arXiv subjects
Publications and source records attributed to J. C. Niemeyer.
In this article we discuss the first simulations of two- and three-dimensional Type Ia supernovae with an improved hydrodynamics code. After describing the various enhancements, the obtained results are compared to those of earlier code versions, observational data and the findings of other researchers in this field.
Following up on earlier work on this topic (Reinecke et al. 1999, A&A 347, pp. 724 and 739), we present an improved set of numerical models for simulations of white dwarfs exploding as Type Ia supernovae (SNe Ia). Two-dimensional simulations were used to test the reliability and numerical robustness of these algorithms; the results indicate that integral quantities like the total energy release are insensitive to changes of the grid resolution (above a certain threshold), which was not the case for our former code. The models were further enhanced to allow fully three-dimensional simulations of SNe Ia. A direct comparison of a 2D and a 3D calculation with identical initial conditions shows that the explosion is considerably more energetic in three dimensions; this is most likely caused by the assumption of axisymmetry in 2D, which inhibits the growth of flame instabilities in the azimuthal direction and thereby decreases the flame surface.
It is shown that varying speed of light cosmology follows from a string-inspired minimal length uncertainty relation. Due to the reduction of the available phase space volume per quantum mode at short wavelengths, the equation of state of ultrarelativistic particles stiffens at very high densities. This causes a stronger than usual deceleration of the scale factor which competes with a higher than usual propagation speed of the particles. Various measures for the effective propagation speed are analyzed: the group and phase velocity in the high energy tail, the thermal average of the group and phase velocity, and the speed of sound. Of these three groups, only the first provides a possible solution to the cosmological horizon problem.
It has been pointed out that the perturbation spectrum predicted by inflation may be sensitive to a natural ultraviolet cutoff, thus potentially providing an experimentally accessible window to aspects of Planck scale physics. A priori, a natural ultraviolet cutoff could take any form, but a fairly general classification of possible Planck scale cutoffs has been given. One of those categorized cutoffs, also appearing in various studies of quantum gravity and string theory, has recently been implemented into the standard inflationary scenario. Here, we continue this approach by investigating its effects on the predicted perturbation spectrum. We find that the size of the effect depends sensitively on the scale separation between cutoff and horizon during inflation.
We investigate the insensitivity of the predictions of inflationary models with respect to modifications of Planck energy physics. The modification we consider consists in replacing the usual dispersion relation by nonlinear ones. This way of addressing the problem has recently recieved attention and contradictory results were found. Our main result is to show that the adiabaticity of the mode propagation and the separation of two scales of interest, the Planck scale and the cosmological horizon scale, are sufficient conditions for the predictions to be unchanged. We then show that almost all models satisfy the first condition if the second is met. Therefore the introduction of a nonlinear dispersion is unlikely to have any discernable effects on the power spectrum of cosmological perturbations.
Type Ia supernovae (SN Ia) are generally believed to be the result of the thermonuclear disruption of Chandrasekhar-mass carbon-oxygen white dwarfs, mainly because such thermonuclear explosions can account for the right amount of nickel, which is needed to explain the light curves and the late-time spectra, and the abundances of intermediate-mass nuclei which dominate the spectra near maximum light. Because of their enormous brightness and apparent homogeneity SN Ia have become an important tool to measure cosmological parameters. In this article the present understanding of the physics of thermonuclear explosions is reviewed. In particular, we focus our attention on subsonic ("deflagration") fronts, i.e. we investigate fronts propagating by heat diffusion and convection rather than by compression. Models based upon this mode of nuclear burning have been applied very successfully to the SN Ia problem, and are able to reproduce many of their observed features remarkably well. However, the models also indicate that SN Ia may differ considerably from each other, which is of importance if they are to be used as standard candles.
The implementation of a Planck-scale high frequency and short wavelength cutoff in quantum theories on expanding backgrounds may have potentially nontrivial implications, such as the breaking of local Lorentz invariance and the existence of a yet unknown mechanism for the creation of vacuum modes. In scenarios where inflation begins close to the cutoff scale, these effects could have observable consequences as trans-Planckian modes are redshifted to cosmological scales. In close analogy with similar studies of Hawking radiation, a simple theory of a minimally coupled scalar field in de Sitter space is studied, with a high frequency cutoff imposed by a nonlinear dispersion relation. Under certain conditions the model predicts deviations from the standard inflationary scenario. We also comment on the difficulties in generalizing fluid models of Hawking radiation to cosmological space-times.
Because calibrated light curves of Type Ia supernovae have become a major tool to determine the local expansion rate of the Universe and also its geometrical structure, considerable attention has been given to models of these events over the past couple of years. There are good reasons to believe that perhaps most Type Ia supernovae are the explosions of white dwarfs that have approached the Chandrasekhar mass, M_ch ~ 1.39 M_sun, and are disrupted by thermonuclear fusion of carbon and oxygen. However, the mechanism whereby such accreting carbon-oxygen white dwarfs explode continues to be uncertain. Recent progress in modeling Type Ia supernovae as well as several of the still open questions are addressed in this review. Although the main emphasis will be on studies of the explosion mechanism itself and on the related physical processes, including the physics of turbulent nuclear combustion in degenerate stars, we also discuss observational constraints.
Type Ia supernovae (SN Ia) are generally believed to be the result of the thermonuclear disruption of Chandrasekhar-mass carbon-oxygen white dwarfs, mainly because such thermonuclear explosions can account for the right amount of Ni-56, which is needed to explain the light curves and the late-time spectra, and the abundances of intermediate-mass nuclei which dominate the spectra near maximum light. Because of their enormous brightness and apparent homogeneity SN Ia have become an important tool to measure cosmological parameters. In this article the present understanding of the physics of thermonuclear explosions is reviewed. In particular, we focus our attention on subsonic (``deflagration'') fronts, i.e. we investigate fronts propagating by heat diffusion and convection rather than by compression. Models based upon this mode of nuclear burning have been applied very successfully to the SN Ia problem, and are able to reproduce many of their observed features remarkably well. However, the models also indicate that SN Ia may differ considerably from each other, which is of importance if they are to be used as standard candles.
We present a new way of modeling turbulent thermonuclear deflagration fronts in Chandrasekhar-mass white dwarfs, consisting of carbon and oxygen, undergoing a type Ia supernova explosion. Our approach is a front capturing/tracking hybrid scheme, based on a level set method, which treats the front as a mathematical discontinuity and allows for full coupling between the front geometry and the flow field. First results of the method applied to the problem of type Ia supernovae are discussed. It will be shown that even in 2-D and even with a physically motivated sub-grid model numerically ``converged'' results are difficult to obtain.
The burning regimes encountered by laminar deflagrations and ZND detonations propagating through helium-rich compositions in the presence of buoyancy-driven turbulence are analyzed. Particular attention is given to models of X-ray bursts which start with a thermonuclear runaway on the surface of a neutron star, and the thin shell helium instability of intermediate-mass stars. In the X-ray burst case, turbulent deflagrations propagating in the lateral or radial directions encounter a transition from the distributed regime to the flamlet regime at a density of 10^8 g cm^{-3}. In the radial direction, the purely laminar deflagration width is larger than the pressure scale height for densities smaller than 10^6 g cm^{-3}. Self-sustained laminar deflagrations travelling in the radial direction cannot exist below this density. Similarily, the planar ZND detonation width becomes larger than the pressure scale height at 10^7 g cm^{-3}, suggesting that a steady-state, self-sustained detonations cannot come into existance in the radial direction. In the thin helium shell case, turbulent deflagrations travelling in the lateral or radial directions encounter the distributed regime at densities below 10^7 g cm^{-3}, and the flamelet regime at larger densities. In the radial direction, the purely laminar deflagration width is larger than the pressure scale height for densities smaller than 10^4 g cm^{-3}, indicating that steady-state laminar deflagrations cannot form below this density. The planar ZND detonation width becomes larger than the pressure scale height at 5 10^4 g cm^{-3}, suggesting that steady-state, self-sustained detonations cannot come into existance in the radial direction.
We present a statistical model which shows the influence of turbulence on a thermonuclear flame propagating in C+O white dwarf matter. Based on a Monte Carlo description of turbulence, it provides a method for investigating the physics in the so-called distributed burning regime. Using this method we perform numerical simulations of turbulent flames and show that in this particular regime the flamelet model for the turbulent flame velocity loses its validity. In fact, at high turbulent intensities burning in the distributed regime can lead to a deceleration of the turbulent flame and thus induces a competing process to turbulent effects that cause a higher flame speed. It is also shown that in dense C+O matter turbulent heat transport is described adequately by the Peclet number, Pe, rather than by the Reynolds number, which means that flame propagation is decoupled from small-scale turbulence. Finally, at the onset of our results we argue that the available turbulent energy in an exploding C+O white dwarf is probably too low in order to make a deflagration to detonation transition possible.
The mechanism for deflagration-detonation-transition (DDT) by turbulent preconditioning, suggested to explain the possible occurrence of delayed detonations in Type Ia supernova explosions, is argued to be conceptually inconsistent. It relies crucially on diffusive heat losses of the burned material on macroscopic scales. Regardless of the amplitude of turbulent velocity fluctuations, the typical gradient scale for temperature fluctuations is shown to be the laminar flame width or smaller, rather than the factor of thousand more required for a DDT. Furthermore, thermonuclear flames cannot be fully quenched in regions much larger than the laminar flame width as a consequence of their simple ``chemistry''. Possible alternative explosion scenarios are briefly discussed.
Microscopic turbulence-flame interactions of thermonuclear fusion flames occuring in Type Ia Supernovae were studied by means of incompressible direct numerical simulations with a highly simplified flame description. The flame is treated as a single diffusive scalar field with a nonlinear source term. It is characterized by its Prandtl number, Pr << 1, and laminar flame speed, S_L. We find that if S_L ~ u', where u' is the rms amplitude of turbulent velocity fluctuations, the local flame propagation speed does not significantly deviate from S_L even in the presence of velocity fluctuations on scales below the laminar flame thickness. This result is interpreted in the context of subgrid-scale modeling of supernova explosions and the mechanism for deflagration-detonation-transitions.
First results of simulations are presented which compute the dynamical evolution of a Chandrasekhar-mass white dwarf, consisting of equal amounts of carbon and oxygen, from the onset of violent thermonuclear burning, by means of a new two-dimensional numerical code. Since in the interior of such a massive white dwarf nuclear burning progresses on microscopic scales as a sharp discontinuity, a so-called flamelet, which cannot be resolved by any numerical scheme, and since on macroscopic scales the burning front propagates due to turbulence, we make an attempt to model both effects explicitly in the framework of a finite-volume hydrodynamics code. Turbulence is included by a sub-grid model, following the spirit of large eddy simulations, and the well-localized burning front is treated by means of a level set, which allows us to compute the geometrical structure of the front more accurately than with previous methods. The only free parameters of our simulations are the location and the amount of nuclear fuel that is ignited as an initial perturbation. We find that models in which explosive carbon burning is ignited at the center remain bound by the time the front reaches low densities, where we stopped the computations because our description of combustion is no longer applicable. In contrast, off-center ignition models give rise to explosions which, however, are still too weak for typical Type Ia supernovae. Possible reasons for this rather disappointing result are discussed.
We present a new way of modeling deflagration fronts in reactive fluids, the main emphasis being on turbulent thermonuclear deflagration fronts in white dwarfs undergoing a Type Ia supernova explosion. Our approach is based on a level set method which treats the front as a mathematical discontinuity and allows full coupling between the front geometry and the flow field. With only minor modifications, this method can also be applied to describe contact discontinuities. Two different implementations are described and their physically correct behaviour for simple testcases is shown. First results of the method applied to the concrete problems of Type Ia supernovae and chemical hydrogen combustion are briefly discussed; a more extensive analysis of our astrophysical simulations is given in (Reinecke et al. 1998, MPA Green Report 1122b).
We present a numerical investigation of the gravitational collapse of horizon-size density fluctuations to primordial black holes (PBHs) during the radiation-dominated phase of the Early Universe. The collapse dynamics of three different families of initial perturbation shapes, imposed at the time of horizon crossing, is computed. The perturbation threshold for black hole formation, needed for estimations of the cosmological PBH mass function, is found to be $δ_{\rm c} \approx 0.7$ rather than the generally employed $δ_{\rm c} \approx 1/3$, if $δ$ is defined as $ΔM/\mh$, the relative excess mass within the initial horizon volume. In order to study the accretion onto the newly formed black holes, we use a numerical scheme that allows us to follow the evolution for long times after formation of the event horizon. In general, small black holes (compared to the horizon mass at the onset of the collapse) give rise to a fluid bounce that effectively shuts off accretion onto the black hole, while large ones do not. In both cases, the growth of the black hole mass owing to accretion is insignificant. Furthermore, the scaling of black hole mass with distance from the formation threshold, known to occur in near-critical gravitational collapse, is demonstrated to apply to primordial black hole formation.
Primordial black holes (PBHs) may form in the early universe when pre-existing adiabatic density fluctuations enter into the cosmological horizon and recollapse. It has been suggested that PBH formation may be facilitated when fluctuations enter into the horizon during a strongly first-order phase transition which proceeds in approximate equilibrium. We employ general-relativistic hydrodynamics numerical simulations in order to follow the collapse of density fluctuations during first-order phase transitions. We find that during late stages of the collapse fluctuations separate into two regimes, an inner part existing exclusively in the high-energy density phase with energy density $ε_{\rm h}$, surrounded by an outer part which exists exclusively in the low-energy density phase with energy density $ε_{\rm h}-L$, where $L$ is the latent heat of the transition. We confirm that the fluctuation density threshold $δε/ε$ required for the formation of PBHs during first-order transitions decreases with increasing $L$ and falls below that for PBH formation during ordinary radiation dominated epochs. Our results imply that, in case PBHs form at all in the early universe, their mass spectrum is likely dominated by the approximate horizon masses during epochs when the universe undergoes phase transitions.