The Thermonuclear Explosion Of Chandrasekhar Mass White Dwarfs

The flame born in the deep interior of a white dwarf that becomes a Type Ia supernova is subject to several instabilities. We briefly review these instabilities and the corresponding flame acceleration. We discuss the conditions necessary for each of the currently proposed explosion mechanisms and the attendant uncertainties. A grid of critical masses for detonation in the range $10^7$ - $2 \times 10^9$ g cm$^{-3}$ is calculated and its sensitivity to composition explored. Prompt detonations are physically improbable and appear unlikely on observational grounds. Simple deflagrations require some means of boosting the flame speed beyond what currently exists in the literature. ``Active turbulent combustion'' and multi-point ignition are presented as two plausible ways of doing this. A deflagration that moves at the ``Sharp-Wheeler'' speed, $0.1 g_{\rm eff} t$, is calculated in one dimension and shows that a healthy explosion is possible in a simple deflagration if the front moves with the speed of the fastest floating bubbles. The relevance of the transition to the ``distributed burning regime'' is discussed for delayed detonations. No model emerges without difficulties, but detonation in the distributed regime is plausible, will produce intermediate mass elements, and warrants further study.Comment: 28 pages, 4 figures included, uses aaspp4.sty. Submitted to Ap

On the Origin of the Type Ia Supernova Width-Luminosity Relation

Brighter Type Ia supernovae (SNe Ia) have broader, more slowly declining B-band light curves than dimmer SNe Ia. We study the physical origin of this width-luminosity relation (WLR) using detailed radiative transfer calculations of Chandrasekhar mass SN Ia models. We find that the luminosity dependence of the diffusion time (emphasized in previous studies) is in fact of secondary relevance in understanding the model WLR. Instead, the essential physics involves the luminosity dependence of the spectroscopic/color evolution of SNe Ia. Following maximum-light, the SN colors are increasingly affected by the development of numerous Fe II/Co II lines which blanket the B-band and, at the same time, increase the emissivity at longer wavelengths. Because dimmer SNe Ia are generally cooler, they experience an earlier onset of Fe III to Fe II recombination in the iron-group rich layers of ejecta, resulting in a more rapid evolution of the SN colors to the red. The faster B-band decline rate of dimmer SNe Ia thus reflects their faster ionization evolution.Comment: 6 pages, submitted to Ap

Carbon Detonation and Shock-Triggered Helium Burning in Neutron Star Superbursts

The strong degeneracy of the 12C ignition layer on an accreting neutron star results in a hydrodynamic thermonuclear runaway, in which the nuclear heating time becomes shorter than the local dynamical time. We model the resulting combustion wave during these superbursts as an upward propagating detonation. We solve the reactive fluid flow and show that the detonation propagates through the deepest layers of fuel and drives a shock wave that steepens as it travels upward into lower density material. The shock is sufficiently strong upon reaching the freshly accreted H/He layer that it triggers unstable 4He burning if the superburst occurs during the latter half of the regular Type I bursting cycle; this is likely the origin of the bright Type I precursor bursts observed at the onset of superbursts. The cooling of the outermost shock-heated layers produces a bright, ~0.1s, flash that precedes the Type I burst by a few seconds; this may be the origin of the spike seen at the burst onset in 4U 1820-30 and 4U 1636-54, the only two bursts observed with RXTE at high time resolution. The dominant products of the 12C detonation are 28Si, 32S, and 36Ar. Gupta et al. showed that a crust composed of such intermediate mass elements has a larger heat flux than one composed of iron-peak elements and helps bring the superburst ignition depth into better agreement with values inferred from observations.Comment: 11 pages, 11 figures, accepted to ApJ; discussion about onset of detonation discussed in new detail, including a new figur

Laser Pulse Heating of Spherical Metal Particles

We consider a general problem of laser pulse heating of spherical metal particles with the sizes ranging from nanometers to millimeters. We employ the exact Mie solutions of the diffraction problem and solve heat-transfer equations to determine the maximum temperature at the particle surface as a function of optical and thermometric parameters of the problem. The main attention is paid to the case when the thermometric conductivity of the particle is much larger than that of the environment, as it is in the case of metal particles in fluids. We show that in this case at any given finite duration of the laser pulse the maximum temperature rise as a function of the particle size reaches an absolute maximum at a certain finite size of the particle, and we suggest simple approximate analytical expressions for this dependence which covers the entire range of variations of the problem parameters and agree well with direct numerical simulations.Comment: 7 pages, 6 figure

A scalar hyperbolic equation with GR-type non-linearity

We study a scalar hyperbolic partial differential equation with non-linear terms similar to those of the equations of general relativity. The equation has a number of non-trivial analytical solutions whose existence rely on a delicate balance between linear and non-linear terms. We formulate two classes of second-order accurate central-difference schemes, CFLN and MOL, for numerical integration of this equation. Solutions produced by the schemes converge to exact solutions at any fixed time $t$ when numerical resolution is increased. However, in certain cases integration becomes asymptotically unstable when $t$ is increased and resolution is kept fixed. This behavior is caused by subtle changes in the balance between linear and non-linear terms when the equation is discretized. Changes in the balance occur without violating second-order accuracy of discretization. We thus demonstrate that a second-order accuracy and convergence at finite $t$ do not guarantee a correct asymptotic behavior and long-term numerical stability. Accuracy and stability of integration are greatly improved by an exponential transformation of the unknown variable.Comment: submitted to Class. Quantum Gra

Polymer globule as a nanoreactor

Peculiarities of chemical reactions inside polymer globules with sizes falling in the nanometric range have been theoretically studied. The simplest example of a polymer-catalyzed bimolecular reaction between two low-molecular-weight compounds has been considered to illustrate the advantages of conducting chemical transformations in globular solution of macromolecules. Under theoretical examination of polymer-analogous transformations of polymer molecules, the possibility has been shown of reaction-induced conformational transitions between their coil and globular states. Besides, a pronounced effect has been revealed of the preferential sorption of low-molecular-weight reagents on composition of copolymers formed

Constraints On The Delayed Transition to Detonation in Type Ia Supernovae

We investigate the possibility of a delayed detonation in a type Ia supernova under the assumption that the transition to detonation is triggered by turbulence only. Our discussion is based on the Zeldovich mechanism and suggests that typical turbulent velocities present during the explosion are not strong enough to allow this transition to occur. Although we are able to show that in carbon-rich matter (e.g., $X(^{12}$C$) = 0.75$) the possibility of a deflagration to detonation transition (DDT) is enhanced, even in this case the turbulent velocities needed are larger than the expected value of $u'(L) \approx 10^7 {cm s}^{-1}$ on a length-scale of $L \approx 10^6$ cm. Thus we conclude that a DDT may not be a common event during a thermonuclear explosion of a Chandrasekhar-mass white dwarf.Comment: 18 pages, 5 figures, accepted for publication in the Ap

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