Presupernova Evolution of Differentially Rotating Massive Stars Including Magnetic Fields

As a massive star evolves through multiple stages of nuclear burning on its way to becoming a supernova, a complex, differentially rotating structure is set up. Angular momentum is transported by a variety of classic instabilities, and also by magnetic torques from fields generated by the differential rotation. We present the first stellar evolution calculations to follow the evolution of rotating massive stars including, at least approximately, all these effects, magnetic and non-magnetic, from the zero-age main sequence until the onset of iron-core collapse. The evolution and action of the magnetic fields is as described by Spruit 2002 and a range of uncertain parameters is explored. In general, we find that magnetic torques decrease the final rotation rate of the collapsing iron core by about a factor of 30 to 50 when compared with the non-magnetic counterparts. Angular momentum in that part of the presupernova star destined to become a neutron star is an increasing function of main sequence mass. That is, pulsars derived from more massive stars will rotate faster and rotation will play a more dominant role in the star's explosion. The final angular momentum of the core is determined - to within a factor of two - by the time the star ignites carbon burning. For the lighter stars studied, around 15 solar masses, we predict pulsar periods at birth near 15 ms, though a factor of two range is easily tolerated by the uncertainties. Several mechanisms for additional braking in a young neutron star, especially by fall back, are also explored.Comment: 32 pages, 3 figures (8 eps files), submitted to Ap

Differential Rotation in Neutron Stars: Magnetic Braking and Viscous Damping

Diffferentially rotating stars can support significantly more mass in equilibrium than nonrotating or uniformly rotating stars, according to general relativity. The remnant of a binary neutron star merger may give rise to such a ``hypermassive'' object. While such a star may be dynamically stable against gravitational collapse and bar formation, the radial stabilization due to differential rotation is likely to be temporary. Magnetic braking and viscosity combine to drive the star to uniform rotation, even if the seed magnetic field and the viscosity are small. This process inevitably leads to delayed collapse, which will be accompanied by a delayed gravitational wave burst and, possibly, a gamma-ray burst. We provide a simple, Newtonian, MHD calculation of the braking of differential rotation by magnetic fields and viscosity. The star is idealized as a differentially rotating, infinite cylinder consisting of a homogeneous, incompressible conducting gas. We solve analytically the simplest case in which the gas has no viscosity and the star resides in an exterior vacuum. We treat numerically cases in which the gas has internal viscosity and the star is embedded in an exterior, low-density, conducting medium. Our evolution calculations are presented to stimulate more realistic MHD simulations in full 3+1 general relativity. They serve to identify some of the key physical and numerical parameters, scaling behavior and competing timescales that characterize this important process.Comment: 11 pages. To appear in ApJ (November 20, 2000

Magnetic fields generated by r-modes in accreting millisecond pulsars

In millisecond pulsars the existence of the Coriolis force allows the development of the so-called Rossby oscillations (r-modes) which are know to be unstable to emission of gravitational waves. These instabilities are mainly damped by the viscosity of the star or by the existence of a strong magnetic field. A fraction of the observed millisecond pulsars are known to be inside Low Mass X-ray Binaries (LMXBs), systems in which a neutron star (or a black hole) is accreting from a donor whose mass is smaller than 1 $M_\odot$. Here we show that the r-mode instabilities can generate strong toroidal magnetic fields by inducing differential rotation. In this way we also provide an alternative scenario for the origin of the magnetars.Comment: 6 pages, 3 figures, Proceedings conference "Theoretical Nuclear Physics", Cortona October 200

Birth kicks as the origin of pulsar rotation

Radio pulsars are thought to born with spin periods of 0.02–0.5 s and space velocities of 100–1,000 kms^(-1), and they are inferred to have initial dipole magnetic fields of 10^(11)–10^(13) G. The average space velocity of their progenitor stars is less than 15 kms^(-1), which means that pulsars must receive a substantial ‘kick’ at birth. Here we propose that the birth characteristics of pulsars have a simple physical connection with each other. Magnetic fields maintained by differential rotation between the core and envelope of the progenitor would keep the whole star in a state of approximately uniform rotation until 10 years before the explosion. Such a slowly rotating core has 1,000 times less angular momentum than required to explain the rotation of pulsars. The specific physical process that ‘kicks’ the neutron star at birth has not been identified, but unless its force is exerted exactly head-on it will also cause the neutron star to rotate. We identify this process as the origin of the spin of pulsars. Such kicks may cause a correlation between the velocity and spin vectors of pulsars. We predict that many neutron stars are born with periods longer than 2 s, and never become radio pulsars

Presupernova Evolution of Rotating Massive Stars and the Rotation Rate of Pulsars

Rotation in massive stars has been studied on the main sequence and during helium burning for decades, but only recently have realistic numerical simulations followed the transport of angular momentum that occurs during more advanced stages of evolution. The results affect such interesting issues as whether rotation is important to the explosion mechanism, whether supernovae are strong sources of gravitational radiation, the star's nucleosynthesis, and the initial rotation rate of neutron stars and black holes. We find that when only hydrodynamic instabilities (shear, Eddington-Sweet, etc.) are included in the calculation, one obtains neutron stars spinning at close to critical rotation at their surface -- or even formally in excess of critical. When recent estimates of magnetic torques (Spruit 2002) are added, however, the evolved cores spin about an order of magnitude slower. This is still more angular momentum than observed in young pulsars, but too slow for the collapsar model for gamma-ray bursts.Comment: 10 pages, 2 figures, to appear in Proc. IAU 215 "Stellar Rotation

Can Extra Mixing in RGB and AGB Stars Be Attributed to Magnetic Mechanisms?

It is known that there must be some weak form of transport (called cool bottom processing, or CBP) acting in low mass RGB and AGB stars, adding nuclei, newly produced near the hydrogen-burning shell, to the convective envelope. We assume that this extra-mixing originates in a stellar dynamo operated by the differential rotation below the envelope, maintaining toroidal magnetic fields near the hydrogen-burning shell. We use a phenomenological approach to the buoyancy of magnetic flux tubes, assuming that they induce matter circulation as needed by CBP models. This establishes requirements on the fields necessary to transport material from zones where some nuclear burning takes place, through the radiative layer, and into the convective envelope. Magnetic field strengths are determined by the transport rates needed by CBP for the model stellar structure of a star of initially 1.5 solar mass, in both the AGB and RGB phases. The field required for the AGB star in the processing zone is B_0 ~ 5x10^6 G; at the base of the convective envelope this yields an intensity B_E < 10^4 G (approximately). For the RGB case, B_0 ~ 5x10^4 to 4x10^5 G, and the corresponding B_E are ~ 450 to 3500 G. These results are consistent with existing observations on AGB stars. They also hint at the basis for high field sources in some planetary nebulae and the very large fields found in some white dwarfs. It is concluded that transport by magnetic buoyancy should be considered as a possible mechanism for extra mixing through the radiative zone, as is required by both stellar observations and the extensive isotopic data on circumstellar condensates found in meteorites.Comment: 26 pages, 4 figures, accepted by Astrophysical Journa

Local Axisymmetric Diffusive Stability of Weakly-Magnetized, Differentially-Rotating, Stratified Fluids

We study the local stability of stratified, differentially-rotating fluids to axisymmetric perturbations in the presence of a weak magnetic field and of finite resistivity, viscosity and heat conductivity. This is a generalization of the Goldreich-Schubert-Fricke (GSF) double-diffusive analysis to the magnetized and resistive, triple-diffusive case. Our fifth-order dispersion relation admits a novel branch which describes a magnetized version of multi-diffusive modes. We derive necessary conditions for axisymmetric stability in the inviscid and perfect-conductor (double-diffusive) limits. In each case, rotation must be constant on cylinders and angular velocity must not decrease with distance from the rotation axis for stability, irrespective of the relative strength of viscous, resistive and heat diffusion. Therefore, in both double-diffusive limits, solid body rotation marginally satisfies our stability criteria. The role of weak magnetic fields is essential to reach these conclusions. The triple-diffusive situation is more complex, and its stability criteria are not easily stated. Numerical analysis of our general dispersion relation confirms our analytic double-diffusive criteria, but also shows that an unstable double-diffusive situation can be significantly stabilized by the addition of a third, ostensibly weaker, diffusion process. We describe a numerical application to the Sun's upper radiative zone and establish that it would be subject to unstable multi-diffusive modes if moderate or strong radial gradients of angular velocity were present.Comment: 29 pages, 1 table, accepted for publication in Ap

Dynamo Action in the Solar Convection Zone and Tachocline: Pumping and Organization of Toroidal Fields

We present the first results from three-dimensional spherical shell simulations of magnetic dynamo action realized by turbulent convection penetrating downward into a tachocline of rotational shear. This permits us to assess several dynamical elements believed to be crucial to the operation of the solar global dynamo, variously involving differential rotation resulting from convection, magnetic pumping, and amplification of fields by stretching within the tachocline. The simulations reveal that strong axisymmetric toroidal magnetic fields (about 3000 G in strength) are realized within the lower stable layer, unlike in the convection zone where fluctuating fields are predominant. The toroidal fields in the stable layer possess a striking persistent antisymmetric parity, with fields in the northern hemisphere largely of opposite polarity to those in the southern hemisphere. The associated mean poloidal magnetic fields there have a clear dipolar geometry, but we have not yet observed any distinctive reversals or latitudinal propagation. The presence of these deep magnetic fields appears to stabilize the sense of mean fields produced by vigorous dynamo action in the bulk of the convection zone.Comment: 4 pages, 3 color figures (compressed), in press at ApJ