Monte-Carlo methods for NLTE spectral synthesis of supernovae

We present JEKYLL, a new code for modelling of supernova (SN) spectra and lightcurves based on Monte-Carlo (MC) techniques for the radiative transfer. The code assumes spherical symmetry, homologous expansion and steady state for the matter, but is otherwise capable of solving the time-dependent radiative transfer problem in non-local-thermodynamic-equilibrium (NLTE). The method used was introduced in a series of papers by Lucy, but the full time-dependent NLTE capabilities of it have never been tested. Here, we have extended the method to include non-thermal excitation and ionization as well as charge-transfer and two-photon processes. Based on earlier work, the non-thermal rates are calculated by solving the Spencer-Fano equation. Using a method previously developed for the SUMO code, macroscopic mixing of the material is taken into account in a statistical sense. In addition, a statistical Markov-chain model is used to sample the emission frequency, and we introduce a method to control the sampling of the radiation field. Except for a description of JEKYLL, we provide comparisons with the ARTIS, SUMO and CMFGEN codes, which show good agreement in the calculated spectra as well as the state of the gas. In particular, the comparison with CMFGEN, which is similar in terms of physics but uses a different technique, shows that the Lucy method does indeed converge in the time-dependent NLTE case. Finally, as an example of the time-dependent NLTE capabilities of JEKYLL, we present a model of a Type IIb SN, taken from a set of models presented and discussed in detail in an accompanying paper. Based on this model we investigate the effects of NLTE, in particular those arising from non-thermal excitation and ionization, and find strong effects even on the bolometric lightcurve. This highlights the need for full NLTE calculations when simulating the spectra and lightcurves of SNe.Comment: Accepted for publication by Astronomy & Astrophysic

The 3-D Structure of SN 1987A's inner Ejecta

Twenty years after the explosion of SN 1987A, we are now able to observe the three-dimensional spatially resolved inner ejecta. Detailed mapping of newly synthesised material and its radioactive decay daughter products sheds light on the explosion mechanism. This may reveal the geometry of the explosion and its connection to the equatorial ring and the outer rings around SN 1987A. We have used integral field spectroscopy to image the supernova ejecta and the equatorial ring in the emission lines of [Si I]+[Fe II] and He I. The spectral information can be mapped into a radial velocity image revealing the expansion of the ejecta both as projected onto the sky and perpendicular to the sky plane. The inner ejecta are spatially resolved in a North-South direction and are clearly asymmetric. We argue that the bulk of the ejecta is situated in the same plane as defined by the equatorial ring and does not form a bipolar structure as has been suggested. The exact shape of the ejecta is modelled and we find that an elongated triaxial ellipsoid fits the observations best. From our spectral analyses of the ejecta spectrum we find that most of the He I, [Si I] and [Fe I-II] emission originates in the core material which has undergone explosive nucleosynthesis. The He I emission may be the result of alpha-rich freeze-out if the positron energy is deposited locally. Our observations clearly indicate a non-symmetric explosion mechanism for SN 1987A. The elongation and velocity asymmetries point towards a large-scale spatial non-spherical distribution as predicted in recent explosion models. The orientation of the ejecta in the plane of the equatorial ring argues against a jet-induced explosion through the poles due to stellar rotation.Comment: Above abstract is abridged. 11 pages, 9 figures. Accepted July 1st 2010 by Astronomy and Astrophysic

Consensus formation on coevolving networks: groups' formation and structure

We study the effect of adaptivity on a social model of opinion dynamics and consensus formation. We analyze how the adaptivity of the network of contacts between agents to the underlying social dynamics affects the size and topological properties of groups and the convergence time to the stable final state. We find that, while on static networks these properties are determined by percolation phenomena, on adaptive networks the rewiring process leads to different behaviors: Adaptive rewiring fosters group formation by enhancing communication between agents of similar opinion, though it also makes possible the division of clusters. We show how the convergence time is determined by the characteristic time of link rearrangement. We finally investigate how the adaptivity yields nontrivial correlations between the internal topology and the size of the groups of agreeing agents.Comment: 10 pages, 3 figures,to appear in a special proceedings issue of J. Phys. A covering the "Complex Networks: from Biology to Information Technology" conference (Pula, Italy, 2007

Three-dimensional modeling of Type Ia supernovae - The power of late time spectra

Late time synthetic spectra of Type Ia supernovae, based on three-dimensional deflagration models, are presented. We mainly focus on one model,"c3_3d_256_10s", for which the hydrodynamics (Roepke 2005) and nucleosynthesis (Travaglio et al. 2004) was calculated up to the homologous phase of the explosion. Other models with different ignition conditions and different resolution are also briefly discussed. The synthetic spectra are compared to observed late time spectra. We find that while the model spectra after 300 to 500 days show a good agreement with the observed Fe II-III features, they also show too strong O I and C I lines compared to the observed late time spectra. The oxygen and carbon emission originates from the low-velocity unburned material in the central regions of these models. To get agreement between the models and observations we find that only a small mass of unburned material may be left in the center after the explosion. This may be a problem for pure deflagration models, although improved initial conditions, as well as higher resolution decrease the discrepancy. The relative intensity from the different ionization stages of iron is sensitive to the density of the emitting iron-rich material. We find that clumping, with the presence of low density regions, is needed to reproduce the observed iron emission, especially in the range between 4000 and 6000 AA. Both temperature and ionization depend sensitively on density, abundances and radioactive content. This work therefore illustrates the importance of including the inhomogeneous nature of realistic three-dimensional explosion models. We briefly discuss the implications of the spectral modeling for the nature of the explosion.Comment: 20 pages, 9 figures, resolution of Fig 1 is reduced to meet astro-ph file size restriction, submitted to A&

The Landscape of Bounds for Binary Search Trees

Binary search trees (BSTs) with rotations can adapt to various kinds of structure in search sequences, achieving amortized access times substantially better than the Theta(log n) worst-case guarantee. Classical examples of structural properties include static optimality, sequential access, working set, key-independent optimality, and dynamic finger, all of which are now known to be achieved by the two famous online BST algorithms (Splay and Greedy). (...) In this paper, we introduce novel properties that explain the efficiency of sequences not captured by any of the previously known properties, and which provide new barriers to the dynamic optimality conjecture. We also establish connections between various properties, old and new. For instance, we show the following. (i) A tight bound of O(n log d) on the cost of Greedy for d-decomposable sequences. The result builds on the recent lazy finger result of Iacono and Langerman (SODA 2016). On the other hand, we show that lazy finger alone cannot explain the efficiency of pattern avoiding sequences even in some of the simplest cases. (ii) A hierarchy of bounds using multiple lazy fingers, addressing a recent question of Iacono and Langerman. (iii) The optimality of the Move-to-root heuristic in the key-independent setting introduced by Iacono (Algorithmica 2005). (iv) A new tool that allows combining any finite number of sound structural properties. As an application, we show an upper bound on the cost of a class of sequences that all known properties fail to capture. (v) The equivalence between two families of BST properties. The observation on which this connection is based was known before - we make it explicit, and apply it to classical BST properties. (...

Nebular Spectra and Explosion Asymmetry of Type Ia Supernovae

The spectral signatures of asymmetry in Type Ia Supernova (SN Ia) explosions are investigated, using a sample of late-time nebular spectra. First, a kinematical model is constructed for SN Ia 2003hv, which can account for the main features in its optical, Near-Infrared (NIR), and Mid-Infrared (Mid-IR) late-time spectra. It is found that an asymmetric off-center model can explain the observed characteristics of SN 2003hv. This model includes a relatively high density, Fe-rich region which displays a large velocity off-set, and a relatively low density, extended 56Ni-rich region which is more spherically distributed. The high density region consists of the inner stable Fe-Ni region and outer 56Ni-rich region. Such a distribution may be the result of a delayed-detonation explosion, in which the first deflagration produces the global asymmetry in the innermost ejecta, while the subsequent detonation can lead to the bulk spherical symmetry. This configuration, if viewed from the direction of the off-set, can consistently explain the blueshift in some of the emission lines and virtually no observed shift in other lines in SN 2003hv. For this model, we then explore the effects of different viewing angles and the implications for SNe Ia in general. The model predicts that a variation of the central wavelength, depending on the viewing angle, should be seen in some lines (e.g., [Ni II]7378), while the strongest lines (e.g., [Fe III] blend at 4700A) will not show this effect. By examining optical nebular spectra of 12 SNe Ia, we have found that such a variation indeed exists. We suggest that the global asymmetry in the innermost ejecta, as likely imprint of the deflagration flame propagation, is a generic feature of SNe Ia (abridged).Comment: 14 pages, 11 figures, 4 tables. Accepted for publication in the Astrophysical Journal. Minor correction

Synchronization in Weighted Uncorrelated Complex Networks in a Noisy Environment: Optimization and Connections with Transport Efficiency

Motivated by synchronization problems in noisy environments, we study the Edwards-Wilkinson process on weighted uncorrelated scale-free networks. We consider a specific form of the weights, where the strength (and the associated cost) of a link is proportional to $(k_{i}k_{j})^{\beta}$ with $k_{i}$ and $k_{j}$ being the degrees of the nodes connected by the link. Subject to the constraint that the total network cost is fixed, we find that in the mean-field approximation on uncorrelated scale-free graphs, synchronization is optimal at $\beta^{*}$$=$-1. Numerical results, based on exact numerical diagonalization of the corresponding network Laplacian, confirm the mean-field results, with small corrections to the optimal value of $\beta^{*}$. Employing our recent connections between the Edwards-Wilkinson process and resistor networks, and some well-known connections between random walks and resistor networks, we also pursue a naturally related problem of optimizing performance in queue-limited communication networks utilizing local weighted routing schemes.Comment: Papers on related research can be found at http://www.rpi.edu/~korniss/Research