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

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 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

Spectra of supernovae in the nebular phase

When supernovae enter the nebular phase after a few months, they reveal spectral fingerprints of their deep interiors, glowing by radioactivity produced in the explosion. We are given a unique opportunity to see what an exploded star looks like inside. The line profiles and luminosities encode information about physical conditions, explosive and hydrostatic nucleosynthesis, and ejecta morphology, which link to the progenitor properties and the explosion mechanism. Here, the fundamental properties of spectral formation of supernovae in the nebular phase are reviewed. The formalism between ejecta morphology and line profile shapes is derived, including effects of scattering and absorption. Line luminosity expressions are derived in various physical limits, with examples of applications from the literature. The physical processes at work in the supernova ejecta, including gamma-ray deposition, non-thermal electron degradation, ionization and excitation, and radiative transfer are described and linked to the computation and application of advanced spectral models. Some of the results derived so far from nebular-phase supernova analysis are discussed.Comment: Book chapter for 'Handbook of Supernovae,' edited by Alsabti and Murdin, Springer. 51 pages, 14 figure

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

Lack of consensus in social systems

We propose an exactly solvable model for the dynamics of voters in a two-party system. The opinion formation process is modeled on a random network of agents. The dynamical nature of interpersonal relations is also reflected in the model, as the connections in the network evolve with the dynamics of the voters. In the infinite time limit, an exact solution predicts the emergence of consensus, for arbitrary initial conditions. However, before consensus is reached, two different metastable states can persist for exponentially long times. One state reflects a perfect balancing of opinions, the other reflects a completely static situation. An estimate of the associated lifetimes suggests that lack of consensus is typical for large systems.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let

Optimally Dense Packings for Fully Asymptotic Coxeter Tilings by Horoballs of Different Types

The goal of this paper to determine the optimal horoball packing arrangements and their densities for all four fully asymptotic Coxeter tilings (Coxeter honeycombs) in hyperbolic 3-space $\mathbb{H}^3$. Centers of horoballs are required to lie at vertices of the regular polyhedral cells constituting the tiling. We allow horoballs of different types at the various vertices. Our results are derived through a generalization of the projective methodology for hyperbolic spaces. The main result states that the known B\"or\"oczky--Florian density upper bound for "congruent horoball" packings of $\mathbb{H}^3$ remains valid for the class of fully asymptotic Coxeter tilings, even if packing conditions are relaxed by allowing for horoballs of different types under prescribed symmetry groups. The consequences of this remarkable result are discussed for various Coxeter tilings.Comment: 26 pages, 10 figure

Optimal transport on wireless networks

We present a study of the application of a variant of a recently introduced heuristic algorithm for the optimization of transport routes on complex networks to the problem of finding the optimal routes of communication between nodes on wireless networks. Our algorithm iteratively balances network traffic by minimizing the maximum node betweenness on the network. The variant we consider specifically accounts for the broadcast restrictions imposed by wireless communication by using a different betweenness measure. We compare the performance of our algorithm to two other known algorithms and find that our algorithm achieves the highest transport capacity both for minimum node degree geometric networks, which are directed geometric networks that model wireless communication networks, and for configuration model networks that are uncorrelated scale-free networks.Comment: 5 pages, 4 figure

Coevolution of Glauber-like Ising dynamics on typical networks

We consider coevolution of site status and link structures from two different initial networks: a one dimensional Ising chain and a scale free network. The dynamics is governed by a preassigned stability parameter $S$, and a rewiring factor $\phi$, that determines whether the Ising spin at the chosen site flips or whether the node gets rewired to another node in the system. This dynamics has also been studied with Ising spins distributed randomly among nodes which lie on a network with preferential attachment. We have observed the steady state average stability and magnetisation for both kinds of systems to have an idea about the effect of initial network topology. Although the average stability shows almost similar behaviour, the magnetisation depends on the initial condition we start from. Apart from the local dynamics, the global effect on the dynamics has also been studied. These parameters show interesting variations for different values of $S$ and $\phi$, which helps in determining the steady-state condition for a given substrate.Comment: 8 pages, 10 figure

Constraining the physical properties of Type II-P supernovae using nebular phase spectra

We present a study of the nebular phase spectra of a sample of Type II-Plateau supernovae with identified progenitors or restrictive limits. The evolution of line fluxes, shapes, and velocities are compared within the sample, and interpreted by the use of a spectral synthesis code. The small diversity within the dataset can be explained by strong mixing occurring during the explosion, and by recognising that most lines have significant contributions from primordial metals in the H envelope, which dominates the total ejecta mass in these type of objects. In particular, when using the [O I] 6300, 6364 Angstrom doublet for estimating the core mass of the star, care has to be taken to account for emission from primordial O in the envelope. Finally, a correlation between the H-alpha line width and the mass of 56Ni is presented, suggesting that higher energy explosions are associated with higher 56Ni production.Comment: 18 pages, 15 figures, accepted for publication in MNRA