Supernova Simulations Research Articles

Numerical simulations of core-collapse supernovae imposing steady shock approximation

We carried out one-dinensional long-term numerical simulations of core-collapse supernovae imposing steady shock approximation. As a result of a computation, we found core does not explode and shock wave stalls within several hundreds milliseconds from bounce. However, we execute long-term numerical simulation until 3.5 seconds from bounce with short CPU time using Personal Computer.

Morphology and evolution of simulated and optical clusters: a comparative analysis

We have made a comparative study of morphological evolution in simulated dark matter (DM) haloes and X-ray brightness distribution, and in optical clusters. Samples of simulated clusters include star formation with supernovae feedback, radiative cooling and simulation in the adiabatic limit at three different redshifts, z= 0.0, 0.10 and 0.25. The optical sample contains 208 Abell, Corwin & Olowin (ACO) clusters within redshift, z≤ 0.25. Cluster morphology, within 0.5 and 1.0 h−1 Mpc from cluster centre, is quantified by multiplicity and ellipticity. We find that the distribution of the DM haloes in the adiabatic simulation appears to be more elongated than the galaxy clusters. Radiative cooling brings halo shapes in excellent agreement with observed clusters; however, cooling along with feedback mechanism makes the haloes more flattened. Our results indicate relatively stronger structural evolution and more clumpy distributions in observed clusters than in the structure of simulated clusters, and slower increase in simulated cluster shapes compared to those in the observed one. Within z≤ 0.1, we note an interesting agreement in the shapes of clusters obtained from the cooling simulations and observation. We also note that the different samples of observed clusters differ significantly in morphological evolution with redshift. We highlight a few possibilities responsible for the discrepancy in morphological evolution of simulated and observed clusters.

Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport

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

Thermonuclear supernova simulations with stochastic ignition

We apply an ad hoc model for dynamical ignition in three-dimensional numerical simulations of thermonuclear supernovae assuming pure deflagrations. The model makes use of the statistical description of temperature fluctuations in the pre-supernova core proposed by Wunsch & Woosley (2004, ApJ, 616, 1102). Randomness in time is implemented by means of a Poisson process. We are able to vary the explosion energy and nucleosynthesis depending on the free parameter of the model which controls the rapidity of the ignition process. However, beyond a certain threshold, the strength of the explosion saturates and the outcome appears to be robust with respect to the number of ignitions. In the most energetic explosions, we find about of iron group elements. Other than in simulations with simultaneous multi-spot ignition, the amount of unburned carbon and oxygen at radial velocities of a few tends to be reduced for an ever increasing number of ignition events and, accordingly, more pronounced layering results.

Effect of electron screening on the prompt explosion energy for type Ⅱ supernova

The effect of electron screening on prompt explosion energy of supernova is discussed in regard to progenitor model WS15M⊙. The average heavy nuclei model is used for calculating the electron capture rates. The simulation results show that electron capture rate is decreased and the collapsing time-scale is prolonged by the electron screening, and the total energy of neutrino leakage increases. Acordingly, by the energy of the shock wave also decreases appreciably. The effect of electron screening on other supernova simulations is estimated.

Exploring the relativistic regime with Newtonian hydrodynamics: an improved effective gravitational potential for supernova simulations

We investigate the possibility approximating relativistic effects in hydrodynamical simulations of stellar core collapse and post-bounce evolution by using a modified gravitational potential in an otherwise standard Newtonian hydrodynamic code. Different modifications of a previously introduced effective relativistic potential are discussed. Corresponding hydrostatic solutions are compared with solutions of the TOV equations, and hydrodynamic simulations with two different codes are compared with fully relativistic results. One code is applied for one- and two-dimensional calculations with a simple equation of state and employs either the modified effective relativistic potential in a Newtonian framework or solves the general relativistic field equations under the assumption of the conformal flatness condition (CFC) for the three-metric. The second code allows for full-scale supernova runs including a microphysical equation of state and neutrino transport based on the solution of the Boltzmann equation and its moments equations. We present prescriptions for the effective relativistic potential for self-gravitating fluids to he used in Newtonian codes, which produce excellent agreement with fully relativistic solutions in spherical symmetry, leading to significant improvements compared to previously published approximations. Moreover, they also approximate qualitatively well relativistic solutions for models with rotation.

Postbounce Evolution of Core‐Collapse Supernovae: Long‐Term Effects of the Equation of State

We study the evolution of supernova core from the beginning of gravitational collapse of a 15Msolar star up to 1 second after core bounce. We present results of spherically symmetric simulations of core-collapse supernovae by solving general relativistic neutrino-radiation-hydrodynamics in the implicit time-differencing. We aim to explore the evolution of shock wave in a long term and investigate the formation of protoneutron star together with supernova neutrino signatures. These studies are done to examine the influence of equation of state (EOS) on the postbounce evolution of shock wave in the late phase and the resulting thermal evolution of protoneutron star. We make a comparison of two sets of EOS, that is, by Lattimer and Swesty (LS-EOS) and by Shen et al.(SH-EOS). We found that, for both EOSs, the core does not explode and the shock wave stalls similarly in the first 100 milliseconds after bounce. The revival of shock wave does not occur even after a long period in either cases. However, the recession of shock wave appears different beyond 200 milliseconds after bounce, having different thermal evolution of central core. A more compact protoneutron star is found for LS-EOS than SH-EOS with a difference in the central density by a factor of ~2 and a difference of ~10 MeV in the peak temperature. Resulting spectra of supernova neutrinos are different to the extent that may be detectable by terrestrial neutrino detectors.

A model for multidimensional delayed detonations in SN Ia explosions

We show that a flame tracking/capturing scheme originally developed for deflagration fronts can be used to model thermonuclear detonations in multidimensional explosion simulations of type Ia supernovae. After testing the accuracy of the front model, we present a set of two-dimensional simulations of delayed detonations with a physically motivated off-center deflagration-detonation-transition point. Furthermore, we demonstrate the ability of the front model to reproduce the full range of possible interactions of the detonation with clumps of burned material. This feature is crucial for assessing the viability of the delayed detonation scenario.

Generalized Boltzmann formalism for oscillating neutrinos

In the standard approaches to neutrino transport in the simulation of core-collapse supernovae, one will often start from the classical Boltzmann equation for the neutrino's spatial, temporal, and spectral evolution. For each neutrino species, and its anti-particle, the classical density in phase space, or the associated specific intensity, will be calculated as a function of time. The neutrino radiation is coupled to matter by source and sink terms on the "right-hand-side" of the transport equation and together with the equations of hydrodynamics this set of coupled partial differential equations for classical densities describes, in principle, the evolution of core collapse and explosion. However, with the possibility of neutrino oscillations between species, a purely quantum-physical effect, how to generalize this set of Boltzmann equations for classical quantities to reflect oscillation physics has not been clear. To date, the formalisms developed have retained the character of quantum operator physics involving complex quantities and have not been suitable for easy incorporation into standard supernova codes. In this paper, we derive generalized Boltzmann equations for quasi-classical, real-valued phase-space densities that retain all the standard oscillation phenomenology, including resonant flavor conversion (the MSW effect), neutrino self-interactions, and the interplay between decohering matter coupling and flavor oscillations. With this formalism, any code(s) that can now handle the solution of the classical Boltzmann or transport equation can easily be generalized to include neutrino oscillations in a quantum-physically consistent fashion.

Exploiting the neutronization burst of a galactic supernova

One of the robust features found in simulations of core-collapse supernovae (SNe) is the prompt neutronization burst, i.e. the first $\sim 25$ milliseconds after bounce when the SN emits with very high luminosity mainly $\nu_e$ neutrinos. We examine the dependence of this burst on variations in the input of current SN models and find that recent improvements of the electron capture rates as well as uncertainties in the nuclear equation of state or a variation of the progenitor mass have only little effect on the signature of the neutronization peak in a megaton water Cherenkov detector for different neutrino mixing schemes. We show that exploiting the time-structure of the neutronization peak allows one to identify the case of a normal mass hierarchy and large 13-mixing angle $\theta_{13}$, where the peak is absent. The robustness of the predicted total event number in the neutronization burst makes a measurement of the distance to the SN feasible with a precision of about 5%, even in the likely case that the SN is optically obscured.

Supernovae, Rotation, and Bipolar Explosions

In this paper, we discuss the possible role of rotation in supernova blast energetics and morphology, and speculate on the origin of Cas A’s and SN1987A’s ejecta fields. Two “explosive” phenomena may be associated with most core collapses, the neutrinodriven supernova itself and an underenergetic jet-like ejection that follows. The latter may be a magnetic wind that easily penetrates the debris created by the much more energetic supernova. We speculate that many core-collapse supernova remnants should have sub-dominant jet-like features. In Cas A, we associate this sub-dominant collimated wind with the “jet/counter-jet” structure observed. We suggest that the actual Cas A explosion itself is at nearly right angles to this jet, along a rotation axis that coincides with the bulk of the ejecta, the iron lobes, and the putative direction of motion of the point source. It may be that when rotation becomes sufficiently rapid that the strong-neutrinodriven-supernova/weak-jet duality switches to a strong-MHD-jet scenario that might be associated with hypernovae, and in some cases GRBs. Finally, we present a calculation using a new 2D multi-group, flux-limited radiation/hydrodynamics code we have recently developed for the simulation of core-collapse supernovae. We discuss the rotation-induced anisotropy in the neutrino radiation field, neutrino heating, and the neutrino flux vectors and speculate on rotation’s possible role in the supernova mechanism. ∗ We acknowledge discussions with Todd Thompson, Jeremiah Murphy, Casey Meakin, Itamar Lichtenstadt, and Moath Jarrah. Support for this work is provided in part by the Scientific Discovery through Advanced Computing (SciDAC) program of the DOE, grant number DE-FC02-01ER41184. In addition, we thank Jeff Fookson and Neal Lauver of the Steward Computer Support Group for their invaluable help with the local Beowulf cluster and acknowledge the use of the NERSC/LBNL/seaborg and ORNL/CCS/cheetah machines.

Toward 2-D and 3-D simulations of core-collapse supernovae with magnetic fields

We describe a code development and integration effort aimed at producing a numerical tool suitable for exploring the effects of stellar rotation and magnetic fields in a neutrino-driven core-collapse supernova environment. A one-dimensional, multi-energy group, flux-limited neutrino diffusion module (MGFLD) has been integrated with ZEUS-MP, a multidimensional, parallel gas hydrodynamics and magnetohydrodynamics code. With the neutrino diffusion module, ZEUS-MP can simulate the core-collapse, bounce, and explosion of a stellar progenitor in two and three space dimensions in which multidimensional hydrodynamics are coupled to 1-D neutrino transport in a ray-by-ray approximation. This paper describes the physics capabilities of the code and the technique for implementing the serial MGFLD module for parallel execution in a multi-dimensional simulation. Because the development and debugging of the integrated code is not yet complete, we provide a current status report of the effort and identify outstanding issues currently under investigation.

Multigroup models of the convective epoch in core collapse supernovae

Understanding the explosion mechanism of core collapse supernovae is a problem that has plagued nuclear astrophysicists since the first computational models of this phenomenon were carried out in the 1960s. Our current theories of this violent phenomenon center around multi-dimensional effects involving radiation-hydrodynamic flows of hot, dense matter and neutrinos. Modeling these multi-dimensional radiative flows presents a computational challenge that will continue to stress high-performance computing beyond the teraflops to the petaflop level. In this paper we describe a few of the scientific discoveries that we have made via terascale computational simulations of supernovae under the auspices of the SciDAC-funded Terascale Supernova Initiative.

Nonuniform neutron-rich matter and coherent neutrino scattering

Nonuniform neutron-rich matter present in both core-collapse supernovae and neutron-star crusts is described in terms of a semiclassical model that reproduces nuclear-matter properties and includes long-range Coulomb interactions. The neutron-neutron correlation function and the corresponding static structure factor are calculated from molecular dynamics simulations involving 40 000 to 100 000 nucleons. The static structure factor describes coherent neutrino scattering which is expected to dominate the neutrino opacity. At low momentum transfers the static structure factor is found to be small because of ion screening. In contrast, at intermediate momentum transfers the static structure factor displays a large peak due to coherent scattering from all the neutrons in a cluster. This peak moves to higher momentum transfers and decreases in amplitude as the density increases. A large static structure factor at zero momentum transfer, indicative of large density fluctuations during a first-order phase transition, may increase the neutrino opacity. However, no evidence of such an increase has been found. Therefore, it is unlikely that the system undergoes a simple first-order phase transition. Further, to compare our results to more conventional approaches, a cluster algorithm is introduced to determine the composition of the clusters in our simulations. Neutrino opacities are then calculated within a single heavy nucleus approximation as is done in most current supernova simulations. It is found that corrections to the single heavy nucleus approximation first appear at a density of the order of ${10}^{13}\phantom{\rule{0.3em}{0ex}}\mathrm{g}∕{\mathrm{cm}}^{3}$ and increase rapidly with increasing density. Thus neutrino opacities are overestimated in the single heavy nucleus approximation relative to the complete molecular dynamics simulations.

Neutral-current neutrino–nucleus cross sections for [formula omitted] nuclei

We study neutral-current neutrino–nucleus reaction cross sections for Mn, Fe, Co and Ni isotopes. An earlier study for a few selected nuclei has shown that in the supernova environment the cross sections are increased for low energy neutrinos due to finite-temperature effects. Our work supports this finding for a much larger set of nuclei. Furthermore we extend previous work to higher neutrino energies considering allowed and forbidden multipole contributions to the cross sections. The allowed contributions are derived from large-scale shell model calculations of the Gamow–Teller strength, while the other multipole contributions are calculated within the random phase approximation. We present the cross sections as functions of initial and final neutrino energies and for a range of supernova-relevant temperatures. These cross sections will allow improved estimates of inelastic neutrino reactions on nuclei in supernova simulations.

The cellular burning regime in type Ia supernova explosions

We present a numerical investigation of the cellular burning regime in Type Ia supernova explosions. This regime holds at small scales (i.e. below the Gibson scale), which are unresolved in large-scale Type Ia supernova simulations. The fundamental effects that dominate the flame evolution here are the Landau-Darrieus instability and its nonlinear stabilization, leading to a stabilization of the flame in a cellular shape. The flame propagation into quiescent fuel is investigated addressing the dependence of the simulation results on the specific parameters of the numerical setup. Furthermore, we investigate the flame stability at a range of fuel densities. This is directly connected to the questions of active turbulent combustion (a mech- anism of flame destabilization and subsequent self-turbulization) and a deflagration-to-detonation transition of the flame. In our simulations we find no substantial destabilization of the flame when propagating into quiescent fuels of densities down to ∼10 7 gc m −3 , corroborating fundamental assumptions of large-scale SN Ia explosion models. For these models, however, we suggest an increased lower cutoff for the flame propagation velocity to take the cellular burning regime into account.

Gravitational radiation from rotational core collapse: Effects of magnetic fields and realistic equations of state

We perform a series of two-dimensional, axisymmetric, magnetohydrodynamic simulations of the rotational collapse of a supernova core. In order to calculate the waveforms of the gravitational wave, we derive the quadrupole formula including the contributions from the electromagnetic fields. Recent stellar evolution calculations imply that the magnetic fields of the toroidal components are much stronger than those of the poloidal ones at the presupernova stage. Thus we systematically investigate the effects of the toroidal magnetic fields on the amplitudes and waveforms of the gravitational wave. Furthermore, we employ two kinds of the realistic equation of states which are often used in supernova simulations. Then, we investigate the effects of the equation of states on the gravitational wave signals. As for microphysics, we take into account the electron capture and neutrino transport by the so-called leakage scheme. With these computations, we find that the peak amplitudes of the gravitational wave are lowered by an order of 10% for models with the strongest toroidal magnetic fields. However, the peak amplitudes are mostly within the sensitivity range of laser interferometers such as TAMA and the first LIGO for a source at a distance of 10 kpc. Furthermore, we point out that the amplitudes of second peaks are still within the detection limit of the first LIGO for the source, although the characteristics of second peaks are reduced by the magnetic fields. We stress the importance of the detection, since it will give us information about the angular momentum distribution of massive evolved stars. When we compare the gravitational waves from the two realistic equations of state, significant differences are not found, except that the typical frequencies of the gravitational wave become slightly higher for the softer equation of state.

The cellular burning regime in type Ia supernova explosions

We present a numerical investigation of the cellular burning regime in Type Ia supernova explosions. This regime holds at small scales (i.e. below the Gibson scale), which are unresolved in large-scale Type Ia supernova simulations. The fundamental effects that dominate the flame evolution here are the Landau-Darrieus instability and its nonlinear stabilization, leading to a stabilization of the flame in a cellular shape. The flame propagation into quiescent fuel is investigated addressing the dependence of the simulation results on the specific parameters of the numerical setup. Furthermore, we investigate the flame stability at a range of fuel densities. This is directly connected to the questions of active turbulent combustion (a mechanism of flame destabilization and subsequent self-turbulization) and a deflagration-to-detonation transition of the flame. In our simulations we find no substantial destabilization of the flame when propagating into quiescent fuels of densities down to ∼, corroborating fundamental assumptions of large-scale SN Ia explosion models. For these models, however, we suggest an increased lower cutoff for the flame propagation velocity to take the cellular burning regime into account.

Cosmic Star Formation History and the Future Observation of Supernova Relic Neutrinos

We investigate the flux and event rate of supernova relic neutrinos (SRNs) and discuss their implications for the cosmic star formation rate. As reference models, we adopt the supernova rate model based on recent observations and the supernova neutrino spectrum numerically calculated by several groups. In the detection energy range E_e>10 MeV, which will possibly be a background-free region in the near future, the SRN event rate is found to be 1-2 yr^{-1} at a water Cerenkov detector with a fiducial volume of 22.5 kton, depending on the adopted neutrino spectrum. We also simulate the expected signal with one set of the reference models by using the Monte Carlo method and then analyze these pseudodata with several free parameters, obtaining the distribution of the best-fit values for them. In particular, we use a parameterization such that R_{SN}(z)=R_{SN}^0 (1+z)^\alpha, where R_{SN}(z) is the comoving supernova rate density at redshift z and R_{SN}^0 and \alpha are free parameters, assuming that the supernova neutrino spectrum and luminosity are well understood by way of a future Galactic supernova neutrino burst or the future development of numerical supernova simulations. The obtained 1\sigma errors for these two parameters are found to be \delta\alpha /\alpha = 30% (7.8%) and \delta R_{SN}^0/ R_{SN}^0 = 28% (7.7%) for a detector with an effective volume of 22.5 kton 5 yr (440 kton 5 yr), where one of the parameters is fixed. On the other hand, if we fix neither of the values for these two parameters, the expected errors become rather large, \delta\alpha /\alpha = 37% and \delta R_{SN}^0/ R_{SN}^0 = 55%, even with an effective volume of 440 kton 5 yr.

Neutron Star Kicks from Asymmetric Collapse

Many neutron stars are observed to be moving with spatial velocities, in excess of 500km/s. A number of mechanisms have been proposed to give neutron stars these high velocities. One of the leading classes of models proposed invokes asymmetries in the core of a massive star just prior to collapse. These asymmetries grow during the collapse, causing the resultant supernova to also be asymmetric. As the ejecta is launched, it pushes off (or ``kicks'') the newly formed neutron star. This paper presents the first 3-dimensional supernova simulations of this process. The ejecta is not the only matter that kicks the newly-formed neutron star. Neutrinos also carry away momentum and the asymmetric collapse leads also to asymmetries in the neutrinos. However, the neutrino asymmetries tend to damp out the neutron star motions and even the most extreme asymmetric collapses presented here do not produce final neutron star velocities above 200km/s.