Evolution of binary stars and its implications for evolutionary population synthesis

Most stars are members of binaries, and the evolution of a star in a close binary system differs from that of an ioslated star due to the proximity of its companion star. The components in a binary system interact in many ways and binary evolution leads to the formation of many peculiar stars, including blue stragglers and hot subdwarfs. We will discuss binary evolution and the formation of blue stragglers and hot subdwarfs, and show that those hot objects are important in the study of evolutionary population synthesis (EPS), and conclude that binary interactions should be included in the study of EPS. Indeed, binary interactions make a stellar population younger (hotter), and the far-ultraviolet (UV) excess in elliptical galaxies is shown to be most likely resulted from binary interactions. This has major implications for understanding the evolution of the far-UV excess and elliptical galaxies in general. In particular, it implies that the far-UV excess is not a sign of age, as had been postulated prviously and predicts that it should not be strongly dependent on the metallicity of the population, but exists universally from dwarf ellipticals to giant ellipticals.Comment: Oral talk on IAUS 262, Brazi

Cataclysmic Variables with Evolved Secondaries and the Progenitors of AM CVn Stars

We present the results of a systematic study of cataclysmic variables (CVs) and related systems, combining detailed binary-population synthesis (BPS) models with a grid of 120 binary evolution sequences calculated with a Henyey-type stellar evolution code. In these sequences, we used 3 masses for the white dwarf (0.6, 0.8, 1.0 Msun) and seven masses for the donor star in the range of 0.6-1.4 Msun. The shortest orbital periods were chosen to have initially unevolved secondaries, and the longest orbital period for each secondary mass was taken to be just longer than the bifurcation period (16 - 22 hr), beyond which systems evolve towards long orbital periods. These calculations show that systems which start with evolved secondaries near the end or just after their main-sequence phase become ultra-compact systems with periods as short as 7 min. These systems are excellent candidates for AM CVn stars. Using a standard BPS code, we show how the properties of CVs at the beginning of mass transfer depend on the efficiency for common-envelope (CE) ejection and the efficiency of magnetic braking. In our standard model, where CE ejection is efficient, some 10 per cent of all CVs have initially evolved secondaries (with a central hydrogen abundance X_c < 0.4) and ultimately become ultra-compact systems (implying a Galactic birthrate for AM CVn-like stars of 10^{-3} yr^{-1}). Almost all CVs with orbital periods longer than 5 hr are found to have initially evolved or relatively massive secondaries. We show that their distribution of effective temperatures is in good agreement with the distribution of spectral types obtained by Beuermann et al. (1998).Comment: 16 pages, 6 figures (Fig. 4 in reduced format). Submitted to MNRA

Constraints on SN Ia progenitor time delays from high-z SNe and the star formation history

We re-assess the question of a systematic time delay between the formation of the progenitor and its explosion in a type Ia supernova (SN Ia) using the Hubble Higher-z Supernova Search sample (Strolger et al. 2004). While the previous analysis indicated a significant time delay, with a most likely value of 3.4 Gyr, effectively ruling out all previously proposed progenitor models, our analysis shows that the time-delay estimate is dominated by systematic errors, in particular due to uncertainties in the star-formation history. We find that none of the popular progenitor models under consideration can be ruled out with any significant degree of confidence. The inferred time delay is mainly determined by the peak in the assumed star-formation history. We show that, even with a much larger Supernova sample, the time delay distribution cannot be reliably reconstructed without better constraints on the star-formation history.Comment: accepted for publication in MNRA

Evanescent wave optical binding forces on spherical microparticles

In this Letter, we demonstrate stable optical binding of spherical microparticles in counter-propagating evanescent optical fields formed by total reflection at a dielectric interface. The microspheres are observed to form one-dimensional chains oriented parallel to the direction of propagation of the beams. We characterize the strength of the optical binding interaction by measuring the extent of Brownian position fluctuations of the optically bound microspheres and relating this to a binding spring constant acting between adjacent particles. A stronger binding interaction is observed for particles near the middle of the chain, and the dependence of the binding strength on incident laser power and number of particles in the chain is determined

The C-flash and the ignition conditions of type Ia supernovae

Thanks to a stellar evolution code able to compute through the C-flash we link the binary population synthesis of single degenerate progenitors of type Ia supernovae (SNe Ia) to their physical condition at the time of ignition. We show that there is a large range of possible ignition densities and we detail how their probability distribution depends on the accretion properties. The low density peak of this distribution qualitatively reminds of the clustering of the luminosities of Branch-normal SNe Ia. We tighten the possible range of initial physical conditions for explosion models: they form a one-parameter family, independent of the metallicity. We discuss how these results may be modified if we were to relax our hypothesis of a permanent Hachisu wind or if we were to include electron captures.Comment: 10 pages, 14 figures, MNRAS accepte

Applications of forward performance processes in dynamic optimal portfolio management

The classical optimal investment models are cast in a finite or infinite horizon setting, assuming an a priori choice of a market model (or a family of models) as well as a priori choice of a utility function of terminal wealth and/or intermediate consumption. Once these choices are made, namely, the horizon, the model and the risk preferences, stochastic optimization technique yield the maximal expected utility (value function) and the optimal policies wither through the Hamilton-Jacobi-Bellman equation in Makovian models or, more generally, via duality in semi-martingale models. A fundamental property of the solution is time-consistency, which follows from the Dynamic Programming Principle (DPP). This principle provides the intuitively pleasing interpretation of the value function as the intermediate (indirect) utility. It also states that the value function is a martingale along the optimal wealth trajectory and a super-martingale along every admissible one. These properties provide a time-consistent framework of the solutions, which ``pastes" naturally one investment period to the next. Despite its mathematical sophistication, the classical expected utility framework cannot accommodate model revision, nor horizon flexibility nor adaptation of risk preferences, if one desires to retain time-consistency. Indeed, the classical formulation is by nature ``backwards" in time and, thus, it does not allow any ``forward in time" changes. For example, on-line learning, which typically occurs in a non-anticipated way, cannot be implemented in the classical setting, simply because the latter evolves backwards while the former progresses forward in time. To alleviate some of these limitations while, at the same time, preserving the time-consistency property, Musiela and Zariphopoulou proposed an alternative criterion, the so-called forward performance process. This process satisfies the DPP forward in time, and generalizes the classical expected utility. For a large family of cases, forward performance processes have been explicitly constructed for general Ito-diffusion markets. While there has already been substantial mathematical work on this criterion, concrete applications to applied portfolio management are lacking. In this thesis, the aim is to focus on applied aspects of the forward performance approach and build meaningful connections with practical portfolio management. The following topics are being studied. Chapter 2 starts with providing an intuitive characterization of the underlying performance measure and the associated risk tolerance process, which are the most fundamental ingredients of the forward approach. It also provides a novel decomposition of the initial condition and, in turn, its inter-temporal preservation as the market evolves. The main steps involve a system of stochastic differential equations modeling various stochastic sensitivities and risk metrics. Chapter 3 focuses on the applications of the above results to lifecycle portfolio management. Investors are firstly classified by their individual risk preference generating measures and, in turn, mapped to different groups that are consistent with the popular practice of age-based de-leveraging. The inverse problem is also studied, namely, how to infer the individual investor-type measure from observed investment behavior. Chapter 4 provides applications of the forward performance to the classical problem of mean-variance analysis. It examines how sequential investment periods can be ``pasted together" in a time-consistent manner from one evaluation period to the next. This is done by mapping the mean-variance to a family of forward quadratic performances with appropriate stochastic and path-dependent coefficients. Quantitative comparisons with the classical approach are provided for a class of market settings, which demonstrate the superiority and flexibility of the forward approach.Information, Risk, and Operations Management (IROM

Spatial-Temporal Deep Embedding for Vehicle Trajectory Reconstruction from High-Angle Video

Spatial-temporal Map (STMap)-based methods have shown great potential to process high-angle videos for vehicle trajectory reconstruction, which can meet the needs of various data-driven modeling and imitation learning applications. In this paper, we developed Spatial-Temporal Deep Embedding (STDE) model that imposes parity constraints at both pixel and instance levels to generate instance-aware embeddings for vehicle stripe segmentation on STMap. At pixel level, each pixel was encoded with its 8-neighbor pixels at different ranges, and this encoding is subsequently used to guide a neural network to learn the embedding mechanism. At the instance level, a discriminative loss function is designed to pull pixels belonging to the same instance closer and separate the mean value of different instances far apart in the embedding space. The output of the spatial-temporal affinity is then optimized by the mutex-watershed algorithm to obtain final clustering results. Based on segmentation metrics, our model outperformed five other baselines that have been used for STMap processing and shows robustness under the influence of shadows, static noises, and overlapping. The designed model is applied to process all public NGSIM US-101 videos to generate complete vehicle trajectories, indicating a good scalability and adaptability. Last but not least, the strengths of the scanline method with STDE and future directions were discussed. Code, STMap dataset and video trajectory are made publicly available in the online repository. GitHub Link: shorturl.at/jklT0

Quantification of the effects of fracture properties on seismic data

Fractures have significant impact on hydrocarbon production planning and management. Their properties directly determine the well location selection, drilling design and oil/gas productivity. The goal of this research is twofold. The first part is to explore and find an efficient modeling method that can describe fractures explicitly embedded in elastic media under for wave propagation modeling. The second part is to establish correlations between fracture properties and seismic response quantitatively using the modeling results. The results will provide essential information for developing a systematic characterization procedures for fractures. In the first part, the discontinuous Galerkin method (DG) is first explored for fracture modeling. Within this method, the displacement discontinuity is incorporated by using a jump function included within the shape functions commonly used in the finite element method. A single fracture model is explored using the DG method. The results are compared with the analytical solutions and found to be in close agreement. From the displacement fields, it is observed that the wave scattering is the main effect of fractures observed in seismic data. However, the expensive computational effort gives rise to challenges in conducting parametric study for several realistic models using DG methods. This poses problems in systematically understanding the effect of fractures on seismic waves. In the second part, an integral based method is implemented for the parametric studies to investigate the effect of fractures on seismic waves in elastic media. This integral based method ensures accuracy at the nodes of the elements and has greater computational efficiency. Using this algorithm, the effects of fracture spacing, density, and azimuth are investigated in a three-dimensional setting. The scattering index is used to evaluate the extent of wave scattering induced by fractures. The quantitative relationships between fracture spacing, azimuth and scattering index are established. These results provide valuable information for future fracture characterization procedures.Geological Science

Binary Evolutionary Models

In this talk, we present the general principles of binary evolution and give two examples. The first example is the formation of subdwarf B stars (sdBs) and their application to the long-standing problem of ultraviolet excess (also known as UV-upturn) in elliptical galaxies. The second is for the progenitors of type Ia supernovae (SNe Ia). We discuss the main binary interactions, i.e., stable Roche lobe overflow (RLOF) and common envelope (CE) evolution, and show evolutionary channels leading to the formation of various binary-related objects. In the first example, we show that the binary model of sdB stars of Han et al. (2002, 2003) can reproduce field sdB stars and their counterparts, extreme horizontal branch (EHB) stars, in globular clusters. By applying the binary model to the study of evolutionary population synthesis, we have obtained an ``a priori'' model for the UV-upturn of elliptical galaxies and showed that the UV-upturn is most likely resulted from binary interactions. This has major implications for understanding the evolution of the UV excess and elliptical galaxies in general. In the second example, we introduce the single degenerate channel and the double degenerate channel for the progenitors of SNe Ia. We give the birth rates and delay time distributions for each channel and the distributions of companion stars at the moment of SN explosion for the single degenerate channel, which would help to search for the remnant companion stars observationally.Comment: 8 pages, 4 figures, invited talk, to appear in the Proceedings of IAU Symp. 252 "The Art of Modelling Stars in the 21st Century", Sanya, China, 6th-11th April 2008, (L. Deng, K.L. Chan & C. Chiosi, eds.