2D Radiation/Hydrodynamic Simulations of Core Collapse

Still of Accetion-Induced Collapse by Dessart et al. (astro-ph/0601603):

Abstract from the paper Features of the Acoustic Mechanism of Core-Collapse Supernova Explosions by Burrows, Livne, Dessart, Ott, and Murphy (accepted to Ap. J., 2006):

In the context of 2D, axisymmetric, multi-group, radiation/hydrodynamic simulations of core-collapse supernovae over the full 180$^{\circ}$ domain, we present an exploration of the progenitor dependence of the acoustic mechanism of explosion. All progenitor models we have tested with our Newtonian code explode. However, some of the cores left behind in our simulations, particularly for the more massive progenitors, have baryon masses that are larger than the canonical $\sim$1.5 M$_{\odot}$ of well-measured pulsars. We investigate the roles of the Standing-Accretion-Shock-Instability (SASI), the excitation of core g-modes, the generation of core acoustic power, the ejection of matter with r-process potential, the wind-like character of the explosion, and the fundamental anisotropy of the blasts. We find that the breaking of spherical symmetry is central to the supernova phenomenon, the delays to explosion can be long, the ejecta are radiation-dominated, and the blasts, when top-bottom asymmetric, are self-collimating. We see indications that the initial explosion energies are larger for the more massive progenitors, and smaller for the less massive progenitors, and that the neutrino contribution to the explosion energy may be an increasing function of progenitor mass. However, the explosion energy is still accumulating by the end of our simulations and has not converged to final values. The degree of explosion asymmetry we obtain is completely consistent with that inferred from the polarization measurements of Type Ic supernovae. Furthermore, we calculate for the first time the magnitude and sign of the net impulse on the core due to anisotropic neutrino emission and suggest that hydrodynamic and neutrino recoils in the context of our asymmetric explosions afford a natural mechanism for observed pulsar proper motions. We conclude that mechanical and fundamentally hydrodynamic mechanisms of supernova explosion may provide viable alternatives to the canonical neutrino mechanism. We discuss the numerical challenges faced when liberating the core to execute its natural multi-dimensional motions in light of the constraints of momentum and energy conservation, the need to treat self-gravity conservatively, and the difficulties of multi-dimensional neutrino transfer.

Abstract from the paper A New Algorithm for 2-D Transport for Astrophysical Simulations: I. General Formulation and Tests for the 1-D Spherical Case by I. Hubeny and A. Burrows (submitted to Ap.J., 2006):

We derive new equations using the {\it mixed-frame} approach for one- and two-dimensional (axisymmetric) time-dependent radiation transport and the associated couplings with matter. Our formulation is multi-group and multi-angle and includes anisotropic scattering, frequency(energy)-dependent scattering and absorption, complete velocity dependence to order $v/c$, rotation, and energy redistribution due to inelastic scattering. Hence, the 2D" realization is actually 6 1/2"-dimensional. The effects of radiation viscosity are automatically incorporated. Moreover, we develop Accelerated-Lambda-Iteration, Krylov subspace (GMRES), Discontinuous-Finite-Element, and Feautrier numerical methods for solving the equations and present the results of one-dimensional numerical tests of the new formalism. The virtues of the mixed-frame approach include simple velocity dependence with no velocity derivatives, straight characteristics, simple physical interpretation, and clear generalization to higher dimensions. Our treatment can be used for both photon and neutrino transport, but we focus on neutrino transport and applications to core-collapse supernova theory in the discussions and examples.

Abstract from the paper A New Mechanism for Core-Collapse Supernova Explosions by Burrows, Livne, Dessart, Ott, and Murphy (Accepted to Ap.J. November 28, 2005):

We present a new mechanism for core-collapse supernova explosions that relies upon acoustic power generated in the inner core as the driver. In our simulation using an 11-solar-mass progenitor, a strong advective-acoustic oscillation a la Foglizzo with a period of ~25-30 milliseconds (ms) arises ~200 ms after bounce. Its growth saturates due to the generation of secondary shocks, and kinks in the resulting shock structure funnel and regulate subsequent accretion onto the inner core. However, this instability is not the primary agent of explosion. Rather, it is the acoustic power generated in the inner turbulent region and most importantly by the excitation and sonic damping of core g-mode oscillations. An l=1 mode with a period of ~3 ms grows to be prominent around ~500 ms after bounce. The accreting protoneutron star is a self-excited oscillator. The associated acoustic power seen in our 11-solar-mass simulation is sufficient to drive the explosion. The angular distribution of the emitted sound is fundamentally aspherical. The sound pulses radiated from the core steepen into shock waves that merge as they propagate into the outer mantle and deposit their energy and momentum with high efficiency. The core oscillation acts like a transducer to convert accretion energy into sound. An advantage of the acoustic mechanism is that acoustic power does not abate until accretion subsides, so that it is available as long as it may be needed to explode the star.

Abstract from the paper A New Mechanism for the Gravitational Wave Signatures of Core-Collapse Supernovae by Ott, Burrows, Dessart, and Livne (accepted to Phys. Rev. Letters, 2006):

We present a new theory for the gravitational wave signatures of core-collapse supernovae. Previous studies identified axisymmetric rotating core collapse, core bounce, postbounce convection, and anisotropic neutrino emission as the primary processes and phases for the radiation of gravitational waves. Our results, which are based on axisymmetric, Newtonian radiation-hydrodynamics supernova simulations (Burrows et al. 2006), indicate that the dominant emission process of gravitational waves in core-collapse supernovae may be the oscillations of the protoneutron star core. The oscillations are predominantly of g-mode character, are excited hundreds of milliseconds after bounce, and typically last for several hundred milliseconds. Our results suggest that even nonrotating core-collapse supernovae should be visible to current LIGO-class detectors throughout the Galaxy, and depending on progenitor structure, possibly out to Megaparsec distances.

Abstract from the paper Multi-Dimensional Radiation-Hydrodynamics Simulations of the Accretion-Induced Collapse of White Dwarfs to Neutron Stars by Luc Dessart, Adam Burrows, Christian Ott, Eli Livne, S.-Y. Yoon, and Norbert Langer (Accepted to Ap.J. 2006):

We present 2.5D radiation-hydrodynamics simulations of the accretion-induced collapse (AIC) of white dwarfs, starting from 2D rotational equilibrium configurations, thereby accounting consistently for the effects of rotation prior to and after core collapse. We focus our study on 1.46-\mo and 1.92-\mo progenitors, with a central density of 5$\times$10$^{10}$\,g\,cm$^{-3}$, and initial rotational to gravitational energy ratios of 7.6$\times$10$^{-3}$ and 8.3$\times$10$^{-2}$. Efficient electron capture leads to the collapse to nuclear densities of these cores a few tens of milliseconds after the start of the simulations. The shock generated at bounce moves slowly, but steadily, outwards. Within 50--100\,ms, the stalled shock breaks out of the white dwarf along the poles. The blast is followed, 200-300\,ms after bounce, by a neutrino-driven wind that develops within the excavated white dwarf, in a cone of $\sim$40$^{\circ}$ opening angle about the pole, with a mass loss rate of 5-8$\times$10$^{-3}$\,\mo\,s$^{-1}$. The ejecta have an entropy on the order of 20-50\,$k_B$/baryon, and the electron fraction is bimodal, with peaks at 0.25 (due to the neutrino-driven wind) and 0.5 (due to the original blast and the wind along the pole). By the end of the simulations, at $\sgreat$600\,ms after bounce, the explosion energy has reached 3-4$\times$10$^{49}$erg and the outflowing mass has reached a few times 10$^{-3}$\,\mo. We estimate the asymptotic explosion energies to be within a factor of $\sim$2 of these values, thus significantly lower than those seen and inferred in the core collapse of massive progenitors. AIC of WDs thus represents one instance where a neutrino mechanism leads undoubtedly to a successful, albeit weak, explosion. While the total electron-neutrino luminosities are comparable to those observed in core collapse simulations, the effects of rotation are to reduce the $\nu_{\mu}$'' and $\bar{\nu}_e$ luminosities, the latter by one order of magnitude. Additionally, the neutron stars resulting from such AIC of white dwarfs are strongly aspherical, with neutrinospheres having disk-like shapes, akin to a polar-pinched oblate surface. In the faster rotating (1.92-\mo) model, this configuration results in a strong latitudinal dependence of the neutrino flux, enhanced in the polar direction and reduced in the equatorial direction compared to a non-rotating case. Such a latitudinal dependence is reminiscent of that observed and modeled in the winds of fast-rotating oblate luminous stars. The deleptonized region connected to the neutrinosphere has a butterfly, rather than a spherical shape. Moreover, the neutrino-driven wind originating in the vicinity of the distorted neutrinosphere sees a lower electron-neutrino flux further away from the poles, resulting in a latitudinal dependence of the electron fraction of the ejected material. In both models, a quasi-Keplerian 0.1-0.5\,\mo disk remains in the equatorial region, that should later be accreted by the neutron star on longer, viscous timescales. Compared to standard core collapse, our AIC simulations show no perceptible signs of convection associated with the negative lepton radial-gradient in the protoneutron star, no $l=1,2$ oscillations associated with the vortical-acoustic instability, no late time (protoneutron star) core oscillations, and no sizable neutron star kick. We estimate the gravitational wave emission by aspherical matter motion and anisotropic neutrino emission from our models. We find that gravitational waves from axisymmetric AIC events may be detected by current and future LIGO-class detectors from anywhere in the Milky Way.

Abstract from the paper Multi-Dimensional Radiation/Hydrodynamic Simulations of Protoneutron Star Convection by Luc Dessart, Adam Burrows, Eli Livne, and Christian Ott (Accepted to Ap.J. 2006):

Based on multi-dimensional multi-group radiation hydrodynamic simulations of core-collapse supernovae with the VULCAN/2D code, we study the physical conditions within and in the vicinity of the nascent protoneutron star (PNS). Conclusions of this work are threefold: First, {\bf as previously demonstrated}, we do not see any large-scale overturn of the inner PNS material. Second, we see no evidence of doubly-diffusive instabilities in the PNS, expected to operate on diffusion timescales of at least a second, but instead observe the presence of convection, within a radius range of 10-20\,km, operating with a timescale of a few milliseconds. Third, we identify unambiguously the presence of gravity waves, predominantly at 200-300\,milliseconds (ms) past core bounce, in the region separating the convective zones inside the PNS and between the PNS surface and the shocked region. Our numerical study is an improvement over past work in a number of ways: we follow the evolution of the collapsing envelope from $\sim$200\,ms before bounce to $\sim$500\,ms after bounce; the spatial grid switches from Cartesian inside to spherical outside, permitting a handling of the inner PNS region at good spatial resolution, all the way inside to the center, and without severe Courant-time limitation; neutrino-transport is treated with a Multi-Group, Flux-Limited-Diffusion (MGFLD) approach, well suited for the study of the PNS, {\it i.e.}, in regions where the neutrino mean-free-path is small. With this configuration, VULCAN/2D has the ability to simulate doubly-diffusive instabilities, if present. Convection, directly connected to the PNS, is found to occur in two distinct regions: between 10 and 20\,km, coincident with the region of negative lepton gradient, and exterior to the PNS above 50\,km. These two regions are separated by an interface, which shows no sizable outward or inward motion and efficiently shelters the inner PNS. The PNS is also the site of gravity waves, excited by the convection in the outer convective zone. In the PNS, convection is always confined to a region between 10 and 20\,km, {\it i.e.}, within the neutrinospheric radii for all neutrino energies above just a few MeV. We find that such motions do not appreciably enhance the $\nu_e$ neutrino luminosity, and that they can enhance the $\bar{\nu}_e$ and $\nu_{\mu}$" luminosities by no more than $\sim$15\% and $\sim$30\%, respectively, during the first post-bounce $\sim$100 ms, after which the optical depth barrier between the inner convection and the neutrinospheres effectively isolates one from the other, terminating even this modest enhancement. PNS convection is thus found to be a secondary feature of the core-collapse phenomenon, rather than a decisive ingredient for a successful explosion. Furthermore, the typical timescale associated with such convective transport is of the order of a few milliseconds, and thus is at least a thousand times faster than typical growth rates for instabilities associated with neutrino-mediated thermal and lepton diffusion. Such doubly-diffusive instabilities are, therefore, unlikely to play a substantial role in the early critical phases of the PNS. We conclude that inner PNS motions do not bear importantly on the potential success of core-collapse supernovae explosions.

Abstract from the paper Anisotropies in the Neutrino Fluxes and Heating Profiles in Two-dimensional, Time-dependent, Multi-group Radiation Hydrodynamics Simulations of Rotating Core-Collapse Supernovae by R. Walder, A. Burrows, C.D. Ott, E. Livne, I. Lichtenstadt, and M. Jarrah (Ap.J., 626, 317, 2005):

Using the 2D multi-group, flux-limited diffusion version of the code VULCAN/2D, that also incorporates rotation, we have calculated the collapse, bounce, shock formation, and early post-bounce evolutionary phases of a core-collapse supernova for a variety of initial rotation rates. This is the first series of such multi-group calculations undertaken in supernova theory with fully multi-D tools. We find that though rotation generates pole-to-equator angular anisotropies in the neutrino radiation fields, the magnitude of the asymmetries is not as large as previously estimated. The finite width of the neutrino decoupling surfaces and the significant emissivity above the $\tau=2/3$ surface moderate the angular contrast. Moreover, we find that the radiation field is always more spherically symmetric than the matter distribution, with its plumes and convective eddies. The radiation field at a point is an integral over many sources from the different contributing directions. As such, its distribution is much smoother than that of the matter and has very little power at high spatial frequencies. We present the dependence of the angular anisotropy of the neutrino fields on neutrino species, neutrino energy, and initial rotation rate. Only for our most rapidly rotating model do we start to see qualitatively different hydrodynamics, but for the lower rates consistent with the pre-collapse rotational profiles derived in the literature the anisotropies, though interesting, are modest. This does not mean that rotation does not play a key role in supernova dynamics. The decrease in the effective gravity due to the centripetal effect can be quite important. Rather, it means that when a realistic mapping between initial and final rotational profiles and 2D multi-group radiation-hydrodynamics are incorporated into collapse simulations the anisotropy of the radiation fields may be only a secondary, not a pivotal factor, in the supernova mechanism.

Abstract from the paper Two-dimensional, Time-dependent, Multi-group, Multi-angle Radiation Hydrodynamics Test Simulation in the Core-Collapse Supernova Context by Livne, Burrows, Walder, et al. (Ap.J., 609, 277, 2004):
We have developed a time-dependent, multi-energy-group, and multi-angle (Sn) Boltzmann transport scheme for radiation hydrodynamics simulations, in one and two spatial dimensions. The implicit transport is coupled to both 1D (spherically-symmetric) and 2D (axially-symmetric) versions of the explicit Newtonian hydrodynamics code VULCAN. The 2D variant, VULCAN/2D, can be operated in general structured or unstructured grids and though the code can address many problems in astrophysics it was constructed specifically to study the core-collapse supernova problem. Furthermore, VULCAN/2D can simulate the radiation/hydrodynamic evolution of differentially rotating bodies. We summarize the equations solved and methods incorporated into the algorithm and present results of a time-dependent 2D test calculation. A more complete description of the algorithm is postponed to another paper. We highlight a 2D test run that follows for 22 milliseconds the immediate post-bounce evolution of a collapsed core. We present the relationship between the anisotropies of the overturning matter field and the distribution of the corresponding flux vectors, as a function of energy group. This is the first 2D multi-group, multi-angle, time-dependent radiation/hydro calculation ever performed in core collapse studies. Though the transport module of the code is not gray and does not use flux limiters (however, there is a flux-limited variant of VULCAN/2D), it still does not include energy redistribution and most velocity-dependent terms.

Movies:

Here below, we present representative movies of 2D radiation-hydrodynamic simulations of core-collapse supernovae using the VULCAN/2D code, either in MGFLD mode or Full transport mode. For further information on this work please feel free to contact Adam Burrows (aburrows@princeton.edu) at your convenience. (Click here for first paper on VULCAN/2D.)

A Selection of Movies (AVI,Mpeg):