Stellar physics and evolution calculations enable a broad range of research in astrophysics. Modules for Experiments in Stellar Astrophysics (MESA) is a suite of open source, robust, efficient, thread-safe libraries for a wide range of applications in computational stellar astrophysics. A one-dimensional stellar evolution module, MESAstar, combines many of the numerical and physics modules for simulations of a wide range of stellar evolution scenarios ranging from very low mass to massive stars, including advanced evolutionary phases. MESAstar solves the fully coupled structure and composition equations simultaneously. It uses adaptive mesh refinement and sophisticated timestep controls, and supports shared memory parallelism based on OpenMP. State-of-the-art modules provide equation of state, opacity, nuclear reaction rates, element diffusion data, and atmosphere boundary conditions. Each module is constructed as a separate Fortran 95 library with its own explicitly defined public interface to facilitate independent development. Several detailed examples indicate the extensive verification and testing that is continuously performed and demonstrate the wide range of capabilities that MESA possesses. These examples include evolutionary tracks of very low mass stars, brown dwarfs, and gas giant planets to very old ages; the complete evolutionary track of a 1 M ☉ star from the pre-main sequence (PMS) to a cooling white dwarf; the solar sound speed profile; the evolution of intermediate-mass stars through the He-core burning phase and thermal pulses on the He-shell burning asymptotic giant branch phase; the interior structure of slowly pulsating B Stars and Beta Cepheids; the complete evolutionary tracks of massive stars from the PMS to the onset of core collapse; mass transfer from stars undergoing Roche lobe overflow; and the evolution of helium accretion onto a neutron star. MESA can be downloaded from the project Web site (http://mesa.sourceforge.net/).

https://iopscience.iop.org/article/10.1088/0067-0049/192/1/3/pdf

Modules for Experiments in Stellar Astrophysics (MESA)

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.

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The evolution and explosion of massive stars

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

Supernova theory, numerical and analytic, has made remarkable progress in the past decade. This progress was made possible by more sophisticated simulation tools, especially for neutrino transport, improved microphysics, and deeper insights into the role of hydrodynamic instabilities. Violent, large-scale nonradial mass motions are generic in supernova cores. The neutrino-heating mechanism, aided by nonradial flows, drives explosions, albeit low-energy ones, of O-Ne-Mg-core and some Fe-core progenitors. The characteristics of the neutrino emission from newborn neutron stars were revised, new features of the gravitational-wave signals were discovered, our notion of supernova nucleosynthesis was shattered, and our understanding of pulsar kicks and explosion asymmetries was significantly improved. But simulations also suggest that neutrino-powered explosions might not explain the most energetic supernovae and hypernovae, which seem to demand magnetorotational driving. Now that modeling is being advanced from...

https://www.annualreviews.org/doi/pdf/10.1146/annurev-nucl-102711-094901

Explosion Mechanisms of Core-Collapse Supernovae

Nucleosynthesis, light curves, explosion energies, and remnant masses are calculated for a grid of supernovae resulting from massive stars with solar metallicity and masses from 9.0 to 120 solar masses. The full evolution is followed using an adaptive reaction network of up to 2000 nuclei. A novel aspect of the survey is the use of a one-dimensional neutrino transport model for the explosion. This explosion model has been calibrated to give the observed energy for SN 1987A, using several standard progenitors, and for the Crab supernova using a 9.6 solar mass progenitor. As a result of using a calibrated central engine, the final kinetic energy of the supernova is variable and sensitive to the structure of the presupernova star. Many progenitors with extended core structures do not explode, but become black holes, and the masses of exploding stars do not form a simply connected set. The resulting nucleosynthesis agrees reasonably well with the sun provided that a reasonable contribution from Type Ia supernovae is also allowed, but with a deficiency of light s-process isotopes. The resulting neutron star IMF has a mean gravitational mass near 1.4 solar masses. The average black hole mass is about 9 solar masses if only the helium core implodes, and 14 solar masses if the entire presupernova star collapses. Only ~10% of supernovae come from stars over 20 solar masses and some of these are Type Ib or Ic. Some useful systematics of Type IIp light curves are explored.

https://iopscience.iop.org/article/10.3847/0004-637X/821/1/38/pdf

Core-Collapse Supernovae from 9 to 120 Solar Masses Based on Neutrino-powered Explosions

Supernova models with a full spectral treatment of the neutrino transport are presented, employing the PROMETHEUS/VERTEX neutrinohydrodynamics code with a variable Eddington factor closure of the O(v/c) moments equations of neutrino number, energy, and momentum. Our ray-by-ray plus approximation developed for two- (or three-) dimensional problems assumes that the local neutrino distribution function is azimuthally symmetric around the radial direction, which implies that the nonradial flux components disappear. Other terms containing the angular velocity components are retained in the moments equations and establish a coupling of the transport at different latitudes by lateral derivatives. Also lateral components of the neutrino pressure gradients are included in the hydrodynamics equations. This approximative approach for neutrino transport in multi-dimensional environments is motivated and critically assessed with respect to its capabilities, limitations, and inaccuracies in the context of supernova simulations. In this first paper of a series, one- (1D) and two-dimensional (2D) core-collapse calculations for a (nonrotating) 15 M ○. star are discussed, uncertainties in the treatment of the equation of state - numerical and physical - are tested, Newtonian results are compared with simulations using a general relativistic potential, bremsstrahlung and interactions of neutrinos of different flavors are investigated, and the standard approximation in neutrino-nucleon interactions with zero energy transfer is replaced by rates that include corrections due to nucleon recoil, thermal motions, weak magnetism, and nucleon correlations. Models with the full implementation of the ray-by-ray plus spectral transport were found not to explode, neither in spherical symmetry nor in 2D when the computational grid is constrained to a lateral wedge (<±45°) around the equator. The success of previous two-dimensional simulations with grey, flux-limited neutrino diffusion can therefore not be confirmed. An explosion is obtained in 2D for the considered 15 M ○. progenitor, when the radial velocity terms in the neutrino momentum equation are omitted. This manipulation increases the neutrino energy density in the convective gain layer by about 20-30% and thus the integral neutrino energy deposition in this region by about a factor of two compared to the non-exploding 2D model with the full transport. The spectral treatment of the transport and detailed description of charged-current processes leads to proton-rich neutrino-heated ejecta, removing the problem that previous explosion models with approximate neutrino treatment overproduced N = 50 closed neutron shell nuclei by large factors.

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Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport. I. Numerical method and results for a 15 M star

Supernova models with a full spectral treatment of the neutrino transport are presented, employing the Prometheus/Vertex neutrino-hydrodynamics code with a ``ray-by-ray plus'' approximation for treating two- (or three-) dimensional problems. The method is described in detail and critically assessed with respect to its capabilities, limitations, and inaccuracies in the context of supernova simulations. In this first paper of a series, 1D and 2D core-collapse calculations for a (nonrotating) 15 M_sun star are discussed, uncertainties in the treatment of the equation of state -- numerical and physical -- are tested, Newtonian results are compared with simulations using a general relativistic potential, bremsstrahlung and interactions of neutrinos of different flavors are investigated, and the standard approximation in neutrino-nucleon interactions with zero energy transfer is replaced by rates that include corrections due to nucleon recoil, thermal motions, weak magnetism, and nucleon correlations. Models with the full implementation of the ``ray-by-ray plus'' spectral transport were found not to explode, neither in spherical symmetry nor in 2D with a 90 degree lateral wedge. The success of previous 2D simulations with grey, flux-limited neutrino diffusion can therefore not be confirmed. Omitting the radial velocity terms in the neutrino momentum equation leads to ``artificial'' explosions by increasing the neutrino energy density in the convective gain layer by about 20--30% and thus the integral neutrino energy deposition in this region by about a factor of two. (abbreviated)

Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport. I. Numerical method and results for a 15 M_sun star

We study hydrodynamic instabilities during the first seconds of core-collapse supernovae by means of 2D simulations with approximative neutrino transport and boundary conditions that parameterize the effects of the contracting neutron star and allow us to obtain sufficiently strong neutrino heating and, hence, neutrino-driven explosions. Confirming more idealised studies, as well as supernova simulations with spectral transport, we find that random seed perturbations can grow by hydrodynamic instabilities to a globally asymmetric mass distribution in the region between the nascent neutron star and the accretion shock, leading to a dominance of dipole ($l=1$) and quadrupole ($l=2$) modes in the explosion ejecta, provided the onset of the supernova explosion is sufficiently slower than the growth time scale of the low-mode instability. By gravitational and hydrodynamic forces, the anisotropic mass distribution causes an acceleration of the nascent neutron star, which lasts for several seconds and can propel the neutron star to velocities of more than 1000 km s -1 . Because the explosion anisotropies develop chaotically and change by small differences in the fluid flow, the magnitude of the kick varies stochastically. No systematic dependence of the average neutron star velocity on the explosion energy or the properties of the considered progenitors is found. Instead, the anisotropy of the mass ejection, and hence of the kick, seems to increase when the nascent neutron star contracts more quickly, and thus low-mode instabilities can grow more rapidly. Our more than 70 models separate into two groups, one with high and the other with low neutron star velocities and accelerations after one second of post-bounce evolution, depending on whether the $l=1$ mode is dominant in the ejecta or not. This leads to a bimodality of the distribution when the neutron star velocities are extrapolated to their terminal values. Establishing a link to the measured distribution of pulsar velocities, however, requires a much larger set of calculations and ultimately 3D modelling.

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Multidimensional supernova simulations with approximative neutrino transport. I. Neutron star kicks and the anisotropy of neutrino-driven explosions in two spatial dimensions

Spherically symmetric (ID) and two-dimensional (2D) supernova simulations for progenitor stars between 11 M ⊙ and 25 M ⊙ are presented, making use of the PROMETHEUS/VERTEX neutrino-hydrodynamics code, which employs a full spectral treatment of neutrino transport and neutrino-matter interactions with a variable Eddington factor closure of the O(v/c) moments equations of neutrino number, energy, and momentum. Multi-dimensional transport aspects are treated by the "ray-by-ray plus" approximation described in Paper I. We discuss in detail the variation of the supernova evolution with the progenitor models, including one calculation for a 15 M ⊙ progenitor whose iron core is assumed to rotate rigidly with an angular frequency of 0.5 rad s -1 before collapse. We also test the sensitivity of our 2D calculations to the angular grid resolution, the lateral wedge size of the computational domain, and to the perturbations which seed convective instabilities in the post-bounce core. In particular, we do not find any important differences depending on whether random perturbations are included already during core collapse or whether such perturbations are imposed on a ID collapse model shortly after core bounce. Convection below the neutrinosphere sets in 30-40 ms after bounce at a density well above 10 12 g cm -3 in all 2D models, and encompasses a layer of growing mass as time goes on. It leads to a more extended proto-neutron star structure with reduced mean energies of the radiated neutrinos, but accelerated lepton number and energy loss and significantly higher muon and tau neutrino luminosities at times later than about 100ms after bounce. While convection inside the nascent neutron star turns out to be insensitive to our variations of the angular cell and grid size, the convective activity in the neutrino-heated postshock layer gains more strength in better resolved models. We find that low (l = 1, 2) convective modes, which require the use of a full 180 degree grid and are excluded in simulations with smaller angular wedges, can qualitatively change the evolution of a model. In case of an 11.2 M ⊙ star, the lowest-mass progenitor we investigate, a probably rather weak explosion by the convectively supported neutrino-heating mechanism develops after about 150ms post-bounce evolution in a 2D simulation with 180 degrees, whereas the same model with 90 degree wedge fails to explode like all other models. This sensitivity demonstrates the proximity of our 2D calculations to the borderline between success and failure, and stresses the need to strive for simulations in 3D, ultimately without the constraints connected with the axis singularity of a polar coordinate grid.

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Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport II. Models for different progenitor stars

We have performed two-dimensional simulations of core collapse supernovae that encompass shock revival by neutrino heating, neutrino-driven convection, explosive nucleosynthesis, the growth of Rayleigh-Taylor instabilities, and the propagation of newly formed metal clumps through the exploding star. A simulation of a type II explosion in a 15 M blue supergiant progenitor is presented, that confirms our earlier type II models and extends their validity to times as late as 5.5 hours after core bounce. We also study a type Ib-like explosion, by simply removing the hydrogen envelope of the progenitor model. This allows for a first comparison of type II and type Ib evolution. We present evidence that the hydrodynamics of core collapse supernovae beyond shock revival diers markedly from the results of simulations that have followed the Rayleigh-Taylor mixing starting from ad hoc energy deposition schemes to initiate the explosion. We find iron group elements to be synthesized in an anisotropic, dense, low-entropy shell that expands with velocities of17 000 km s 1 shortly after shock revival. The growth of Rayleigh-Taylor instabilities at the Si/ Oa nd (C+O)/He composition interfaces of the progenitor, seeded by the flow-structures resulting from neutrino-driven convection, leads to a fragmentation of this shell into metal-rich "clumps". This fragmentation starts already 20 s after core bounce and is complete within the first few minutes of the explosion. During this time the clumps are slowed down by drag, and by the positive pressure gradient in the unstable layers. However, at t 300 s they decouple from the flow and start to propagate ballistically and subsonically through the He core, with the maximum velocities of metals remaining constant at3500 5500 km s 1 . This early "clump decoupling" leads to significantly higher 56 Ni velocities at t= 300 s than in one-dimensional models of the explosion, demonstrating that multi-dimensional eects which are at work within the first minutes, and which have been neglected in previous studies (especially in those which dealt with the mixing in type II supernovae), are crucial. Despite comparably high initial maximum nickel velocities in both our type II and our type Ib-like model, we find that there are large dierences in the final maximum nickel velocities between both cases. In the "type Ib" model the maximum velocities of metals remain frozen in at3500 5500 km s 1 for t 300 s, while in the type II model they drop significantly for t > 1500 s. In the latter case, the massive hydrogen envelope of the progenitor forces the supernova shock to slow down strongly, leaving behind a reverse shock and a dense helium shell (or "wall") below the He/H interface. After penetrating into this dense material the metal-rich clumps possess supersonic speeds, before they are slowed down by drag forces to1200 km s 1 at a time of 20 000 s post-bounce. While, due to this deceleration, the maximum velocities of iron-group elements in SN 1987 A cannot be reproduced in case of the considered 15 M progenitor, the "type Ib" model is in fairly good agreement with observed clump velocities and the amount of mixing inferred for type Ib supernovae. Thus it appears promising for calculations of synthetic spectra and light curves. Furthermore, our simulations indicate that for type Ib explosions the pattern of clump formation in the ejecta is correlated with the structure of the convective pattern prevailing during the shock-revival phase. This might be used to deduce observational constraints for the dynamics during this early phase of the evolution, and the role of neutrino heating in initiating the explosion.

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Non-spherical core collapse supernovae. I. Neutrino-driven convection, Rayleigh-Taylor instabilities, and the formation and propagation of metal clumps

Konstantinos Kifonidis

Papers

Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport. I. Numerical method and results for a 15 M star

Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport. I. Numerical method and results for a 15 M_sun star

Multidimensional supernova simulations with approximative neutrino transport. I. Neutron star kicks and the anisotropy of neutrino-driven explosions in two spatial dimensions

Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport II. Models for different progenitor stars

Non-spherical core collapse supernovae. I. Neutrino-driven convection, Rayleigh-Taylor instabilities, and the formation and propagation of metal clumps