BETHE-Hydro: An Arbitrary Lagrangian-Eulerian Multi-dimensional Hydrodynamics Code for Astrophysical Simulations

In this paper, we describe a new hydrodynamics code for 1D and 2D astrophysical simulations, BETHE-hydro, that uses time-dependent, arbitrary, unstructured grids. The core of the hydrodynamics algorithm is an arbitrary Lagrangian-Eulerian (ALE) approach, in which the gradient and divergence operators are made compatible using the support-operator method. We present 1D and 2D gravity solvers that are finite differenced using the support-operator technique, and the resulting system of linear equations are solved using the tridiagonal method for 1D simulations and an iterative multigrid-preconditioned conjugate-gradient method for 2D simulations. Rotational terms are included for 2D calculations using cylindrical coordinates. We document an incompatibility between a subcell pressure algorithm to suppress hourglass motions and the subcell remapping algorithm and present a modified subcell pressure scheme that avoids this problem. Strengths of this code include a straightforward structure, enabling simple inclusion of additional physics packages, the ability to use a general equation of state, and most importantly, the ability to solve self-gravitating hydrodynamic flows on time-dependent, arbitrary grids. In what follows, we describe in detail the numerical techniques employed and, with a large suite of tests, demonstrate that BETHE-hydro finds accurate solutions with 2$^{nd}$-order convergence.Comment: 51 pages in emulateapj, including 25 figures, replace with version accepted to ApJS, corrected typos and included minor referee's comment

Dimensional Dependence of the Hydrodynamics of Core-Collapse Supernovae

The multidimensional character of the hydrodynamics in core-collapse supernova (CCSN) cores is a key facilitator of explosions. Unfortunately, much of this work has necessarily been performed assuming axisymmetry and it remains unclear whether or not this compromises those results. In this work, we present analyses of simplified two- and three-dimensional CCSN models with the goal of comparing the multidimensional hydrodynamics in setups that differ only in dimension. Not surprisingly, we find many differences between 2D and 3D models. While some differences are subtle and perhaps not crucial to understanding the explosion mechanism, others are quite dramatic and make interpreting 2D CCSN models problematic. In particular, we find that imposing axisymmetry artificially produces excess power at the largest spatial scales, power that has been deemed critical in the success of previous explosion models and has been attributed solely to the standing accretion shock instability. Nevertheless, our 3D models, which have an order of magnitude less power on large scales compared to 2D models, explode earlier. Since we see explosions earlier in 3D than in 2D, the vigorous sloshing associated with the large scale power in 2D models is either not critical in any dimension or the explosion mechanism operates differently in 2D and 3D. Possibly related to the earlier explosions in 3D, we find that about 25% of the accreted material spends more time in the gain region in 3D than in 2D, being exposed to more integrated heating and reaching higher peak entropies, an effect we associate with the differing characters of turbulence in 2D and 3D. Finally, we discuss a simple model for the runaway growth of buoyant bubbles that is able to quantitatively account for the growth of the shock radius and predicts a critical luminosity relation.Comment: Submitted to the Astrophysical Journa

A Force Explosion Condition for Spherically Symmetric Core-collapse Supernovae

Understanding which stars explode leaving behind neutron stars and which stars collapse forming black holes remains a fundamental astrophysical problem. We derive an analytic explosion condition for spherically symmetric core-collapse supernovae. The derivation starts with the exact governing equations, considers the balance of integral forces, includes the important dimensionless parameters, and includes an explicit set of self-consistent approximations. The force explosion condition is $\tilde{L}_\nu\tau_g - 0.06 \tilde{\kappa} > 0.38$, and only depends upon two dimensionless parameters. The first compares the neutrino power deposited in the gain region with the accretion power, $\tilde{L}_\nu \tau_g = L_{\nu} \tau_g R_{\rm NS}/ ( G \dot{M} M_{\rm NS})$. The second, $\tilde{\kappa} = \kappa \dot{M} / \sqrt{G M_{\rm NS} R_{\rm NS}}$, parameterizes the neutrino optical depth in the accreted matter near the neutron-star surface. Over the years, many have proposed approximate explosion conditions: the critical neutrino-luminosity, ante-sonic, and timescale conditions. We are able to derive these other conditions from the force explosion condition, which unifies them all. Using numerical, steady-state and fully hydrodynamic solutions, we test the explosion condition. The success of these tests is promising in two ways. One, the force explosion condition helps to illuminate the underlying physics of explosions. Two, this condition may be a useful explosion diagnostic for more realistic, three-dimensional radiation hydrodynamic core-collapse simulations.Comment: Figure 10 most clearly highlights the fidelity and the efficacy of the Force Explosion Condition. If you are interested in testing the explosion condition with CCSN simulations, feel free to contact u

Criteria for Core-Collapse Supernova Explosions by the Neutrino Mechanism

We investigate the criteria for successful core-collapse supernova explosions by the neutrino mechanism. We find that a critical-luminosity/mass-accretion-rate condition distinguishes non-exploding from exploding models in hydrodynamic one-dimensional (1D) and two-dimensional (2D) simulations. We present 95 such simulations that parametrically explore the dependence on neutrino luminosity, mass accretion rate, resolution, and dimensionality. While radial oscillations mediate the transition between 1D accretion (non-exploding) and exploding simulations, the non-radial standing accretion shock instability characterizes 2D simulations. We find that it is useful to compare the average dwell time of matter in the gain region with the corresponding heating timescale, but that tracking the residence time distribution function of tracer particles better describes the complex flows in multi-dimensional simulations. Integral quantities such as the net heating rate, heating efficiency, and mass in the gain region decrease with time in non-exploding models, but for 2D exploding models, increase before, during, and after explosion. At the onset of explosion in 2D, the heating efficiency is $\sim$2% to $\sim$5% and the mass in the gain region is $\sim$0.005 M_{\sun} to $\sim$0.01 M_{\sun}. Importantly, we find that the critical luminosity for explosions in 2D is $\sim$70% of the critical luminosity required in 1D. This result is not sensitive to resolution or whether the 2D computational domain is a quadrant or the full 180$^{\circ}$. We suggest that the relaxation of the explosion condition in going from 1D to 2D (and to, perhaps, 3D) is of a general character and is not limited by the parametric nature of this study.Comment: 32 pages in emulateapj, including 17 figures, accepted for publication in ApJ, included changes suggested by the refere

The Force Explosion Condition is Consistent with Spherically Symmetric CCSN Explosions

One of the major challenges in Core-collapse Supernova (CCSN) theory is to predict which stars explode and which collapse to black holes. Gogilashvili and Murphy (2022) derived an analytic force explosion condition (FEC) and showed that the FEC is consistent with CCSN simulations that use the light-bulb approximation for neutrino heating and cooling. In this follow-up manuscript, we show that the FEC is consistent with the explosion condition when using actual neutrino transport in GR1D simulations (O'CONNOR 2015). Since most 1D simulations do not explode, to facilitate this test, we enhance the heating efficiency within the gain region. To compare the analytic FEC and radiation-hydrodynamic simulations, this manuscript also presents a practical translation of the physical parameters. For example: we replace the neutrino power deposited in the gain region, $L_\nu\tau_g$, with the net neutrino heating in the gain region; rather than assuming that $\dot{M}$ is the same everywhere, we calculate $\dot{M}$ within the gain region; and we use the neutrino opacity at the gain radius. With small, yet practical modifications, we show that the FEC predicts the explosion conditions in spherically symmetric CCSN simulations that use neutrino transport.Comment: Figure 5 most clearly highlights the fidelity and the efficacy of the Force Explosion Conditio