R. M. Cabezón

PULSATING REVERSE DETONATION MODELS OF TYPE Ia SUPERNOVAE. II. EXPLOSION

Observational evidences point to a common explosion mechanism of Type Ia supernovae based on a delayed detonation of a white dwarf (WD). However, all attempts to find a convincing ignition mechanism based on a delayed detonation in a destabilized, expanding, white dwarf have been elusive so far. One of the possibilities that has been invoked is that an inefficient deflagration leads to pulsation of a Chandrasekhar-mass WD, followed by formation of an accretion shock that confines a carbon–oxygen rich core, while transforming the kinetic energy of the collapsing halo into thermal energy of the core, until an inward moving detonation is formed. This chain of events has been termed Pulsating Reverse Detonation (PRD). In this work, we present three-dimensional numerical simulations of PRD models from the time of detonation initiation up to homologous expansion. Different models characterized by the amount of mass burned during the deflagration phase, Mdefl, give explosions spanning a range of kinetic energies, K ∼ (1.0–1.2)×1051 erg, and 56Ni masses, M(56Ni) ∼ 0.6–0.8 M , which are compatible with what is expected for typical Type Ia supernovae. Spectra and light curves of angle-averaged spherically symmetric versions of the PRD models are discussed. Type Ia supernova spectra pose the most stringent requirements on PRD models.

Improving smoothed particle hydrodynamics with an integral approach to calculating gradients

Context. The smoothed particle hydrodynamics (SPH) technique is a well-known numerical method that has been applied to simulate the evolution of a wide variety of systems. Modern astrophysical applications of the method rely on the Lagrangian formulation of fluid Euler equations, which is fully conservative. A different scheme, based on a matrix approach to the SPH equations is currently being used in computational fluid dynamics. These matrix formulations achieve better interpolations of the physical magnitudes but they are, in general, not fully conservative. The matrix approach to the Euler equations has never been used in astrophysics. Aims. We develop and test a fully conservative SPH scheme based on a tensor formulation that can be applied to simulate astrophysical systems. Methods. In the proposed scheme, derivatives are calculated from an integral expression that leads to a tensor (instead of a vectorial) estimation of gradients and reduces to the standard formulation in the continuum limit. The new formulation improves the interpolation of physical magnitudes, leading to a set of conservative equations that resembles those of standard SPH. The resulting scheme is verified using a variety of well-known tests, all of them simulated in two dimensions. We also discuss an application of the proposed tensor method to astrophysics by simulating the stability of a Sun-like polytrope calculated in three dimensions. Results. The proposed scheme is able to improve the results of standard SPH in the two-dimensional tests, especially in the simulation of subsonic hydrodynamic instabilities. Our results for the stability of the Sun-like polytrope suggest that the new method can be used in astrophysics to carry out three-dimensional calculations with a computational cost that is only slightly higher (i.e. ≤50% for a serial code) than that of a standard SPH formulation. Conclusions. A formalism based on a matrix approach to Euler SPH equations was developed and checked. The new scheme is more accurate because of the re-normalization imposed on the interpolations, which is fully conservative and probably less prone to undergo the tensile instability. The analysis of several test cases suggest that the method may improve the simulation of both subsonic and supersonic systems. An application of the tensor method to astrophysics is, for the first time, successfully carried out. These encouraging results indicates that more work should be invested in the applications of matrix SPH formulations to astrophysics.Context. The smoothed particle hydrodynamics (SPH) technique is a well-known numerical method that has been applied to simulate the evolution of a wide variety of systems. Modern astrophysical applications of the method rely on the Lagrangian formulation of fluid Euler equations, which is fully conservative. A different scheme, based on a matrix approach to the SPH equations is currently being used in computational fluid dynamics. These matrix formulations achieve better interpolations of the physical magnitudes but they are, in general, not fully conservative. The matrix approach to the Euler equations has never been used in astrophysics. Aims. We develop and test a fully conservative SPH scheme based on a tensor formulation that can be applied to simulate astrophysical systems. Methods. In the proposed scheme, derivatives are calculated from an integral expression that leads to a tensor (instead of a vectorial) estimation of gradients and reduces to the standard formulation in the continuum limit. The new formulation improves the interpolation of physical magnitudes, leading to a set of conservative equations that resembles those of standard SPH. The resulting scheme is verified using a variety of well-known tests, all of them simulated in two dimensions. We also discuss an application of the proposed tensor method to astrophysics by simulating the stability of a Sun-like polytrope calculated in three dimensions. Results. The proposed scheme is able to improve the results of standard SPH in the two-dimensional tests, especially in the simulation of subsonic hydrodynamic instabilities. Our results for the stability of the Sun-like polytrope suggest that the new method can be used in astrophysics to carry out three-dimensional calculations with a computational cost that is only slightly higher (i.e. ≤50% for a serial code) than that of a standard SPH formulation. Conclusions. A formalism based on a matrix approach to Euler SPH equations was developed and checked. The new scheme is more accurate because of the re-normalization imposed on the interpolations, which is fully conservative and probably less prone to undergo the tensile instability. The analysis of several test cases suggest that the method may improve the simulation of both subsonic and supersonic systems. An application of the tensor method to astrophysics is, for the first time, successfully carried out. These encouraging results indicates that more work should be invested in the applications of matrix SPH formulations to astrophysics.

High-resolution simulations of the head-on collision of white dwarfs

The direct impact of white dwarfs has been suggested as a plausible channel for type Ia supernovae. In spite of their (a priori) rareness, in highly populated globular clusters and in galactic centers, where the amount of white dwarfs is considerable, the rate of violent collisions between two of them might be non-negligible. Even more, there are indications that binary white dwarf systems orbited by a third stellar-mass body have an important chance to induce a clean head-on collision. Therefore, this scenario represents a source of contamination for the supernova light-curves sample that it is used as standard candles in cosmology, and it deserves further investigation. Some groups have conducted numerical simulations of this scenario, but their results show several differences. In this paper we address some of the possible sources of these differences, presenting the results of high resolution hydrodynamical simulations jointly with a detailed nuclear post-processing of the nuclear abundances, to check the viability of white dwarf collisions to produce significant amounts of 56Ni. To that purpose, we use a 2D-axial symmetric smoothed particle hydrodynamic code to obtain a resolution considerably higher than in previous studies. In this work, we also study how the initial mass and nuclear composition affect the results. The gravitational wave emission is also calculated, as this is a unique signature of this kind of events. All calculated models produce a significant amount of 56Ni, ranging from 0.1 Msun to 1.1 Msun, compatible not only with normal-Branch type Ia supernova but also with the subluminous and super-Chandrasekhar subset. Nevertheless, the distribution mass-function of white dwarfs favors collisions among 0.6-0.7 Msun objects, leading to subluminous events.

Axisymmetric smoothed particle hydrodynamics with self‐gravity

The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation of a Sun-like star), gas dynamics (wall heating problem, collision of two streams of gas) and inertial confinement fusion (ablative implosion of a small capsule). New material concerning the standard SPH formalism is given. That includes the numerical handling of those mass points which move close to the singularity axis, more accurate expressions for the artificial viscosity and the heat conduction term and an easy way to incorporate self-gravity in the simulations. The algorithm developed to compute gravity does not rely in any sort of grid, leading to a numerical scheme totally compatible with the Lagrangian nature of the SPH equations.

Merging in the common envelope and the origin of early R-type stars

Context. Binary systems experiencing one or two common envelope episodes during the red giant branch or the Hertzsprung gap phases can produce a single star, evolving along the Hayashi track, as a final outcome. Even if these objects are expected to be very common in nature, a proper description of their evolution and physical properties is still missing. Moreover, this scenario (red giant merging scenario) has been invoked as the progenitor systems of early-R stars, by assuming that the physical conditions developed as a consequence of the cores merging could produce the mixing into the convective envelope of fresh carbon that was synthesized during the He-flash. Aims. We analyze in detail the red giant merging scenario to verify if the resulting star develops the physical conditions suitable for a dredge-up of C-enriched material from the core to the envelope. Methods. We performed 3D simulations of the merging stars, to check whether He is burnt efficiently during the formation of a self-sustained disk. We therefore did 1D computations of the accretion phase occurring after the merging and of the following evolution up to the settling of quiescent He-burning in the center. We adopted different assumptions on the amount of angular momentum transferred from the disk to the core and on the angular momentum transport. Results. Efficient He-burning does not occur during the merging, because a very high temperature (T > 10 8 K) at the disk/He-core interface develops only for a few minutes. Our computations show that the accretion process is the leading parameter in determining the final properties of the merged object. In particular, the thermal energy delivered by the accreted matter determines the heating of the whole newborn core, thus preventing the developing of highly degenerate physical conditions. This occurrence determines the onset of the He-burning with an He-flash milder and closer to the center, as compared to standard RGB stars. Rotation and different angular momentum transport efficiency plays a secondary role by determining the exact location of the first He-flash. In none of the computed models is material formed in the He-core mixed into the convective envelope, because the H-burning shell, which always active during the He-flashes and later on, acts as a barrier. Conclusions. In the red giant merging scenario, the physical conditions suitable for both a peculiar He-flash and the dredging-up of C-enriched material never occur. Our results speak against the possibility that such an evolutionary scenario could represent the progenitor system of early R-stars.

An Advanced Leakage Scheme for Neutrino Treatment in Astrophysical Simulations

We present an Advanced Spectral Leakage (ASL) scheme to model neutrinos in the context of core-collapse supernovae (CCSNe) and compact binary mergers. Based on previous gray leakage schemes, the ASL scheme computes the neutrino cooling rates by interpolating local production and diffusion rates (relevant in optically thin and thick regimes, respectively) separately for discretized values of the neutrino energy. Neutrino trapped components are also modeled, based on equilibrium and timescale arguments. The better accuracy achieved by the spectral treatment allows a more reliable computation of neutrino heating rates in optically thin conditions. The scheme has been calibrated and tested against Boltzmann transport in the context of Newtonian spherically symmetric models of CCSNe. ASL shows a very good qualitative and a partial quantitative agreement for key quantities from collapse to a few hundreds of milliseconds after core bounce. We have proved the adaptability and flexibility of our ASL scheme, coupling it to an axisymmetric Eulerian and to a three-dimensional smoothed particle hydrodynamics code to simulate core collapse. Therefore, the neutrino treatment presented here is ideal for large parameter-space explorations, parametric studies, high-resolution tests, code developments, and long-term modeling of asymmetric configurations, where more detailed neutrino treatments are not available or are currently computationally too expensive.

Constraining Deflagration Models of Type Ia Supernovae through Intermediate-Mass Elements

The physical structure of a nuclear flame is a basic ingredient of the theory of Type Ia supernovae (SNe Ia). Assuming an exponential density reduction with several characteristic times, we have followed the evolution of a planar nuclear flame in an expanding background from an initial density of 6.6 × 107 g cm-3 down to 2 × 106 g cm-3. The total amount of synthesized intermediate-mass elements (IMEs), from silicon to calcium, was monitored during the calculation. We have used the computed mass fractions, XIME, of these elements to estimate the total amount of IMEs synthesized during the deflagration of a massive white dwarf. Using XIME and adopting the usual hypothesis that the relevant flame speed is actually the turbulent speed on the integral length scale, we have built a simple geometrical approach to model the region where IMEs are thought to be produced. It turns out that a healthy production of IMEs involves the combination of not-too-short expansion times, τc ≥ 0.2 s, and high turbulent intensities. According to our results, it could be difficult to produce much more than 0.2 M☉ of intermediate-mass elements within the standard deflagrative paradigm. The calculations also suggest that the mass of the IMEs scales with the mass of the Fe-peak elements, making it difficult to reconcile energetic explosions with low ejected nickel masses, as in the well-observed supernova SN 1991bg or in SN 1998de. Thus, a large production of Si-peak elements, especially in combination with a low or moderate production of iron, could be better addressed either by the delayed detonation route in standard Chandrasekhar-mass models or, perhaps, by the off-center helium detonation in the sub-Chandrasekhar-mass scenario.

MODA: a new algorithm to compute optical depths in multidimensional hydrodynamic simulations

Aims. We introduce the multidimensional optical depth algorithm (MODA) for the calculation of optical depths in approximate multidimensional radiative transport schemes, equally applicable to neutrinos and photons. Motivated by (but not limited to) neutrino transport in three-dimensional simulations of core-collapse supernovae and neutron star mergers, our method makes no assumptions about the geometry of the matter distribution, apart from expecting optically transparent boundaries. Methods. Based on local information about opacities, the algorithm figures out an escape route that tends to minimize the optical depth without assuming any predefined paths for radiation. Its adaptivity makes it suitable for a variety of astrophysical settings with complicated geometry (e.g., core-collapse supernovae, compact binary mergers, tidal disruptions, star formation, etc.). We implement the MODA algorithm into both a Eulerian hydrodynamics code with a fixed, uniform grid and into an SPH code where we use a tree structure that is otherwise used for searching neighbors and calculating gravity. Results. In a series of numerical experiments, we compare the MODA results with analytically known solutions. We also use snapshots from actual 3D simulations and compare the results of MODA with those obtained with other methods, such as the global and local ray-by-ray method. It turns out that MODA achieves excellent accuracy at a moderate computational cost. In appendix we also discuss implementation details and parallelization strategies.

Testing the concept of integral approach to derivatives within the smoothed particle hydrodynamics technique in astrophysical scenarios

Context. The smoothed particle hydrodynamics (SPH) technique is a well-known numerical method that has been applied to simulating the evolution of a wide variety of systems. Modern astrophysical applications of the method rely on the Lagrangian formulation of fluid Euler equations, which is fully conservative. A different scheme, based on a matrix approach to the SPH equations is currently being used in computational fluid dynamics. An original matrix formulation of SPH based on an integral approach to the derivatives, called IAD0, has been recently proposed and is fully conservative and well-suited to simulating astrophysical processes. Aims. The behavior of the IAD0 scheme is analyzed in connection with several astrophysical scenarios, and compared to the same simulations carried out with the standard SPH technique. Methods. The proposed hydrodynamic scheme is validated using a variety of numerical tests that cover important topics in astrophysics, such as the evolution of supernova remnants, the stability of self-gravitating bodies, and the coalescence of compact objects. Results. The analysis of the hydrodynamical simulations of the above-mentioned astrophysical scenarios suggests that the SPH scheme built with the integral approach to the derivatives improves the results of the standard SPH technique. In particular, there is a better development of hydrodynamic instabilities, a good description of self-gravitating structures in equilibrium and a reasonable description of the process of coalescence of two white dwarfs. We also observed good conservations of energy and both linear and angular momenta that were generally better than those of standard SPH. In addition the new scheme is less susceptible to pairing instability. Conclusions. We present a formalism based on a tensor approach to Euler SPH equations that we checked using a variety of three-dimensional tests of astrophysical interest. This new scheme is more accurate because of the re-normalization imposed on the interpolations, which is fully conservative and less prone to undergoing the pairing instability. The analysis of these test cases suggests that the method may improve the simulation of many astrophysical problems with only a moderate computational overload.Context. The smoothed particle hydrodynamics (SPH) technique is a well-known numerical method that has been applied to simulating the evolution of a wide variety of systems. Modern astrophysical applications of the method rely on the Lagrangian formulation of fluid Euler equations, which is fully conservative. A different scheme, based on a matrix approach to the SPH equations is currently being used in computational fluid dynamics. An original matrix formulation of SPH based on an integral approach to the derivatives, called IAD0, has been recently proposed and is fully conservative and well-suited to simulating astrophysical processes. Aims. The behavior of the IAD0 scheme is analyzed in connection with several astrophysical scenarios, and compared to the same simulations carried out with the standard SPH technique. Methods. The proposed hydrodynamic scheme is validated using a variety of numerical tests that cover important topics in astrophysics, such as the evolution of supernova remnants, the stability of self-gravitating bodies, and the coalescence of compact objects. Results. The analysis of the hydrodynamical simulations of the above-mentioned astrophysical scenarios suggests that the SPH scheme built with the integral approach to the derivatives improves the results of the standard SPH technique. In particular, there is a better development of hydrodynamic instabilities, a good description of self-gravitating structures in equilibrium and a reasonable description of the process of coalescence of two white dwarfs. We also observed good conservations of energy and both linear and angular momenta that were generally better than those of standard SPH. In addition the new scheme is less susceptible to pairing instability. Conclusions. We present a formalism based on a tensor approach to Euler SPH equations that we checked using a variety of three-dimensional tests of astrophysical interest. This new scheme is more accurate because of the re-normalization imposed on the interpolations, which is fully conservative and less prone to undergoing the pairing instability. The analysis of these test cases suggests that the method may improve the simulation of many astrophysical problems with only a moderate computational overload.

Type Ia supernovae: Can Coriolis force break the symmetry of the gravitational confined detonation explosion mechanism?

© 2016. The American Astronomical Society. All rights reserved.. Currently the number of models aimed at explaining the phenomena of type Ia supernovae is high and distinguishing between them is a must. In this work we explore the influence of rotation on the evolution of the nuclear flame that drives the explosion in the so-called gravitational confined detonation models. Assuming that the flame starts in a pointlike region slightly above the center of the white dwarf (WD) and adding a moderate amount of angular velocity to the star we follow the evolution of the deflagration using a smoothed particle hydrodynamics code. We find that the results are very dependent on the angle between the rotational axis and the line connecting the initial bubble of burned material with the center of the WD at the moment of ignition. The impact of rotation is larger for angles close to 90° because the Coriolis force on a floating element of fluid is maximum and its principal effect is to break the symmetry of the deflagration. Such symmetry breaking weakens the convergence of the nuclear flame at the antipodes of the initial ignition volume, changing the environmental conditions around the convergence region with respect to non-rotating models. These changes seem to disfavor the emergence of a detonation in the compressed volume at the antipodes and may compromise the viability of the so-called gravitational confined detonation mechanism.