Transport in Transitory Dynamical Systems

We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case. This requires knowing only the "action" of relevant heteroclinic orbits at the intersection of invariant manifolds of "forward" and "backward" hyperbolic orbits. These manifolds can be easily computed by leveraging the autonomous nature of the vector fields on either side of the time-dependent transition. As illustrative examples we consider a two-dimensional fluid flow in a rotating double-gyre configuration and a simple one-and-a-half degree of freedom model of a resonant particle accelerator. We compare our results to those obtained using finite-time Lyapunov exponents and to adiabatic theory, discussing the benefits and limitations of each method.Comment: Updated and corrected version. LaTeX, 29 pages, 21 figure

Analysis of the accuracy and convergence of equation-free projection to a slow manifold

In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis, and A. Zagaris, Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes, SIAM J. Appl. Dyn. Syst. 4 (2005) 711-732], we developed a class of iterative algorithms within the context of equation-free methods to approximate low-dimensional, attracting, slow manifolds in systems of differential equations with multiple time scales. For user-specified values of a finite number of the observables, the m-th member of the class of algorithms (m = 0, 1, ...) finds iteratively an approximation of the appropriate zero of the (m+1)-st time derivative of the remaining variables and uses this root to approximate the location of the point on the slow manifold corresponding to these values of the observables. This article is the first of two articles in which the accuracy and convergence of the iterative algorithms are analyzed. Here, we work directly with explicit fast--slow systems, in which there is an explicit small parameter, epsilon, measuring the separation of time scales. We show that, for each m = 0, 1, ..., the fixed point of the iterative algorithm approximates the slow manifold up to and including terms of O(epsilon^m). Moreover, for each m, we identify explicitly the conditions under which the m-th iterative algorithm converges to this fixed point. Finally, we show that when the iteration is unstable (or converges slowly) it may be stabilized (or its convergence may be accelerated) by application of the Recursive Projection Method. Alternatively, the Newton-Krylov Generalized Minimal Residual Method may be used. In the subsequent article, we will consider the accuracy and convergence of the iterative algorithms for a broader class of systems-in which there need not be an explicit small parameter-to which the algorithms also apply

Modeling Ultraviolet Wind Line Variability in Massive Hot Stars

We model the detailed time-evolution of Discrete Absorption Components (DACs) observed in P Cygni profiles of the Si IV lam1400 resonance doublet lines of the fast-rotating supergiant HD 64760 (B0.5 Ib). We adopt the common assumption that the DACs are caused by Co-rotating Interaction Regions (CIRs) in the stellar wind. We perform 3D radiative transfer calculations with hydrodynamic models of the stellar wind that incorporate these large-scale density- and velocity-structures. We develop the 3D transfer code Wind3D to investigate the physical properties of CIRs with detailed fits to the DAC shape and morphology. The CIRs are caused by irregularities on the stellar surface that change the radiative force in the stellar wind. In our hydrodynamic model we approximate these irregularities by circular symmetric spots on the stellar surface. We use the Zeus3D code to model the stellar wind and the CIRs, limited to the equatorial plane. We constrain the properties of large-scale wind structures with detailed fits to DACs observed in HD 64760. A model with two spots of unequal brightness and size on opposite sides of the equator, with opening angles of 20 +/- 5 degr and 30 +/- 5 degr diameter, and that are 20 +/- 5 % and 8 +/- 5 % brighter than the stellar surface, respectively, provides the best fit to the observed DACs. The recurrence time of the DACs compared to the estimated rotational period corresponds to spot velocities that are 5 times slower than the rotational velocity. The mass-loss rate of the structured wind model for HD 64760 does not exceed the rate of the spherically symmetric smooth wind model by more than 1 %. The fact that DACs are observed in a large number of hot stars constrains the clumping that can be present in their winds, as substantial amounts of clumping would tend to destroy the CIRs.Comment: 58 pages, 16 figures, 1 animation. Accepted for publication in The Astrophysical Journal, Main Journal. More information and animations are available at http://alobel.freeshell.org/hotstars.htm

Dynamical Masses for the Large Magellanic Cloud Massive Binary System [L72] LH 54-425

We present results from an optical spectroscopic investigation of the massive binary system [L72] LH~54-425 in the LH 54 OB association in the Large Magellanic Cloud. We revise the ephemeris of [L72] LH 54-425 and find an orbital period of 2.247409 +/- 0.000010 days. We find spectral types of O3 V for the primary and O5 V for the secondary. We made a combined solution of the radial velocities and previously published V-band photometry to determine the inclination for two system configurations, i = 52 degrees for the configuration of the secondary star being more tidally distorted and i = 55 degrees for the primary as the more tidally distorted star. We argue that the latter case is more probable, and this solution yields masses and radii of M_1 = 47 +/- 2 M_Sun and R_1 = 11.4 +/- 0.1 R_Sun for the primary, and M_2 = 28 +/- 1 M_Sun and R_2 = 8.1 +/- 0.1 R_Sun for the secondary. Our analysis places LH 54-425 amongst the most massive stars known. Based on the position of the two stars plotted on a theoretical HR diagram, we find the age of the system to be about 1.5 Myr.Comment: 21 pages, 6 figures. Accepted in ApJ. To appear vol. 683, Aug. 10t

Large Interstellar Polarisation Survey. LIPS I: FORS2 spectropolarimetry in the Southern Hemisphere

Polarimetric studies of light transmitted through interstellar clouds may give constraints on the properties of the interstellar dust grains. Traditionally, broadband linear polarisation (BBLP) measurements have been considered an important diagnostic tool for the study of the interstellar dust, while comparatively less attention has been paid to spectropolarimetric measurements. However, spectropolarimetry may offer stronger constraints than BBLP, for example by revealing narrowband features, and by allowing us to distinguish the contribution of dust from the contribution of interstellar gas. Therefore, we have decided to carry out a Large Interstellar Polarisation Survey (LIPS) using spectropolarimetric facilities in both hemispheres. Here we present the results obtained in the Southern Hemisphere with the FORS2 instrument of the ESO Very Large Telescope. Our spectra cover the wavelength range 380--950\,nm at a spectral resolving power of about 880. We have produced a publicly available catalogue of 127 linear polarisation spectra of 101 targets. We also provide the Serkowski-curve parameters, as well as the wavelength gradient of the polarisation position angle for the interstellar polarisation along 76 different lines of sight. In agreement with previous literature, we found that the best-fit parameters of the Serkowski-curve are not independent of each other. However, the relationships that we obtained are not always consistent with what was found in previous studies.Comment: Accepted by A&A (replaced on 12 October 2017 simply to correct a Metadata error

The Rich Mid-Infrared Environments of Two Highly-Obscured X-ray Binaries: Spitzer Observations of IGR J16318-4848 and GX 301-2

We present the results of Spitzer mid-infrared spectroscopic observations of two highly-obscured massive X-ray binaries: IGR J16318-4848 and GX301-2. Our observations reveal for the first time the extremely rich mid-infrared environments of this type of source, including multiple continuum emission components (a hot component with T > 700 K and a warm component with T ~ 180 K) with apparent silicate absorption features, numerous HI recombination lines, many forbidden ionic lines of low ionization potentials, and pure rotational H2 lines. This indicates that both sources have hot and warm circumstellar dust, ionized stellar winds, extended low-density ionized regions, and photo-dissociated regions. It appears difficult to attribute the total optical extinction of both sources to the hot and warm dust components, which suggests that there could be an otherwise observable colder dust component responsible for the most of the optical extinction and silicate absorption features. The observed mid-infrared spectra are similar to those from Luminous Blue Variables, indicating that the highly-obscured massive X-ray binaries may represent a previously unknown evolutionary phase of X-ray binaries with early-type optical companions. Our results highlight the importance and utility of mid-infrared spectroscopy to investigate highly-obscured X-ray binaries.Comment: To appear in ApJ Letter

Ultra-short pulses in linear and nonlinear media

We consider the evolution of ultra-short optical pulses in linear and nonlinear media. For the linear case, we first show that the initial-boundary value problem for Maxwell's equations in which a pulse is injected into a quiescent medium at the left endpoint can be approximated by a linear wave equation which can then be further reduced to the linear short-pulse equation. A rigorous proof is given that the solution of the short pulse equation stays close to the solutions of the original wave equation over the time scales expected from the multiple scales derivation of the short pulse equation. For the nonlinear case we compare the predictions of the traditional nonlinear Schr\"odinger equation (NLSE) approximation which those of the short pulse equation (SPE). We show that both equations can be derived from Maxwell's equations using the renormalization group method, thus bringing out the contrasting scales. The numerical comparison of both equations to Maxwell's equations shows clearly that as the pulse length shortens, the NLSE approximation becomes steadily less accurate while the short pulse equation provides a better and better approximation