. Conclusions. According to our numerical simulations, a fossil magnetic field cannot prevent the radiative spread of the tachocline, and thus it is unable to enforce uniform rotation in the radiation zone. Neither can the observed thinness of that layer be invoked as a proof for such an internal fossil magnetic field.

/pdf/magnetic-confinement-of-the-solar-tachocline-1r8jqbisd5.pdf

Magnetic confinement of the solar tachocline

Context The understanding of fossil fields’ origin, topology, and stability is one of the corner stones of the stellar magnetism theory On one hand, since they survive on secular time scales, they may modify the structure and the evolution of their host stars On the other hand, they must have a complex stable structure since it has been demonstrated that the simplest purely poloidal or toroidal fields are unstable on dynamical time scales In this context, the only stable configuration found today is the one resulting from a numerical simulation by Braithwaite and collaborators who studied the evolution of an initial stochastic magnetic field, which is found to relax on a mixed stable configuration (poloidal and toroidal) that seems to be in equilibrium and then diffuses Aims We investigate an equilibrium field in a semi-analytical way In this first article, we study the barotropic magnetohydrostatic equilibrium states Methods The problem reduces to a Grad-Shafranov-like equation with arbitrary functions These functions are constrained by deriving the lowest-energy equilibrium states for given invariants of the considered axisymmetric problem, in particular for a given helicity known to be one of the causes of such problems These theoretical results were applied to realistic stellar cases, the solar radiative core and the envelope of an Ap star, and discussed In both cases we assumed that the field is initially confined in the stellar radiation zone Results The generalization of the force-free Taylor’s relaxation states studied in laboratory experiments (in spheromaks) that become non force-free in the self-gravitating stellar case are obtained The case of general baroclinic equilibrium states will be studied in Paper II

/pdf/relaxed-equilibrium-configurations-to-model-fossil-fields-i-58tefwgg80.pdf

Relaxed equilibrium configurations to model fossil fields I. A first family

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.

/pdf/magnetically-driven-crustquakes-in-neutron-stars-vdgl438ir5.pdf

R. J. Tayler

Papers

The adiabatic stability of stars containing magnetic fields. IV - Mixed poloidal and toroidal fields