arXiv subjects

A. M. Khokhlov

Publications and source records attributed to A. M. Khokhlov.

15 recordsLinked to original sources

arXiv2012

A Physical Model for SN 2001ay, a normal, bright, extremely slowly declining Type Ia supernova

We present a study of the peculiar Type Ia supernova 2001ay (SN 2001ay). The defining features of its peculiarity are: high velocity, broad lines, and a fast rising light curve, combined with the slowest known rate of decline. It is one magnitude dimmer than would be predicted from its observed value of Delta-m15, and shows broad spectral features. We base our analysis on detailed calculations for the explosion, light curves, and spectra. We demonstrate that consistency is key for both validating the models and probing the underlying physics. We show that this SN can be understood within the physics underlying the Delta-m15 relation, and in the framework of pulsating delayed detonation models originating from a Chandrasekhar mass, white dwarf, but with a progenitor core composed of 80% carbon. We suggest a possible scenario for stellar evolution which leads to such a progenitor. We show that the unusual light curve decline can be understood with the same physics as has been used to understand the Delta-m15 relation for normal SNe Ia. The decline relation can be explained by a combination of the temperature dependence of the opacity and excess or deficit of the peak luminosity, alpha, measured relative to the instantaneous rate of radiative decay energy generation. What differentiates SN 2001ay from normal SNe Ia is a higher explosion energy which leads to a shift of the Ni56 distribution towards higher velocity and alpha < 1. This result is responsible for the fast rise and slow decline. We define a class of SN 2001ay-like SNe Ia, which will show an anti-Phillips relation.

astro-ph.SR↗

arXiv2009

Secondary Parameters of Type Ia Supernova Light Curves

High-quality observations of $B$ and $V$ light curves obtained at Las Campanas Observatory for local Type Ia Supernovae (SNe Ia) show clear evidence that SNe Ia with the same brightness decline or stretch may have systematic and independent deviations at times < 5 days before and at times > 30 days after maximum light. This suggests the existence of two independent secondary parameters which control the shape of SN Ia light curves in addition to the brightness decline relation. stretch. The differences are consistent in morphology of the time dependence and size with predictions by models within the delayed detonation scenario. The secondary parameters may reflect two independent physical effects caused by variations in the progenitor and accretion rates, and link the LC variations in shape with the intrinsic, absolute brightness.

astro-ph.CO↗

arXiv2006

Well-posed constrained evolution of 3+1 formulations of General Relativity

We present an analysis of well-posedness of constrained evolution of 3+1 formulations of GR. In this analysis we explicitly take into account the energy and momentum constraints as well as possible algebraic constraints on the evolution of high-frequency perturbations of solutions of Einstein's equations. In this respect, our approach is principally different from standard analyses of well-posedness of free evolution in general relativity. Our study reveals the existence of subsets of the linearized Einstein's equations that control the well-posedness of constrained evolution. It is demonstrated that the well-posedness of ADM, BSSN and other 3+1 formulations derived from ADM by adding combinations of constraints to the right-hand-side of ADM and/or by linear transformation of the dynamical ADM variables depends entirely on the properties of the gauge. For certain classes of gauges we formulate conditions for well-posedness of constrained evolution. This provides a new basis for constructing stable numerical integration schemes for a classical Arnowitt--Deser--Misner (ADM) and many other 3+1 formulations of general relativity.

gr-qc↗

arXiv2006

Computation of Fluid Flows in Non-inertial Contracting, Expanding, and Rotating Reference Frames

We present the method for computation of fluid flows that are characterized by the large degree of expansion/contraction and in which the fluid velocity is dominated by the bulk component associated with the expansion/contraction and/or rotation of the flow. We consider the formulation of Euler equations of fluid dynamics in a homologously expanding/contracting and/or rotating reference frame. The frame motion is adjusted to minimize local fluid velocities. Such approach allows to accommodate very efficiently large degrees of change in the flow extent. Moreover, by excluding the contribution of the bulk flow to the total energy the method eliminates the high Mach number problem in the flows of interest. An important practical advantage of the method is that it can be easily implemented with virtually any implicit or explicit Eulerian hydrodynamic scheme and adaptive mesh refinement (AMR) strategy. We also consider in detail equation invariance and existence of conservative formulation of equations for special classes of expanding/contracting reference frames. Special emphasis is placed on extensive numerical testing of the method for a variety of reference frame motions, which are representative of the realistic applications of the method. We study accuracy, conservativity, and convergence properties of the method both in problems which are not its optimal applications as well as in systems in which the use of this method is maximally beneficial. Such detailed investigation of the numerical solution behavior is used to define the requirements that need to be considered in devising problem-specific fluid motion feedback mechanisms.

astro-ph↗

arXiv2003

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.

gr-qc↗

arXiv2003

Exponential stretch-rotation (ESR) formulation of general relativity

We study a tensorial exponential transformation of a three-dimensional metric of space-like hypersurfaces embedded in a four-dimensional space-time, $γ_{ij} = e^{ε_{ikm}θ_m} e^{ϕ_k} e^{-ε_{jkn}θ_n}$, where $ϕ_k$ are logarithms of the eigenvalues of $γ_{ij}$, $θ_k$ are rotation angles, and $ε_{ijk}$ is a fully anti-symmetric symbol. Evolution part of Einstein's equations, formulated in terms of $ϕ_k$ and $θ_k$, describes time evolution of the metric at every point of a hyper-surface as a continuous stretch and rotation of a local coordinate system in a tangential space. The exponential stretch-rotation (ESR) transformation generalizes particular exponential transformations used previously in cases of spatial symmetry. The ESR 3+1 formulation of Einstein's equations may have certain advantages for long-term stable integration of these equations.

gr-qc↗

arXiv2002

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.

astro-ph↗

arXiv2000

Three-Dimensional Modeling of the Deflagration Stage of a Type Ia Supernova Explosion

The paper describes a physical model and numerical algorithm for modeling Type Ia supernova (SNIa) explosions in three dimensions and presents first results of modeling a deflagration explosion in a nonrotating, Chandrasekhar-mass carbon-oxygen (CO) white dwarf. Simulations show that the turbulent flame speed grows exponentially, reaches approximately 30% of the speed of sound, and then declines as the large-scale turbulence is frozen by expansion. The freezing of turbulent motions appears to be a crucial physical mechanism regulating the rate of deflagration in SNIa. The energy of the explosion is comparable to that of a typical SNIa. However, the presence of the outer layer of unburned CO and the formation of intermediate mass elements and pockets of unburned CO near the center pose problems for the modeling of SNIa spectra. Delayed detonation is a way to alleviate these problems and to produce consistent spectra.

astro-ph↗

arXiv1999

Deflagration to Detonation

Thermonuclear explosions of Type Ia supernovae (SNIa) involve turbulent deflagrations, detonations, and possibly a deflagration-to-detonation transition. A phenomenological delayed detonation model of SNIa successfully explains many observational properties of SNIa including monochromatic light curves, spectra, brightness - decline and color - decline relations. Observed variations among SNia are explained as a result of varying nickel mass synthesised in an explosion of a Chandrasekhar mass C/O white dwarf. Based on theoretical models of SNIa, the value of the Hubble constant H_o \simeq 67km/s/Mpc was determined without the use of secondary distance indicators. The cause for the nickel mass variations in SNIa is still debated. It may be a variation of the initial C/O ratio in a supernova progenitor, rotation, or other effects.

astro-ph↗

arXiv1999

The Santa Barbara cluster comparison project: a comparison of cosmological hydrodynamics solutions

We have simulated the formation of an X-ray cluster in a cold dark matter universe using 12 different codes. The codes span the range of numerical techniques and implementations currently in use, including SPH and grid methods with fixed, deformable or multilevel meshes. The goal of this comparison is to assess the reliability of cosmological gas dynamical simulations of clusters in the simplest astrophysically relevant case, that in which the gas is assumed to be non-radiative. We compare images of the cluster at different epochs, global properties such as mass, temperature and X-ray luminosity, and radial profiles of various dynamical and thermodynamical quantities. On the whole, the agreement among the various simulations is gratifying although a number of discrepancies exist. Agreement is best for properties of the dark matter and worst for the total X-ray luminosity. Even in this case, simulations that adequately resolve the core radius of the gas distribution predict total X-ray luminosities that agree to within a factor of two. Other quantities are reproduced to much higher accuracy. For example, the temperature and gas mass fraction within the virial radius agree to about 10%, and the ratio of specific kinetic to thermal energies of the gas agree to about 5%. Various factors contribute to the spread in calculated cluster properties, including differences in the internal timing of the simulations. Based on the overall consistency of results, we discuss a number of general properties of the cluster we have modelled.

astro-ph↗

arXiv1999

Jet-Induced Explosions of Core Collapse Supernovae

We numerically studied the explosion of a supernova caused by supersonic jets present in its center. The jets are assumed to be generated by a magneto-rotational mechanism when a stellar core collapses into a neutron star. We simulated the process of the jet propagation through the star, jet breakthrough, and the ejection of the supernova envelope by the lateral shocks generated during jet propagation. The end result of the interaction is a highly nonspherical supernova explosion with two high-velocity jets of material moving in polar directions, and a slower moving, oblate, highly distorted ejecta containing most of the supernova material. The jet-induced explosion is entirely due to the action of the jets on the surrounding star and does not depend on neutrino transport or re-acceleration of a stalled shock. The jet mechanism can explain the observed high polarization of Type Ib,c and Type II supernovae, pulsar kicks, very high velocity material observed in supernova remnants, indications that radioactive material was carried to the hydrogen-rich layers in SN1987A, and some others observations that are very difficult or impossible to explain by the neutrino energy deposition mechanism. The breakout of the jet from a compact, hydrogen- deficient core may account for the gamma-ray bursts and radio outburst associated with SN1998bw/GRB980425.

astro-ph↗

arXiv1998

The QSE-reduced αNetwork

Examination of the process of silicon burning, the burning stage that leads to the production of the iron peak nuclei, reveals that the nuclear evolution is dominated by large groups of nuclei in mutual equilibrium. These quasi-equilibrium (QSE) groups form well in advance of the global Nuclear Statistical Equilibrium (NSE). We present an improved ``minimal'' nuclear network, which takes advantage of quasi-equilibrium in order to calculate the nuclear evolution and energy generation while further reducing the computational cost compared to a conventional α-chain network. During silicon burning, the resultant \emph{QSE-reduced} αnetwork is twice as fast as the full αnetwork it replaces and requires the tracking of only half as many abundance variables, without significant loss of accuracy. When the QSE-reduced αnetwork is used in combination with a conventional αnetwork stretching from He to Si, the combined \alpha7 network provides an accurate approximation for all of the burning stages from He burning to NSE, while tracking only 7 abundances. These reductions in computational cost and the number of species evolved make the \alpha7 network well suited for inclusion within hydrodynamic simulations, particularly those in multi-dimension.

astro-ph↗

arXiv1996

Deflagration to Detonation Transition in Thermonuclear Supernovae

We derive the criteria for deflagration to detonation transition (DDT) in a Type Ia supernova. The theory is based on the two major assumptions: (i) detonation is triggered via the Zeldovich gradient mechanism inside a region of mixed fuel and products, (ii) the mixed region is produced by a turbulent mixing of fuel and products either inside an active deflagration front or during the global expansion and subsequent contraction of an exploding white dwarf. We determine the critical size of the mixed region required to initiate a detonation in a degenerate carbon-oxygen mixture. This critical length is much larger than the width of the reaction front of a Chapman-Jouguet detonation. However, at densities greater than simeq 5 x 10^6 g cm^-3, it is much smaller than the size of a white dwarf. We derive the critical turbulent intensity required to create the mixed region inside an active deflagration front in which a detonation can form. We conclude that the density rho_tr at which a detonation can form in a carbon-oxygem white dwarf is low, less than 2 - 5 x 10^7 g cm^-3, but greater than 5 x 10^6 g cm^-3.

astro-ph↗

arXiv1996

Theory of DDT in Unconfined Flames

This paper outlines a theoretical approach for predicting the onset of detonation in unconfined turbulent flames which is relevant both to problems of terrestrial combustion and to thermonuclear burning in Type Ia supernovae. Two basic assumuptions are made: 1) the gradient mechanism is the inherent mechanism that leads to DDT in unconfined conditions, and 2) the sole mechanism for preparing the gradient in induction time is by turbulent mixing and local flame quenching. The criterion for DDT is derived in terms of the one-dimensional detonation wave thickness, the laminar flame speed, and the laminar flame thickness in the reactive gas. This approach gives a lower-bound criterion for DDT for conditions where shock preheating, wall effects, and interactions with obstacles are absent. Regions in parameter space where unconfined DDT can and cannot occur are determined. A subsequent paper will address these issues specifically in the astrophysical context.

astro-ph↗

arXiv1996

Three-dimensional Combustion in Type Ia Supernovae

Turbulent combustion is three-dimensional. Turbulence in a Type Ia supernova is driven on large scales by the buoyancy of burning products. The turbulent cascade penetrates down to very small scales, and makes the rate of deflagration independent of the microphysics. The competition between the turbulent cascade and the freeze-out of turbulent motions due to stellar expansion determines the largest scale participating in the cascade. This sets the bulk rate of a deflagration in a supernova. The freeze-out limits the bulk rate of deflagration to a value that makes a powerful explosion impossible. Two-dimensional simulations cannot capture these essential elements of turbulent combustion, even in principle. A powerful delayed detonation explosion can take place if the burning makes a transition to a detonation. A deflagration to detonation transition (DDT) can occur in a layer of mixed cold fuel and hot burning products created either inside an active turbulent burning region by a high intensity of turbulence, or by mixing cold fuel with ashes of a dead deflagration front during the global pulsation of a star, or by both.

astro-ph↗