Isotropic Diffusion Source Approximation Research Articles

Stellar Mass Black Hole Formation and Multimessenger Signals from Three-dimensional Rotating Core-collapse Supernova Simulations

Abstract We present self-consistent 3D core-collapse supernova simulations of a 40 M ⊙ progenitor model using the isotropic diffusion source approximation for neutrino transport and an effective general relativistic potential up to ∼0.9 s postbounce. We consider three different rotational speeds with initial angular velocities of Ω 0 = 0 , 0.5, and 1 rad s−1 and investigate the impact of rotation on shock dynamics, black hole (BH) formation, and gravitational wave (GW) signals. The rapidly rotating model undergoes an early explosion at ∼250 ms postbounce and shows signs of the low T / ∣ W ∣ instability. We do not find BH formation in this model within ∼460 ms postbounce. In contrast, we find BH formation at 776 ms postbounce and 936 ms postbounce for the nonrotating and slowly rotating models, respectively. The slowly rotating model explodes at ∼650 ms postbounce, and the subsequent fallback accretion onto the proto–neutron star (PNS) results in BH formation. In addition, the standing accretion shock instability induces rotation of the PNS in the model that started with a nonrotating progenitor. Assuming conservation of specific angular momentum during BH formation, this corresponds to a BH spin parameter of a = J/M = 0.046. However, if no explosion sets in, all the angular momentum will eventually be accreted by the BH, resulting in a nonspinning BH. The successful explosion of the slowly rotating model drastically slows down the accretion onto the PNS, allowing continued cooling and contraction that results in an extremely high GW frequency (f ∼ 3000 Hz) at BH formation, while the nonrotating model generates GW signals similar to our corresponding 2D simulations.

The impact of different neutrino transport methods on multidimensional core-collapse supernova simulations

Neutrinos play a crucial role in the core-collapse supernova (CCSN) explosion mechanism. The requirement of accurately calculating the transport of neutrinos makes simulations of the CCSN mechanism extremely challenging and computationally expensive. Historically, this stiff challenge has been met by making approximations to the full transport equation. In this work, we compare CCSN simulations in one- and two-dimensions with three approximate neutrino transport schemes, each implemented in the FLASH simulation framework. We compare a two-moment M1 scheme with an analytic closure (M1), the isotropic diffusion source approximation (IDSA), and the advanced spectral leakage method. We identify and discuss the advantages and disadvantages of each scheme. For each approximate transport scheme, we use identical grid setups, hydrodynamics, and gravity solvers to investigate the transport effects on supernova shock dynamics and neutrino quantities. We find that the transport scheme has a small effect on the evolution of protoneutron star (PNS) radius, PNS mass, and the mass accretion rate. The neutrino luminosities, mean energies, and shock radii have a ∼10%–20% quantitative difference but the overall qualitative trends are fairly consistent between all three approximations. We find larger differences in the gain region properties, including the gain region mass and the net heating rate in the gain region, as well as the strength of PNS convection in the core. We investigate the progenitor, nuclear equation of state, and stochastic perturbation dependence of our simulations and find similar magnitudes of impact on key quantities. We also compare the computational expense of the various approximations.

Core-collapse supernovae in the hall of mirrors

Context. Modeling core-collapse supernovae (SNe) with neutrino transport in three dimensions (3D) requires tremendous computing resources and some level of approximation. We present a first comparison study of core-collapse SNe in 3D with different physics approximations and hydrodynamics codes. Aims. The objective of this work is to assess the impact of the hydrodynamics code, approximations for the neutrino, gravity treatments, and rotation on the simulation of core-collapse SNe in 3D. Methods. We use four different hydrodynamics codes in this work (ELEPHANT, FLASH, fGR1, and SPHYNX) in combination with two different neutrino treatments, the isotropic diffusion source approximation (IDSA) and two-moment M1, and three different gravity treatments (Newtonian, 1D General Relativity correction, and full General Relativity). Additional parameters discussed in this study are the inclusion of neutrino-electron scattering via a parametrized deleptonization and the influence of rotation. Results. The four codes compared in this work include Eulerian and fully Lagrangian (smoothed particle hydrodynamics) codes for the first time. They show agreement in the overall evolution of the collapse phase and early post-bounce within the range of 10% (20% in some cases). The comparison of the different neutrino treatments highlights the need to further investigate the antineutrino luminosities in IDSA, which tend to be relatively high. We also demonstrate the requirement for a more detailed heavy-lepton neutrino leakage. When comparing with a full General Relativity code, including an M1 transport method, we confirm the influence of neutrino-electron scattering during the collapse phase, which is adequately captured by the parametrized deleptonization scheme. Also, the effective general relativistic potential reproduces the overall dynamic evolution correctly in all Newtonian codes. Additionally, we verify that rotation aids the shock expansion and estimate the overall angular momentum losses for each code in rotating scenarios.

Equation of State Dependent Dynamics and Multi-messenger Signals from Stellar-mass Black Hole Formation

Abstract We investigate axisymmetric black hole (BH) formation and its gravitational wave (GW) and neutrino signals with self-consistent core-collapse supernova simulations of a non-rotating 40 M ⊙ progenitor star using the isotropic diffusion source approximation for the neutrino transport and a modified gravitational potential for general relativistic effects. We consider four different neutron star (NS) equations of state (EoS): LS220, SFHo, BHBΛϕ, and DD2, and study the impact of the EoS on BH formation dynamics and GW emission. We find that the BH formation time is sensitive to the EoS from 460 to >1300 ms and is delayed in multiple dimensions for ∼100–250 ms due to the finite entropy effects. Depending on the EoS, our simulations show the possibility that shock revival can occur along with the collapse of the proto-neutron star (PNS) to a BH. The gravitational waveforms contain four major features that are similar to previous studies but show extreme values: (1) a low-frequency signal (∼300–500 Hz) from core-bounce and prompt convection, (2) a strong signal from the PNS g-mode oscillation among other features, (3) a high-frequency signal from the PNS inner-core convection, and (4) signals from the standing accretion shock instability and convection. The peak frequency at the onset of BH formation reaches to ∼2.3 kHz. The characteristic amplitude of a 10 kpc object at peak frequency is detectable but close to the noise threshold of the Advanced LIGO and KAGRA, suggesting that the next-generation GW detector will need to improve the sensitivity at the kHz domain to better observe stellar-mass BH formation from core-collapse supernovae or failed supernovae.

Impact of Neutrino Opacities on Core-collapse Supernova Simulations

Abstract The accurate description of neutrino opacities is central to both the core-collapse supernova (CCSN) phenomenon and the validity of the explosion mechanism itself. In this work, we study in a systematic fashion the role of a variety of well-selected neutrino opacities in CCSN simulations where the multi-energy, three-flavor neutrino transport is solved using the isotropic diffusion source approximation (IDSA) scheme. To verify our code, we first present results from one-dimensional (1D) simulations following the core collapse, bounce, and ∼250 ms postbounce of a star using a standard set of neutrino opacities by Bruenn. A detailed comparison with published results supports the reliability of our three-flavor IDSA scheme using the standard opacity set. We then investigate in 1D simulations how individual opacity updates lead to differences with the baseline run with the standard opacity set. Through detailed comparisons with previous work, we check the validity of our implementation of each update in a step-by-step manner. Individual neutrino opacities with the largest impact on the overall evolution in 1D simulations are selected for systematic comparisons in our two-dimensional (2D) simulations. Special attention is given to the criterion of explodability in the 2D models. We discuss the implications of these results as well as its limitations and the requirements for future, more elaborate CCSN modeling.

The IDSA and the homogeneous sphere: Issues and possible improvements

In this paper, we are concerned with the study of the Isotropic Diffusion Source Approximation (IDSA) [6] of radiative transfer. After having recalled well-known limits of the radiative transfer equation, we present the IDSA and adapt it to the case of the homogeneous sphere. We then show that for this example the IDSA suffers from severe numerical difficulties. We argue that these difficulties originate in the min-max switch coupling mechanism used in the IDSA. To overcome this problem we reformulate the IDSA to avoid the problematic coupling. This allows us to access the modeling error of the IDSA for the homogeneous sphere test case. The IDSA is shown to overestimate the streaming component, hence we propose a new version of the IDSA, which is numerically shown to be more accurate than the old one. Analytical results and numerical tests are provided to support the accuracy of the new proposed approximation.

Three-dimensional simulations of rapidly rotating core-collapse supernovae: finding a neutrino-powered explosion aided by non-axisymmetric flows

Abstract We report results from a series of three-dimensional (3D) rotational core-collapse simulations for 11.2 and 27 M⊙ stars employing neutrino transport scheme by the isotropic diffusion source approximation. By changing the initial strength of rotation systematically, we find a rotation-assisted explosion for the 27 M⊙ progenitor , which fails in the absence of rotation. The unique feature was not captured in previous two-dimensional (2D) self-consistent rotating models because the growing non-axisymmetric instabilities play a key role. In the rapidly rotating case, strong spiral flows generated by the so-called low T/|W| instability enhance the energy transport from the proto-neutron star (PNS) to the gain region, which makes the shock expansion more energetic. The explosion occurs more strongly in the direction perpendicular to the rotational axis, which is different from previous 2D predictions.

Parametric initial conditions for core-collapse supernova simulations

We investigate a method to construct parametrized progenitor models for core-collapse supernova simulations. Different from all modern core-collapse supernova studies, which rely on progenitor models from stellar evolution calculations, we follow the methodology of Baron & Cooperstein (1990) to construct initial models. Choosing parametrized spatial distributions of entropy and electron fraction as a function of mass coordinate and solving the equation of hydrostatic equilibrium, we obtain the initial density structures of our progenitor models. First, we calculate structures with parameters fitting broadly the evolutionary model s11.2 of Woosley et al. (2002). We then demonstrate the reliability of our method by performing general relativistic hydrodynamic simulations in spherical symmetry with the isotropic diffusion source approximation to solve the neutrino transport. Our comprehensive parameter study shows that initial models with a small central entropy ($\lesssim 0.4\,k_B$ nucleon$^{-1}$) can explode even in spherically symmetric simulations. Models with a large entropy ($\gtrsim 6\,k_B$ nucleon$^{-1}$) in the Si/O layer have a rather large explosion energy ($\sim 4\times 10^{50}$ erg) at the end of the simulations, which is still rapidly increasing.

TWO-DIMENSIONAL CORE-COLLAPSE SUPERNOVA SIMULATIONS WITH THE ISOTROPIC DIFFUSION SOURCE APPROXIMATION FOR NEUTRINO TRANSPORT

ABSTRACT The neutrino mechanism of core-collapse supernova is investigated via non-relativistic, two-dimensional (2D), neutrino radiation–hydrodynamic simulations. For the transport of electron flavor neutrinos, we use the interaction rates defined by Bruenn and the isotropic diffusion source approximation (IDSA) scheme, which decomposes the transported particles into trapped-particle and streaming-particle components. Heavy neutrinos are described by a leakage scheme. Unlike the “ray-by-ray” approach in some other multidimensional supernova models, we use cylindrical coordinates and solve the trapped-particle component in multiple dimensions, improving the proto-neutron star resolution and the neutrino transport in angular and temporal directions. We provide an IDSA verification by performing one-dimensional (1D) and 2D simulations with 15 and 20 M ⊙ progenitors from Woosley et al. and discuss the difference between our IDSA results and those existing in the literature. Additionally, we perform Newtonian 1D and 2D simulations from prebounce core collapse to several hundred milliseconds postbounce with 11, 15, 21, and 27 M ⊙ progenitors from Woosley et al. with the HS(DD2) equation of state. General-relativistic effects are neglected. We obtain robust explosions with diagnostic energies E dia ≳ 0.1–0.5 B (1 B ≡ 1051 erg) for all considered 2D models within approximately 100–300 ms after bounce and find that explosions are mostly dominated by the neutrino-driven convection, although standing accretion shock instabilities are observed as well. We also find that the level of electron deleptonization during collapse dramatically affects the postbounce evolution, e.g., the neglect of neutrino–electron scattering during collapse will lead to a stronger explosion.

Systematic features of axisymmetric neutrino-driven core-collapse supernova models in multiple progenitors

Abstract We present an overview of two-dimensional (2D) core-collapse supernova simulations employing a neutrino transport scheme by the isotropic diffusion source approximation. We study 101 solar-metallicity, 247 ultra metal-poor, and 30 zero-metal progenitors covering zero-age main sequence mass from 10.8 M⊙ to 75.0 M⊙. Using the 378 progenitors in total, we systematically investigate how the differences in the structures of these multiple progenitors impact the hydrodynamics evolution. By following a long-term evolution over 1.0 s after bounce, most of the computed models exhibit neutrino-driven revival of the stalled bounce shock at ∼200–800 ms postbounce, leading to the possibility of explosion. Pushing the boundaries of expectations in previous one-dimensional studies, our results confirm that the compactness parameter ξ that characterizes the structure of the progenitors is also a key in 2D to diagnosing the properties of neutrino-driven explosions. Models with high ξ undergo high ram pressure from the accreting matter onto the stalled shock, which affects the subsequent evolution of the shock expansion and the mass of the protoneutron star under the influence of neutrino-driven convection and the standing accretion-shock instability. We show that the accretion luminosity becomes higher for models with high ξ, which makes the growth rate of the diagnostic explosion energy higher and the synthesized nickel mass bigger. We find that these explosion characteristics tend to show a monotonic increase as a function of the compactness parameter ξ.

PUSHING CORE-COLLAPSE SUPERNOVAE TO EXPLOSIONS IN SPHERICAL SYMMETRY. I. THE MODEL AND THE CASE OF SN 1987A

We report on a method, PUSH, for triggering core-collapse supernova explosions of massive stars in spherical symmetry. We explore basic explosion properties and calibrate PUSH such that the observables of SN1987A are reproduced. Our simulations are based on the general relativistic hydrodynamics code AGILE combined with the detailed neutrino transport scheme IDSA for electron neutrinos and ALS for the muon and tau neutrinos. To trigger explosions in the otherwise non-exploding simulations, we rely on the neutrino-driven mechanism. The PUSH method locally increases the energy deposition in the gain region through energy deposition by the heavy neutrino flavors. Our setup allows us to model the explosion for several seconds after core bounce. We explore the progenitor range 18-21M$_{\odot}$. Our studies reveal a distinction between high compactness (HC) and low compactness (LC) progenitor models, where LC models tend to explore earlier, with a lower explosion energy, and with a lower remnant mass. HC models are needed to obtain explosion energies around 1 Bethe, as observed for SN1987A. However, all the models with sufficiently high explosion energy overproduce $^{56}$Ni. We conclude that fallback is needed to reproduce the observed nucleosynthesis yields. The nucleosynthesis yields of $^{57-58}$Ni depend sensitively on the electron fraction and on the location of the mass cut with respect to the initial shell structure of the progenitor star. We identify a progenitor and a suitable set of PUSH parameters that fit the explosion properties of SN1987A when assuming 0.1M$_{\odot}$ of fallback. We predict a neutron star with a gravitational mass of 1.50M$_{\odot}$. We find correlations between explosion properties and the compactness of the progenitor model in the explored progenitors. However, a more complete analysis will require the exploration of a larger set of progenitors with PUSH.

A COMPARISON OF TWO- AND THREE-DIMENSIONAL NEUTRINO-HYDRODYNAMICS SIMULATIONS OF CORE-COLLAPSE SUPERNOVAE

We present numerical results on two- (2D) and three-dimensional (3D) hydrodynamic core-collapse simulations of an 11.2$M_\odot$ star. By changing numerical resolutions and seed perturbations systematically, we study how the postbounce dynamics is different in 2D and 3D. The calculations were performed with an energy-dependent treatment of the neutrino transport based on the isotropic diffusion source approximation scheme, which we have updated to achieve a very high computational efficiency. All the computed models in this work including nine 3D models and fifteen 2D models exhibit the revival of the stalled bounce shock, leading to the possibility of explosion. All of them are driven by the neutrino-heating mechanism, which is fostered by neutrino-driven convection and the standing-accretion-shock instability (SASI). Reflecting the stochastic nature of multi-dimensional (multi-D) neutrino-driven explosions, the blast morphology changes from models to models. However, we find that the final fate of the multi-D models whether an explosion is obtained or not, is little affected by the explosion stochasticity. In agreement with some previous studies, higher numerical resolutions lead to slower onset of the shock revival in both 3D and 2D. Based on the self-consistent supernova models leading to the possibility of explosions, our results systematically show that the revived shock expands more energetically in 2D than in 3D.

ON THE IMPORTANCE OF THE EQUATION OF STATE FOR THE NEUTRINO-DRIVEN SUPERNOVA EXPLOSION MECHANISM

By implementing widely-used equations of state (EOS) from Lattimer & Swesty (LS) and H. Shen et al. (SHEN) in core-collapse supernova simulations, we explore possible impacts of these EOS on the post-bounce dynamics prior to the onset of neutrino-driven explosions. Our spherically symmetric (1D) and axially symmetric (2D) models are based on neutrino radiation hydrodynamics including spectral transport, which is solved by the isotropic diffusion source approximation. We confirm that in 1D simulations neutrino-driven explosions cannot be obtained for any of the employed EOS. Impacts of the EOS on the post-bounce hydrodynamics are more clearly visible in 2D simulations. In 2D models of a 15 M_sun progenitor using the LS EOS, the stalled bounce shock expands to increasingly larger radii, which is not the case using the SHEN EOS. Keeping in mind that the omission of the energy drain by heavy-lepton neutrinos in the present scheme could facilitate explosions, we find that 2D models of an 11.2 M_sun progenitor produce neutrino-driven explosions for all the EOS under investigation. Models using the LS EOS are slightly more energetic compared to those with the SHEN EOS. The more efficient neutrino heating in the LS models coincides with a higher electron antineutrino luminosity and a larger mass that is enclosed within the gain region. The models based on the LS EOS also show a more vigorous and aspherical downflow of accreting matter to the surface of the protoneutron star (PNS). The accretion pattern is essential for the production and strength of outgoing pressure waves, that can push in turn the shock to larger radii and provide more favorable conditions for the explosion. [abbreviated]

Derivation of the Isotropic Diffusion Source Approximation (IDSA) for Supernova Neutrino Transport by Asymptotic Expansions

We present Chapman--Enskog and Hilbert expansions applied to the $\BigO(v/c)$ Boltzmann equation for the radiative transfer of neutrinos in core-collapse supernovae. Based on the Legendre expansion of the scattering kernel for the collision integral truncated after the second term, we derive the diffusion limit for the Boltzmann equation by truncation of Chapman--Enskog or Hilbert expansions with reaction and collision scaling. We also give asymptotically sharp results obtained by the use of an additional time scaling. The diffusion limit determines the diffusion source in the \emph{Isotropic Diffusion Source Approximation (IDSA)} of Boltzmann's equation for which the free streaming limit and the reaction limit serve as limiters. Here, we derive the reaction limit as well as the free streaming limit by truncation of Chapman--Enskog or Hilbert expansions using reaction and collision scaling as well as time scaling, respectively. Finally, we motivate why limiters are a good choice for the definition of the source term in the IDSA.

A mathematical description of the IDSA for supernova neutrino transport, its discretization and a comparison with a finite volume scheme for Boltzmann’s equation

In this paper we give an introduction to the Boltzmann equation for neutrino transport used in core collapse supernova models as well as a detailed mathematical description of the \emph{Isotropic Diffusion Source Approximation} (IDSA). Furthermore, we present a numerical treatment of a reduced Boltzmann model problem based on time splitting and finite volumes and revise the discretization of the IDSA for this problem. Discretization error studies carried out on the reduced Boltzmann model problem and on the IDSA show that the errors are of order one in both cases. By a numerical example, a detailed comparison of the reduced model and the IDSA is carried out and interpreted. For this example the IDSA modeling error with respect to the reduced Boltzmann model is numerically determined and localized.

THREE-DIMENSIONAL HYDRODYNAMIC CORE-COLLAPSE SUPERNOVA SIMULATIONS FOR AN 11.2M☉STAR WITH SPECTRAL NEUTRINO TRANSPORT

We present numerical results on three-dimensional (3D) hydrodynamic core-collapse simulations of an $11.2 M_{\odot}$ star. By comparing one-(1D) and two-dimensional(2D) results with those of 3D, we study how the increasing spacial multi-dimensionality affects the postbounce supernova dynamics. The calculations were performed with an energy-dependent treatment of the neutrino transport that is solved by the isotropic diffusion source approximation scheme. By performing a tracer-particle analysis, we show that the maximum residency time of material in the gain region is shown to be longer for 3D due to non-axisymmetric flow motions than 2D, which is one of advantageous aspects of 3D models to obtain neutrino-driven explosions. Our results show that convective matter motions below the gain radius become much more violent in 3D than 2D, making the neutrino luminosity larger for 3D. Nevertheless the emitted neutrino energies are made smaller due to the enhanced cooling. Our results indicate whether these advantages for driving 3D explosions could or could not overwhelm the disadvantages is sensitive to the employed numerical resolutions. An encouraging finding is that the shock expansion tends to become more energetic for models with finer resolutions. To draw a robust conclusion, 3D simulations with much more higher numerical resolutions and also with more advanced treatment of neutrino transport as well as of gravity is needed, which could be hopefully practicable by utilizing forthcoming Petaflops-class supercomputers.

3D hydrodynamic core-collapse SN simulations for an 11.2 M⊙ star with spectral neutrino transport

AbstractWe have performed three-dimensional (3D) hydrodynamical simulations of core-collapse supernovae (SNe) with multigroup neutrino transport to study non-axisymmetric effects in the context of neutrino heating explosion mechanism. By comparing one- (1D) and two dimensional (2D) results with those of 3D, we study how the increasing spatial multi-dimensionality affects the postbounce SN dynamics. The calculations were performed with an energy-dependent treatment of the neutrino transport that is solved by the isotropic diffusion source approximation scheme. In agreement with previous studies, our 1D model does not produce explosions for the 11.2 M⊙ star, while the neutrino-driven revival of the stalled bounce shock is obtained both in the 2D and 3D models. Our results show that convective matter motions below the gain radius become much more violent in 3D than 2D, making the neutrino luminosity larger for 3D. Enhanced by the large neutrino luminosity, the shock of the 3D model expands faster than that of the 2D. Our results show that the evolution of the shock is sensitive to the employed numerical resolutions. To draw a robust conclusion, 3D simulations with much higher numerical resolution and more advanced treatment of neutrino transport and gravity is needed.

Explosion Geometry of a Rotating 13 $\ M_{\odot}$ Star Driven by the SASI-Aided Neutrino-Heating Supernova Mechanism

Abstract By performing axisymmetric hydrodynamic simulations of core-collapse supernovae with spectral neutrino transport based on the isotropic diffusion source approximation scheme, we support the assumption that the neutrino-heating mechanism aided by the standing accretion shock instability (SASI) and convection can initiate an explosion of a 13$\ M_{\odot}$ star. Our results show that bipolar explosions are more likely to be associated with models that include rotation. We point out that models that form a north–south symmetric bipolar explosion can lead to larger explosion energies than the corresponding unipolar explosions can.