White Dwarf Mergers on Adaptive Meshes I. Methodology and Code Verification

The Type Ia supernova progenitor problem is one of the most perplexing and exciting problems in astrophysics, requiring detailed numerical modeling to complement observations of these explosions. One possible progenitor that has merited recent theoretical attention is the white dwarf merger scenario, which has the potential to naturally explain many of the observed characteristics of Type Ia supernovae. To date there have been relatively few self-consistent simulations of merging white dwarf systems using mesh-based hydrodynamics. This is the first paper in a series describing simulations of these systems using a hydrodynamics code with adaptive mesh refinement. In this paper we describe our numerical methodology and discuss our implementation in the compressible hydrodynamics code CASTRO, which solves the Euler equations, and the Poisson equation for self-gravity, and couples the gravitational and rotation forces to the hydrodynamics. Standard techniques for coupling gravitation and rotation forces to the hydrodynamics do not adequately conserve the total energy of the system for our problem, but recent advances in the literature allow progress and we discuss our implementation here. We present a set of test problems demonstrating the extent to which our software sufficiently models a system where large amounts of mass are advected on the computational domain over long timescales. Future papers in this series will describe our treatment of the initial conditions of these systems and will examine the early phases of the merger to determine its viability for triggering a thermonuclear detonation.Comment: Accepted for publication in the Astrophysical Journa

Trend-based analysis of a population model of the AKAP scaffold protein

We formalise a continuous-time Markov chain with multi-dimensional discrete state space model of the AKAP scaffold protein as a crosstalk mediator between two biochemical signalling pathways. The analysis by temporal properties of the AKAP model requires reasoning about whether the counts of individuals of the same type (species) are increasing or decreasing. For this purpose we propose the concept of stochastic trends based on formulating the probabilities of transitions that increase (resp. decrease) the counts of individuals of the same type, and express these probabilities as formulae such that the state space of the model is not altered. We define a number of stochastic trend formulae (e.g. weakly increasing, strictly increasing, weakly decreasing, etc.) and use them to extend the set of state formulae of Continuous Stochastic Logic. We show how stochastic trends can be implemented in a guarded-command style specification language for transition systems. We illustrate the application of stochastic trends with numerous small examples and then we analyse the AKAP model in order to characterise and show causality and pulsating behaviours in this biochemical system

On variations of the brightness of type Ia supernovae with the age of the host stellar population

Recent observational studies of type Ia supernovae (SNeIa) suggest correlations between the peak brightness of an event and the age of the progenitor stellar population. This trend likely follows from properties of the progenitor white dwarf (WD), such as central density, that follow from properties of the host stellar population. We present a statistically well-controlled, systematic study utilizing a suite of multi-dimensional SNeIa simulations investigating the influence of central density of the progenitor WD on the production of Fe-group material, particularly radioactive Ni-56, which powers the light curve. We find that on average, as the progenitor's central density increases, production of Fe-group material does not change but production of Ni-56 decreases. We attribute this result to a higher rate of neutronization at higher density. The central density of the progenitor is determined by the mass of the WD and the cooling time prior to the onset of mass transfer from the companion, as well as the subsequent accretion heating and neutrino losses. The dependence of this density on cooling time, combined with the result of our central density study, offers an explanation for the observed age-luminosity correlation: a longer cooling time raises the central density at ignition thereby producing less Ni-56 and thus a dimmer event. While our ensemble of results demonstrates a significant trend, we find considerable variation between realizations, indicating the necessity for averaging over an ensemble of simulations to demonstrate a statistically significant result.Comment: 5 pages, 4 figures, 1 table, accepted to ApJ

Evaluating Systematic Dependencies of Type Ia Supernovae: The Influence of Deflagration to Detonation Density

We explore the effects of the deflagration to detonation transition (DDT) density on the production of Ni-56 in thermonuclear supernova explosions (type Ia supernovae). Within the DDT paradigm, the transition density sets the amount of expansion during the deflagration phase of the explosion and therefore the amount of nuclear statistical equilibrium (NSE) material produced. We employ a theoretical framework for a well-controlled statistical study of two-dimensional simulations of thermonuclear supernovae with randomized initial conditions that can, with a particular choice of transition density, produce a similar average and range of Ni-56 masses to those inferred from observations. Within this framework, we utilize a more realistic "simmered" white dwarf progenitor model with a flame model and energetics scheme to calculate the amount of Ni-56 and NSE material synthesized for a suite of simulated explosions in which the transition density is varied in the range 1-3x10^7 g/cc. We find a quadratic dependence of the NSE yield on the log of the transition density, which is determined by the competition between plume rise and stellar expansion. By considering the effect of metallicity on the transition density, we find the NSE yield decreases by 0.055 +/- 0.004 solar masses for a 1 solar metallicity increase evaluated about solar metallicity. For the same change in metallicity, this result translates to a 0.067 +/- 0.004 solar mass decrease in the Ni-56 yield, slightly stronger than that due to the variation in electron fraction from the initial composition. Observations testing the dependence of the yield on metallicity remain somewhat ambiguous, but the dependence we find is comparable to that inferred from some studies.Comment: 15 pages, 13 figures, accepted to ApJ on July 6, 201

Simulations of Astrophysical Fluid Instabilities

We present direct numerical simulations of mixing at Rayleigh-Taylor unstable interfaces performed with the FLASH code, developed at the ASCI/Alliances Center for Astrophysical Thermonuclear Flashes at the University of Chicago. We present initial results of single-mode studies in two and three dimensions. Our results indicate that three-dimensional instabilities grow significantly faster than two-dimensional instabilities and that grid resolution can have a significant effect on instability growth rates. We also find that unphysical diffusive mixing occurs at the fluid interface, particularly in poorly resolved simulations.Comment: 3 pages, 1 figure. To appear in the proceedings of the 20th Texas Symposium on Relativistic Astrophysic

A Consideration of Biomarkers to be Used for Evaluation of Inflammation in Human Nutritional Studies

To monitor inflammation in a meaningful way, the markers used must be valid: they must reflect the inflammatory process under study and they must be predictive of future health status. In 2009, the Nutrition and Immunity Task Force of the International Life Sciences Institute, European Branch, organized an expert group to attempt to identify robust and predictive markers, or patterns or clusters of markers, which can be used to assess inflammation in human nutrition studies in the general population. Inflammation is a normal process and there are a number of cells and mediators involved. These markers are involved in, or are produced as a result of, the inflammatory process irrespective of its trigger and its location and are common to all inflammatory situations. Currently, there is no consensus as to which markers of inflammation best represent low-grade inflammation or differentiate between acute and chronic inflammation or between the various phases of inflammatory responses. There are a number of modifying factors that affect the concentration of an inflammatory marker at a given time, including age, diet and body fatness, among others. Measuring the concentration of inflammatory markers in the bloodstream under basal conditions is probably less informative compared with data related to the concentration change in response to a challenge. A number of inflammatory challenges have been described. However, many of these challenges are poorly standardised. Patterns and clusters may be important as robust biomarkers of inflammation. Therefore, it is likely that a combination of multiple inflammatory markers and integrated readouts based upon kinetic analysis following defined challenges will be the most informative biomarker of inflammation. Copyright © ILSI Europe 2013.Peer Reviewe