Those massive stars that give rise to gamma-ray bursts (GRBs) during their deaths must be endowed with an unusually large amount of angular momentum in their inner regions, 1-2 orders of magnitude greater than the ones that make common pulsars. Yet the inclusion of mass loss and angular momentum transport by magnetic torques during the precollapse evolution is known to sap the core of the necessary rotation. Here we explore the evolution of very rapidly rotating massive stars, including stripped-down helium cores that might result from mergers or mass transfer in a binary, and single stars that rotate unusually rapidly on the main sequence. For the highest possible rotation rates (about 400 km s-1), a novel sort of evolution is encountered in which single stars mix completely on the main sequence, never becoming red giants. Such stars, essentially massive "blue stragglers," produce helium-oxygen cores that rotate unusually rapidly. Such stars might comprise roughly 1% of all stars above 10 M☉ and can, under certain circumstances, retain enough angular momentum to make GRBs. Because this possibility is very sensitive to mass loss, GRBs are much more probable in regions of low metallicity.

https://iopscience.iop.org/article/10.1086/498500/pdf

The Progenitor stars of gamma-ray bursts

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 nonmagnetic, 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 in 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 30-50 when compared with the nonmagnetic 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 rotate faster and rotation plays a more important role in the star's explosion. The final angular momentum of the core has been determined—to within a factor of 2—by the time the star ignites carbon burning. For the lighter stars studied, around 15 M☉, we predict pulsar periods at birth near 15 ms, though a factor of 2 range is easily tolerated by the uncertainties. Several mechanisms for additional braking in a young neutron star, especially by fallback, are explored.

https://iopscience.iop.org/article/10.1086/429868/pdf

Presupernova evolution of differentially rotating massive stars including magnetic fields

We investigate the birth and evolution of Galactic isolated radio pulsars. We begin by estimating their birth space velocity distribution from proper-motion measurements of Brisken and coworkers. We find no evidence for multimodality of the distribution and favor one in which the absolute one-dimensional velocity components are exponentially distributed and with a three-dimensional mean velocity of 380 km s-1. We then proceed with a Monte Carlo-based population synthesis, modeling the birth properties of the pulsars, their time evolution, and their detection in the Parkes and Swinburne Multibeam surveys. We present a population model that appears generally consistent with the observations. Our results suggest that pulsars are born in the spiral arms, with a galactocentric radial distribution that is well described by the functional form proposed by Yusifov & Kucuk, in which the pulsar surface density peaks at radius ~3 kpc. The birth spin period distribution extends to several hundred milliseconds, with no evidence of multimodality. Models that assume the radio luminosities of pulsars to be independent of the spin periods and period derivatives are inadequate, as they lead to the detection of too many old simulated pulsars in our simulations. Dithered radio luminosities proportional to the square root of the spin-down luminosity accommodate the observations well and provide a natural mechanism for the pulsars to dim uniformly as they approach the death line, avoiding an observed pileup on the latter. There is no evidence for significant torque decay (due to magnetic field decay or otherwise) over the lifetime of the pulsars as radio sources (~100 Myr). Finally, we estimate the pulsar birthrate and total number of pulsars in the Galaxy.

https://iopscience.iop.org/article/10.1086/501516/pdf

Birth and Evolution of Isolated Radio Pulsars

Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information they might yield about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on equilibrium properties and on nonaxisymmetric oscillations and instabilities in f-modes and r-modes have been updated. Several new sections have been added on equilibria in modified theories of gravity, approximate universal relationships, the one-arm spiral instability, on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity including both hydrodynamic and magnetohydrodynamic studies of these objects.

/pdf/rotating-stars-in-relativity-2icxwvd68c.pdf

Rotating Stars in Relativity

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.

Presupernova Evolution of Differentially Rotating Massive Stars Including Magnetic Fields

Rossby waves (r-modes) in rapidly rotating neutron stars are unstable because of the emission of gravitational radiation. As a result, the stellar rotational energy is converted into both gravitational waves and r-mode energy. The saturation level for the r-mode energy is a fundamental parameter needed to determine how fast the neutron star spins down, as well as whether gravitational waves will be detectable. In this paper we study saturation by nonlinear transfer of energy to the sea of stellar "inertial" oscillation modes that arise in rotating stars with negligible buoyancy and elastic restoring forces. We present detailed calculations of stellar inertial modes in the WKB limit, their linear damping by bulk and shear viscosity, and the nonlinear coupling forces among these modes. The saturation amplitude is derived in the extreme limits of strong or weak driving by radiation reaction, as compared to the damping rate of low-order inertial modes. In the weak driving case, energy can be stably transferred to a small number of modes, which damp the energy as heat or neutrinos. In the strong driving case, we show that a turbulent cascade develops, with a constant flux of energy to large wavenumbers and small frequencies where it is damped by shear viscosity. We find that the saturation energy is extremely small, at least 4 orders of magnitude smaller than that found by previous investigators. We show that the large saturation energy found in the simulations of Lindblom and coworkers is an artifact of their unphysically large radiation reaction force. In most physical situations of interest, for either nascent, rapidly rotating neutron stars or neutron stars being spun up by accretion in low-mass X-ray binaries (LMXBs), the strong driving limit is appropriate and the saturation energy is roughly E_(r-mode)/(0.5Mr^2_+Ω^2) sime 0.1γgr/Ω ≃ 10^(-6)(ν_(spin)/10^3 Hz)^5, where M and r* are the stellar mass and radius, respectively, γ_(gr) is the driving rate by gravitational radiation, Ω is the angular velocity of the star, and ν_(spin) is the spin frequency. At such a low saturation amplitude, the characteristic time for the star to exit the region of r-mode instability is ≳ 10^3-10^4 yr, depending sensitively on the instability curve. Although our saturation amplitude is smaller than that found by previous investigators, it is still sufficiently large to explain the observed period clustering in LMXBs. We find that the r-mode signal from both newly born neutron stars and LMXBs in the spin-down phase of Levin's limit cycle will be detectable by enhanced LIGO detectors out to ~100-200 kpc.

http://iopscience.iop.org/article/10.1086/374657/pdf

Saturation of the R mode instability

Rossby waves (r-modes) in rapidly rotating neutron stars are unstable because of the emission of gravitational radiation. We study saturation of this instability by nonlinear transfer of energy to stellar "inertial" oscillation modes. We present detailed calculations of stellar inertial modes in the WKB limit, their linear damping by bulk and shear viscosity, and the nonlinear coupling forces among these modes. The saturation amplitude is derived in the extreme limits of strong or weak driving by radiation reaction, as compared to the damping rate of low order inertial modes. We find the saturation energy is {\it extremely small}, at least four orders of magnitude smaller than that found by previous investigators. We discuss the consequences of this result for spin evolution of young neutron stars, and neutron stars being spun up by accretion in Low Mass X-ray Binaries.We also discuss the detection of these gravitational waves by LIGO.

https://arxiv.org/pdf/astro-ph/0202345.pdf

Saturation of the R-mode Instability

We present a method for constructing equilibrium disks with net angular momentum in general relativity The method solves the relativistic Vlasov equation coupled to Einstein's equations for the gravitational field We apply the method to construct disks that are relativistic versions of Newtonian Kalnajs disks In Newtonian gravity these disks are analytic and are stable against ring formation for certain ranges of their velocity dispersion We investigate the existence of fully general relativistic equilibrium sequences for differing values of the velocity dispersion These models are the first rotating, relativistic disk solutions of the collisionless Boltzmann equation

/pdf/hot-rotating-disks-in-general-relativity-collisionless-a7sbf660w1.pdf

A. Katrin Schenk

Papers

Saturation of the R mode instability

Saturation of the R-mode Instability

Hot, Rotating Disks in General Relativity: Collisionless Equilibrium Models