Magnetic fields and rotation in white dwarfs and neutron stars

Recent spectropolarimetric observations of Ap and Bp stars with improved sensitivity have suggested that most Ap and Bp stars are magnetic with dipolar fields of at least a few hundred gauss. These new estimates suggest that the range of magnetic fluxes found for the majority of magnetic white dwarfs is similar to that of main-sequence Ap–Bp stars, thus strengthening the empirical evidence for an evolutionary link between magnetism on the main sequence and magnetism in white dwarfs. We draw parallels between the magnetic white dwarfs and the magnetic neutron stars and argue that the observed range of magnetic fields in isolated neutron stars  ( B_p ∼ 10¹¹–10¹⁵ G)  could also be explained if their mainly O-type progenitors have effective dipolar fields in the range of a few gauss to a few kilogauss, assuming approximate magnetic flux conservation with the upper limit being consistent with the recent measurement of a field of   B_p ∼ 1100 G  for θ Orion C.
In the magnetic field–rotation diagram, the magnetic white dwarfs can be divided into three groups of different origin: a significant group of strongly magnetized slow rotators  ( P _rot∼ 50 –100 yr)  that have originated from single-star evolution, a group of strongly magnetized fast rotators  ( P _rot∼ 700 s)  , typified by EUVE J0317–853, that have originated from a merger, and a group of modest rotators ( P _rot∼ hours–days) of mixed origin (single-star and CV-type binary evolution). We propose that the neutron stars may similarly divide into distinct classes at birth , and suggest that the magnetars may be the counterparts of the slowly rotating high-field magnetic white dwarfs.     

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)     

On the Line Formation in Stellar Magnetized Atmospheres

1 INTRODUCTIONIn the previous paper (on et al. 1999, hereafter Paper I), we investigated the wavelength-dependence of four colltribution functions (CFs) derived from dmerent formal solutions andreferring to different emergellt quantities in the unpolarized case. Because one cannot generallyassign a single formation region to the whole line band in a real stellar atmosphere, e.g., the solaratmosphere, instead, the line formation region can be defined as the layers deviating farthestfrom t…     

Stellar forensics — I. Cooling curves

The presence of low-mass, degenerate secondaries in millisecond pulsar binaries offers the opportunity to determine an age for the binary system independently of the rotational properties of the pulsar. To this end, we present here a detailed calculation of the evolution of a grid of low-mass (< 0.05 M⊙) helium core white dwarfs. We investigate the effects of different hydrogen layer masses and provide results for well-known optical bandpasses. We supplement the OPAL opacity calculations with our own calculations for low effective temperatures ( T _eff < 6000 K) and also provide fitting formulae for the gravity as a function of mass and effective temperature. In Paper II we apply these results to individual cases.     

Theoretical model of a magnetic white dwarf

In this paper a theoretical model of a magnetic white dwarf is studied. All numerical calculations are performed under the assumption of a spherically symmetric star. The obtained equation of state is stiffer with the increase of value of the magnetic field (B). Numerical values of the maximum mass and radius are presented. The influence of the magnetic field on the results is evident. Finally the departure from the condition of isothermality of a degenerate electron gas in the gravitational field is discussed.     

Axisymmetric magnetic fields in stars: relative strengths of poloidal and toroidal components

In this third paper in a series on stable magnetic equilibria in stars, I look at the stability of axisymmetric field configurations and, in particular, the relative strengths of the toroidal and poloidal components. Both toroidal and poloidal fields are unstable on their own, and stability is achieved by adding the two together in some ratio. I use Tayler's stability conditions for toroidal fields and other analytic tools to predict the range of stable ratios and then check these predictions by running numerical simulations. If the energy in the poloidal component as a fraction of the total magnetic energy is written as E_p / E , it is found that the stability condition is a ( E / U ) < E_p / E ≲ 0.8 where E /U is the ratio of magnetic to gravitational energy in the star and a is some dimensionless factor whose value is of order 10 in a main-sequence star and of order 10³ in a neutron star. In other words, whilst the poloidal component cannot be significantly stronger than the toroidal, the toroidal field can be very much stronger than the poloidal–given that in realistic stars we expect E / U < 10⁻⁶. The implications of this result are discussed in various contexts such as the emission of gravitational waves by neutron stars, free precession and a 'hidden' energy source for magnetars.     

On non-axisymmetric magnetic equilibria in stars

In previous work, stable approximately axisymmetric equilibrium configurations for magnetic stars were found by numerical simulation. Here, I investigate the conditions under which more complex, non-axisymmetric configurations can form. I present numerical simulations of the formation of stable equilibria from turbulent initial conditions and demonstrate the existence of non-axisymmetric equilibria consisting of twisted flux tubes lying horizontally below the surface of the star, meandering around the star in random patterns. Whether such a non-axisymmetric equilibrium or a simple axisymmetric equilibrium forms depends on the radial profile of the strength of the initial magnetic field. The results could explain observations of non-dipolar fields on stars such as the B0.2 main-sequence star τ Sco or the pulsar 1E 1207.4-5209. The secular evolution of these equilibria due to Ohmic and buoyancy processes is also examined.     

Type Ia supernovae and remnant neutron stars

On the basis of the current observational evidence, we put forward the case that the merger of two CO white dwarfs produces both a Type Ia supernova explosion and a stellar remnant, the latter in the form of a magnetar. The estimated occurrence rates raise the possibility that many, if not most, Type Ia supernovae might result from white dwarf mergers.     

Saa有挠引力模型下慢旋转磁中子星的电磁场

导出在Saa有挠引力模型下慢旋转磁中子星电磁场所满足的方程，并研究其外部解，得出如下结论：其一，选规范．A^0=0，电磁场存在某种形式的特解；其二，选规范A^0≠0，电磁场根本不存在此特解．故可通过观测中子星外部电磁场的形式判断挠率是否存在．     

Models of rapidly rotating neutron stars: remnants of accretion-induced collapse

Equilibrium models of differentially rotating nascent neutron stars are constructed, which represent the result of the accretion-induced collapse of rapidly rotating white dwarfs. The models are built in a two-step procedure: (1) a rapidly rotating pre-collapse white dwarf model is constructed; (2) a stationary axisymmetric neutron star having the same total mass and angular momentum distribution as the white dwarf is constructed. The resulting collapsed objects consist of a high-density central core of size roughly 20 km, surrounded by a massive accretion torus extending over 1000 km from the rotation axis. The ratio of the rotational kinetic energy to the gravitational potential energy of these neutron stars ranges from 0.13 to 0.26, suggesting that some of these objects may have a non-axisymmetric dynamical instability that could emit a significant amount of gravitational radiation.     

Stellar forensics — II. Millisecond pulsar binaries

We use the grid of models described in Paper I to analyse those millisecond pulsar binaries whose secondaries have been studied optically. In particular, we find cooling ages for these binary systems that range from < 1 to ∼ 15 Gyr. Comparison of cooling ages and characteristic spin-down ages allows us to constrain the initial spin periods and spin-up histories for individual systems, showing that at least some millisecond pulsars had sub-Eddington accretion rates and long magnetic field decay times.     

The effect of a magnetosphere on asynchronous magnetic torques in AM Herculis binaries

The interaction is investigated between a white dwarf magnetosphere and a red dwarf secondary star in an asynchronous AM Herculis binary. The poloidal magnetic field diffuses into the secondary and shearing motions, due to differential rotation between the star and the magnetosphere, generate azimuthal field. The effects of diffusion and field advection caused by a poloidal flow induced by magnetospheric motions are calculated. Outward radial motions reduce the amount of field penetration and limit the stellar magnetic torque at higher degrees of asynchronism. A resonance torque curve results, similar to the case of a precessing magnetic field with vacuum surroundings. Inward motions in the secondary increase field penetration, allowing the torque to reach higher values for larger degrees of asynchronism.     

Stellar parameters of young brown dwarfs

We present X‐shooter observations of two brown dwarf candidates. We focus on the determination of stellar parameters and their errors. The targets, an accreting class II and a non‐accreting class III objects, are members of the σ Orionis star‐forming region. We derive the spectroscopic spectral types from the VIS spectrum and the stellar parameters. We find that the uncertainties on the stellar parameters have a minor effect on the determination of the mass accretion rate for the accreting star, thus confirming that the discrepancies between the mass accretion rate estimates found with different (simultaneous) tracers are probably due to different physical conditions where the accretion/wind indicators are produced (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic deformation of the white dwarf surface structure

The influence of strong, large‐scale magnetic fields on the structure and temperature distribution in white dwarf atmospheres is investigated. Magnetic fields may provide an additional component of pressure support, thus possibly inflating the atmosphere compared to the non‐magnetic case. Since the magnetic forces are not isotropic, atmospheric properties may significantly deviate from spherical symmetry. In this paper the magnetohydrostatic equilibrium is calculated numerically in the radial direction for either for small deviations from different assumptions for the poloidal current distribution. We generally find indication that the scale height of the magnetic white dwarf atmosphere enlarges with magnetic field strength and/or poloidal current strength. This is in qualitative agreement with recent spectropolarimetric observations of Grw+10°8247. Quantitatively, we .nd for e.g. a mean surface poloidal field strength of 100 MG and a toroidal field strength of 2‐10 MG an increase of scale height by a factor of 10. This is indicating that already a small deviation from the initial force‐free dipolar magnetic field may lead to observable effects. We further propose the method of finite elements for the solution of the two‐dimensional magnetohydrostatic equilibrium including radiation transport in the diffusive approximation. We present and discuss preliminary solutions, again indicating on an expansion of the magnetized atmosphere.     

Heating and cooling of magnetars with accreted envelopes

We study the thermal structure and evolution of magnetars as cooling neutron stars with a phenomenological heat source in an internal layer. We focus on the effect of magnetized (   B ≳ 10¹⁴  G) non-accreted and accreted outermost envelopes composed of different elements, from iron to hydrogen or helium. We discuss a combined effect of thermal conduction and neutrino emission in the outer neutron star crust and calculate the cooling of magnetars with a dipole magnetic field for various locations of the heat layer, heat rates and magnetic field strengths. Combined effects of strong magnetic fields and light-element composition simplify the interpretation of magnetars in our model: these effects allow one to interpret observations assuming less extreme (therefore, more realistic) heating. Massive magnetars, with fast neutrino cooling in their cores, can have higher thermal surface luminosity.