Using a two-dimensional hydrodynamics code (PROMETHEUS), we explore the continued evolution of rotating helium stars, Mα 10 M☉, in which iron-core collapse does not produce a successful outgoing shock but instead forms a black hole of 2-3 M☉. The model explored in greatest detail is the 14 M☉ helium core of a 35 M☉ main-sequence star. The outcome is sensitive to the angular momentum. For j16 ≡ j/(1016 cm2 s-1) 3, material falls into the black hole almost uninhibited. No outflows are expected. For j16 20, the infalling matter is halted by centrifugal force outside 1000 km where neutrino losses are negligible. The equatorial accretion rate is very low, and explosive oxygen burning may power a weak equatorial explosion. For 3 j16 20, however, a reasonable value for such stars, a compact disk forms at a radius at which the gravitational binding energy can be efficiently radiated as neutrinos or converted to beamed outflow by magnetohydrodynamical (MHD) processes. These are the best candidates for producing gamma-ray bursts (GRBs). Here we study the formation of such a disk, the associated flow patterns, and the accretion rate for disk viscosity parameter α ≈ 0.001 and 0.1. Infall along the rotational axis is initially uninhibited, and an evacuated channel opens during the first few seconds. Meanwhile the black hole is spun up by the accretion (to a ≈ 0.9), and energy is dissipated in the disk by MHD processes and radiated by neutrinos. For the α = 0.1 model, appreciable energetic outflows develop between polar angles of 30° and 45°. These outflows, powered by viscous dissipation in the disk, have an energy of up to a few times 1051 ergs and a mass ~1 M☉ and are rich in 56Ni. They constitute a supernova-like explosion by themselves. Meanwhile accretion through the disk is maintained for approximately 10-20 s but is time variable (±30%) because of hydrodynamical instabilities at the outer edge in a region where nuclei are experiencing photodisintegration. Because the efficiency of neutrino energy deposition is sensitive to the accretion rate, this instability leads to highly variable energy deposition in the polar regions. Some of this variability, which has significant power at 50 ms and overtones, may persist in the time structure of the burst. During the time followed, the average accretion rate for the standard α = 0.1 and j16 = 10 model is 0.07 M☉ s-1. The total energy deposited along the rotational axes by neutrino annihilation is (1-14) × 1051 ergs, depending upon the evolution of the Kerr parameter and uncertain neutrino efficiencies. Simulated deposition of energy in the polar regions, at a constant rate of 5 × 1050 ergs s-1 per pole, results in strong relativistic outflow jets beamed to about 1% of the sky. These jets may be additionally modulated by instabilities in the sides of the "nozzle" through which they flow. The jets blow aside the accreting material, remain highly focused, and are capable of penetrating the star in ~10 s. After the jet breaks through the surface of the star, highly relativistic flow can emerge. Because of the sensitivity of the mass ejection and jets to accretion rate, angular momentum, and disk viscosity, and the variation of observational consequences with viewing angle, a large range of outcomes is possible, ranging from bright GRBs like GRB 971214 to faint GRB-supernovae like SN 1998bw. X-ray precursors are also possible as the jet first breaks out of the star. While only a small fraction of supernovae make GRBs, we predict that collapsars will always make supernovae similar to SN 1998bw. However, hard, energetic GRBs shorter than a few seconds will be difficult to produce in this model and may require merging neutron stars and black holes for their explanation.

https://iopscience.iop.org/article/10.1086/307790/pdf

Collapsars: Gamma-ray bursts and explosions in 'failed supernovae'

How massive stars die-what sort of explosion and remnant each produces-depends chiefly on the masses of their helium cores and hydrogen envelopes at death. For single stars, stellar winds are the only means of mass loss, and these are a function of the metallicity of the star. We discuss how metallicity, and a simplified prescription for its effect on mass loss, affects the evolution and final fate of massive stars. We map, as a function of mass and metallicity, where black holes and neutron stars are likely to form and where different types of supernovae are produced. Integrating over an initial mass function, we derive the relative populations as a function of metallicity. Provided that single stars rotate rapidly enough at death, we speculate on stellar populations that might produce gamma-ray bursts and jet-driven supernovae.

/pdf/how-massive-single-stars-end-their-life-3v2i056c9w.pdf

How Massive Single Stars End Their Life

Observations show that at least some gamma-ray bursts (GRBs) happen simultaneously with core-collapse supernovae (SNe), thus linking by a common thread nature's two grandest explosions. We review here the growing evidence for and theoretical implications of this association, and conclude that most long-duration soft-spectrum GRBs are accompanied by massive stellar explosions (GRB-SNe). The kinetic energy and luminosity of well-studied GRB-SNe appear to be greater than those of ordinary SNe, but evidence exists, even in a limited sample, for considerable diversity. The existing sample also suggests that most of the energy in the explosion is contained in nonrelativistic ejecta (producing the supernova) rather than in the relativistic jets responsible for making the burst and its afterglow. Neither all SNe, nor even all SNe of Type Ibc produce GRBs. The degree of differential rotation in the collapsing iron core of massive stars when they die may be what makes the difference.

The Supernova Gamma-Ray Burst Connection

Gamma-ray bursts are the most luminous explosions in the Universe, and their origin and mechanism are the focus of intense research and debate. More than three decades after their discovery, and after pioneering breakthroughs from space and ground experiments, their study is entering a new phase with the recently launched Swift satellite. The interplay between these observations and theoretical models of the prompt gamma-ray burst and its afterglow is reviewed.

https://iopscience.iop.org/article/10.1088/0034-4885/69/8/R01/pdf

Gamma-ray bursts

The evolution of rotating stars with zero-age main-sequence (ZAMS) masses in the range 8-25 M☉ is followed through all stages of stable evolution. The initial angular momentum is chosen such that the star's equatorial rotational velocity on the ZAMS ranges from zero to ~ 70% of breakup. The stars rotate rigidly on the ZAMS as a consequence of angular momentum redistribution during the pre-main-sequence evolution. Redistribution of angular momentum and chemical species are then followed as a consequence of Eddington-Sweet circulation, Solberg-Hoiland instability, the Goldreich-Schubert-Fricke instability, and secular and dynamic shear instability. The effects of the centrifugal force on the stellar structure are included. Convectively unstable zones are assumed to tend toward rigid rotation, and uncertain mixing efficiencies are gauged by observations. We find, as noted in previous work, that rotation increases the helium core masses and enriches the stellar envelopes with products of hydrogen burning. We determine, for the first time, the angular momentum distribution in typical presupernova stars along with their detailed chemical structure. Angular momentum loss due to (nonmagnetic) stellar winds and the redistribution of angular momentum during core hydrogen burning are of crucial importance for the specific angular momentum of the core. Neglecting magnetic fields, we find angular momentum transport from the core to the envelope to be unimportant after core helium burning. We obtain specific angular momenta for the iron core and overlying material of 1016-1017 cm2 s-1. These values are insensitive to the initial angular momentum and to uncertainties in the efficiencies of rotational mixing. They are small enough to avoid triaxial deformations of the iron core before it collapses, but could lead to neutron stars which rotate close to breakup. They are also in the range required for the collapsar model of gamma-ray bursts. The apparent discrepancy with the measured rotation rates of young pulsars is discussed.

https://iopscience.iop.org/article/10.1086/308158/pdf

Presupernova Evolution of Rotating Massive Stars. I. Numerical Method and Evolution of the Internal Stellar Structure

A variety of current models of gamma-ray bursts (GRBs) suggest a common engine: a black hole of several solar masses accreting matter from a disk at a rate of 0.01 to 10 M☉ s-1. Using a numerical model for relativistic disk accretion, we have studied steady state accretion at these high rates. Outside about 108 cm, the disk is advection dominated; energy released by dissipation is carried in by the optically thick gas, and the disk does not cool. Inside this radius, for accretion rates greater than about 0.01 M☉ s-1 a global state of balanced power comes to exist between neutrino losses, chiefly pair capture on nucleons, and dissipation. As a result of these losses, the temperature is reduced, the density is raised, and the disk scale height is reduced compared to the advective solution. The sudden onset of neutrino losses (due to the high temperature dependence) and photodisintegration leads to an abrupt thinning of the disk that may provide a favorable geometry for jet production. The inner disk remains optically thin to neutrinos for accretion rates of up to about 1 M☉ s-1. The energy emitted in neutrinos is less, and in the case of low accretion rates, very much less, than the maximum efficiency factor for black hole accretion (0.057 for no rotation; 0.42 for extreme Kerr rotation) times the accretion rate, c2. Neutrino temperatures at the last stable orbit range from 2 MeV (no rotation, slow accretion) to 13 MeV (Kerr geometry, rapid accretion), and the density ranges from 109 to 1012 g cm-3. The efficiency for producing a pair fireball along the rotational axis by neutrino annihilation is calculated and found to be highly variable and very sensitive to the accretion rate. For some of the higher accretion rates studied, it can be several percent or more; for accretion rates less than 0.05 M☉ s-1, it is essentially zero. The efficiency of the Blandford-Znajek mechanism in extracting rotational energy from the black hole is also estimated. In light of these results, the viability of various gamma-ray burst models is discussed, and the sensitivity of the results to disk viscosity, black hole rotation rate, and black hole mass is explored. A diverse range of GRB energies seems unavoidable, and neutrino annihilation in hyperaccreting black hole systems can explain bursts of up to 1052 ergs. Larger energies can be inferred for beaming systems.

https://iopscience.iop.org/article/10.1086/307259/pdf

Hyperaccreting black holes and gamma-ray bursts

A variety of current models for gamma-ray bursts (GRBs) suggest a common engine - a black hole of several solar masses accreting matter from a disk at a rate 0.01 to 10 solar masses per second. Using a numerical model for relativistic disk accretion, we have studied steady-state accretion at these high rates. Inside a radius ~ 10**8 cm, for accretion rates greater than about 0.01 solar masses per second, a global state of balanced power comes to exist between neutrino losses, chiefly pair capture on nucleons, and dissipation. Energy emitted in neutrinos is less, and in the case of low accretion rates, very much less, than the maximum efficiency factor for black hole accretion (0.057 for no rotation; 0.42 for extreme Kerr rotation) times Mdot c**2. The efficiency for producing a pair fireball along the rotational axis by neutrino annihilation is calculated and found to be highly variable and very sensitive to the accretion rate. For some of the higher accretion rates studied, it can be several per cent or more; for accretion rates less than 0.05 solar masses per second, it is essentially zero. The efficiency of the Blandford-Znajek mechanism in extracting rotational energy from the black hole is also estimated. In light of these results, the viability of various gamma-ray burst models is discussed and the sensitivity of the results to disk viscosity, black hole rotation rate, and black hole mass explored. A diverse range of GRB energies seems unavoidable and neutrino annihilation in hyper-accreting black hole systems can explain bursts up to 10**52 erg. Larger energies may be inferred for beaming systems.

Hyper-Accreting Black Holes and Gamma-Ray Bursts

Dwarf nova oscillations (DNOs) have been observed in a number of cataclysmic variables. I propose that these oscillations could be produced by a non-axisymmetric bulge at the transition between the optically thick disc and the optically thin boundary layer region. This would naturally explain the observed oscillation periods and the dependence of the oscillation amplitude on photon energy. The transition radius moves inward and outward with changing mass accretion rate, which explains the correlation between period and flux, and the time-scale for period variations. The underlying cause of the non-axisymmetry that produces the oscillations is not known, so it is not possible to predict the oscillation amplitude from first principles.

Robert Popham

Papers

Hyperaccreting black holes and gamma-ray bursts

Hyper-Accreting Black Holes and Gamma-Ray Bursts

A boundary layer origin for dwarf nova oscillations

Hyper-Accreting Black Holes and Gamma-ray Bursts