Core-collapse Supernova Simulations Research Articles

New equations of state constrained by nuclear physics, observations, and QCD calculations of high-density nuclear matter

We present new equations of state for applications in core-collapse supernova and neutron star merger simulations. We start by introducing an effective mass parametrization that is fit to recent microscopic calculations up to twice saturation density. This is important to capture the predicted thermal effects, which have been shown to determine the proto--neutron star contraction in supernova simulations. The parameter range of the energy-density functional underlying the equation of state is constrained by chiral effective field theory results at nuclear densities as well as by functional renormalization group computations at high densities based on QCD. We further implement observational constraints from measurements of heavy neutron stars, the gravitational wave signal of GW170817, and from the recent NICER results. Finally, we study the resulting allowed ranges for the equation of state and for properties of neutron stars, including the predicted ranges for the neutron star radius and maximum mass.

Three-dimensional Hydrodynamics Simulations of Precollapse Shell Burning in the Si- and O-rich Layers

Abstract We present 3D hydrodynamics simulations of shell burning in two progenitors with zero-age main-sequence masses of 22 and 27 M ⊙ for ∼65 and 200 s up to the onset of gravitational collapse, respectively. The 22 and 27 M ⊙ stars are selected from a suite of 1D progenitors. The former and the latter have an extended Si- and O-rich layer with a width of ∼109 cm and ∼5 × 109 cm, respectively. Our 3D results show that turbulent mixing occurs in both of the progenitors with the angle-averaged turbulent Mach number exceeding ∼0.1 at the maximum. We observe that an episodic burning of O and Ne, which takes place underneath the convection bases, enhances the turbulent mixing in the 22 and 27 M ⊙ models, respectively. The distribution of nucleosynthetic yields is significantly different from that in 1D simulations, namely, in 3D more homogeneous and inhomogeneous in the radial and angular direction, respectively. By performing a spectrum analysis, we investigate the growth of turbulence and its role of material mixing in the convective layers. We also present a scalar spherical harmonics mode analysis of the turbulent Mach number. This analytical formula would be helpful for supernova modelers to implement the precollapse perturbations in core-collapse supernova simulations. Based on the results, we discuss implications for the possible onset of the perturbation-aided neutrino-driven supernova explosion.

Impact of a Magnetic Field on Neutrino–Matter Interactions in Core-collapse Supernovae

Abstract We explore the impact of a magnetic field on neutrino–matter interactions in core-collapse supernovae. We first derive the modified source terms for neutrino–nucleon scattering and neutrino absorption and emission processes in the moment formalism. Then, we perform full relativistic, three-dimensional, magnetorotational core-collapse supernova simulations of a star with spectral neutrino transport. Our simulations self-consistently treat the parity-violation effects of weak interaction in the presence of an external magnetic field. The result shows significant global asymmetry, mostly confined in the proto-neutron star, clearly reflecting the magnetic field structure. The asymmetric property arises from two factors: the angle between the neutrino flux and magnetic field, and the term that is parallel to the magnetic field and is also proportional to the deviation of the distribution function of neutrinos from thermal equilibrium. The typical correction value amounts to ∼1% relative to the total neutrino–matter interaction rate for the magnetic field strength of G. Although these asymmetric properties do not immediately affect the explosion dynamics, our results imply that they would be significant once the neutrinos diffuse out of the proto-neutron- star core carrying those asymmetries away. We also show that, during our simulation time of ∼370 ms after bounce, our results indicate that the correction value due to the modified inelastic scattering process dominates over that of the modified neutrino absorption and emission process.

Medium modifications for light and heavy nuclear clusters in simulations of core collapse supernovae: Impact on equation of state and weak interactions

The present article investigates the role of heavy nuclear clusters and weakly bound light nuclear clusters based on a newly developed equation of state for core collapse supernova studies. A novel approach is brought forward for the description of nuclear clusters, taking into account the quasiparticle approach and continuum correlations. It demonstrates that the commonly employed nuclear statistical equilibrium approach, based on non-interacting particles, for the description of light and heavy clusters becomes invalid for warm nuclear matter near the saturation density. This has important consequences for studies of core collapse supernovae. To this end, we implement this nuclear equation of state provided for arbitrary temperature, baryon density and isospin asymmetry, to spherically symmetric core collapse supernova simulations in order to study the impact on the dynamics as well as on the neutrino emission. For the inclusion of a set of weak processes involving light clusters the rate expressions are derived, including medium modifications at the mean field level. A substantial impact from the inclusion of a variety of weak reactions involving light clusters on the post bounce dynamics nor on the neutrino emission could not be found.

Explosion energies for core-collapse supernovae I: analytic, spherically symmetric solutions

ABSTRACT Recent multidimensional simulations of core-collapse supernovae are producing successful explosions and explosion-energy predictions. In general, the explosion-energy evolution is monotonic and relatively smooth, suggesting a possible analytic solution. We derive analytic solutions for the expansion of the gain region under the following assumptions: spherical symmetry, one-zone shell, and powered by neutrinos and α particle recombination. We consider two hypotheses: (I) explosion energy is powered by neutrinos and α recombination and (II) explosion energy is powered by neutrinos alone. Under these assumptions, we derive the fundamental dimensionless parameters and analytic scalings. For the neutrino-only hypothesis (II), the asymptotic explosion energy scales as $E_{\infty } \approx 1.5 M_\mathrm{ g}\nu _0^2 \eta ^{2/3}$, where Mg is the gain mass, $\nu _0$ is the free-fall velocity at the shock, and η is a ratio of the heating and dynamical time-scales. Including both neutrinos and recombination (hypothesis I), the asymptotic explosion energy is $E_{\infty } \approx M_g \nu _0^2 (1.5\eta ^{2/3} + \beta f(\rho _0))$, where β is the dimensionless recombination parameter. We use Bayesian inference to fit these analytic models to simulations. Both hypotheses fit the simulations of the lowest progenitor masses that tend to explode spherically. The fits do not prefer hypothesis I or II; however, prior investigations suggest that α recombination is important. As expected, neither hypothesis fits the higher mass simulations that exhibit aspherical explosions. In summary, this explosion energy theory is consistent with the spherical explosions of low progenitor masses; the inconsistency with higher progenitor-mass simulations suggests that a theory for them must include aspherical dynamics.

Simulations of the Early Postbounce Phase of Core-collapse Supernovae in Three-dimensional Space with Full Boltzmann Neutrino Transport

Abstract We report on the core-collapse supernova simulation we conducted for a 11.2M ⊙ progenitor model in three-dimensional space up to 20 ms after bounce, using a radiation-hydrodynamics code with full Boltzmann neutrino transport. We solve the six-dimensional Boltzmann equations for three neutrino species and the three-dimensional compressible Euler equations with Furusawa and Togashi's nuclear equation of state. We focus on the prompt convection at ∼10 ms after bounce and investigate how neutrinos are transported in the convective matter. We apply a new analysis based on the eigenvalues and eigenvectors of the Eddington tensor and make a comparison between the Boltzmann transport results and the M1 closure approximation in the transition regime between the optically thick and thin limits. We visualize the eigenvalues and eigenvectors using an ellipsoid, in which each principal axis is parallel to one of the eigenvectors and has a length proportional to the corresponding eigenvalue. This approach enables us to understand the difference between the Eddington tensor derived directly from the Boltzmann simulation and the one given by the M1 prescription from a new perspective. We find that the longest principal axis of the ellipsoid is almost always nearly parallel to the energy flux in the M1 closure approximation, whereas in the Boltzmann simulation it becomes perpendicular in some transition regions, where the mean free path is ∼0.1 times the radius. In three spatial dimensions, the convective motions make it difficult to predict where this happens and to possibly improve the closure relation there.

Retrieval of energy spectra for all flavours of neutrinos from core-collapse supernova with multiple detectors

ABSTRACT We present a new method by which to retrieve energy spectrum for all falvours of neutrinos from core-collapse supernova (CCSN). In the retrieval process, we do not assume any analytic formulas to express the energy spectrum of neutrinos but rather take a direct way of spectrum reconstruction from the observed data; the singular value decomposition algorithm with a newly developed adaptive energy-gridding technique is adopted. We employ three independent reaction channels having different flavour sensitivity to neutrinos. Two reaction channels, inverse beta decay on proton and elastic scattering on electrons, from a water Cherenkov detector such as Super-Kamiokande (SK) and Hyper-Kamiokande (HK), and a charged current reaction channel with Argon from the Deep Underground Neutrino Experiment (DUNE) are adopted. Given neutrino oscillation models, we iteratively search the neutrino energy spectra at the CCSN source until they provide the consistent event counts in the three reaction channels. We test the capability of our method by demonstrating the spectrum retrieval to a theoretical neutrino data computed by our recent three-dimensional CCSN simulation. Although the energy spectrum with either electron-type or electron-type antineutrinos at the CCSN source has relatively large error compared to that of other species, the joint analysis with HK + DUNE or SK + DUNE will provide precise energy spectrum of all flavours of neutrinos at the source. Finally, we discuss perspectives for improvements of our method by using neutrino data of other detectors.

Core-collapse supernova neutrino emission and detection informed by state-of-the-art three-dimensional numerical models

ABSTRACT Based on our recent three-dimensional core-collapse supernova (CCSN) simulations including both exploding and non-exploding models, we study the detailed neutrino signals in representative terrestrial neutrino observatories, namely Super-Kamiokande (Hyper-Kamiokande), DUNE, JUNO, and IceCube. We find that the physical origin of difference in the neutrino signals between 1D and 3D is mainly proto-neutron-star convection. We study the temporal and angular variations of the neutrino signals and discuss the detectability of the time variations driven by the spiral standing accretion shock instability (spiral SASI) when it emerges for non-exploding models. In addition, we determine that there can be a large angular asymmetry in the event rate (${\gtrsim} 50 {{\ \rm per\ cent}}$), but the time-integrated signal has a relatively modest asymmetry (${\lesssim} 20 {{\ \rm per\ cent}}$). Both features are associated with the lepton-number emission self-sustained asymmetry and the spiral SASI. Moreover, our analysis suggests that there is an interesting correlation between the total neutrino energy (TONE) and the cumulative number of neutrino events in each detector, a correlation that can facilitate data analyses of real observations. We demonstrate the retrieval of neutrino energy spectra for all flavours of neutrino by applying a novel spectrum reconstruction technique to the data from multiple detectors. We find that this new method is capable of estimating the TONE within the error of ∼20 per cent if the distance to the CCSN is ≲6 kpc.

Coupling neutrino oscillations and simulations of core-collapse supernovae

At the present time even the most sophisticated, multi-dimensional simulations of core-collapse supernovae do not (self-consistently) include neutrino flavor transformation. This physics is missing despite the importance of neutrinos in the core-collapse explosion paradigm. Because of this dependence, any flavor transformation that occurs in the region between the proto-neutron star and the shock could result in major effects upon the dynamics of the explosion. We present the first hydrodynamic core-collapse supernova simulation which simultaneously includes flavor transformation of the free-streaming neutrinos in the neutrino transport. These oscillation calculations are dynamically updated and evolve self-consistently alongside the hydrodynamics. Using a $M=20\;{\rm M_{\odot}}$ progenitor, we find that while the oscillations have an effect on the neutrino emission and the heating rates, flavor transformation alone does not lead to a successful explosion of this progenitor in spherical symmetry.

The Boltzmann-radiation-hydrodynamics Simulations of Core-collapse Supernovae with Different Equations of State: The Role of Nuclear Composition and the Behavior of Neutrinos

Abstract Using the Boltzmann-radiation-hydrodynamics code, which solves the Boltzmann equation for neutrino transport, we present the results of the simulations with the nuclear equations of state (EOSs) of Lattimer and Swesty (LS) and Furusawa and Shen (FS). We extend the simulation time of the LS model and conduct thorough investigations, though our previous paper briefly reported some of the results. Only the LS model shows the shock revival. This seems to originate from the nuclear composition: the different nuclear composition results in the different energy loss by photodissociation and hence the different strength of the prompt convection and the later neutrino-driven convection. The protoneutron star seen in the FS model is more compact than that in the LS model because the existence of multinuclear species softens the EOS. For the behavior of neutrinos, we examined the flux and the Eddington tensor of neutrinos. In the optically thick region, the diffusion of neutrinos and the dragging by the motion of matter determine the flux. In the optically thin region, the free-streaming determines it. The Eddington tensor is compared with that obtained from the M1-closure relation. The M1-closure scheme overestimates the contribution from the velocity-dependent terms in the semitransparent region.

Potential Impact of Fast Flavor Oscillations on Neutrino-driven Winds and Their Nucleosynthesis

Abstract The wind driven by the intense neutrino emission from a protoneutron star (PNS) is an important site for producing nuclei heavier than the Fe group. Because of certain features in the neutrino angular distributions, the so-called fast flavor oscillations may occur very close to the PNS surface, effectively resetting the neutrino luminosities and energy spectra that drive the wind. Using the unoscillated neutrino emission characteristics from two core-collapse supernova simulations representative of relevant progenitors at the lower and higher mass end, we study the potential effects of fast flavor oscillations on neutrino-driven winds and their nucleosynthesis. We find that such oscillations can increase the total mass loss by factors up to ∼1.5–1.7 and lead to significantly more proton-rich conditions. The latter effect can greatly enhance the production of 64Zn and the so-called light p-nuclei 74Se, 78Kr, and 84Sr. Implications for abundances in metal-poor stars, Galactic chemical evolution in general, and isotopic anomalies in meteorites are discussed.

Charged-current muonic reactions in core-collapse supernovae

The steady advance in core-collapse supernova simulations requires a more precise description of neutrino processes in hot and dense matter. In this work, we study the rates of charged-current (CC) weak processes with (anti)muons in supernova matter. At the relativistic mean field level, we derive results for the rates of CC neutrino-nucleon reactions, taking into account full kinematics, weak magnetism and pseudoscalar terms, and $q^2$-dependent nucleon form factors in the hadronic current. In addition to muonic semileptonic processes we also consider purely leptonic processes. In particular, we show that inverse muon decay can dominate the opacities for low energy $\nu_\mu$ and $\bar\nu_e$ at densities $\gtrsim 10^{13}~\rm{g~ cm^{-3}}$.

Generalized Kompaneets formalism for inelastic neutrino-nucleon scattering in supernova simulations

Based on the Kompaneets approximation, we develop a robust methodology to calculate spectral redistribution via inelastic neutrino-nucleon scattering in the context of core-collapse supernova simulations. The resulting equations conserve lepton number to machine precision and scale linearly, not quadratically, with number of energy groups. The formalism also provides an elegant means to derive the rate of energy transfer to matter which, as it must, automatically goes to zero when the neutrino radiation field is in thermal equilibrium. Furthermore, we derive the next-higher-order in {\epsilon}/mc2 correction to the neutrino Kompaneets equation. Unlike other Kompaneets schema, ours also generalizes to the case of anisotropic angular distributions, while retaining the conservative form that is a hallmark of the classical Kompaneets equation. Our formalism enables immediate incorporation into supernova codes that follow the spectral angular moments of the neutrino radiation fields.

Magnetorotational Explosion of a Massive Star Supported by Neutrino Heating in General Relativistic Three-dimensional Simulations

Abstract 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.

Three-dimensional core-collapse supernova simulations of massive and rotating progenitors

ABSTRACT We present 3D simulations of the core-collapse of massive rotating and non-rotating progenitors performed with the general relativistic neutrino hydrodynamics code coconut-fmt. The progenitor models include Wolf-Rayet stars with initial helium star masses of $39\, \mathrm{ M}_{\odot }$ and $20\, \mathrm{ M}_{\odot }$, and an $18\, \mathrm{ M}_{\odot }$ red supergiant. The $39\, \mathrm{ M}_{\odot }$ model is a rapid rotator, whereas the two other progenitors are non-rotating. Both Wolf-Rayet models produce healthy neutrino-driven explosions, whereas the red supergiant model fails to explode. By the end of the simulations, the explosion energies have already reached $1.1\times 10^{51}\, $ and $0.6\times 10^{51}\, \mathrm{erg}$ for the $39\, \mathrm{ M}_{\odot }$ and $20\, \mathrm{ M}_{\odot }$ model, respectively. They produce neutron stars of relatively high mass, but with modest kicks. Due to the alignment of the bipolar explosion geometry with the rotation axis, there is a relatively small misalignment of 30° between the spin and the kick in the rapidly rotating $39\, \mathrm{ M}_{\odot }$ model. For this model, we find that rotation significantly changes the dependence of the characteristic gravitational-wave frequency of the f-mode on the proto-neutron star parameters compared to the non-rotating case. Its gravitational-wave amplitudes would make it detectable out to almost 2 Mpc by the Einstein Telescope. The other two progenitors have considerably smaller detection distances, despite significant low-frequency emission in the most sensitive frequency band of current gravitational-wave detectors.

Consistent perturbative modeling of pseudo-Newtonian core-collapse supernova simulations

We write down and apply the linearized fluid and gravitational equations consistent with pseudo-Newtonian simulations, whereby Newtonian hydrodynamics is used with a pseudo-Newtonian monopole and standard Newtonian gravity for higher multipoles. We thereby eliminate the need to use mode function matching to identify the active non-radial modes in pseudo-Newtonian core-collapse supernova simulations, in favor of the less complex and less costly mode frequency matching method. In doing so, we are able to measure appropriate boundary conditions for a mode calculation.

Effects of Symmetry Energy on the Equation of State for Simulations of Core-collapse Supernovae and Neutron-star Mergers

Abstract We construct a new equation of state (EOS) for numerical simulations of core-collapse supernovae and neutron-star mergers based on an extended relativistic mean-field model with a small symmetry energy slope L, which is compatible with both experimental nuclear data and recent observations of neutron stars. The new EOS table (EOS4) based on the extended TM1 (TM1e) model with L = 40 MeV is designed in the same tabular form and compared with the commonly used Shen EOS (EOS2) based on the original TM1 model with . This is convenient and useful for performing numerical simulations and examining the influences of symmetry energy and its density dependence on astrophysical phenomena. In comparison with the TM1 model used in EOS2, the TM1e model provides a similar maximum neutron-star mass but smaller radius and tidal deformability for a 1.4M ⊙ neutron star, which is more consistent with current constraints. By comparing the phase diagram and thermodynamic quantities between EOS4 and EOS2, it is found that the TM1e model predicts a relatively larger region of nonuniform matter and softer EOS for neutron-rich matter. Significant differences between EOS4 and EOS2 are observed in the case with low proton fraction, while the properties of symmetric matter remain unchanged.

A systematic study of proto-neutron star convection in three-dimensional core-collapse supernova simulations

ABSTRACT This paper presents the first systematic study of proto-neutron star (PNS) convection in three dimensions (3D) based on our latest numerical fornax models of core-collapse supernova (CCSN). We confirm that PNS convection commonly occurs, and then quantify the basic physical characteristics of the convection. By virtue of the large number of long-term models, the diversity of PNS convective behaviour emerges. We find that the vigour of PNS convection is not correlated with CCSN dynamics at large radii, but rather with the mass of PNS − heavier masses are associated with stronger PNS convection. We find that PNS convection boosts the luminosities of νμ, ντ, $\bar{\nu }_{\mu }$, and $\bar{\nu }_{\tau }$ neutrinos, while the impact on other species is complex due to a competition of factors. Finally, we assess the consequent impact on CCSN dynamics and the potential for PNS convection to generate pulsar magnetic fields.

Matter Mixing in Aspherical Core-collapse Supernovae: Three-dimensional Simulations with Single-star and Binary Merger Progenitor Models for SN 1987A

Abstract We perform three-dimensional hydrodynamic simulations of aspherical core-collapse supernovae, focusing on the matter mixing in SN 1987A. The impacts of four progenitor (pre-supernova) models and parameterized aspherical explosions are investigated. The four pre-supernova models include a blue supergiant (BSG) model based on a slow-merger scenario developed recently for the progenitor of SN 1987A (Urushibata et al. 2018). The others are a BSG model based on a single-star evolution and two red supergiant (RSG) models. Among the investigated explosion (simulation) models, a model with the binary merger progenitor model and an asymmetric bipolar-like explosion, which invokes a jetlike explosion, best reproduces constraints on the mass of high-velocity 56Ni, as inferred from the observed [Fe ii] line profiles. The advantage of the binary merger progenitor model for the matter mixing is the flat and less extended ρ r 3 profile of the C+O core and the helium layer, which may be characterized by the small helium core mass. From the best explosion model, the direction of the bipolar explosion axis (the strongest explosion direction) and the neutron star (NS) kick velocity and direction are predicted. Other related implications and future prospects are also given.

Influence of Density Dependence of Symmetry Energy in Hot and Dense Matter for Supernova Simulations

Abstract We study the influence of density-dependent symmetry energy at high densities in simulations of core-collapse supernovae, black hole formation, and proto–neutron star cooling by extending the relativistic mean field (RMF) theory used for the Shen equation-of-state (EOS) table. We adopt the extended RMF theory to examine the density dependence of the symmetry energy with a small value of the slope parameter L, while the original properties of the symmetric nuclear matter are unchanged. In order to assess matter effects at high densities, we perform numerical simulations of gravitational collapse of massive stars adopting the EOS table at high densities beyond 1014 g cm−3 with the small L value, which is in accord with the experimental and observational constraints, and compare them with the results obtained by using the Shen EOS. Numerical results for 11.2 and 15 M ⊙ stars exhibit minor effects around the core bounce and in the following evolution for 200 ms. Numerical results for 40 and 50 M ⊙ stars reveal a shorter duration toward the black hole formation with a smaller maximum mass for the small-L case. Numerical simulations of proto–neutron star cooling over 10 s through neutrino emissions demonstrate increasing effects of the symmetry energy at high densities. Neutrino cooling drastically proceeds in a relatively long timescale with high luminosities and average energies with the small symmetry energy. Evolution toward the cold neutron star is affected because of the different behavior of neutron-rich matter, while supernova dynamics around core bounce remains similar in less neutron-rich environments.