Context. Due to the ever increasing number of observations during the past decades, Type Ia supernovae are nowadays regarded as a heterogeneous class of optical transients consisting of several subtypes. One of the largest of these subclasses is the class of Type Iax supernovae. They have been suggested to originate from pure deflagrations in carbon-oxygen Chandrasekhar mass white dwarfs because the outcome of this explosion scenario is in general agreement with their subluminous nature. Aims. Although a few deflagration studies have already been carried out, the full diversity of the class has not been captured yet. This, in particular, holds for the faint end of the subclass. We therefore present a parameter study of single-spot ignited deflagrations in Chandrasekhar mass white dwarfs varying the location of the ignition spark, the central density, the metallicity, and the composition of the white dwarf. We also explore a rigidly rotating progenitor to investigate whether the effect of rotation can spawn additional trends. Methods. We carried out three-dimensional hydrodynamic simulations employing the LEAFS code. Subsequently, detailed nucleosynthesis results were obtained with the nuclear network code YANN. In order to compare our results to observations, we calculated synthetic spectra and light curves with the ARTIS code. Results. The new set of models extends the range in brightness covered by previous studies to the lower end. Our single-spot ignited explosions produce 56Ni masses from 5.8 × 10−3 to 9.2 × 10−2 M⊙. In spite of the wide exploration of the parameter space, the main characteristics of the models are primarily driven by the mass of 56Ni and form a one-dimensional sequence. Secondary parameters seem to have too little impact to explain the observed trend in the faint part of the Type Iax supernova class. We report kick velocities of the gravitationally bound explosion remnants from 6.9 to 369.8 km s−1. The magnitude as well as the direction of the natal kick is found to depend on the strength of the deflagration. Conclusions. This work corroborates the results of previous studies of deflagrations in Chandrasekhar mass white dwarfs. The wide exploration of the parameter space in initial conditions and viewing angle effects in the radiative transfer lead to a significant spread in the synthetic observables. The trends in observational properties toward the faint end of the class are, however, not reproduced. This motivates a quantification of the systematic uncertainties in the modeling procedure and the influence of the 56Ni-rich bound remnant to get to the bottom of these discrepancies. Moreover, while the pure deflagration scenario remains a favorable explanation for bright and intermediate luminosity Type Iax supernovae, our results suggest that other mechanisms also contribute to this class of events.
In 1974, Harris proposed his celebrated criterion: Continuous phase transitions in d-dimensional systems are stable against quenched spatial randomness whenever dν>2, where ν is the clean critical exponent of the correlation length. Forty years later, motivated by violations of the Harris criterion for certain lattices such as Voronoi-Delaunay triangulations of random point clouds, Barghathi and Vojta put forth a modified criterion for topologically disordered systems: aν>1, where a is the disorder decay exponent, which measures how fast coordination number fluctuations decay with increasing length scale. Here we present a topologically disordered lattice with coordination number fluctuations that decay as slowly as those of conventional uncorrelated randomness, but for which the clean universal behavior is preserved, hence violating even the modified criterion.
We study the two-dimensional Ising model on networks with quenched topological (connectivity) disorder. In particular, we construct random lattices of constant coordination number and perform large-scale Monte Carlo simulations in order to obtain critical exponents using finite-size scaling relations. We find disorder-dependent effective critical exponents, similar to diluted models, showing thus no clear universal behavior. Considering the very recent results for the two-dimensional Ising model on proximity graphs and the coordination number correlation analysis suggested by Barghathi and Vojta [Phys. Rev. Lett. 113, 120602 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.120602], our results indicate that the planarity and connectedness of the lattice play an important role on deciding whether the phase transition is stable against quenched topological disorder.
The Voronoi construction is ubiquitous across the natural sciences and engineering. In statistical mechanics, though, critical phenomena have so far been only investigated on the Delaunay triangulation, the dual of a Voronoi graph. In this paper we set to fill this gap by studying the two most prominent systems of classical statistical mechanics, the equilibrium spin-1/2 Ising model and the non-equilibrium contact process, on two-dimensional random Voronoi graphs. Particular motivation comes from the fact that these graphs have vertices of constant coordination number, making it possible to isolate topological effects of quenched disorder from node-intrinsic coordination number disorder. Using large-scale numerical simulations and finite-size-scaling techniques, we are able to demonstrate that both systems belong to their respective clean universality classes. Therefore, quenched disorder introduced by the randomness of the lattice is irrelevant and does not influence the character of the phase transitions. We report the critical points of both models to considerable precision and, for the Ising model, also the first correction-to-scaling exponent.
We establish how the Breitenlohner-Freedman (BF) bound is realized on tilings of two-dimensional Euclidean Anti-de Sitter space. For the continuum case and for scalar modes, the BF bound states that on Anti-de Sitter spaces, fluctuation modes remain stable for small negative mass squared. We solve the Klein-Gordon equation both analytically and numerically for finite cutoff. We then numerically calculate the BF bound for both cases. The results agree and are independent of the specific tiling. We also propose a model for a hyperbolic electric circuit and find again numerical agreement with the modified BF bound. This circuit is readily accessible in the laboratory, allowing for the experimental verification of our results.
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