Nonaxisymmetric Magnetorotational Instability in Proto-Neutron Stars

We investigate the stability of differentially rotating proto-neutron stars (PNSs) with a toroidal magnetic field. Stability criteria for nonaxisymmetric MHD instabilities are derived using a local linear analysis. PNSs are expected to have much stronger radial shear in the rotation velocity compared to normal stars. We find that nonaxisymmetric magnetorotational instability (NMRI) with a large azimuthal wavenumber $m$ is dominant over the kink mode ($m=1$) in differentially rotating PNSs. The growth rate of the NMRI is of the order of the angular velocity $\Omega$ which is faster than that of the kink-type instability by several orders of magnitude. The stability criteria are analogous to those of the axisymmetric magnetorotational instability with a poloidal field, although the effects of leptonic gradients are considered in our analysis. The NMRI can grow even in convectively stable layers if the wavevectors of unstable modes are parallel to the restoring force by the Brunt-V\"ais\"al\"a oscillation. The nonlinear evolution of NMRI could amplify the magnetic fields and drive MHD turbulence in PNSs, which may lead to enhancement of the neutrino luminosity.Comment: 24pages, 7figures, Accepted for publication in the Astrophysical Journal (December 12, 2005

The stability of toroidal fields in stars

We present numerical models of hydromagnetic instabilities under the conditions prevailing in a stably stratified, non-convective stellar interior, and compare them with previous results of analytic work on instabilities in purely toroidal fields. We confirm that an $m=1$ mode (`kink') is the dominant instability in a toroidal field in which the field strength is proportional to distance from the axis, such as the field formed by the winding up of a weak field by differential rotation. We measure the growth rate of the instability as a function of field strength and rotation rate $\Omega$, and investigate the effects of a stabilising thermal stratification as well as magnetic and thermal diffusion on the stability. Where comparison is computationally feasible, the results agree with analytic predictions.Comment: 13 pages, 14 figures, comments welcom

Bounds on the Magnetic Fields in the Radiative Zone of the Sun

We discuss bounds on the strength of the magnetic fields that could be buried in the radiative zone of the Sun. The field profiles and decay times are computed for all axisymmetric toroidal Ohmic decay eigenmodes with lifetimes exceeding the age of the Sun. The measurements of the solar oblateness yield a bound <~ 7 MG on the strength of the field. A comparable bound is expected to come from the analysis of the splitting of the solar oscillation frequencies. The theoretical analysis of the double diffusive instability also yields a similar bound. The oblateness measurements at their present level of sensitivity are therefore not expected to measure a toroidal field contribution.Comment: 15 pages, 6 figure

Dynamo action by differential rotation in a stably stratified stellar interior

Magnetic fields can be created in stably stratified (non-convective) layers in a differentially rotating star. A magnetic instability in the toroidal field (wound up by differential rotation) replaces the role of convection in closing the field amplification loop. Tayler instability is likely to be the most relevant magnetic instability. A dynamo model is developed from these ingredients, and applied to the problem of angular momentum transport in stellar interiors. It produces a prodominantly horizontal field. This dynamo process might account for the observed pattern of rotation in the solar core.Comment: Expanded version as accepted by Astron. Astrophy

Non-axisymmetric instabilities of neutron star with toroidal magnetic fields

The aim of this paper is to clarify the stabilities of neutron stars with strong toroidal magnetic fields against non-axisymmetric perturbation. The motivation comes from the fact that super magnetized neutron stars of $\sim 10^{15}$G, magnetars, and magnetized proto-neutron stars born after the magnetically-driven supernovae are likely to have such strong toroidal magnetic fields. Long-term, three-dimensional general relativistic magneto-hydrodynamic simulations are performed, preparing isentropic neutron stars with toroidal magnetic fields in equilibrium as initial conditions. To explore the effects of rotations on the stability, simulations are done for both non-rotating and rigidly rotating models. We find the emergence of the Parker and/or Tayler instabilities in both the non-rotating and rotating models. For both non-rotating and rotating models, the Parker instability is the primary instability as predicted by the local linear perturbation analysis. The interchange instability also appears in the rotating models. It is found that rapid rotation is not enough to suppress the Parker instability, and this finding does not agree with the perturbation analysis. The reason for this is that rigidly and rapidly rotating stars are marginally stable, and hence, in the presence of stellar pulsations by which the rotational profile is deformed, unstable regions with negative gradient of angular momentum profile is developed. After the onset of the instabilities, a turbulence is excited. Contrary to the axisymmetric case, the magnetic fields never reach an equilibrium state after the development of the turbulence. This conclusion suggests that three-dimensional simulation is indispensable for exploring the formation of magnetars or prominence activities of magnetars such as giant flares.Comment: 19 pages, 11 figures, to be published in A&

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.Comment: To appear in Astronomische Nachrichten (Astronomical Notes) as part of the Proceedings of the 5th Potsdam Thinkshop, "Meridional Circulation, Differential Rotation, Solar and Stellar Activity", held 2007 June 24-29. 5 pages, no figure

Stellar evolution of massive stars with a radiative alpha-omega dynamo

Models of rotationally-driven dynamos in stellar radiative zones have suggested that magnetohydrodynamic transport of angular momentum and chemical composition can dominate over the otherwise purely hydrodynamic processes. A proper consideration of the interaction between rotation and magnetic fields is therefore essential. Previous studies have focused on a magnetic model where the magnetic field strength is derived as a function of the stellar structure and angular momentum distribution. We have adapted our one-dimensional stellar rotation code, RoSE, to model the poloidal and toroidal magnetic field strengths with a pair of time-dependent advection-diffusion equations coupled to the equations for the evolution of the angular momentum distribution and stellar structure. This produces a much more complete, though still reasonably simple, model for the magnetic field evolution. Our model reproduces well observed surface nitrogen enrichment of massive stars in the Large Magellanic Cloud. In particular it reproduces a population of slowly-rotating nitrogen-enriched stars that cannot be explained by rotational mixing alone alongside the traditional rotationlly-enriched stars. The model further predicts a strong mass-dependency for the dynamo-driven field. Above a threshold mass, the strength of the magnetic dynamo decreases abruptly and so we predict that more massive stars are much less likely to support a dynamo-driven field than less massive stars.Comment: Accepted for publication in MNRAS. 15 pages, 13 figure

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 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 timescale on which this happens depends critically on the magnetisation and helicity of the outflow as well as on properties of the surrounding ICM. If the outflow is strongly magnetised, the magnetic field undergoes reconnection on a short timescale, 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 timescale, whereas a low-helicity outflow results in no global equilibrium being reached and at the time of observation reconnection will be ongoing. However, localised flux-tube equilibria will form. If, on the other hand, the outflow is very weakly magnetised, 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, their interaction with 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.Comment: MNRAS accepted. 15 pages, 10 figures

Magnetic field structure of relativistic jets without current sheets

We present an analytical class of equilibrium solutions for the structure of relativistic sheared and rotating magnetized jets that contain no boundary current sheets. We demonstrate the overall dynamical stability of these solutions and, most importantly, a better numerical resistive stability than the commonly employed force-free structures which inevitably require the presence of dissipative surface currents. The jet is volumetrically confined by the external pressure, with no pressure gradient on the surface. We calculate the expected observed properties of such jets. Given the simplicity of these solution we suggest them as useful initial conditions for relativistic jet simulations.Comment: 13 pages, 13 figures, Accepted by MNRA

Active region formation through the negative effective magnetic pressure instability

The negative effective magnetic pressure instability operates on scales encompassing many turbulent eddies and is here discussed in connection with the formation of active regions near the surface layers of the Sun. This instability is related to the negative contribution of turbulence to the mean magnetic pressure that causes the formation of large-scale magnetic structures. For an isothermal layer, direct numerical simulations and mean-field simulations of this phenomenon are shown to agree in many details in that their onset occurs at the same depth. This depth increases with increasing field strength, such that the maximum growth rate of this instability is independent of the field strength, provided the magnetic structures are fully contained within the domain. A linear stability analysis is shown to support this finding. The instability also leads to a redistribution of turbulent intensity and gas pressure that could provide direct observational signatures.Comment: 19 pages, 10 figures, submitted to Solar Physic