Jonathan Braithwaite

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 r Sco or the pulsar 1E 1207.4-5209. The secular evolution of these equilibria due to Ohmic and buoyancy processes is also examined.

Magnetic spots on hot massive stars

Context. Hot luminous stars show a variety of phenomena in their photospheres and winds which still lack clear physical explanation. Among these phenomena are photospheric turbulence, line profile variability (LPV), non-thermal emission, non-radial pulsations, discrete absorption components (DACs) and wind clumping. It has been argued that a convection zone close to the stellar surface could be responsible for some of these phenomena. This convective zone is caused by a peak in the opacity associated with iron-group elements and is referred to as the “iron convection zone” (FeCZ). Aims. Assuming dynamo action producing magnetic fields at equipartition in the FeCZ, we investigate the occurrence of subsurface magnetism in OB stars. Then we study the surface emergence of these magnetic fields and discuss possible observational signatures of magnetic spots. Methods. Simple estimates are made using the subsurface properties of massive stars, as calculated in 1D stellar evolution models. Results. We find that magnetic fields of sufficient amplitude to affect the wind could emerge at the surface via magnetic buoyancy. While at this stage it is difficult to predict the geometry of these features, we show that magnetic spots of size comparable to the local pressure scale height can manifest themselves as hot, bright spots. Conclusions. Localized magnetic fields could be widespread in those early type stars that have subsurface convection. This type of surface magnetism could be responsible for photometric variability and play a role in X-ray emission and wind clumping.

ON THE STABILITY OF NON-FORCE-FREE MAGNETIC EQUILIBRIA IN STARS

The existence of stable magnetic configurations in white dwarfs, neutron stars, and various non-convective stellar regions is now well recognized. It has recently been shown numerically that various families of equilibria, including axisymmetric mixed poloidal-toroidal configurations, are stable. Here we test the stability of an analytically derived non-force-free magnetic equilibrium resulting from an initial relaxation (self-organization) process, using three-dimensional magnetohydrodynamic simulations: the obtained mixed configuration is compared with the dynamical evolution of its purely poloidal and purely toroidal components, both known to be unstable. The mixed equilibrium shows no sign of instability under white noise perturbations. This configuration therefore provides a good description of magnetic equilibrium topology inside non-convective stellar objects and will be useful to initialize magneto-rotational transport in stellar evolution codes and in multi-dimensional magnetohydrodynamic simulations.

Weak magnetic fields in early-type stars: failed fossils

Weak magnetic fields have recently been detected in Vega and Sirius. Here, we explore the possibility that these fields are the remnants of some field inherited or created during or shortly after star formation and, unlike true fossil fields, are still evolving as we observe them. The timescale of this evolution is given in terms of the Alfven timescale and the rotation frequency by tau_evol ~ tau_A^2 Omega, which would be comparable to the age of the star. It is shown that it is likely that all intermediate- and high-mass stars contain fields of at least the order of the strength found so far in Vega and Sirius. Faster rotators are expected to have stronger magnetic fields. Stars may experience an increase in field strength during their early main-sequence, but for most of their lives field strength will decrease slowly. The length scale of the magnetic structure on the surface may be small in very young stars but should quickly increase to at least very approximately a fifth of the stellar radius.

Magnetohydrodynamic relaxation of AGN ejecta: radio bubbles in the intracluster medium

X-ray images of galaxy clusters often display underdense bubbles which are apparently inflated by active galactic nucleus (AGN) outflow. I consider the evolution of the magnetic field inside such a bubble, using a mixture of analytic and numerical methods. It is found that the field relaxes into an equilibrium, filling the entire volume of the bubble. The time-scale on which this happens depends critically on the magnetization and helicity of the outflow as well as on the properties of the surrounding intracluster medium (ICM). If the outflow is strongly magnetized, the magnetic field undergoes reconnection on a short time-scale, magnetic energy being converted into heat whilst the characteristic length-scale of the field rises; this process stops when a global equilibrium is reached. The strength of the equilibrium field is determined by the magnetic helicity injected into the bubble by the AGN: if the outflow has a consistent net flux and consequently a large helicity then a global equilibrium will be reached on a short time-scale, whereas a low-helicity outflow results in no global equilibrium being reached and at the time of observation reconnection will be ongoing. However, localized flux-tube equilibria will form. If, on the other hand, the outflow is very weakly magnetized, no reconnection occurs and the magnetic field inside the bubble remains small-scale and passive. These results have implications for the internal composition of the bubbles, for their interaction with the ICM – in particular to explain how bubbles could move a large distance through the ICM without breaking up – as well as for the cooling flow problem in general. In addition, reconnection sites in a bubble could be a convenient source of energetic particles, circumventing the problem of synchrotron emitters having a shorter lifetime than the age of the bubble they inhabit.

Instability of magnetic equilibria in barotropic stars

ABSTRACT In stably stratified stars, numerical magneto-hydrodynamics simulations have shownthat arbitrary initial magnetic fields evolve into stable equilibrium configurations,usually containing nearly axisymmetric, linked poloidal and toroidal fields that sta-bilize each other. In this work, we test the hypothesis that stable stratification is arequirement for the existence of such stable equilibria. For this purpose, we follownumerically the evolution of magnetic fields in barotropic (and thus neutrally stable)stars, starting from two different types of initial conditions, namely random disorderedmagnetic fields, as well as linked poloidal-toroidal configurations resembling the previ-ously found equilibria. With many trials, we always find a decay of the magnetic fieldover a few Alfv´en times, never a stable equilibrium. This strongly suggests that thereare no stable equilibria in barotropic stars, thus clearly invalidating the assumptionof barotropic equations of state often imposed on the search of magnetic equilibria. Italso supports the hypothesis that, as dissipative processes erode the stable stratifica-tion, they might destabilize previously stable magnetic field configurations, leading totheir decay.

Flame Propagation on the Surfaces of Rapidly Rotating Neutron Stars during Type I X-ray Bursts

We present the first vertically resolved hydrodynamic simulations of a laterally propagating, deflagrating flame in the thin helium ocean of a rotating accreting neutron star. We use a new hydrodynamics solver tailored to deal with the large discrepancy in horizontal and vertical length scales typical of neutron star oceans, and which filters out sound waves that would otherwise limit our timesteps. We find that the flame moves horizontally with velocities of the order of 10 5 cm s 1 , crossing the ocean in a few seconds, broadly consistent with the rise times of Type I X-ray bursts. We address the open question of what drives flame propagation, and find that heat is transported from burning to unburnt fuel by a combination of topto-bottom conduction and mixing driven by a baroclinic instability. The speed of the flame propagation is therefore a sensitive function of the ocean conductivity and spin: we explore this dependence for an astrophysically relevant range of parameters and find that in general flame propagation is faster for slower rotation and higher conductivity.

BURN OUT OR FADE AWAY? ON THE X-RAY AND MAGNETIC DEATH OF INTERMEDIATE MASS STARS

The nature of the mechanisms apparently driving X-rays from intermediate mass stars lacking strong convection zones or massive winds remains poorly understood, and the possible role of hidden, lower mass close companions is still unclear. A 20 ks Chandra HRC-I observation of HR 4796A, an 8 Myr old main sequence A0 star devoid of close stellar companions, has been used to search for a signature or remnant of magnetic activity from the Herbig Ae phase. X-rays were not detected and the X-ray luminosity upper limit was LX ≤ 1.3 × 1027 erg s–1. The result is discussed in the context of various scenarios for generating magnetic activity, including rotational shear and subsurface convection. A dynamo driven by natal differential rotation is unlikely to produce observable X rays, chiefly because of the difficulty in getting the dissipated energy up to the surface of the star. A subsurface convection layer produced by the ionization of helium could host a dynamo that should be effective throughout the main sequence but can only produce X-ray luminosities of the order 1025 erg s–1. This luminosity lies only moderately below the current detection limit for Vega. Our study supports the idea that X-ray production in Herbig Ae/Be stars is linked largely to the accretion process rather than the properties of the underlying star, and that early A stars generally decline in X-ray luminosity at least 100,000 fold in only a few million years.

Rotational effects in thermonuclear type I bursts: equatorial crossing and directionality of flame spreading

In a previous study on thermonuclear (type I) bursts on accreting neutron stars, we addressed and demonstrated the importance of the effects of rotation, through the Coriolis force, on the propagation of the burning flame. However, that study only analysed cases of longitudinal propagation, where the Coriolis force coefficient 2Ωcos θ was constant. In this paper, we study the effects of rotation on propagation in the meridional (latitudinal) direction, where the Coriolis force changes from its maximum at the poles to zero at the equator. We find that the zero Coriolis force at the equator, while affecting the structure of the flame, does not prevent its propagation from one hemisphere to another. We also observe structural differences between the flame propagating towards the equator and that propagating towards the pole, the second being faster. In the light of the recent discovery of the low spin frequency of burster IGR J17480-2446 rotating at 11 Hz (for which Coriolis effects should be negligible), we also extend our simulations to slow rotation.

Structure of magnetic fields in intracluster cavities

ABSTRACT Observations of clusters of galaxies show ubiquitous presence of X-ray cavities, pre-sumably blown by the AGN jets. We consider magnetic eld structures of these cav-ities. Stability requires that they contain both toroidal and poloidal magnetic elds,while realistic con gurations should have vanishing magnetic eld on the boundary.For axisymmetric con gurations embedded in unmagnetized plasma, the continuityof poloidal and toroidal magnetic eld components on the surface of the bubble thenrequires solving the elliptical Grad-Shafranov equation with both Dirichlet and Neu-mann boundary conditions. This leads to a double eigenvalue problem, relating thepressure gradients and the toroidal magnetic eld to the radius of the bubble. Wehave found fully analytical stable solutions. This result is con rmed by numericalsimulation. We present synthetic X-ray images and synchrotron emission pro les andevaluate the rotation measure for radiation traversing the bubble.Key words: MHD { methods: analytical { methods: numerical { galaxies: clusters:intracluster medium { plasmas, X-rays: galaxies: clusters.