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

Solar differential rotation and meridional flow: The role of a subadiabatic tachocline for the Taylor-Proudman balance

We present a simple model for the solar differential rotation and meridional circulation based on a mean field parameterization of the Reynolds stresses that drive the differential rotation. We include the subadiabatic part of the tachocline and show that this, in conjunction with turbulent heat conductivity within the convection zone and overshoot region, provides the key physics to break the Taylor-Proudman constraint, which dictates differential rotation with contour lines parallel to the axis of rotation in case of an isentropic stratification. We show that differential rotation with contour lines inclined by 10 - 30 degrees with respect to the axis of rotation is a robust result of the model, which does not depend on the details of the Reynolds stress and the assumed viscosity, as long as the Reynolds stress transports angular momentum toward the equator. The meridional flow is more sensitive with respect to the details of the assumed Reynolds stress, but a flow cell, equatorward at the base of the convection zone and poleward in the upper half of the convection zone, is the preferred flow pattern.Comment: 15 pages, 7 figure

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

Generation of strong magnetic fields by r-modes in millisecond accreting neutron stars: induced deformations and gravitational wave emission

Differential rotation induced by the r-mode instability can generate very strong toroidal fields in the core of accreting, millisecond spinning neutron stars. We introduce explicitly the magnetic damping term in the evolution equations of the r-modes and solve them numerically in the Newtonian limit, to follow the development and growth of the internal magnetic field. We show that the strength of the latter can reach large values, $B \sim 10^{14}$ G, in the core of the fastest accreting neutron stars. This is strong enough to induce a significant quadrupole moment of the neutron star mass distribution, corresponding to an ellipticity |\epsilon_B}| \sim 10^{-8}. If the symmetry axis of the induced magnetic field is not aligned with the spin axis, the neutron star radiates gravitational waves. We suggest that this mechanism may explain the upper limit of the spin frequencies observed in accreting neutron stars in Low Mass X-Ray Binaries. We discuss the relevance of our results for the search of gravitational waves.Comment: 11 pages, 8 figure

A new model for mixing by double-diffusive convection (semi-convection): I. The conditions for layer formation

The process referred to as "semi-convection" in astrophysics and "double-diffusive convection in the diffusive regime" in Earth and planetary sciences, occurs in stellar and planetary interiors in regions which are stable according to the Ledoux criterion but unstable according to the Schwarzschild criterion. In this series of papers, we analyze the results of an extensive suite of 3D numerical simulations of the process, and ultimately propose a new 1D prescription for heat and compositional transport in this regime which can be used in stellar or planetary structure and evolution models. In a preliminary study of the phenomenon, Rosenblum et al. (2011) showed that, after saturation of the primary instability, a system can evolve in one of two possible ways: the induced turbulence either remains homogeneous, with very weak transport properties, or transitions into a thermo-compositional staircase where the transport rate is much larger (albeit still smaller than in standard convection). In this paper, we show that this dichotomous behavior is a robust property of semi-convection across a wide region of parameter space. We propose a simple semi-analytical criterion to determine whether layer formation is expected or not, and at what rate it proceeds, as a function of the background stratification and of the diffusion parameters (viscosity, thermal diffusivity and compositional diffusivity) only. The theoretical criterion matches the outcome of our numerical simulations very adequately in the numerically accessible "planetary" parameter regime, and can easily be extrapolated to the stellar parameter regime. Subsequent papers will address more specifically the question of quantifying transport in the layered case and in the non-layered case.Comment: Submitted to Ap

General Relativistic Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell

We show that, at first order in the angular velocity, the general relativistic description of Rossby-Haurwitz waves (the analogues of r-waves on a thin shell) can be obtained from the corresponding Newtonian one after a coordinate transformation. As an application, we show that the results recently obtained by Rezzolla and Yoshida (2001) in the analysis of Newtonian Rossby-Haurwitz waves of a slowly and differentially rotating, fluid shell apply also in General Relativity, at first order in the angular velocity.Comment: 4 pages. Comment to Class. Quantum Grav. 18(2001)L8

Properties of r modes in rotating magnetic neutron stars. II. Evolution of the r modes and stellar magnetic field

The evolution of the r-mode instability is likely to be accompanied by secular kinematic effects which will produce differential rotation with large scale drifts of fluid elements, mostly in the azimuthal direction. As first discussed by Rezzolla, Lamb and Shapiro 2000, the interaction of these secular velocity fields with a pre-existing neutron star magnetic field could result in the generation of intense and large scale toroidal fields. Following their derivation in the companion paper, we here discuss the numerical solution of the evolution equations for the magnetic field. The values of the magnetic fields obtained in this way are used to estimate the conditions under which the r-mode instability might be prevented or suppressed. We also assess the impact of the generation of large magnetic fields on the gravitational wave detectability of r-mode unstable neutron stars. Our results indicate that the signal to noise ratio in the detection of gravitational waves from the r-mode instability might be considerably decreased if the latter develops in neutron stars with initial magnetic fields larger than 10^10 G.Comment: 16 pages, 12 figures. To appear in Phys. Rev.

Comparison of the thin flux tube approximation with 3D MHD simulations

The structure and dynamics of small vertical photospheric magnetic flux concentrations has been often treated in the framework of an approximation based upon a low-order truncation of the Taylor expansions of all quantities in the horizontal direction, together with the assumption of instantaneous total pressure balance at the boundary to the non-magnetic external medium. Formally, such an approximation is justified if the diameter of the structure (a flux tube or a flux sheet) is small compared to all other relevant length scales (scale height, radius of curvature, wavelength, etc.). The advent of realistic 3D radiative MHD simulations opens the possibility of checking the consistency of the approximation with the properties of the flux concentrations that form in the course of a simulation. We carry out a comparative analysis between the thin flux tube/sheet models and flux concentrations formed in a 3D radiation-MHD simulation. We compare the distribution of the vertical and horizontal components of the magnetic field in a 3D MHD simulation with the field distribution in the case of the thin flux tube/sheet approximation. We also consider the total (gas plus magnetic) pressure in the MHD simulation box. Flux concentrations with super-equipartition fields are reasonably well reproduced by the second-order thin flux tube/sheet approximation. The differences between approximation and simulation are due to the asymmetry and the dynamics of the simulated structures

Relationships between magnetic foot points and G-band bright structures

Magnetic elements are thought to be described by flux tube models, and are well reproduced by MHD simulations. However, these simulations are only partially constrained by observations. We observationally investigate the relationship between G-band bright points and magnetic structures to clarify conditions, which make magnetic structures bright in G-band. The G-band filtergrams together with magnetograms and dopplergrams were taken for a plage region covered by abnormal granules as well as ubiquitous G-band bright points, using the Swedish 1-m Solar Telescope (SST) under very good seeing conditions. High magnetic flux density regions are not necessarily associated with G-band bright points. We refer to the observed extended areas with high magnetic flux density as magnetic islands to separate them from magnetic elements. We discover that G-band bright points tend to be located near the boundary of such magnetic islands. The concentration of G-band bright points decreases with inward distance from the boundary of the magnetic islands. Moreover, G-band bright points are preferentially located where magnetic flux density is higher, given the same distance from the boundary. There are some bright points located far inside the magnetic islands. Such bright points have higher minimum magnetic flux density at the larger inward distance from the boundary. Convective velocity is apparently reduced for such high magnetic flux density regions regardless of whether they are populated by G-band bright points or not. The magnetic islands are surrounded by downflows.These results suggest that high magnetic flux density, as well as efficient heat transport from the sides or beneath, are required to make magnetic elements bright in G-band.Comment: 9 pages, 14 figures, accepted for publication in A&