Development of a density inversion in driven granular gases

Granular materials fluidized by a rapidly vibrating bottom plate often develop a fascinating density inversion: a heavier layer of granulate supported by a lower-density region. We employ the Navier-Stokes granular hydrodynamics to follow a density inversion as it develops in time. Assuming a dilute low-Mach-number flow, we derive a reduced time-dependent model of the late stage of the dynamics. The model looks especially simple in the Lagrangian coordinates. The time-dependent solution describes the growth of a density peak at an intermediate height. A transient temperature minimum is predicted to develop in the region of the density peak. The temperature minimum disappears at later times, as the system approaches the steady state. At late times, the predictions of the low-Mach-number model are in good agreement with a numerical solution of the full hydrodynamic equations. At an early stage of the dynamics, pressure oscillations are predicted.Comment: 13 pages, 6 figures. To appear in "Granular Gas Dynamics", ed. by T. Poeschel and N. Brilliantov, vol. 624 of "Lecture Notes in Physics", Springe

Imploding ignition waves: I. one dimensional analysis

We show that converging spherical and cylindrical shock waves may ignite a detonation wave in a combustible medium, provided the radius at which the shocks become strong exceeds a critical radius, R_c. An approximate analytic expression for R_c is derived for an ideal gas equation of state and a simple (power-law-Arrhenius) reaction law, and shown to reproduce the results of numerical solutions. For typical acetylene-air experiments we find R_c~0.1 mm (spherical) and R_c~1 mm (cylindrical). We suggest that the deflagration to detonation transition (DDT) observed in these systems may be due to converging shocks produced by the turbulent deflagration flow, which reaches sub (but near) sonic velocities on scales >>R_c. Our suggested mechanism differs from that proposed by Zel'dovich et al., in which a fine-tuned spatial gradient in the chemical induction time is required to be maintained within the turbulent deflagration flow. Our analysis may be readily extended to more complicated equations of state and reaction laws. An order of magnitude estimate of R_c within a white dwarf at the pre-detonation conditions believed to lead to Type Ia supernova explosions is 0.1 km, suggesting that our proposed mechanism may be relevant for DDT initiation in these systems. The relevance of our proposed ignition mechanism to DDT initiation may be tested by both experiments and numerical simulations.Comment: 12 pages, 10 figures. Somewhat modified, published in Ap

Early emission from type Ia supernovae

A unique feature of deflagration-to-detonation (DDT) white dwarf explosion models of SNe of type Ia is the presence of a strong shock wave propagating through the outer envelope. We consider the early emission expected in such models, which is produced by the expanding shock-heated outer part of the ejecta and precedes the emission driven by radioactive decay. We expand on earlier analyses by considering the modification of the pre-detonation density profile by the weak-shocks generated during the deflagration phase, the time evolution of the opacity, and the deviation of the post-shock equation of state from that obtained for radiation pressure domination. A simple analytic model is presented and shown to provide an acceptable approximation to the results of 1D numerical DDT simulations. Our analysis predicts a thousand second long UV/optical flash with a luminosity of ~1 to 3*1e39 erg/s. Lower luminosity corresponds to faster (turbulent) deflagration velocity. The predicted luminosity of the UV flash is an order of magnitude lower than that of earlier estimates, and is expected to be strongly suppressed at times longer than an hour due to the deviation from pure radiation domination.Comment: 10 pages, 4 figure

Multi-Dimensional Explorations in Supernova Theory

In this paper, we bring together various of our published and unpublished findings from our recent 2D multi-group, flux-limited radiation hydrodynamic simulations of the collapse and explosion of the cores of massive stars. Aided by 2D and 3D graphical renditions, we motivate the acoustic mechanism of core-collapse supernova explosions and explain, as best we currently can, the phases and phenomena that attend this mechanism. Two major foci of our presentation are the outer shock instability and the inner core g-mode oscillations. The former sets the stage for the latter, which damp by the generation of sound. This sound propagates outward to energize the explosion and is relevant only if the core has not exploded earlier by some other means. Hence, it is a more delayed mechanism than the traditional neutrino mechanism that has been studied for the last twenty years since it was championed by Bethe and Wilson. We discuss protoneutron star convection, accretion-induced-collapse, gravitational wave emissions, pulsar kicks, the angular anisotropy of the neutrino emissions, a subset of numerical issues, and a new code we are designing that should supercede our current supernova code VULCAN/2D. Whatever ideas last from this current generation of numerical results, and whatever the eventual mechanism(s), we conclude that the breaking of spherical symmetry will survive as one of the crucial keys to the supernova puzzle.Comment: To be published in the "Centennial Festschrift for Hans Bethe," Physics Reports (Elsevier: Holland), ed. G.E. Brown, E. van den Heuvel, and V. Kalogera, 200

Type II-Plateau supernova radiation: dependencies on progenitor and explosion properties

We explore the properties of Type II-Plateau (II-P) supernovae (SNe) together with their red-supergiant (RSG) star progenitors. Using MESA STAR, we modulate the parameters (e.g., mixing length, overshoot, rotation, metallicity) that control the evolution of a 15Msun main-sequence star to produce a variety of physical pre-SN models and SN II-P ejecta. We extend previous modeling of SN II-P radiation to include photospheric and nebular phases, as well as multi-band light curves and spectra. Our treatment does not assume local thermodynamic equilibrium, is time dependent, treats explicitly the effects of line blanketing, and incorporates non-thermal processes. We find that the color properties of SNe II-P require large model atoms for FeI and FeII, much larger than adopted in Dessart & Hillier (2011). The color properties also imply RSG progenitors of limited extent (~500Rsun) --- larger progenitor stars produce a SN II-P radiation that remains too blue for too long. This finding calls for a reduction of RSG radii, perhaps through a strengthening of convective energy transport in RSG envelopes. Increased overshoot and rotation reduce the ratio of ejecta to helium-core mass, similarly to an increase in main-sequence mass, and thus complicate the inference ofprogenitor masses. In contrast to the great sensitivity on progenitor radius, SN II-P color evolution appears insensitive to variations in explosion energy. Finally, we document the numerous SN II-P signatures that vary with progenitor metallicity, revealing their potential for metallicity determinations in the nearby and distant Universe.Comment: Paper accepted to MNRA

Results From Core-Collapse Simulations with Multi-Dimensional, Multi-Angle Neutrino Transport

We present new results from the only 2D multi-group, multi-angle calculations of core-collapse supernova evolution. The first set of results from these calculations was published in Ott et al. (2008). We have followed a nonrotating and a rapidly rotating 20 solar mass model for ~400 ms after bounce. We show that the radiation fields vary much less with angle than the matter quantities in the region of net neutrino heating. This obtains because most neutrinos are emitted from inner radiative regions and because the specific intensity is an integral over sources from many angles at depth. The latter effect can only be captured by multi-angle transport. We then compute the phase relationship between dipolar oscillations in the shock radius and in matter and radiation quantities throughout the postshock region. We demonstrate a connection between variations in neutrino flux and the hydrodynamical shock oscillations, and use a variant of the Rayleigh test to estimate the detectability of these neutrino fluctuations in IceCube and Super-K. Neglecting flavor oscillations, fluctuations in our nonrotating model would be detectable to ~10 kpc in IceCube, and a detailed power spectrum could be measured out to ~5 kpc. These distances are considerably lower in our rapidly rotating model or with significant flavor oscillations. Finally, we measure the impact of rapid rotation on detectable neutrino signals. Our rapidly rotating model has strong, species-dependent asymmetries in both its peak neutrino flux and its light curves. The peak flux and decline rate show pole-equator ratios of up to ~3 and ~2, respectively.Comment: 13 pages, 9 figures, ApJ accepted. Replaced with accepted versio