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.
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