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Supernova Simulations
Abstract
Magnetohydrodynamic simulations of core-collapse supernovae have become increasingly mature and important in recent years. Magnetic fields take center stage in scenarios for explaining hypernova explosions, but are now also considered in supernova theory more broadly as an important factor even in neutrino-driven explosions, especially in the context of neutron star birth properties. Here we present an overview of simulation approaches currently used for magnetohydrodynamic supernova simulations and sketch essential physical concepts for understanding the role of magnetic fields in supernovae of slowly or rapidly rotating massive stars. We review progress on simulations of neutrino-driven supernovae, magnetorotational supernovae, and the relevant field amplification processes. Recent results on the nucleosynthesis and gravitational wave emission from magnetorotational supernovae are also discussed. We highlight efforts to provide better initial conditions for magnetohydrodynamic supernova models by simulating short phases of the progenitor evolution in 3D to address uncertainties in the treatment of rotation and magnetic fields in current stellar evolution models.
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The production of heavy elements is one of the main by-products of the explosive end of massive stars. A long sought goal is finding differentiated patterns in the nucleosynthesis yields, which could permit identifying a number of properties of the explosive core. Among them, the traces of the magnetic field topology are particularly important for extreme supernova (SN) explosions, most likely hosted by magnetorotational effects. We investigate the nucleosynthesis of five state-of-the-art magnetohydrodynamic models with fast rotation that have been previously calculated in full 3D and that involve an accurate neutrino transport (M1). One of the models does not contain any magnetic field and synthesizes elements around the iron group, in agreement with other CC-SNe models in literature. All other models host a strong magnetic field of the same intensity, but with different topology. For the first time, we investigate the nucleosynthesis of MR-SNe models with a quadrupolar magnetic field and a 90° tilted dipole. We obtain a large variety of ejecta compositions reaching from iron nuclei to nuclei up to the third r-process peak. We assess the robustness of our results by considering the impact of different nuclear physics uncertainties such as different nuclear masses, β−-decays and β−-delayed neutron emission probabilities, neutrino reactions, fission, and a feedback of nuclear energy on the temperature. We find that the qualitative results do not change with different nuclear physics input. The properties of the explosion dynamics and the magnetic field configuration are the dominant factors determining the ejecta composition.
We investigate the influence of magnetic field amplification on the core-collapse supernovae in highly magnetized progenitors through three-dimensional simulations. By considering rotating models, we observe a strong correlation between the exponential growth of the magnetic field in the gain region and the initiation of shock revival, with a faster onset compared to the non-rotating model. We highlight that the mean magnetic field experiences exponential amplification as a result of α-effect in the dynamo process, which works efficiently with the increasing kinetic helicity of the turbulence within the gain region. Our findings indicate that the significant amplification of the mean magnetic fields leads to the development of locally intense turbulent magnetic fields, particularly in the vicinity of the poles, thereby promoting the revival of the shock by neutrino heating.
Spectroscopy is an important tool for providing insights into the structure of core-collapse supernova explosions. We use the Monte Carlo radiative transfer code Artis to compute synthetic spectra and light curves based on a two-dimensional explosion model of an ultra-stripped supernova. These calculations are designed both to identify observable fingerprints of ultra-stripped supernovae and as a proof-of-principle for using synthetic spectroscopy to constrain the nature of stripped-envelope supernovae more broadly. We predict characteristic spectral and photometric features for our ultra-stripped explosion model, and find that these do not match observed ultra-stripped supernova candidates like SN 2005ek. With a peak bolometric luminosity of 6.8 × 1041 erg s−1, a peak magnitude of −15.9 mag in R–band, and Δm15, R = 3.50, the model is even fainter and evolves even faster than SN 2005ek as the closest possible analogue in photometric properties. The predicted spectra are extremely unusual. The most prominent features are Mg II lines at 2,800 Å and 4,500 Å and the infrared Ca triplet at late times. The Mg lines are sensitive to the multi-dimensional structure of the model and are viewing-angle dependent. They disappear due to line blanketing by iron group elements in a spherically averaged model with additional microscopic mixing. In future studies, multi-D radiative transfer calculations need to be applied to a broader range of models to elucidate the nature of observed Type Ib/c supernovae.
We present a first 3D magnetohydrodynamic (MHD) simulation of oxygen, neon and carbon shell burning in a rapidly rotating 16M⊙ core-collapse supernova progenitor. We also run a purely hydrodynamic simulation for comparison. After ( 15 and 7 convective turnovers respectively), the magnetic fields in the oxygen and neon shells achieve saturation at 1011G and 5 × 1010G. The strong Maxwell stresses become comparable to the radial Reynolds stresses and eventually suppress convection. The suppression of mixing by convection and shear instabilities results in the depletion of fuel at the base of the burning regions, so that the burning shell eventually move outward to cooler regions, thus reducing the energy generation rate. The strong magnetic fields efficiently transport angular momentum outwards, quickly spinning down the rapidly rotating convective oxygen and neon shells and forcing them into rigid rotation. The hydrodynamic model shows complicated redistribution of angular momentum and develops regions of retrograde rotation at the base of the convective shells. We discuss implications of our results for stellar evolution and for the subsequent core-collapse supernova. The rapid redistribution of angular momentum in the MHD model casts some doubt on the possibility of retaining significant core angular momentum for explosions driven by millisecond magnetars. However, findings from multi-D models remain tentative until stellar evolution calculations can provide more consistent rotation profiles and estimates of magnetic field strengths to initialise multi-D simulations without substantial numerical transients. We also stress the need for longer simulations, resolution studies, and an investigation of non-ideal effects.
Convection is one of the most important mixing processes in stellar interiors. Hydrodynamic mass entrainment can bring fresh fuel from neighboring stable layers into a convection zone, modifying the structure and evolution of the star. Because flows in stellar convection zones are highly turbulent, multidimensional hydrodynamic simulations are fundamental to accurately capture the physics of mixing processes. Under some conditions, strong magnetic fields can be sustained by the action of a turbulent dynamo, adding another layer of complexity and possibly altering the dynamics in the convection zone and at its boundaries. In this study, we used our fully compressible S EVEN -L EAGUE H YDRO code to run detailed and highly resolved three-dimensional magnetohydrodynamic simulations of turbulent convection, dynamo amplification, and convective boundary mixing in a simplified setup whose stratification is similar to that of an oxygen-burning shell in a star with an initial mass of 25 M ⊙ . We find that the random stretching of magnetic field lines by fluid motions in the inertial range of the turbulent spectrum (i.e., a small-scale dynamo) naturally amplifies the seed field by several orders of magnitude in a few convective turnover timescales. During the subsequent saturated regime, the magnetic-to-kinetic energy ratio inside the convective shell reaches values as high as 0.33, and the average magnetic field strength is ∼10 ¹⁰ G. Such strong fields efficiently suppress shear instabilities, which feed the turbulent cascade of kinetic energy, on a wide range of spatial scales. The resulting convective flows are characterized by thread-like structures that extend over a large fraction of the convective shell. The reduced flow speeds and the presence of magnetic fields with strengths up to 60% of the equipartition value at the upper convective boundary diminish the rate of mass entrainment from the stable layer by ≈20% as compared to the purely hydrodynamic case.
Formed in the aftermath of a core-collapse supernova or neutron star merger, a hot proto–neutron star (PNS) launches an outflow driven by neutrino heating lasting for up to tens of seconds. Though such winds are considered potential sites for the nucleosynthesis of heavy elements via the rapid neutron capture process ( r -process), previous work has shown that unmagnetized PNS winds fail to achieve the necessary combination of high entropy and/or short dynamical timescale in the seed nucleus formation region. We present three-dimensional general-relativistic magnetohydrodynamical simulations of PNS winds which include the effects of a dynamically strong ( B ≳ 10 ¹⁵ G) dipole magnetic field. After initializing the magnetic field, the wind quickly develops a helmet-streamer configuration, characterized by outflows along open polar magnetic field lines and a “closed” zone of trapped plasma at lower latitudes. Neutrino heating within the closed zone causes the thermal pressure of the trapped material to rise in time compared to the polar outflow regions, ultimately leading to the expulsion of this matter from the closed zone on a timescale of ∼60 ms, consistent with the predictions of Thompson. The high entropies of these transient ejecta are still growing at the end of our simulations and are sufficient to enable a successful second-peak r -process in at least a modest ≳1% of the equatorial wind ejecta.
The Tayler-Spruit dynamo is one of the most promising mechanisms proposed to explain angular momentum transport during stellar evolution. Its development in proto-neutron stars spun-up by supernova fallback has also been put forward as a scenario to explain the formation of very magnetized neutron stars called magnetars. Using three-dimensional direct numerical simulations, we model the proto-neutron star interior as a stably stratified spherical Couette flow with the outer sphere that rotates faster than the inner one. We report the existence of two subcritical dynamo branches driven by the Tayler instability. They differ by their equatorial symmetry (dipolar or hemispherical) and the magnetic field scaling, which is in agreement with different theoretical predictions (by Fuller and Spruit, respectively). The magnetic dipole of the dipolar branch is found to reach intensities compatible with observational constraints on magnetars.
In this paper, we analyze the neutrino-driven winds that emerge in 12 unprecedentedly long-duration 3D core-collapse supernova simulations done using the code F ornax . The 12 models cover progenitors with zero-age main-sequence mass between 9 and 60 solar masses. In all our models, we see transonic outflows that are at least 2 times as fast as the surrounding ejecta and that originate generically from a proto−neutron star surface atmosphere that is turbulent and rotating. We find that winds are common features of 3D simulations, even if there is anisotropic early infall. We find that the basic dynamical properties of 3D winds behave qualitatively similarly to those inferred in the past using simpler 1D models, but that the shape of the emergent wind can be deformed, very aspherical, and channeled by its environment. The thermal properties of winds for less massive progenitors very approximately recapitulate the 1D stationary solutions, while for more massive progenitors they deviate significantly owing to aspherical accretion. The Y e temporal evolution in winds is stochastic, and there can be some neutron-rich phases. Though no strong r -process is seen in any model, a weak r -process can be produced, and isotopes up to ⁹⁰ Zr are synthesized in some models. Finally, we find that there is at most a few percent of a solar mass in the integrated wind component, while the energy carried by the wind itself can be as much as 10%–20% of the total explosion energy.
Magnetic fields on small scales are ubiquitous in the Universe. Although they can often be observed in detail, their generation mechanisms are not fully understood. One possibility is the so-called small-scale dynamo (SSD). Prevailing numerical evidence, however, appears to indicate that an SSD is unlikely to exist at very low magnetic Prandtl numbers (PrM) such as those that are present in the Sun and other cool stars. Here we have performed high-resolution simulations of isothermal forced turbulence using the lowest PrM values achieved so far. Contrary to earlier findings, the SSD not only turns out to be possible for PrM down to 0.0031 but also becomes increasingly easier to excite for PrM below about 0.05. We relate this behaviour to the known hydrodynamic phenomenon referred to as the bottleneck effect. Extrapolating our results to solar values of PrM indicates that an SSD would be possible under such conditions.
We perform three-dimensional simulations of magnetorotational supernovae using a 39 M⊙ progenitor star with two different initial magnetic field strengths of 1010 G and 1012 G in the core. Both models rapidly undergo shock revival and their explosion energies asymptote within a few hundred milliseconds to values of ≳ 2 × 1051 erg after conservatively correcting for the binding energy of the envelope. Magnetically collimated, non-relativistic jets form in both models, though the jets are subject to non-axisymmetric instabilities. The jets do not appear crucial for driving the explosion, as they only emerge once the shock has already expanded considerably. Our simulations predict moderate neutron star kicks of about 150 km s−1, no spin-kick alignment, and rapid early spin-down that would result in birth periods of about 20 ms, too slow to power an energetic gamma-ray burst jet. More than 0.2 M⊙ of iron-group material are ejected, but we estimate that the mass of ejected 56Ni will be considerably smaller as the bulk of this material is neutron-rich. Explosive burning does not contribute appreciable amounts of 56Ni because the burned material originates from the slightly neutron-rich silicon shell. The iron-group ejecta also show no pronounced bipolar geometry by the end of the simulations. The models thus do not immediately fit the characteristics of observed hypernovae, but may be representative of other transients with moderately high explosion energies. The gravitational-wave emission reaches high frequencies of up to 2000 Hz and amplitudes of over 100 cm. The gravitational-wave emission is detectable out to distances of ∼4 Mpc in the planned Cosmic Explorer detector.
In contrast to regular core-collapse supernovae, explosions of rapidly rotating massive stars can develop jets, fast collimated outflows directed along the rotational axis. Depending on the rate of rotation and the magnetic field strength before collapse as well as on possible mechanisms amplifying the magnetic field, such a core can explode magnetorotationally rather than via the standard supernova mechanism based on neutrino heating. This scenario can explain the highest kinetic energies observed in the class of hypernovae. On longer time scales, rotation and magnetic fields can play an important role in the engine of long gamma-ray burst powered by proto-magnetars or hyperaccreting black holes in collapsars. Both classes of events are characterized by relativistic jets and winds driven by neutrinos or magnetic spin-down of the central objects. The nucleosynthesis in these events includes the production of Fe group elements, including a possibly enhanced synthesis of radioactive 56Ni leading to high peak luminosities. Additionally, these events are, out of all stellar core-collapse events the ones most likely to allow for the formation of the heaviest nuclei via rapid neutron captures. Increasingly sophisticated numerical simulations indicate that at least a limited r-process is possible, though it remains open how robust this result is against variations in the numerical methods and the initial conditions. If so, supernovae with jets could contribute to the observed galactic chemical enrichment, in particular at early times before neutron-star mergers might be able to set in.
Long-duration γ -ray bursts (GRBs) accompany the collapse of massive stars and carry information about the central engine. However, no 3D models have been able to follow these jets from their birth via black hole (BH) to the photosphere. We present the first such 3D general-relativity magnetohydrodynamic simulations, which span over six orders of magnitude in space and time. The collapsing stellar envelope forms an accretion disk, which drags inwardly the magnetic flux that accumulates around the BH, becomes dynamically important, and launches bipolar jets. The jets reach the photosphere at ∼10 ¹² cm with an opening angle θ j ∼ 6° and a Lorentz factor Γ j ≲ 30, unbinding ≳90% of the star. We find that (i) the disk–jet system spontaneously develops misalignment relative to the BH rotational axis. As a result, the jet wobbles with an angle θ t ∼ 12°, which can naturally explain quiescent times in GRB lightcurves. The effective opening angle for detection θ j + θ t suggests that the intrinsic GRB rate is lower by an order of magnitude than standard estimates. This suggests that successful GRBs are rarer than currently thought and emerge in only ∼0.1% of supernovae Ib/c, implying that jets are either not launched or choked inside most supernova Ib/c progenitors. (ii) The magnetic energy in the jet decreases due to mixing with the star, resulting in jets with a hybrid composition of magnetic and thermal components at the photosphere, where ∼10% of the gas maintains magnetization σ ≳ 0.1. This indicates that both a photospheric component and reconnection may play a role in the prompt emission.
Magnetars are isolated young neutron stars characterised by the most intense magnetic fields known in the Universe, which power a wide variety of high-energy emissions from giant flares to fast radio bursts. The origin of their magnetic field is still a challenging question. In situ magnetic field amplification by dynamo action could potentially generate ultra-strong magnetic fields in fast-rotating progenitors. However, it is unclear whether the fraction of progenitors harbouring fast core rotation is sufficient to explain the entire magnetar population. To address this point, we propose a new scenario for magnetar formation involving a slowly rotating progenitor, in which a slow-rotating proto-neutron star is spun up by the supernova fallback. We argue that this can trigger the development of the Tayler-Spruit dynamo while other dynamo processes are disfavoured. Using the findings of previous studies of this dynamo and simulation results characterising the supernova fallback, we derive equations modelling the coupled evolution of the proto-neutron star rotation and magnetic field. Their time integration for different accreted masses is successfully compared with analytical estimates of the amplification timescales and saturation value of the magnetic field. We find that the magnetic field is amplified within 20 − 40 s after the core bounce, and that the radial magnetic field saturates at intensities between ∼10 ¹³ and 10 ¹⁵ G, therefore spanning the full range of a magnetar’s dipolar magnetic fields. The toroidal magnetic field is predicted to be a factor of 10–100 times stronger, lying between ∼10 ¹⁵ and 3 × 10 ¹⁶ G. We also compare the saturation mechanisms proposed respectively by H.C. Spruit and J. Fuller, showing that magnetar-like magnetic fields can be generated for a neutron star spun up to rotation periods of ≲8 ms and ≲28 ms, corresponding to accreted masses of ≳ 4 × 10 ⁻² M ⊙ and ≳ 1.1 × 10 ⁻² M ⊙ , respectively. Therefore, our results suggest that magnetars can be formed from slow-rotating progenitors for accreted masses compatible with recent supernova simulations and leading to plausible initial rotation periods of the proto-neutron star.
The dynamo driven by the magnetorotational instability (MRI) is believed to play an important role in the dynamics of accretion discs and may also explain the origin of the extreme magnetic fields present in magnetars. Its saturation level is an important open question known to be particularly sensitive to the diffusive processes through the magnetic Prandtl number Pm (the ratio of viscosity to resistivity). Despite its relevance to proto-neutron stars and neutron star merger remnants, the numerically challenging regime of high Pm is still largely unknown. Using zero-net flux shearing box simulations in the incompressible approximation, we studied MRI-driven dynamos at unprecedentedly high values of Pm reaching 256. The simulations show that the stress and turbulent energies are proportional to Pm up to moderately high values (Pm ∼ 50). At higher Pm, they transition to a new regime consistent with a plateau independent of Pm for . This trend is independent of the Reynolds number, which may suggest an asymptotic regime where the energy injection and dissipation are independent of the diffusive processes. Interestingly, large values of Pm not only lead to intense small-scale magnetic fields but also to a more efficient dynamo at the largest scales of the box.
Context. Magnetars are highly magnetized neutron stars that can produce a wide diversity of X-ray and soft gamma-ray emissions that are powered by magnetic dissipation. Their magnetic dipole is constrained in the range of 10 ¹⁴ –10 ¹⁵ G by the measurement of their spin-down. In addition to fast rotation, these strong fields are also invoked to explain extreme stellar explosions, such as hypernovae, which are associated with long gamma-ray bursts and superluminous supernovae. A promising mechanism for explaining magnetar formation is the amplification of the magnetic field by the magnetorotational instability (MRI) in fast-rotating protoneutron stars (PNS). This scenario is supported by recent global incompressible models, which showed that a dipole field with magnetar-like intensity can be generated from small-scale turbulence. However, the impact of important physical ingredients, such as buoyancy and density stratification, on the efficiency of the MRI in generating a dipole field is still unknown.
Aims. We assess the impact of the density and entropy profiles on the MRI dynamo in a global model of a fast-rotating PNS. The model focuses on the outer stratified region of the PNS that is stable to convection.
Methods. Using the pseudo-spectral code MagIC, we performed 3D Boussinesq and anelastic magnetohydrodynamics simulations in spherical geometry with explicit diffusivities and with differential rotation forced at the outer boundary. The thermodynamic background of the anelastic models was retrieved from the data of 1D core-collapse supernova simulations from the Garching group. We performed a parameter study in which we investigated the influence of different approximations and the effect of the thermal diffusion through the Prandtl number.
Results. We obtain a self-sustained turbulent MRI-driven dynamo. This confirms most of our previous incompressible results when they are rescaled for density. The MRI generates a strong turbulent magnetic field and a nondominant equatorial dipole, which represents about 4.3% of the averaged magnetic field strength. Interestingly, an axisymmetric magnetic field at large scales is observed to oscillate with time, which can be described as a mean-field α Ω dynamo. By comparing these results with models without buoyancy or density stratification, we find that the key ingredient explaining the appearance of this mean-field behavior is the density gradient. Buoyancy due to the entropy gradient damps turbulence in the equatorial plane, but it has a relatively weak influence in the low Prandtl number regime overall, as expected from neutrino diffusion. However, the buoyancy starts to strongly impact the MRI dynamo for Prandtl numbers close to unity.
Conclusions. Our results support the hypothesis that the MRI is able to generate magnetar-like large-scale magnetic fields. The results furthermore predict the presence of a α Ω dynamo in the protoneutron star, which could be important to model in-situ magnetic field amplification in global models of core-collapse supernovae or binary neutron star mergers.
The impact of the magnetic field on postbounce supernova dynamics of non-rotating stellar cores is studied by performing three-dimensional magnetohydrodynamics simulations with spectral neutrino transport. The explodability of strongly and weakly magnetized models of 20 and 27 M⊙ pre-supernova progenitors are compared. We find that although the efficiency for the conversion of the neutrino heating into turbulent energy including magnetic fields in the gain region is not significantly different between the strong and weak field models, the amplified magnetic field due to the neutrino-driven convection on large hot bubbles just behind stalled shock results in a faster and more energetic explosion in the strongly magnetized models. In addition, by comparing the difference between the 2nd- and 5th-order spatial accuracy of the simulation in the strong field model for 27 M⊙ progenitor, we also find that the higher order accuracy in space is beneficial to the explosion because it enhances the growth of neutrino-driven convection in the gain region. Based on our results of core-collapse supernova simulations for the non-rotating model, a new possibility for the origin of the magnetic field of the protoneutron star (PNS) is proposed. The magnetic field is accumulated and amplified to magnetar level, that is, G, in the convectively stable shell near the PNS surface.
To study properties of magnetohydrodynamic (MHD) convection and resultant dynamo activities in proto-neutron stars (PNSs), we construct a “PNS in a box” simulation model and solve the compressible MHD equation coupled with a nuclear equation of state (EOS) and simplified leptonic transport. As a demonstration, we apply it to two types of PNS model with different internal structures: a fully convective model and a spherical-shell convection model. By varying the spin rate of the models, the rotational dependence of convection and the dynamo that operate inside the PNS is investigated. We find that, as a consequence of turbulent transport by rotating stratified convection, large-scale structures of flow and thermodynamic fields are developed in all models. Depending on the spin rate and the depth of the convection zone, various profiles of the large-scale structures are obtained, which can be physically understood as steady-state solutions to the “mean-field” equation of motion. Additionally to those hydrodynamic structures, a large-scale magnetic component of ( 10 15 ) G is also spontaneously organized in disordered tangled magnetic fields in all models. The higher the spin rate, the stronger the large-scale magnetic component grows. Intriguingly, as an overall trend, the fully convective models have a stronger large-scale magnetic component than that in the spherical-shell convection models. The deeper the convection zone extends, the larger the size of the convective eddies becomes. As a result, rotationally constrained convection seems to be more easily achieved in the fully convective model, resulting in a higher efficiency of the large-scale dynamo there. To gain a better understanding of the origin of the diversity of a neutron star’s magnetic field, we need to study the PNS dynamo in a wider parameter range.
Magnetic fields can play a major role in the dynamics of outstanding explosions associated to violent events such as GRBs and hypernovae, since they provide a natural mechanism to harness the rotational energy of the central proto-neutron star and power relativistic jets through the stellar progenitor. As the structure of such fields is quite uncertain, most numerical models of MHD-driven core-collapse supernovae consider an aligned dipole as initial magnetic field, while the field’s morphology can actually be much more complex. We present three-dimensional simulations of core-collapse supernovae with more realistic magnetic structures, such as quadrupolar fields and, for the first time, an equatorial dipolar field. Configurations other than an aligned dipole produce weaker explosions and less collimated outflows, but can at the same time be more efficient in extracting the rotational energy from the PNS. This energy is then stored in the surroundings of the PNS, rather than powering the polar jets. A significant axial dipolar component is also produced by models starting with a quadrupolar field, pointing to an effective dynamo mechanism operating in proximity of the PNS surface.
Context. Magnetars are isolated neutron stars characterized by their variable high-energy emission, which is powered by the dissipation of enormous internal magnetic fields. The measured spin-down of magnetars constrains the magnetic dipole to be in the range of 10 ¹⁴ − 10 ¹⁵ G. The magnetorotational instability (MRI) is considered to be a promising mechanism to amplify the magnetic field in fast-rotating protoneutron stars and form magnetars. This scenario is supported by many local studies that have shown that magnetic fields could be amplified by the MRI on small scales. However, the efficiency of the MRI at generating a dipole field is still unknown.
Aims. To answer this question, we study the MRI dynamo in an idealized global model of a fast rotating protoneutron star with differential rotation.
Methods. Using the pseudo-spectral code MagIC, we performed three-dimensional incompressible magnetohydrodynamics simulations in spherical geometry with explicit diffusivities where the differential rotation is forced at the outer boundary. We performed a parameter study in which we varied the initial magnetic field and investigated different magnetic boundary conditions. These simulations were compared to local shearing box simulations performed with the code Snoopy.
Results. We obtain a self-sustained turbulent MRI-driven dynamo, whose saturated state is independent of the initial magnetic field. The MRI generates a strong turbulent magnetic field of B ≥ 2 × 10 ¹⁵ G and a nondominant magnetic dipole, which represents systematically about 5% of the averaged magnetic field strength. Interestingly, this dipole is tilted toward the equatorial plane. By comparing these results with shearing box simulations, we find that local models can reproduce fairly well several characteristics of global MRI turbulence such as the kinetic and magnetic spectra. The turbulence is nonetheless more vigorous in the local models than in the global ones. Moreover, overly large boxes allow for elongated structures to develop without any realistic curvature constraint, which may explain why these models tend to overestimate the field amplification.
Conclusions. Overall, our results support the ability of the MRI to form magnetar-like large-scale magnetic fields. They furthermore predict the presence of a stronger small-scale magnetic field. The resulting magnetic field could be important to power outstanding stellar explosions, such as superluminous supernovae and gamma-ray bursts.
The proposal that core collapse supernovae are neutrino driven is still the subject of active investigation more than 50 years after the seminal paper by Colgate and White. The modern version of this paradigm, which we owe to Wilson, proposes that the supernova shock wave is powered by neutrino heating, mediated by the absorption of electron-flavor neutrinos and antineutrinos emanating from the proto-neutron star surface, or neutrinosphere. Neutrino weak interactions with the stellar core fluid, the theory of which is still evolving, are flavor and energy dependent. The associated neutrino mean free paths extend over many orders of magnitude and are never always small relative to the stellar core radius. Thus, neutrinos are never always fluid like. Instead, a kinetic description of them in terms of distribution functions that determine the number density of neutrinos in the six-dimensional phase space of position, direction, and energy, for both neutrinos and antineutrinos of each flavor, or in terms of angular moments of these neutrino distributions that instead provide neutrino number densities in the four-dimensional phase-space subspace of position and energy, is needed. In turn, the computational challenge is twofold: (i) to map the kinetic equations governing the evolution of these distributions or moments onto discrete representations that are stable, accurate, and, perhaps most important, respect physical laws such as conservation of lepton number and energy and the Fermi–Dirac nature of neutrinos and (ii) to develop efficient, supercomputer-architecture-aware solution methods for the resultant nonlinear algebraic equations. In this review, we present the current state of the art in attempts to meet this challenge.
We study the effects of the magnetic field on the dynamics of non-rotating stellar cores by performing 2D, magnetohydrodynamic (MHD) simulations. To this end, we have updated our neutrino-radiation-hydrodynamics supernova code to include MHD employing a divergence cleaning method with both careful treatments of finite volume and area reconstructions. By changing the initial strength of the magnetic field, the evolution of 15.0, 18.4, and pre-supernova progenitors is investigated. An intriguing finding in our study is that the neutrino-driven explosion occurs regardless of the strength of the initial magnetic field. For the 2D models presented in this work, the neutrino heating is the main driver for the explosion, whereas the magnetic field secondary contributes to the pre-explosion dynamics. Our results show that the strong magnetic field weakens the growth of the neutrino-driven turbulence in the small scale compared to the weak magnetic field. This results in the slower increase of the turbulent kinetic energy in the post-shock region, leading to the slightly delayed onset of the shock revival for models with the stronger initial magnetic field.
We present results of three-dimensional (3D), radiation-magnetohydrodynamics (MHD) simulations of core-collapse supernovae in full general relativity (GR) with spectral neutrino transport. In order to study the effects of the progenitor’s rotation and magnetic fields, we compute three models, where the precollapse rotation rate and magnetic fields are included parametrically to a 20 M ⊙ star. While we find no shock revival in our two nonmagnetized models during our simulation times (∼500 ms after bounce), the magnetorotational (MR) driven shock expansion immediately initiates after bounce in our rapidly rotating and strongly magnetized model. We show that the expansion of the MR-driven flows toward the polar directions is predominantly driven by the magnetic pressure, whereas the shock expansion toward the equatorial direction is supported by neutrino heating. Our detailed analysis indicates that the growth of the so-called kink instability may hinder the collimation of jets, resulting in the formation of broader outflows. Furthermore, we find a dipole emission of lepton number, only in the MR explosion model, whose asymmetry is consistent with the explosion morphology. Although it is similar to the lepton number emission self-sustained asymmetry (LESA), our analysis shows that the dipole emission occurs not from the proto–neutron star convection zone but from above the neutrino sphere, indicating that it is not associated with the LESA. We also report several unique neutrino signatures, which are significantly dependent on both the time and the viewing angle, if observed, possibly providing rich information regarding the onset of the MR-driven explosion.
Multi-dimensional fluid flow plays a paramount role in the explosions of massive stars as core-collapse supernovae. In recent years, three-dimensional (3D) simulations of these phenomena have matured significantly. Considerable progress has been made towards identifying the ingredients for shock revival by the neutrino-driven mechanism, and successful explosions have already been obtained in a number of self-consistent 3D models. These advances also bring new challenges, however. Prompted by a need for increased physical realism and meaningful model validation, supernova theory is now moving towards a more integrated view that connects multi-dimensional phenomena in the late convective burning stages prior to collapse, the explosion engine, and mixing instabilities in the supernova envelope. Here we review our current understanding of multi-D fluid flow in core-collapse supernovae and their progenitors. We start by outlining specific challenges faced by hydrodynamic simulations of core-collapse supernovae and of the late convective burning stages. We then discuss recent advances and open questions in theory and simulations.
The release of spin-down energy by a magnetar is a promising scenario to power several classes of extreme explosive transients. However, it lacks a firm basis because magnetar formation still represents a theoretical challenge. Using the first three-dimensional simulations of a convective dynamo based on a protoneutron star interior model, we demonstrate that the required dipolar magnetic field can be consistently generated for sufficiently fast rotation rates. The dynamo instability saturates in the magnetostrophic regime with the magnetic energy exceeding the kinetic energy by a factor of up to 10. Our results are compatible with the observational constraints on galactic magnetar field strength and provide strong theoretical support for millisecond protomagnetar models of gamma-ray burst and superluminous supernova central engines.
About ten per cent of ‘massive’ stars (those of more than 1.5 solar masses) have strong, large-scale surface magnetic fields1–3. It has been suggested that merging of main-sequence and pre-main-sequence stars could produce such strong fields4,5, and the predicted fraction of merged massive stars is also about ten per cent6,7. The merger hypothesis is further supported by a lack of magnetic stars in close binaries8,9, which is as expected if mergers produce magnetic stars. Here we report three-dimensional magnetohydrodynamical simulations of the coalescence of two massive stars and follow the evolution of the merged product. Strong magnetic fields are produced in the simulations, and the merged star rejuvenates such that it appears younger and bluer than other coeval stars. This can explain the properties of the magnetic ‘blue straggler’ star τ Sco in the Upper Scorpius association that has an observationally inferred, apparent age of less than five million years, which is less than half the age of its birth association¹⁰. Such massive blue straggler stars seem likely to be progenitors of magnetars, perhaps giving rise to some of the enigmatic fast radio bursts observed¹¹, and their supernovae may be affected by their strong magnetic fields¹².
Magnetorotational supernovae are a rare type of core-collapse supernovae where the magnetic field and rotation play a central role in the dynamics of the explosion. We present the post-processed nucleosynthesis of state-of-the-art neutrino-MHD supernova models that follow the post explosion evolution for few seconds. We find three different dynamical mechanisms to produce heavy r-process elements: (i) a prompt ejection of matter right after core bounce, (ii) neutron-rich matter that is ejected at late times due to a reconfiguration of the protoneutronstar shape, (iii) small amount of mass ejected with high entropies in the centre of the jet. We investigate total ejecta yields, including the ones of unstable nuclei such as 26Al, 44Ti, 56Ni, and 60Fe. The obtained 56Ni masses vary between . The latter maximum is compatible with hypernova observations. Furthermore, all of our models synthesize Zn masses in agreement with observations of old metal-poor stars. We calculate simplified light curves to investigate whether our models can be candidates for superluminous supernovae. The peak luminosities obtained from taking into account only nuclear heating reach up to a few . Under certain conditions, we find a significant impact of the 66Ni decay chain that can raise the peak luminosity up to compared to models including only the 56Ni decay chain. This work reinforces the theoretical evidence on the critical role of magnetorotational supernovae to understand the occurrence of hypernovae, superluminous supernovae, and the synthesis of heavy elements.
We analyze the properties of 42 rapidly rotating, low-metallicity, quasi-chemically homogeneously evolving stellar models in the mass range between 4 and 45 at the time of core collapse. Such models were proposed as progenitors for both superluminous supernovae (SLSNe) and long-duration gamma-ray bursts (lGRBs) and the Type Ic-BL supernovae (SNe) that are associated with them. Our findings suggest that whether these models produce a magnetar-driven SLSN explosion or a near-critically rotating black hole is not a monotonic function of the initial mass. Rather, their explodability varies nonmonotonically depending on the late core evolution, once chemical homogeneity is broken. Using different explodability criteria, we find that our models have a clear preference to produce SLSNe at lower masses and lGRBs at higher masses, but we find several exceptions, expecting lGRBs to form from stars as low as 10 and SLSNe with progenitors as massive as 30 . In general, our models reproduce the predicted angular momenta, ejecta masses, and magnetic field strengths at core collapse inferred for SLSNe and lGRBs and suggest significant interaction with their circumstellar medium, particularly for explosions with low ejecta mass.
We investigate the impact of strong initial magnetic fields in core-collapse supernovae of non-rotating progenitors by simulating the collapse and explosion of a 16.9 M⊙ star for a strong- and weak-field case assuming a twisted-torus field with initial central field strengths of and . The strong-field model has been set up with a view to the fossil-field scenario for magnetar formation and emulates a pre-collapse field configuration that may occur in massive stars formed by a merger. This model undergoes shock revival already 100 ms after bounce and reaches an explosion energy of 9.3 × 1050 erg at 310 ms, in contrast to a more delayed and less energetic explosion in the weak-field model. The strong magnetic fields help trigger a neutrino-driven explosion early on, which results in a rapid rise and saturation of the explosion energy. Dynamically, the strong initial field leads to a fast build-up of magnetic fields in the gain region to 40% of kinetic equipartition and also creates sizable pre-shock ram pressure perturbations that are known to be conducive to asymmetric shock expansion. For the strong-field model, we find an extrapolated neutron star kick of , a spin period of , and no spin-kick alignment. The dipole field strength of the proto-neutron star is 2 × 1014 G by the end of the simulation with a declining trend. Surprisingly, the surface dipole field in the weak-field model is stronger, which argues against a straightforward connection between pre-collapse fields and the birth magnetic fields of neutron stars.
In the seconds following their formation in core-collapse supernovae, ‘proto’-magnetars drive neutrino-heated magnetocentrifugal winds. Using a suite of two-dimensional axisymmetric magnetohydrodynamic simulations, we show that relatively slowly rotating magnetars with initial spin periods of P⋆0 = 50–500 ms spin down rapidly during the neutrino Kelvin–Helmholtz cooling epoch. These initial spin periods are representative of those inferred for normal Galactic pulsars, and much slower than those invoked for gamma-ray bursts and superluminous supernovae. Since the flow is non-relativistic at early times, and because the Alfvén radius is much larger than the proto-magnetar radius, spin-down is millions of times more efficient than the typically used dipole formula. Quasi-periodic plasmoid ejections from the closed zone enhance spin-down. For polar magnetic field strengths B0 ≳ 5 × 1014 G, the spin-down time-scale can be shorter than the Kelvin–Helmholtz time-scale. For B0 ≳ 1015 G, it is of the order of seconds in early phases. We compute the spin evolution for cooling proto-magnetars as a function of B0, P⋆0, and mass (M). Proto-magnetars born with B0 greater than spin down to periods >1 s in just the first few seconds of evolution, well before the end of the cooling epoch and the onset of classic dipole spin-down. Spin-down is more efficient for lower M and for larger P⋆0. We discuss the implications for observed magnetars, including the discrepancy between their characteristic ages and supernova remnant ages. Finally, we speculate on the origin of 1E 161348−5055 in the remnant RCW 103, and the potential for other ultra-slowly rotating magnetars.
The final collapse of the cores of massive stars can lead to a wide variety of outcomes in terms of electromagnetic and kinetic energies, nucleosynthesis, and remnants. The association of this wide spectrum of explosion and remnant types with the properties of the progenitors remains an open issue. The rotation and magnetic fields in Wolf–Rayet stars of subsolar metallicity may explain extreme events such as superluminous supernovae and gamma-ray bursts powered by proto-magnetars or collapsars. Continuing with numerical studies of magnetorotational core collapse, including detailed neutrino physics, we focus on progenitors with zero-age main-sequence masses in the range between 5 and 39 . The pre-collapse stars are 1D models employing prescriptions for the effects of rotation and magnetic fields. Eight of the 10 stars we consider are the results of chemically homogeneous evolution owing to enhanced rotational mixing . All but one of them produce explosions driven by neutrino heating (more likely for low-mass progenitors up to 8 ) and non-spherical flows or by magnetorotational stresses (more frequent above 26 ). In most of them and for the one non-exploding model, ongoing accretion leads to black hole formation. Rapid rotation makes subsequent collapsar activity plausible. Models not forming black holes show proto-magnetar-driven jets. Conditions for the formation of nickel are more favourable in magnetorotationally driven models, although our rough estimates fall short of the requirements for extremely bright events if these are powered by radioactive decay. However, the approximate light curves of our models suggest that a proto-magnetar or black hole spin-down may fuel luminous transients (with peak luminosities ).
We present a suite of the first 3D GRMHD collapsar simulations, which extend from the self-consistent jet launching by an accreting Kerr black hole (BH) to the breakout from the star. We identify three types of outflows, depending on the angular momentum, l, of the collapsing material and the magnetic field, B, on the BH horizon: (i) subrelativistic outflow (low l and high B), (ii) stationary accretion shock instability (SASI; high l and low B), (iii) relativistic jets (high l and high B). In the absence of jets, free-fall of the stellar envelope provides a good estimate for the BH accretion rate. Jets can substantially suppress the accretion rate, and their duration can be limited by the magnetization profile in the star. We find that progenitors with large (steep) inner density power-law indices (≳ 2), face extreme challenges as gamma-ray burst (GRB) progenitors due to excessive luminosity, global time evolution in the lightcurve throughout the burst and short breakout times, inconsistent with observations. Our results suggest that the wide variety of observed explosion appearances (supernova/supernova+GRB/low-luminosity GRBs) and the characteristics of the emitting relativistic outflows (luminosity and duration) can be naturally explained by the differences in the progenitor structure. Our simulations reveal several important jet features: (i) strong magnetic dissipation inside the star, resulting in weakly magnetized jets by breakout that may have significant photospheric emission and (ii) spontaneous emergence of tilted accretion disk-jet flows, even in the absence of any tilt in the progenitor.
We investigate the impact of rotation and magnetic fields on the dynamics and gravitational wave emission in 2D core-collapse supernova simulations with neutrino transport. We simulate 17 different models of 15 M⊙ and 39 M⊙ progenitor stars with various initial rotation profiles and initial magnetic fields strengths up to 1012 G, assuming a dipolar field geometry in the progenitor. Strong magnetic fields generally prove conducive to shock revival, though this trend is not without exceptions. The impact of rotation on the post-bounce dynamics is more variegated, in line with previous studies. A significant impact on the time-frequency structure of the gravitational wave signal is found only for rapid rotation or strong initial fields. For rapid rotation, the angular momentum gradient at the proto-neutron star surface can appreciably affect the frequency of the dominant mode, so that known analytic relations for the high-frequency emission band no longer hold. In case of two magnetorotational explosion models, the deviation from these analytic relations is even more pronounced. One of the magnetorotational explosions has been evolved to more than half a second after the onset of the explosion and shows a subsidence of high-frequency emission at late times. Its most conspicuous gravitational wave signature is a high-amplitude tail signal. We also estimate the maximum detection distances for our waveforms. The magnetorotational models do not stick out for higher detectability during the post-bounce and explosion phase.
We study differential rotation in late-stage shell convection in a 3D hydrodynamic simulation of a rapidly rotating 16 M⊙ helium star with a particular focus on the convective oxygen shell. We find that the oxygen shell develops a quasi-stationary pattern of differential rotation that is neither described by uniform angular velocity as assumed in current stellar evolution models of supernova progenitors, nor by uniform specific angular momentum. Instead, the oxygen shell develops a positive angular velocity gradient with faster rotation at the equator than at the pole by tens of percent. We show that the angular momentum transport inside the convection zone is not adequately captured by a diffusive mixing-length flux proportional to the angular velocity or angular momentum gradient. Zonal flow averages reveal stable large-scale meridional flow and an entropy deficit near the equator that mirrors the patterns in the angular velocity. The structure of the flow is reminiscent of simulations of stellar surface convection zones and the differential rotation of the Sun, suggesting that similar effects are involved; future simulations will need to address in more detail how the interplay of buoyancy, inertial forces, and turbulent stresses shapes differential rotation during late-stage convection in massive stars. If convective regions develop positive angular velocity gradients, angular momentum could be shuffled out of the core region more efficiently, potentially making the formation of millisecond magnetars more difficult. Our findings have implications for neutron star birth spin periods and supernova explosion scenarios that involve rapid core rotation.
Gravitational waves provide a unique and powerful opportunity to constrain the dynamics in the interior of proto-neutron stars during core collapse supernovae. Convective motions play an important role in generating neutron stars magnetic fields, which could explain magnetar formation in the presence of fast rotation. We compute the gravitational wave emission from proto-neutron star convection and its associated dynamo, by post-processing three-dimensional MHD simulations of a model restricted to the convective zone in the anelastic approximation. We consider two different proto-neutron star structures representative of early times (with a convective layer) and late times (when the star is almost entirely convective). In the slow rotation regime, the gravitational wave emission follows a broad spectrum peaking at about three times the turnover frequency. In this regime, the inclusion of magnetic fields slightly decreases the amplitude without changing the spectrum significantly compared to a non-magnetised simulation. Fast rotation changes both the amplitude and spectrum dramatically. The amplitude is increased by a factor of up to a few thousands. The spectrum is characterized by several peaks associated to inertial modes, whose frequency scales with the rotation frequency. Using simple physical arguments, we derive scalings that reproduce quantitatively several aspects of these numerical results. We also observe an excess of low-frequency gravitational waves, which appears at the transition to a strong field dynamo characterized by a strong axisymmetric toroidal magnetic field. This signature of dynamo action could be used to constrain the dynamo efficiency in a proto-neutron star with future gravitational wave detections.
Nonspherical structure in massive stars at the point of iron core collapse can have a qualitative impact on the properties of the ensuing core-collapse supernova explosions and the multimessenger signals they produce. Strong perturbations can aid successful explosions by strengthening turbulence in the postshock region. Here we report on a set of 4 π 3D hydrodynamic simulations of O- and Si-shell burning in massive star models of varied initial masses using MESA and the FLASH simulation framework. We evolve four separate 3D models for roughly the final 10 minutes prior to and including iron core collapse. We consider initial 1D MESA models with masses of 14, 20, and 25 M ⊙ to survey a range of O/Si-shell density and compositional configurations. We characterize the convective shells in our 3D models and compare them to the corresponding 1D models. In general, we find that the angle-average convective speeds in our 3D simulations near collapse are three to four times larger than the convective speeds predicted by MESA at the same epoch for our chosen mixing length parameter of α MLT = 1.5. In three of our simulations, we observe significant power in the spherical harmonic decomposition of the radial velocity field at harmonic indices of ℓ = 1–3 near collapse. Our results suggest that large-scale modes are common in massive stars near collapse and should be considered a key aspect of presupernova progenitor models.
Code comparisons are a valuable tool for the verification of supernova simulation codes and the quantification of model uncertainties. Here we present a first comparison of axisymmetric magnetohydrodynamic (MHD) supernova simulations with the CoCoNuT-FMT and Aenus-Alcar codes, which use distinct methods for treating the MHD induction equation and the neutrino transport. We run two sets of simulations of a rapidly rotating 35M⊙ gamma-ray burst progenitor model with different choices for the initial field strength, namely 1012 G for the maximum poloidal and toroidal field in the strong-field case and 1010 G in the weak-field case. We also investigate the influence of the Riemann solver and the resolution in CoCoNuT-FMT. The dynamics is qualitatively similar for both codes and robust with respect to these numerical details, with a rapid magnetorotational explosion in the strong-field case and a delayed neutrino-driven explosion in the weak-field case. Despite relatively similar shock trajectories, we find sizeable differences in many other global metrics of the dynamics, like the explosion energy and the magnetic energy of the proto-neutron star. Further differences emerge upon closer inspection, for example, the disk-like surface structure of the proto-neutron star proves highly sensitives to numerical details. The electron fraction distribution in the ejecta as a crucial determinant for the nucleosynthesis is qualitatively robust, but the extent of neutron- or proton-rich tails is sensitive to numerical details. Due to the complexity of the dynamics, the ultimate cause of model differences can rarely be uniquely identified, but our comparison helps gauge uncertainties inherent in current MHD supernova simulations.
To date, modern three-dimensional (3D) supernova (SN) simulations have not demonstrated that explosion energies of 10 ⁵¹ erg (=1 bethe=1 B) or more are possible for neutrino-driven SNe of non/slow-rotating M < 20 M ⊙ progenitors. We present the first such model, considering a nonrotating, solar-metallicity 18.88 M ⊙ progenitor, whose final 7 minutes of convective oxygen-shell burning were simulated in 3D and showed a violent oxygen–neon shell merger prior to collapse. A large set of 3D SN models was computed with the Prometheus-Vertex code, whose improved convergence of the two-moment equations with Boltzmann closure allows now to fully exploit the implicit neutrino-transport treatment. Nuclear burning is treated with a 23-species network. We vary the angular grid resolution and consider different nuclear equations of state and muon formation in the proto-neutron star (PNS), which requires six-species transport with coupling of all neutrino flavors across all energy–momentum groups. Elaborate neutrino transport was applied until ∼2 s after bounce. In one case, the simulation was continued to >7 s with an approximate treatment of neutrino effects that allows for seamless continuation without transients. A spherically symmetric neutrino-driven wind does not develop. Instead, accretion downflows to the PNS and outflows of neutrino-heated matter establish a monotonic rise of the explosion energy until ∼7 s post-bounce, when the outgoing shock reaches ∼50,000 km and enters the He layer. The converged value of the explosion energy at infinity (with overburden subtracted) is ∼1 B and the ejected ⁵⁶ Ni mass ≲0.087 M ⊙ , both within a few 10% of the SN 1987A values. The final NS mass and kick are ∼1.65 M ⊙ and >450 km s ⁻¹ , respectively.
We present a first 3D magnetohydrodynamic (MHD) simulation of convective oxygen and neon shell burning in a non-rotating star shortly before core collapse to study the generation of magnetic fields in supernova progenitors. We also run a purely hydrodynamic control simulation to gauge the impact of the magnetic fields on the convective flow and on convective boundary mixing. After about 17 convective turnover times, the magnetic field is approaching saturation levels in the oxygen shell with an average field strength of , and does not reach kinetic equipartition. The field remains dominated by small-to-medium scales, and the dipole field strength at the base of the oxygen shell is only . The angle-averaged diagonal components of the Maxwell stress tensor mirror those of the Reynolds stress tensor, but are about one order of magnitude smaller. The shear flow at the oxygen–neon shell interface creates relatively strong fields parallel to the convective boundary, which noticeably inhibit the turbulent entrainment of neon into the oxygen shell. The reduced ingestion of neon lowers the nuclear energy generation rate in the oxygen shell and thereby slightly slows down the convective flow. Aside from this indirect effect, we find that magnetic fields do not appreciably alter the flow inside the oxygen shell. We discuss the implications of our results for the subsequent core-collapse supernova and stress the need for longer simulations, resolution studies, and an investigation of non-ideal effects for a better understanding of magnetic fields in supernova progenitors.
We explore the influence of non-axisymmetric modes on the dynamics of the collapsed core of rotating, magnetized high-mass stars in three-dimensional simulations of a rapidly rotating star with an initial mass of endowed with four different pre-collapse configurations of the magnetic field, ranging from moderate to very strong field strength and including the field predicted by the stellar evolution model. The model with the weakest magnetic field achieves shock revival due to neutrino heating in a gain layer characterized by a large-scale, hydrodynamic m = 1 spiral mode. Later on, the growing magnetic field of the proto neutron star launches weak outflows into the early ejecta. Their orientation follows the evolution of the rotational axis of the proto neutron star, which starts to tilt from the original orientation due to the asymmetric accretion flows impinging on its surface. The models with stronger magnetization generate mildly relativistic, magnetically driven polar outflows propagating over a distance of 104 km within a few . These jets are stabilized against disruptive non-axisymmetric instabilities by their fast propagation and by the shear of their toroidal magnetic field. Within the simulation times of around , the explosions reach moderate energies and the growth of the proto neutron star masses ceases at values substantially below the threshold for black hole formation, which, in combination with the high rotational energies, might suggest a possible later proto-magnetar activity.
We present the nucleosynthesis of magneto-rotational supernovae (MR-SNe) including neutrino-driven and magneto-rotational-driven ejecta based, for the first time, on two-dimensional simulations with accurate neutrino transport. The models analysed here have different rotation and magnetic fields, allowing us to explore the impact of these two key ingredients. The accurate neutrino transport of the simulations is critical to analyse the slightly neutron rich and proton rich ejecta that are similar to the, also neutrino-driven, ejecta in standard supernovae. In the model with strong magnetic field, the r-process produces heavy elements up to the third r-process peak (A ∼ 195), in agreement with previous works. This model presents a jet-like explosion with proton-rich jets surrounded by neutron rich material where the r-process occurs. We have estimated a lower limit for 56Ni of 2.5 × 10−2M⊙, which is still well below the expected hypernova value. Longer simulations including the accretion disk evolution are required to get a final prediction. In addition, we have found that the late evolution is critical in a model with weak magnetic field in which lately ejected neutron rich matter produces elements up to the second r-process peak. Even if we cannot yet provide conclusions for hypernova nucleosynthesis, our results agree with observations of old stars and radioactive isotopes in supernova remnants. This makes MR-SNe a good additional scenario to neutron star mergers for the synthesis of heavy elements and brings us closer to understand their origin and the role of MR-SNe in the early galaxy nucleosynthesis.
Hypernovae powered by magnetic jets launched from the surface of rapidly rotating millisecond magnetars are one of the leading models to explain broad-lined Type Ic supernovae (SNe Ic-BL), and have been implicated as an important source of metal enrichment in the early Universe. We investigate the nucleosynthesis in such jet-driven hypernovae using a parameterised, but physically motivated, approach that analytically relates an artificially injected jet energy flux to the power available from the energy in differential rotation in the proto-neutron star. We find ejected 56Ni masses of in our most energetic models with explosion energy >1052 erg. This is in good agreement with the range of observationally inferred values for SNe Ic-BL. The 56Ni is mostly synthesised in the shocked stellar envelope, and is therefore only moderately sensitive to the jet composition. Jets with a high electron fraction Ye = 0.5 eject more 56Ni by a factor of 2 than neutron-rich jets. We can obtain chemical abundance profiles in good agreement with the average chemical signature observed in extremely metal-poor (EMP) stars presumably polluted by hypernova ejecta. Notably, [Zn/Fe] ≳ 0.5 is consistently produced in our models. For neutron-rich jets, there is a significant r-process component, and agreement with EMP star abundances in fact requires either a limited contribution from neutron-rich jets or a stronger dilution of r-process material in the interstellar medium than for the slow SN ejecta outside the jet. The high [C/Fe] ≳ 0.7 observed in many EMP stars cannot be consistently achieved due to the large mass of iron in the ejecta, however, and remains a challenge for jet-driven hypernovae based on the magneto-rotational mechanism.
We derive the scaling of differential rotation in both slowly and rapidly rotating convection zones using order of magnitude methods. Our calculations apply across stars and fluid planets and all rotation rates, as well as to both magnetized and purely hydrodynamic systems. We find shear |R∇Ω| of order the angular frequency Ω for slowly rotating systems with Ω ≪ |N|, where N is the Brünt–Väisälä frequency, and find that it declines as a power law in Ω for rapidly rotating systems with Ω ≫ |N|. We further calculate the meridional circulation rate and baroclinicity and examine the magnetic field strength in the rapidly rotating limit. Our results are in general agreement with simulations and observations and we perform a detailed comparison with those in a companion paper.
Differential rotation is central to a great many mysteries in stars and planets. In part I, we predicted the order of magnitude and scaling of the differential rotation in both hydrodynamic and magnetohydrodynamic convection zones. Our results apply to both slowly and rapidly rotating systems, and provide a general picture of differential rotation in stars and fluid planets. We further calculated the scalings of the meridional circulation, entropy gradient, and baroclinicity. In this companion paper, we compare these predictions with a variety of observations and numerical simulations. With a few exceptions, we find that these are consistent in both the slowly rotating and rapidly rotating limits. Our results help to localize core–envelope shear in red giant stars, suggest a rotation-dependent frequency shift in the internal gravity waves of massive stars, and potentially explain observed deviations from von Zeipel’s gravity darkening in late-type stars.
About 10 per cent of stars more massive than have strong, large-scale surface magnetic fields and are being discussed as progenitors of highly magnetic white dwarfs and magnetars. The origin of these fields remains uncertain. Recent three-dimensional (3D) magnetohydrodynamical simulations have shown that strong magnetic fields can be generated in the merger of two massive stars. Here, we follow the long-term evolution of such a 3D merger product in a 1D stellar evolution code. During a thermal relaxation phase after the coalescence, the merger product reaches critical surface rotation, sheds mass and then spins down primarily because of internal mass readjustments. The spin of the merger product after thermal relaxation is mainly set by the co-evolution of the star–torus structure left after coalescence. This evolution is still uncertain, so we also consider magnetic braking and other angular momentum-gain and -loss mechanisms that may influence the final spin of the merged star. Because of core compression and mixing of carbon and nitrogen in the merger, enhanced nuclear burning drives a transient convective core that greatly contributes to the rejuvenation of the star. Once the merger product relaxed back to the main sequence, it continues its evolution similar to that of a genuine single star of comparable mass. It is a slow rotator that matches the magnetic blue straggler τ Sco. Our results show that merging is a promising mechanism to explain some magnetic massive stars and it may also be key to understand the origin of the strong magnetic fields of highly magnetic white dwarfs and magnetars.
We study the impact of a small-scale dynamo in core-collapse supernovae using a 3D neutrino magnetohydrodynamics (MHD) simulation of a 15 M⊙ progenitor. The weak seed field is amplified exponentially in the gain region once neutrino-driven convection develops, and remains dominated by small-scale structures. About after bounce, the field energy in the gain region reaches of kinetic equipartition. This supports the development of a neutrino-driven explosion with modest global anisotropy, which does not occur in a corresponding model without magnetic fields. Our results suggest that magnetic fields may play a beneficial subsidiary role in neutrino-driven supernovae even without rapid progenitor rotation. Further investigation into the nature of MHD turbulence in the supernova core is required.
The design and implementation of a new framework for adaptive mesh refinement calculations are described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design enables its use for a wide variety of physics. The framework works with both uniform and nonuniform grids in Cartesian and curvilinear coordinate systems. It adopts a dynamic execution model based on a simple design called a “task list” that improves parallel performance by overlapping communication and computation, simplifies the inclusion of a diverse range of physics, and even enables multiphysics models involving different physics in different regions of the calculation. We describe physics modules implemented in this framework for both nonrelativistic and relativistic magnetohydrodynamics (MHD). These modules adopt mature and robust algorithms originally developed for the Athena MHD code and incorporate new extensions: support for curvilinear coordinates, higher-order time integrators, more realistic physics such as a general equation of state, and diffusion terms that can be integrated with super-time-stepping algorithms. The modules show excellent performance and scaling, with well over 80% parallel efficiency on over half a million threads. The source code has been made publicly available.
We present a 7 minute long 4 π -3D simulation of a shell merger event in a nonrotating 18.88 M ⊙ supernova progenitor before the onset of gravitational collapse. The key motivation is to capture the large-scale mixing and asymmetries in the wake of the shell merger before collapse using a self-consistent approach. The 4 π geometry is crucial, as it allows us to follow the growth and evolution of convective modes on the largest possible scales. We find significant differences between the kinematic, thermodynamic, and chemical evolution of the 3D and 1D models. The 3D model shows vigorous convection leading to more efficient mixing of nuclear species. In the 3D case, the entire oxygen shell attains convective Mach numbers of ≈0.1, whereas in the 1D model, the convective velocities are much lower, and there is negligible overshooting across convective boundaries. In the 3D case, the convective eddies entrain nuclear species from the neon (and carbon) layers into the deeper part of the oxygen-burning shell, where they burn and power a violent convection phase with outflows. This is a prototypical model of a convective–reactive system. Due to the strong convection and resulting efficient mixing, the interface between the neon layer and the silicon-enriched oxygen layer disappears during the evolution, and silicon is mixed far out into the merged oxygen/neon shell. Neon entrained inward by convective downdrafts burns, resulting in lower neon mass in the 3D model compared to the 1D model at the time of collapse. In addition, the 3D model develops remarkable large-scale, large-amplitude asymmetries, which may have important implications for the impending gravitational collapse and subsequent explosion.
The internal rotational dynamics of massive stars are poorly understood. If angular momentum (AM) transport between the core and the envelope is inefficient, the large core AM upon core-collapse will produce rapidly rotating neutron stars (NSs). However, observations of low-mass stars suggest an efficient AM transport mechanism is at work, which could drastically reduce NS spin rates. Here, we study the effects of the baroclinic instability and the magnetic Tayler instability in differentially rotating radiative zones. Although the baroclinic instability may occur, the Tayler instability is likely to be more effective for AM transport. We implement Tayler torques as prescribed by Fuller, Piro, and Jermyn into models of massive stars, finding they remove the vast majority of the core’s AM as it contracts between the main-sequence and helium-burning phases of evolution. If core AM is conserved during core-collapse, we predict natal NS rotation periods of P_(NS) ≈ 50−200ms, suggesting these torques help explain the relatively slow rotation rates of most young NSs, and the rarity of rapidly rotating engine-driven supernovae. Stochastic spin-up via waves just before core-collapse, asymmetric explosions, and various binary evolution scenarios may increase the initial rotation rates of many NSs.
With myriads of detection events from a prospective Galactic core-collapse supernova, current and future neutrino detectors will be able to sample detailed, time-dependent neutrino fluxes and spectra. This will offer significant possibilities of inferring supernova physics from the various phases of the neutrino signal, ranging from the neutronization burst through the accretion and early explosion phases to the cooling phase. The signal will constrain the time evolution of bulk parameters of the young proto–neutron star, such as its mass and radius, as well as the structure of the progenitor; probe multidimensional phenomena in the supernova core; and constrain the dynamics of the early explosion phase. Aside from further astrophysical implications, supernova neutrinos may also shed light on the properties of matter at supranuclear densities and on open problems in particle physics.
Expected final online publication date for the Annual Review of Nuclear and Particle Science, Volume 69 is October 21, 2019. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.