Dynamo action by differential rotation in a stably stratified stellar interior
TL;DR: In this article, a dynamo model is developed from these ingredients, and applied to the problem of angular momentum transport in stellar interiors, which is found to be more effective in transporting angular momentum than the known hydrodynamic mechanisms.
Abstract: 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 predominantly horizontal field. This dynamo process is found to be more effective in transporting angular momentum than the known hydrodynamic mechanisms. It might account for the observed pattern of rotation in the solar core.
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TL;DR: Modules for Experiments in Stellar Astrophysics (MESA) as discussed by the authors is an open source software package for modeling the evolution of stellar structures and composition. But it is not suitable for large-scale systems such as supernovae.
Abstract: We substantially update the capabilities of the open source software package Modules for Experiments in Stellar Astrophysics (MESA), and its one-dimensional stellar evolution module, MESA star. Improvements in MESA star's ability to model the evolution of giant planets now extends its applicability down to masses as low as one-tenth that of Jupiter. The dramatic improvement in asteroseismology enabled by the space-based Kepler and CoRoT missions motivates our full coupling of the ADIPLS adiabatic pulsation code with MESA star. This also motivates a numerical recasting of the Ledoux criterion that is more easily implemented when many nuclei are present at non-negligible abundances. This impacts the way in which MESA star calculates semi-convective and thermohaline mixing. We exhibit the evolution of 3-8 M ? stars through the end of core He burning, the onset of He thermal pulses, and arrival on the white dwarf cooling sequence. We implement diffusion of angular momentum and chemical abundances that enable calculations of rotating-star models, which we compare thoroughly with earlier work. We introduce a new treatment of radiation-dominated envelopes that allows the uninterrupted evolution of massive stars to core collapse. This enables the generation of new sets of supernovae, long gamma-ray burst, and pair-instability progenitor models. We substantially modify the way in which MESA star solves the fully coupled stellar structure and composition equations, and we show how this has improved the scaling of MESA's calculational speed on multi-core processors. Updates to the modules for equation of state, opacity, nuclear reaction rates, and atmospheric boundary conditions are also provided. We describe the MESA Software Development Kit that packages all the required components needed to form a unified, maintained, and well-validated build environment for MESA. We also highlight a few tools developed by the community for rapid visualization of MESA star results.
2,761 citations
Cites background or methods from "Dynamo action by differential rotat..."
...Magnetic fields generated by differential rotation in radiative regions have been implemented following the work of Spruit (2002) and in the same fashion as in Petrovic et al. (2005) and Heger et al. (2005)....
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...We refer to Spruit (2002) for a description of the physics of the dynamo loop and to Maeder & Meynet (2003), Maeder & Meynet (2004) and Heger et al. (2005) for a discussion of its inclusion in stellar evolution codes....
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...As expected, these fields are generated only in radiative regions of the star and Bφ > Br (Spruit 2002)....
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TL;DR: In this article, the authors discuss how metallicity affects the evolution and final fate of massive stars, and derive the relative populations of stellar populations as a function of metallity.
Abstract: 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.
2,007 citations
Cites background from "Dynamo action by differential rotat..."
...If the estimates of magnetic torques by Spruit (2002) are valid, then single stars are unlikely to produce collapsars and rotation is probably not a factor in the explosion of common supernovae....
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...Recently, Spruit (2002) has discussed a ‘‘ dynamo ’’ mechanism based on the interchange instability that allows the estimation of magnetic torques to be included in models for stellar evolution....
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TL;DR: In this article, the authors examined the current understanding of the lives and deaths of massive stars, with special attention to the relevant nuclear and stellar physics, and focused on their post-helium-burning evolution.
Abstract: amount of energy, a tiny fraction of which is sufficient to explode the star as a supernova. The authors examine our current understanding of the lives and deaths of massive stars, with special attention to the relevant nuclear and stellar physics. Emphasis is placed upon their post-helium-burning evolution. Current views regarding the supernova explosion mechanism are reviewed, and the hydrodynamics of supernova shock propagation and ‘‘fallback’’ is discussed. The calculated neutron star masses, supernova light curves, and spectra from these model stars are shown to be consistent with observations. During all phases, particular attention is paid to the nucleosynthesis of heavy elements. Such stars are capable of producing, with few exceptions, the isotopes between mass 16 and 88 as well as a large fraction of still heavier elements made by the r and p processes.
1,981 citations
TL;DR: In this paper, a set of models for solar metallicity, where the effects of rotation are accounted for in a homogeneous way, is presented, and a grid of 48 different stellar evolutionary tracks, both rotating and non-rotating, at Z ǫ = 0.014, spanning a wide mass range from 0.8 to 120 m ⊙.
Abstract: Aims. Many topical astrophysical research areas, such as the properties of planet host stars, the nature of the progenitors of different types of supernovae and gamma ray bursts, and the evolution of galaxies, require complete and homogeneous sets of stellar models at different metallicities in order to be studied during the whole of cosmic history. We present here a first set of models for solar metallicity, where the effects of rotation are accounted for in a homogeneous way.Methods. We computed a grid of 48 different stellar evolutionary tracks, both rotating and non-rotating, at Z = 0.014, spanning a wide mass range from 0.8 to 120 M ⊙ . For each of the stellar masses considered, electronic tables provide data for 400 stages along the evolutionary track and at each stage, a set of 43 physical data are given. These grids thus provide an extensive and detailed data basis for comparisons with the observations. The rotating models start on the zero-age main sequence (ZAMS) with a rotation rate υ ini /υ crit = 0.4. The evolution is computed until the end of the central carbon-burning phase, the early asymptotic giant branch (AGB) phase, or the core helium-flash for, respectively, the massive, intermediate, and both low and very low mass stars. The initial abundances are those deduced by Asplund and collaborators, which best fit the observed abundances of massive stars in the solar neighbourhood. We update both the opacities and nuclear reaction rates, and introduce new prescriptions for the mass-loss rates as stars approach the Eddington and/or the critical velocity. We account for both atomic diffusion and magnetic braking in our low-mass star models.Results. The present rotating models provide a good description of the average evolution of non-interacting stars. In particular, they reproduce the observed main-sequence width, the positions of the red giant and supergiant stars in the Hertzsprung-Russell (HR) diagram, the observed surface compositions and rotational velocities. Very interestingly, the enhancement of the mass loss during the red-supergiant stage, when the luminosity becomes supra-Eddington in some outer layers, help models above 15−20 M ⊙ to lose a significant part of their hydrogen envelope and evolve back into the blue part of the HR diagram. This result has interesting consequences for the blue to red supergiant ratio, the minimum mass for stars to become Wolf-Rayet stars, and the maximum initial mass of stars that explode as type II−P supernovae.
1,654 citations
TL;DR: In this article, it was shown that most long-duration soft-spectrum gamma-ray bursts are accompanied by massive stellar explosions (GRB-SNe) and 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.
Abstract: 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.
1,389 citations
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TL;DR: In this article, a linear analysis is presented of the instability, which is local and extremely powerful; the maximum growth rate which is of the order of the angular rotation velocity, is independent of the strength of the magnetic field.
Abstract: A broad class of astronomical accretion disks is presently shown to be dynamically unstable to axisymmetric disturbances in the presence of a weak magnetic field, an insight with consequently broad applicability to gaseous, differentially-rotating systems. In the first part of this work, a linear analysis is presented of the instability, which is local and extremely powerful; the maximum growth rate, which is of the order of the angular rotation velocity, is independent of the strength of the magnetic field. Fluid motions associated with the instability directly generate both poloidal and toroidal field components. In the second part of this investigation, the scaling relation between the instability's wavenumber and the Alfven velocity is demonstrated, and the independence of the maximum growth rate from magnetic field strength is confirmed.
4,265 citations
Book•
01 Jan 1990TL;DR: In this paper, the theory of the internal structure of stars and their evolution in time is introduced and the basic physics of stellar interiors, methods for solving the underlying equations, and the most important results necessary for understanding the wide variety of stellar types and phenomena.
Abstract: This book introduces the theory of the internal structure of stars and their evolution in time. It presents the basic physics of stellar interiors, methods for solving the underlying equations, and the most important results necessary for understanding the wide variety of stellar types and phenomena. The evolution of stars is discussed from their birth through normal evolution to possibly spectacular final stages. Chapters on stellar oscillations and rotation are included.
2,450 citations
TL;DR: In this paper, the angular momenta for the iron core and overlying material of typical presupernova stars along with their detailed chemical structure are determined, for the first time, the angular momentum distribution in typical pre-main-sequence stars.
Abstract: 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.
981 citations
"Dynamo action by differential rotat..." refers background in this paper
...If only these known processes are included, pre-supernova cores rotate much too fast to explain the majority of supernovae (Heger et al. 2000), though they may rotate at the right rate for the collapsar model of gamma-ray bursts (McFadyen et al. 2001 and references therein)....
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TL;DR: In this article, the authors report on joint helioseismic analyses of solar rotation in the convection zone and in the outer part of the radiative core using the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft.
Abstract: The splitting of the frequencies of the global resonant acoustic modes of the Sun by large-scale flows and rotation permits study of the variation of angular velocity Ω with both radius and latitude within the turbulent convection zone and the deeper radiative interior. The nearly uninterrupted Doppler imaging observations, provided by the Solar Oscillations Investigation (SOI) using the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft positioned at the L1 Lagrangian point in continuous sunlight, yield oscillation power spectra with very high signal-to-noise ratios that allow frequency splittings to be determined with exceptional accuracy. This paper reports on joint helioseismic analyses of solar rotation in the convection zone and in the outer part of the radiative core. Inversions have been obtained for a medium-l mode set (involving modes of angular degree l extending to about 250) obtained from the first 144 day interval of SOI-MDI observations in 1996. Drawing inferences about the solar internal rotation from the splitting data is a subtle process. By applying more than one inversion technique to the data, we get some indication of what are the more robust and less robust features of our inversion solutions. Here we have used seven different inversion methods. To test the reliability and sensitivity of these methods, we have performed a set of controlled experiments utilizing artificial data. This gives us some confidence in the inferences we can draw from the real solar data. The inversions of SOI-MDI data have confirmed that the decrease of Ω with latitude seen at the surface extends with little radial variation through much of the convection zone, at the base of which is an adjustment layer, called the tachocline, leading to nearly uniform rotation deeper in the radiative interior. A prominent rotational shearing layer in which Ω increases just below the surface is discernible at low to mid latitudes. Using the new data, we have also been able to study the solar rotation closer to the poles than has been achieved in previous investigations. The data have revealed that the angular velocity is distinctly lower at high latitudes than the values previously extrapolated from measurements at lower latitudes based on surface Doppler observations and helioseismology. Furthermore, we have found some evidence near latitudes of 75° of a submerged polar jet which is rotating more rapidly than its immediate surroundings. Superposed on the relatively smooth latitudinal variation in Ω are alternating zonal bands of slightly faster and slower rotation, each extending some 10° to 15° in latitude. These relatively weak banded flows have been followed by inversion to a depth of about 5% of the solar radius and appear to coincide with the evolving pattern of torsional oscillations reported from earlier surface Doppler studies.
959 citations
"Dynamo action by differential rotat..." refers background in this paper
...The very small degree of differential rotation in the core of the Sun, and the small difference in rotation rate between the core and the convective envelope (Schou et al. 1998; Charbonneau et al. 1999) requires the presence a process with two special properties....
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806 citations
"Dynamo action by differential rotat..." refers methods in this paper
...This view is much closer to semiempirical models of the cycle like those of Leighton (1969), the development of which was eclipsed by the mathematically more interesting turbulent dynamo models....
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