Thermonuclear Flames Research Articles

Spreading of Thermonuclear Flames on the Neutron Star in SAX J1808.4-3658: An Observational Tool

We analyse archival Rossi X-Ray Timing Explorer (RXTE) proportional counter array (PCA) data of thermonuclear X-ray bursts from the 2002 outburst of the accreting millisecond pulsar SAX 51808.4-3658. We present evidence of a complex frequency modulation of oscillations during burst rise, and correlations among the time evolution of the oscillation frequency, amplitude, and the inferred burning region area. We discuss these findings in the context of a model, based on thermonuclear flame spreading on the neutron star surface, that can qualitatively explain these features. From our model, we infer that for the 2002 Oct. 15 thermonuclear burst, the ignition likely occurred in the mid-latitudes, the burning region took approx. 0.2 s to nearly encircle the equatorial region of the neutron star, and after that the lower amplitude oscillation originated from the remaining asymmetry of the burning front in the same hemisphere where the burst ignited. We emphasize that studies of the evolution of burst oscillation properties during burst rise can provide a powerful tool to understand thermonuclear flame spreading on neutron star surfaces under extreme physical conditions.

The ignition of thermonuclear flames in type Ia supernovae

In the framework of the Chandrasekar-mass deflagration model for Type Ia supernovae, a persisting free parameter is the initial location of the flame front, which is linked to the ignition process in the progenitor white dwarf. Previous analytical models indicate that the thermal runaway is driven by temperature perturbations (bubbles'') developing in the white dwarf's convective core. In this work, numerical 2D simulations of buoyant bubbles in the white dwarf interior are presented and discussed, in order to probe the bubble features at ignition (diameters, temperatures and evolutionary time scales). The results support the multi-point scenario as the most favored ignition model for the SN Ia explosion.

Dynamics of bubbles in supernovae and turbulent vortices

We consider the motion of a bubble in a central acceleration field created by gravity or a centrifugal force. In the former case, the bubble moves outwards from and, in the latter, towards the center. We have calculated the characteristic time needed for a bubble to leave or reach the center. The solution obtained provides insight into the processes of thermonuclear supernovae and combustion; in other words, into the interaction between a flame and a turbulent vortex. In the case of combustion, a light bubble of burnt material propagates towards the axis of a strong turbulent vortex faster than it drifts in the direction of rotation of the vortex. It is expected that the development of bubbles should prevent the formation of “pockets” at the flame front, similar to those predicted by a simplified model of turbulent combustion in a constant density flux. In the case of a thermonuclear supernova in a deflagration burning regime, it is shown that light products of burning rise from the center of the white dwarf substantially more rapidly than the thermonuclear flame front propagates. As a result, a flame cannot completely burn the central part of the star, and instead is pushed to the outer layers of the white dwarf. The effect of bubble motion (large-scale convection) makes spherically symmetric models for thermonuclear supernovae unrealistic, which is of prime importance for the supernova spectrum and energy. The motion of bubbles is even faster in the case of a rotating white dwarf; under certain conditions, the centrifugal force may dominate over the gravitational force. To test this theory, we have carried out numerical simulations of supernovae explosions for various sizes of the burned region in the core of the presupernova. We have derived a relation between the rate of large-scale convection and the size of the burned region, which is specified by the rate of the deflagration in the thermonuclear burning.

Signature of Temporary Burning Front Stalling from a Non-Photospheric Radius Expansion Double-peaked Burst

Non-photospheric-radius-expansion (non-PRE) double-peaked bursts may be explained in terms of spreading (and temporary stalling) of thermonuclear flames on the neutron star surface, as we argued in a previous study of a burst assuming polar ignition. Here we analyze Rossi X-ray Timing Explorer (RXTE) Proportional Counter Array (PCA) data of such a burst (but with a considerably different intensity profile from the previous one) from the low mass X-ray binary (LMXB) system 4U 1636-536, and show that this model can qualitatively explain the observed burst profile and spectral evolution, if we assume an off-polar, but high-latitude ignition, and burning front stalling at a higher latitude compared to that for the previous burst. The off-polar ignition can account for the millisecond period brightness oscillations detected from this burst. This is the first time oscillations have been seen from such a burst. Our model can qualitatively explain the oscillation amplitude measured during the first (weaker) peak, and the absence of oscillations during the second peak. The higher latitude front stalling facilitates the first clear detection of a signature of this stalling, which is the primary result of this work, and may be useful for understanding thermonuclear flame spreading on neutron stars.

A Non-PRE Double-peaked Burst from 4U 1636-536: Evidence of Burning Front Propagation

We analyse Rossi X-ray Timing Explorer (RXTE) Proportional Counter Array (PCA) data of a double-peaked burst from the low mass X-ray binary (LMXB) 4U 1636-536 that shows no evidence for photospheric radius expansion (PRE). We find that the X-ray emitting area on the star increases with time as the burst progresses, even though the photosphere does not expand. We argue that this is a strong indication of thermonuclear flame spreading on the stellar surface during such bursts. We propose a model for such double-peaked bursts, based on thermonuclear flame spreading, that can qualitatively explain their essential features, as well as the rarity of these bursts.

Evidence for Harmonic Content and Frequency Evolution of Oscillations during the Rising Phase of X-Ray Bursts from 4U 1636-536

We report on a study of the evolution of burst oscillation properties during the rising phase of X-ray bursts from 4U 1636-536 observed with the proportional counter array (PCA) on board the Rossi X-Ray Timing Explorer (RXTE) . We present evidence for significant harmonic structure of burst oscillation pulses during the early rising phases of bursts. This is the first such detection in burst rise oscillations, and is very important for constraining neutron star structure parameters and the equation of state models of matter at the core of a neutron star. The detection of harmonic content only during the initial portions of the burst rise is consistent with the theoretical expectation that with time the thermonuclear burning region becomes larger, and hence the fundamental and harmonic amplitudes both diminish. We also find, for the first time from this source, strong evidence of oscillation frequency increase during the burst rise. The timing behavior of harmonic content, amplitude, and frequency of burst rise oscillations may be important in understanding the spreading of thermonuclear flames under the extreme physical conditions on neutron star surfaces.

Level set simulations of turbulent thermonuclear deflagration in degenerate carbon and oxygen

We study the dynamics of thermonuclear flames propagating in fuel stirred by stochastic forcing. The fuel consists of carbon and oxygen in a state which is encountered in white dwarfs close to the Chandrasekhar limit. The level set method is applied to represent the flame fronts numerically. The computational domain for the numerical simulations is cubic, and periodic boundary conditions are imposed. The goal is the development of a suitable flame speed model for the small-scale dynamics of turbulent deflagration in thermonuclear supernovae. Because the burning process in a supernova explosion is transient and spatially inhomogeneous, the localized determination of subgrid scale closure parameters is essential. We formulate a semi-localized model based on the dynamical equation for the subgrid scale turbulence energy k sgs. The turbulent flame speed s t is of the order √2k sgs. In particular, the subgrid scale model features a dynamic procedure for the calculation of the turbulent energy transfer from resolved toward subgrid scales, which has been successfully applied to combustion problems in engineering. The options of either including or suppressing inverse energy transfer in the turbulence production term are compared. In combination with the piece-wise parabolic method for the hydrodynamics, our results favour the latter option. Moreover, different choices for the constant of proportionality in the asymptotic flame speed relation, s t∝√2k sgs, are investigated.

On the Stability of Thermonuclear Burning Fronts in Type Ia Supernovae

SummaryThe propagation of cellularly stabilized thermonuclear flames is investigated by means of numerical simulations. In Type Ia supernova explosions the corresponding burning regime establishes at scales below the Gibson length. The cellular flame stabilization - which is a result of an interplay between the Landau-Darrieus instability and a nonlinear stabilization mechanism - is studied for the case of propagation into quiescent fuel as well as interaction with vortical fuel flows. Our simulations indicate that in thermonuclear supernova explosions stable cellular flames develop around the Gibson scale and that a deflagration-to-detonation transition is unlikely to be triggered from flame evolution effects here.

The physics of flames in Type Ia supernovae

We extend a low Mach number hydrodynamics method developed for terrestrial combustion, to the study of thermonuclear flames in Type Ia supernovae. We discuss the differences between 2-D and 3-D Rayleigh-Taylor unstable flame simulations, and give detailed diagnostics on the turbulence, showing that the kinetic energy power spectrum obeys Bolgiano-Obukhov statistics in 2-D, but Kolmogorov statistics in 3-D. Preliminary results from 3-D reacting bubble calculations are shown, and their implications for ignition are discussed.

Three‐dimensional Delayed‐Detonation Model of Type Ia Supernovae

We study a Type Ia supernova explosion using large-scale three-dimensional numerical simulations based on reactive fluid dynamics with a simplified mechanism for nuclear reactions and energy release. The initial deflagration stage of the explosion involves a subsonic turbulent thermonuclear flame propagating in the gravitational field of an expanding white dwarf. The deflagration produces an inhomogeneous mixture of unburned carbon and oxygen with intermediate-mass and iron-group elements in central parts of the star. During the subsequent detonation stage, a supersonic detonation wave propagates through the material unburned by the deflagration. The total energy released in this delayed-detonation process, (1.3-1.6) × 1051 ergs, is consistent with a typical range of kinetic energies obtained from observations. In contrast to the deflagration model, which releases only about 0.6 × 1051 ergs, the delayed-detonation model does not leave carbon, oxygen, and intermediate-mass elements in central parts of a white dwarf. This removes the key disagreement between three-dimensional simulations and observations, and makes a delayed detonation the mostly likely mechanism for Type Ia supernova explosions.

Direct Numerical Simulations of Type Ia Supernovae Flames. I. The Landau‐Darrieus Instability

Planar flames are intrinsically unstable in open domains because of thermal expansion across the burning front, i.e., the Landau-Darrieus instability. This instability leads to wrinkling and growth of the flame surface and corresponding acceleration of the flame, until it is stabilized by cusp formation. We look at the Landau-Darrieus instability for C/O thermonuclear flames at conditions relevant to the late stages of a Type Ia supernova explosion. Two-dimensional direct numerical simulations of both single-mode and multimode perturbations using a low Mach number hydrodynamics code are presented. We show the effect of the instability on the flame speed as a function of both the density and domain size, demonstrate the existence of the small-scale cutoff to the growth of the instability, and look for the proposed breakdown of the nonlinear stabilization at low densities. The effects of curvature on the flame are quantified through measurements of the growth rate and computation of the corresponding Markstein number. While accelerations of a few percent are observed, they are too small to have any direct outcome on the supernova explosion.

Asymmetric explosions of thermonuclear supernovae

A type Ia supernova explosion starts in a white dwarf as a laminar deflagration at the center of the star and soon several hydrodynamic instabilities (in particular, the Rayleigh-Taylor (R-T) instability) begin to act. In previous work (Ghezzi, de Gouveia Dal Pino, & Horvath 2001), we addressed the propagation of an initially laminar thermonuclear flame in presence of a magnetic field assumed to be dipolar. We were able to show that, within the framework of a fractal model for the flame velocity, the front is affected by the field through the quenching of the R-T instability growth in the direction perpendicular to the field lines. As a consequence, an asymmetry develops between the magnetic polar and the equatorial axis that gives a prolate shape to the burning front. We have here computed numerically the total integrated asymmetry as the flame front propagates outward through the expanding shells of decreasing density of the magnetized white dwarf progenitor, for several chemical compositions, and found that a total asymmetry of about 50 % is produced between the polar and equatorial directions for progenitors with a surface magnetic field B ~ 5 x 10^{7} G, and a composition C12 = 0.2 and O16 = 0.8 (in this case, the R-T instability saturates at scales \~ 20 times the width of the flame front). This asymmetry is in good agreement with the inferred asymmetries from spectropolarimetric observations of very young supernova remnants, which have recently revealed intrinsic linear polarization interpreted as evidence of an asymmetric explosion in several objects,such as SN1999by, SN1996X, and SN1997dt. Larger magnetic field strengths will produce even larger asymmetries. We have also found that for lighter progenitors the total asymmetry is larger.

The Response of Model and Astrophysical Thermonuclear Flames to Curvature and Stretch

Critically understanding the standard candle-like behavior of Type Ia supernovae requires understanding their explosion mechanism. One family of models for Type Ia supernovae begins with a deflagration in a carbon-oxygen white dwarf that greatly accelerates through wrinkling and flame instabilities. While the planar speed and behavior of astrophysically relevant flames is increasingly well understood, more complex behavior, such as the flame's response to stretch and curvature, has not been extensively explored in the astrophysical literature; this behavior can greatly enhance or suppress instabilities and local flame-wrinkling, which in turn can increase or decrease the bulk burning rate. In this paper, we explore the effects of curvature on both nuclear flames and simpler model flames to understand the effect of curvature on the flame structure and speed.

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.

Propagation of Thermonuclear Flames on Rapidly Rotating Neutron Stars: Extreme Weather during Type I X‐Ray Bursts

We analyze the global hydrodynamic flow in the ocean of an accreting, rapidly rotating, nonmagnetic neutron star in a low-mass X-ray binary during a type I X-ray burst. We use both analytical arguments and numerical simulations of simplified models for ocean burning. Our analysis extends previous work by taking into account the rapid rotation of the star and the lift-up of the burning ocean during the burst. We find a new regime for the spreading of a nuclear burning front, where the flame is carried along a coherent shear flow across the front. If turbulent viscosity is weak, the speed of flame propagation is v_(flame) ~ (gh)^(1/2)/ft_n ~ 20 km s^(-1), where h is the scale height of the burning ocean, g is the local gravitational acceleration, t_n is the timescale for fast nuclear burning during the burst, and f is the Coriolis parameter, i.e., twice the local vertical component of the spin vector. If turbulent viscosity is dynamically important, the flame speed increases and reaches the maximum value, v^(max)_(flame_ ~ (gh/ft_n)^(1/2) ~ 300 km s^(-1), when the eddy overturn frequency is comparable to the Coriolis parameter f. We show that, as a result of rotationally reduced gravity, the thermonuclear runaway which ignites the ocean is likely to begin on the equator. The equatorial belt is ignited at the beginning of the burst, and the flame then propagates from the equator to the poles. Inhomogeneous cooling (equator first, poles second) of the hot ashes drives strong zonal currents which may be unstable to the formation of Jupiter-type vortices; we conjecture that these vortices are responsible for coherent modulation of X-ray flux in the tails of some bursts. We consider the effect of strong zonal currents on the frequency of modulation of the X-ray flux and show that the large values of the frequency drifts observed in some bursts can be accounted for within our model combined with the model of homogeneous radial expansion. Additionally, if vortices or other inhomogeneities are trapped in the forward zonal flows around the propagating burning front, fast chirps with large frequency ranges (~25-500 Hz) may be detectable during the burst rise. Finally, we argue that an MHD dynamo within the burning front can generate a small-scale magnetic field, which may enforce vertically rigid flow in the front's wake and can explain the coherence of oscillations in the burst tail.

FLASH: An Adaptive Mesh Hydrodynamics Code for Modeling Astrophysical Thermonuclear Flashes

We report on the completion of the first version of a new-generation simulation code, FLASH. The FLASH code solves the fully compressible, reactive hydrodynamic equations and allows for the use of adaptive mesh refinement. It also contains state-of-the-art modules for the equations of state and thermonuclear reaction networks. The FLASH code was developed to study the problems of nuclear flashes on the surfaces of neutron stars and white dwarfs, as well as in the interior of white dwarfs. We expect, however, that the FLASH code will be useful for solving a wide variety of other problems. This first version of the code has been subjected to a large variety of test cases and is currently being used for production simulations of X-ray bursts, Rayleigh-Taylor and Richtmyer-Meshkov instabilities, and thermonuclear flame fronts. The FLASH code is portable and already runs on a wide variety of massively parallel machines, including some of the largest machines now extant.

Distributed Burning in Type Ia Supernovae: A Statistical Approach

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 induce 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 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 to make a deflagration-to-detonation transition possible.

Small‐Scale Interaction of Turbulence with Thermonuclear Flames in Type Ia Supernovae

Microscopic turbulence-flame interactions of thermonuclear fusion flames occurring 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, Slam. We find that if Slam ≥ u', where u' is the rms amplitude of turbulent velocity fluctuations, the local flame propagation speed does not significantly deviate from Slam 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.

Can Deflagration-Detonation Transitions Occur in Type I[CLC]a[/CLC] Supernovae?

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.

Mechanisms of supernova explosion

Abstract The modern status of supernova mechanisms is reviewed with special emphasis on physical processes involved. An extensive study of supernovae (both observational and theoretical) during the last decade, prompted by the outburst of close Supernova 1987A in the Large Magellanic Cloud, led to general consensus that Type Ia supernovae are the result of thermonuclear explosion of carbon-oxygen white dwarfs whereas other types supernovae (especially Type II) are triggered by the gravitational collapse of stellar iron cores. However, there is still much left to do to understand the details of the two supernova mechanisms. The main difficulties are due to the lack of a comprehensive theory of thermonuclear flame in degenerate stellar matter for Type Ia supernovae and a very complicated (essentially three-dimensional) picture of the energy transfer from a dense collapsed remnant (neutron star) to the expelled stellar envelope in the case of other type supernovae—the interaction of neutrino flux with large-scale convective eddies and possible role of stellar rotation and magnetic fields make it very difficult to construct a consistent unambiguous quantitative model of Type II supernovae.