Maximum Brightness and Post-Maximum Decline of Light Curves of SN~Ia: A Comparison of Theory and Observations

We compare the observed correlations between the maximum brightness, postmaximum decline rate and color at maximum light of Type Ia supernovae (SN Ia) with model predictions. The observations are based on a total of 40 SN Ia with 29 SN of the Calan Tololo Supernova Search and 11 local SN which cover a range of 2 mag in the absolute visual brightness. The observed correlations are not tight, one dimensional relations. Supernovae with the same postmaximum decline or the same color have a spread in visual magnitude of about 0.7 mag. The dispersion in the color-magnitude relation may result from uncertainties in the distance determinations or the interstellar reddening within the host galaxy. The dispersion in the decline rate-magnitude relation suggests that an intrinsic spread in the supernova properties exists that cannot be accounted for by any single relation between visual brightness and postmaximum decline. Theoretical correlations are derived from a grid of models which encompasses delayed detonations, pulsating delayed detonations, the merging scenario and helium detonations. We find that the observed correlations can be understood in terms of explosions of Chandrasekhar mass white dwarfs. Our models show an intrinsic spread in the relations of about 0.5 mag in the maximum brightness and about 0.1 mag in the B-V color. Our study provides strong evidence against the mechanism of helium detonation for subluminous, red SN Ia.Comment: 7 pages, 3 figures, macros ''aaspp.sty'. LaTeX Style. Astrophysical Journal Letters, submitted Jul. 1995, revised Aug. 1995, resubmitted Sep. 199

Local Ignition in Carbon/Oxygen White Dwarfs -- I: One-zone Ignition and Spherical Shock Ignition of Detonations

The details of ignition of Type Ia supernovae remain fuzzy, despite the importance of this input for any large-scale model of the final explosion. Here, we begin a process of understanding the ignition of these hotspots by examining the burning of one zone of material, and then investigate the ignition of a detonation due to rapid heating at single point. We numerically measure the ignition delay time for onset of burning in mixtures of degenerate material and provide fitting formula for conditions of relevance in the Type Ia problem. Using the neon abundance as a proxy for the white dwarf metallicity, we then find that ignition times can decrease by ~20% with addition of even 5% of neon by mass. When temperature fluctuations that successfully kindle a region are very rare, such a reduction in ignition time can increase the probability of ignition by orders of magnitude. If the neon comes largely at the expense of carbon, a similar increase in the ignition time can occur. We then consider the ignition of a detonation by an explosive energy input in one localized zone, eg a Sedov blast wave leading to a shock-ignited detonation. Building on previous work on curved detonations, we find that surprisingly large inputs of energy are required to successfully launch a detonation, leading to required matchheads of ~4500 detonation thicknesses - tens of centimeters to hundreds of meters - which is orders of magnitude larger than naive considerations might suggest. This is a very difficult constraint to meet for some pictures of a deflagration-to-detonation transition, such as a Zel'dovich gradient mechanism ignition in the distributed burning regime.Comment: 29 pages; accepted to ApJ. Comments welcome at http://www.cita.utoronto.ca/~ljdursi/thisweek/ . Updated version addressing referee comment

Nucleosynthesis in Type Ia Supernovae

Among the major uncertainties involved in the Chandrasekhar mass models for Type Ia supernovae are the companion star of the accreting white dwarf (or the accretion rate that determines the carbon ignition density) and the flame speed after ignition. We present nucleosynthesis results from relatively slow deflagration (1.5 - 3 % of the sound speed) to constrain the rate of accretion from the companion star. Because of electron capture, a significant amount of neutron-rich species such as ^{54}Cr, ^{50}Ti, ^{58}Fe, ^{62}Ni, etc. are synthesized in the central region. To avoid the too large ratios of ^{54}Cr/^{56}Fe and ^{50}Ti/^{56}Fe, the central density of the white dwarf at thermonuclear runaway must be as low as \ltsim 2 \e9 \gmc. Such a low central density can be realized by the accretion as fast as \dot M \gtsim 1 \times 10^{-7} M_\odot yr^{-1}. These rapidly accreting white dwarfs might correspond to the super-soft X-ray sources.Comment: 10 page LaTeX, 7 PostScript figures, to appear in Nuclear Physics A, Vol. A621 (1997

Exact asymptotic expansions for the cylindrical Poisson-Boltzmann equation

The mathematical theory of integrable Painleve/Toda type systems sheds new light on the behavior of solutions to the Poisson-Boltzmann equation for the potential due to a long rod-like macroion. We investigate here the case of symmetric electrolytes together with that of 1:2 and 2:1 salts. Short and large scale features are analyzed, with a particular emphasis on the low salinity regime. Analytical expansions are derived for several quantities relevant for polyelectrolytes theory, such as the Manning radius. In addition, accurate and practical expressions are worked out for the electrostatic potential, which improve upon previous work and cover the full range of radial distances

On the small-scale stability of thermonuclear flames in Type Ia supernovae

We present a numerical model which allows us to investigate thermonuclear flames in Type Ia supernova explosions. The model is based on a finite-volume explicit hydrodynamics solver employing PPM. Using the level-set technique combined with in-cell reconstruction and flux-splitting schemes we are able to describe the flame in the discontinuity approximation. We apply our implementation to flame propagation in Chandrasekhar-mass Type Ia supernova models. In particular we concentrate on intermediate scales between the flame width and the Gibson-scale, where the burning front is subject to the Landau-Darrieus instability. We are able to reproduce the theoretical prediction on the growth rates of perturbations in the linear regime and observe the stabilization of the flame in a cellular shape. The increase of the mean burning velocity due to the enlarged flame surface is measured. Results of our simulation are in agreement with semianalytical studies.Comment: 9 pages, 7 figures, Uses AASTEX, emulateapj5.sty, onecolfloat.sty. Replaced with accepted version (ApJ), Figures 1 and 3 are ne

Physics of the interior of a spherical, charged black hole with a scalar field

We analyse the physics of nonlinear gravitational processes inside a spherical charged black hole perturbed by a self-gravitating massless scalar field. For this purpose we created an appropriate numerical code. Throughout the paper, in addition to investigation of the properties of the mathematical singularities where some curvature scalars are equal to infinity, we analyse the properties of the physical singularities where the Kretschmann curvature scalar is equal to the planckian value. Using a homogeneous approximation we analyse the properties of the spacetime near a spacelike singularity in spacetimes influenced by different matter contents namely a scalar field, pressureless dust and matter with ultrarelativistic isotropic pressure. We also carry out full nonlinear analyses of the scalar field and geometry of spacetime inside black holes by means of an appropriate numerical code with adaptive mesh refinement capabilities. We use this code to investigate the nonlinear effects of gravitational focusing, mass inflation, matter squeeze, and these effects dependence on the initial boundary conditions. It is demonstrated that the position of the physical singularity inside a black hole is quite different from the positions of the mathematical singularities. In the case of the existence of a strong outgoing flux of the scalar field inside a black hole it is possible to have the existence of two null singularities and one central $r=0$ singularity simultaneously

Can differences in the nickel abundance in Chandrasekhar mass models explain the relation between brightness and decline rate of normal Type Ia Supernovae?

The use of Type Ia supernovae as distance indicators relies on the determination of their brightness. This is not constant, but it can be calibrated using an observed relation between the brightness and the properties of the optical light curve (decline rate, width, shape), which indicates that brighter SNe have broader, slower light curves. However, the physical basis for this relation is not yet fully understood. Among possible causes are different masses of the progenitor white dwarfs or different opacities in Chandrasekhar-mass explosions. We parametrise the Chandrasekhar-mass models presented by Iwamoto et al (1999), which synthesize different amounts of Ni, and compute bolometric light curves and spectra at various epochs. Since opacity in SNe Ia is due mostly to spectral lines, it should depend on the mass of Fe-peak elements synthesized in the explosion, and on the temperature in the ejecta. Bolometric light curves computed using these prescriptions for the optical opacity reproduce the relation between brightness and decline rate. Furthermore, when spectra are calculated, the change in colour between maximum and two weeks later allows the observed relation between M_B(Max) and Dm_{15}(B) to be reproduced quite nicely. Spectra computed at various epochs compare well with corresponding spectra of spectroscopically normal SNeIa selected to cover a similar range of Dm_{15}(B) values.Comment: 25 pages, including 6 figures. Accepted for publication in Ap

Direct Numerical Simulations of Type Ia Supernovae Flames II: The Rayleigh-Taylor Instability

A Type Ia supernova explosion likely begins as a nuclear runaway near the center of a carbon-oxygen white dwarf. The outward propagating flame is unstable to the Landau-Darrieus, Rayleigh-Taylor, and Kelvin-Helmholtz instabilities, which serve to accelerate it to a large fraction of the speed of sound. We investigate the Rayleigh-Taylor unstable flame at the transition from the flamelet regime to the distributed-burning regime, around densities of $10^7$ g/cc, through detailed, fully resolved simulations. A low Mach number, adaptive mesh hydrodynamics code is used to achieve the necessary resolution and long time scales. As the density is varied, we see a fundamental change in the character of the burning--at the low end of the density range the Rayleigh-Taylor instability dominates the burning, whereas at the high end the burning suppresses the instability. In all cases, significant acceleration of the flame is observed, limited only by the size of the domain we are able to study. We discuss the implications of these results on the potential for a deflagration to detonation transition.Comment: submitted to ApJ, some figures degraded due to size constraint

Thermonuclear Supernovae: Simulations of the Deflagration Stage and Their Implications

Large-scale three-dimensional numerical simulations of the deflagration stage of a thermonuclear supernova explosion show the formation and evolution of a highly convoluted turbulent flame in a gravitational field of an expanding carbon-oxygen white dwarf. The flame dynamics is dominated by the gravity-induced Rayleigh-Taylor instability that controls the burning rate. The thermonuclear deflagration releases enough energy to produce a healthy explosion. The turbulent flame, however, leaves large amounts of unburnt and partially burnt material near the star center, whereas observations imply these materials only in outer layers. This disagreement could be resolved if the deflagration triggers a detonation.Comment: 17 pages, 5 figures. To appear in Science, January 200