Multidimensional thermal structure of magnetized neutron star envelopes

Recently launched X-ray telescopes have discovered several candidate isolated neutron stars. The thermal radiation from these objects may potentially constrain our understanding of nuclear physics in a realm inaccessible to terrestrial experiments. To translate the observed fluxes from neutron stars into constraints, one needs precise calculations of the heat transfer through the thin insulating envelopes of neutron stars. We describe models of the thermal structure of the envelopes of neutron stars with magnetic fields up to 10¹⁴ G. Unlike earlier work, we infer the properties of envelope models in two dimensions and precisely account for the quantization of the electron phase-space. Both dipole and uniformly magnetized envelopes are considered.     

On the meaning and inapplicability of the Zeldovich relations of magnetohydrodynamics

Considering a plasma with an initially weak large scale field subject to nonhelical turbulent stirring, Zeldovich (1957), for two‐dimensions, followed by others for three dimensions, have presented formulae of the form 〈b²〉 = f(R_M) . Such “Zeldovich relations” have sometimes been interpreted to provide steady‐state relations between the energy associated with the fluctuating magnetic field and that associated with a large scale or mean field multiplied by a function f that depends on spatial dimension and a magnetic Reynolds number R_M. Here we dissect the origin of these relations and pinpoint pitfalls that show why they are inapplicable to realistic, dynamical MHD turbulence and that they disagree with many numerical simulations. For 2D, we show that when the total magnetic field is determined by a vector potential, the standard Zeldovich relation applies only transiently, characterizing a maximum possible value that the field energy can reach before necessarily decaying. In 3D, we show that the standard Zeldovich relations are derived by balancing subdominant terms. In contrast, balancing the dominant terms shows that the fluctuating field can grow to a value independent of R_M and the initially imposed , as seen in numerical simulations. We also emphasize that these Zeldovich relations of nonhelical turbulence imply nothing about the amount mean field growth in a helical dynamo. In short, by re‐analyzing the origin of the Zeldovich relations, we highlight that they are inapplicable to realistic steady‐states of large R_M MHD turbulence. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Equilibrium configurations of strongly magnetized neutron stars with realistic equations of state

We investigate equilibrium sequences of magnetized rotating stars with four kinds of realistic equations of state (EOSs) of SLy, FPS, Shen and LS, employing the Tomimura–Eriguchi scheme to construct the equilibrium configurations. We study the basic physical properties of the sequences in the framework of Newtonian gravity. In addition, we take a new step by taking into account a general relativistic effect to the magnetized rotating configurations. With these computations, we find that the properties of the Newtonian magnetized stars, e.g. structure of magnetic field, highly depends on the EOSs. The toroidal magnetic fields concentrate rather near the surface for Shen and LS EOSs than those for SLy and FPS EOSs. The poloidal fields are also affected by the toroidal configurations. Paying attention to the stiffness of the EOSs, we analyse this tendency in detail. In the general relativistic stars, we find that the difference due to the EOSs becomes small because all the employed EOSs become sufficiently stiff for the large maximum density, typically greater than  10¹⁵ g cm⁻³  . The maximum baryon mass of the magnetized stars with axis ratio   q ∼ 0.7  increases about up to 20 per cent for that of spherical stars. We furthermore compute equilibrium sequences at finite temperature, which should serve as an initial condition for the hydrodynamic study of newly born magnetars. Our results suggest that we may obtain information about the EOSs from the observation of the masses of magnetars.     

The influence of Hall drift on the magnetic fields of neutron stars

We consider the evolution of magnetic fields under the influence of Hall drift and Ohmic decay. The governing equation is solved numerically, in a spherical shell with   r _i / r _o = 0.75  . Starting with simple free-decay modes as initial conditions, we then consider the subsequent evolution. The Hall effect induces so-called helicoidal oscillations, in which energy is redistributed among the different modes. We find that the amplitude of these oscillations can be quite substantial, with some of the higher harmonics becoming comparable with the original field. Nevertheless, this transfer of energy to the higher harmonics is not sufficient to accelerate significantly the decay of the original field, at least not at the   R _B = O (100)  parameter values accessible to us, where this Hall parameter   R _B   measures the ratio of the Ohmic time-scale to the Hall time-scale. We do find clear evidence though of increasingly fine structures developing for increasingly large   R _B   , suggesting that perhaps this Hall-induced cascade to ever-shorter length-scales is eventually sufficiently vigorous to enhance the decay of the original field. Finally, the implications for the evolution of neutron star magnetic fields are discussed.     

Relativistic models of magnetars: the twisted torus magnetic field configuration

We find general relativistic solutions of equilibrium magnetic field configurations in magnetars, extending previous results of Colaiuda et al. Our method is based on the solution of the relativistic Grad–Shafranov equation, to which Maxwell's equations can be reduced. We obtain equilibrium solutions with the toroidal magnetic field component confined into a finite region inside the star, and the poloidal component extending to the exterior. These so-called twisted torus configurations have been found to be the final outcome of dynamical simulations in the framework of Newtonian gravity, and appear to be more stable than other configurations. The solutions include higher-order multipoles, which are coupled to the dominant dipolar field. We use arguments of minimal energy to constrain the ratio of the toroidal to the poloidal field.     

A new numerical scheme for structures of rotating magnetic stars

We have developed a new numerical scheme for obtaining structures of rapidly rotating stars with strong magnetic fields. In our scheme, both poloidal and toroidal magnetic fields can be treated for stars with compressibility and infinite conductivity. By introducing the vector potential and its integral representation, we can treat the boundary condition for the magnetic fields across the surface properly. We show structures and distributions of magnetic fields as well as the distributions of the currents of rotating magnetic polytropic stars with polytropic index   N = 1.5  . The shapes of magnetic stars are oblate as long as the magnetic vector potential decreases as 1/ r when   r →∞  . For extremely strong magnetic fields, equilibrium configurations can be of toroidal shapes.     

On the incidence of magnetic fields in slowly pulsating B, β Cephei and B-type emission-line stars

We have obtained 40 high-resolution circular spectropolarimetric measurements of 12 slowly pulsating B (SPB) stars, eight β Cephei stars and two Be stars with the Echelle Spectropolarimetric Device for the Observation of Stars at CFHT (ESPaDOnS) and Narval spectropolarimeters. The aim of these observations is to evaluate recent claims of a high incidence of magnetic field detections in stars of these types obtained using low-resolution spectropolarimetry by Hubrig et al. The precision achieved is generally comparable to or superior to that obtained by Hubrig et al., although our new observations are distinguished by their resolution of metallic and He line profiles, and their consequent sensitivity to magnetic fields of zero net longitudinal component. In the SPB stars, we confirm the detection of magnetic field in one star (16 Peg), but find no evidence of the presence of fields in the remaining 11. In the β Cep stars, we detect a field in  ξ¹  CMa, but not in any of the remaining seven stars. Finally, neither of the two B-type emission-line stars shows any evidence of magnetic field. Based on our results, we conclude that fields are not common in SPB, β Cep and B-type emission-line stars, consistent with the general rarity of fields in the broader population of main sequence B-type stars. A relatively small, systematic underestimation of the error bars associated with the UV Focal Reducer and Low Dispersion Spectrograph for the Very Large Telescope (FORS1) longitudinal field measurements of Hubrig et al. could in large part explain the discrepancy between their results and those presented here.     

Relating stellar cycle periods to dynamo calculations

Stellar magnetic activity in slowly rotating stars is often cyclic, with the period of the magnetic cycle depending critically on the rotation rate and the convective turnover time of the star. Here we show that the interpretation of this law from dynamo models is not a simple task. It is demonstrated that the period is (unsurprisingly) sensitive to the precise type of non-linearity employed. Moreover the calculation of the wave-speed of plane-wave solutions does not (as was previously supposed) give an indication of the magnetic period in a more realistic dynamo model, as the changes in length-scale of solutions are not easily captured by this approach. Progress can be made, however, by considering a realistic two-dimensional model, in which the radial length-scale of waves is included. We show that it is possible in this case to derive a more robust relation between cycle period and dynamo number. For all the non-linearities considered in the most realistic model, the magnetic cycle period is a decreasing function of | D | (the amplitude of the dynamo number). However, discriminating between different non-linearities is difficult in this case and care must therefore be taken before advancing explanations for the magnetic periods of stars.     

Mode enslavement in a two-layer stellar dynamo

We consider a conventional stellar  α²ω  -dynamo with dynamo generators localized in two spherical shells separated by a passive layer. The signs of the α-effect as well as rotational shear in the dynamo active layers can be chosen to give dynamo waves that propagate in opposite directions (poleward and equatorward) if the layers are considered separately in the framework of the Parker migratory dynamo. In a sequence of numerical experiments we show that the variety of dynamo-generated magnetic configurations in the system under discussion is quite rich. We identify the possibility of almost independent dynamo waves existing in the two layers as well as enslavement of one layer by the other, and of activity waves generated by a joint action of the two layers. We suggest some qualitative explanations of the behaviour and discuss also the limited nature of these explanations. This variety of phenomena suggests previously underexploited freedoms to understand how predictions of dynamo theory may accommodate the observed solar and stellar activity phenomenology.     

Atmospheres and spectra of strongly magnetized neutron stars

We construct atmosphere models for strongly magnetized neutron stars with surface fields     and effective temperatures     . The atmospheres directly determine the characteristics of thermal emission from isolated neutron stars, including radio pulsars, soft gamma-ray repeaters, and anomalous X-ray pulsars. In our models, the atmosphere is composed of pure hydrogen or helium and is assumed to be fully ionized. The radiative opacities include free–free absorption and scattering by both electrons and ions computed for the two photon polarization modes in the magnetized electron–ion plasma. Since the radiation emerges from deep layers in the atmosphere with     , plasma effects can significantly modify the photon opacities by changing the properties of the polarization modes. In the case where the magnetic field and the surface normal are parallel, we solve the full, angle-dependent, coupled radiative transfer equations for both polarization modes. We also construct atmosphere models for general field orientations based on the diffusion approximation of the transport equations and compare the results with models based on full radiative transport. In general, the emergent thermal radiation exhibits significant deviation from blackbody, with harder spectra at high energies. The spectra also show a broad feature     around the ion cyclotron resonance     , where Z and A are the atomic charge and atomic mass of the ion, respectively; this feature is particularly pronounced when     . Detection of the resonance feature would provide a direct measurement of the surface magnetic fields on magnetars.     

Magnetic field evolution in neutron stars

Neutron stars contain persistent, ordered magnetic fields that are the strongest known in the Universe. However, their magnetic fluxes are similar to those in magnetic A and B stars and white dwarfs, suggesting that flux conservation during gravitational collapse may play an important role in establishing the field, although it might also be modified substantially by early convection, differential rotation, and magnetic instabilities. The equilibrium field configuration, established within hours (at most) of the formation of the star, is likely to be roughly axisymmetric, involving both poloidal and toroidal components. The stable stratification of the neutron star matter (due to its radial composition gradient) probably plays a crucial role in holding this magnetic structure inside the star. The field can evolve on long time scales by processes that overcome the stable stratification, such as weak interactions changing the relative abundances and ambipolar diffusion of charged particles with respect to neutrons. These processes become more effective for stronger magnetic fields, thus naturally explaining the magnetic energy dissipation expected in magnetars, at the same time as the longer-lived, weaker fields in classical and millisecond pulsars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Catalogue of averaged stellar effective magnetic fields – II. Re-discussion of chemically peculiar A and B stars

This paper presents a catalogue and the method of determining averaged quadratic effective magnetic fields  〈 B _e〉  for 1212 main-sequence and giant stars, and 11 white dwarf stars. The catalogue includes stars that are members of several open clusters. We have compiled measurements of the longitudinal magnetic field for those stars, which were scattered in the existing literature. A new parameter, magnetization (MA), has been defined, and we present values of MA for stars of various spectral classes. Our sample includes a subset of 610 chemically peculiar early-type stars. We confirm the conclusion of our previous study that the number distribution of all chemically peculiar stars versus the averaged magnetic field strength is described by a decreasing exponential function. Relations of this type also hold for stars of all the analysed subclasses of chemical peculiarity. Magnetization tends to correlate with the effective temperature only at high MA, for He-weak and He-rich stars.