Two classes of nonlocal Evolution Equations related by a shared Traveling Wave Problem

We consider reaction-diffusion equations and Korteweg-de Vries-Burgers (KdVB) equations, i.e. scalar conservation laws with diffusive-dispersive regularization. We review the existence of traveling wave solutions for these two classes of evolution equations. For classical equations the traveling wave problem (TWP) for a local KdVB equation can be identified with the TWP for a reaction-diffusion equation. In this article we study this relationship for these two classes of evolution equations with nonlocal diffusion/dispersion. This connection is especially useful, if the TW equation is not studied directly, but the existence of a TWS is proven using one of the evolution equations instead. Finally, we present three models from fluid dynamics and discuss the TWP via its link to associated reaction-diffusion equations

Physics of rotation in stellar models

In these lecture notes, we present the equations presently used in stellar interior models in order to compute the effects of axial rotation. We discuss the hypotheses made. We suggest that the effects of rotation might play a key role at low metallicity.Comment: 32 pages, 7 figures, lectures, CNRS school, will be published by Springe

Presupernova Structure of Massive Stars

Issues concerning the structure and evolution of core collapse progenitor stars are discussed with an emphasis on interior evolution. We describe a program designed to investigate the transport and mixing processes associated with stellar turbulence, arguably the greatest source of uncertainty in progenitor structure, besides mass loss, at the time of core collapse. An effort to use precision observations of stellar parameters to constrain theoretical modeling is also described.Comment: Proceedings for invited talk at High Energy Density Laboratory Astrophysics conference, Caltech, March 2010. Special issue of Astrophysics and Space Science, submitted for peer review: 7 pages, 3 figure

CoRoT\,102699796, the first metal-poor Herbig Ae pulsator: a hybrid δ\delta Sct-γ\gamma Dor variable?

We present the analysis of the time series observations of CoRoT\,102699796 obtained by the CoRoT satellite that show the presence of five independent oscillation frequencies in the range 3.6-5 c/d. Using spectra acquired with FLAMES@VLT, we derive the following stellar parameters: spectral type F1V, T$_{\rm eff}$=7000$\pm$200 K, log(g)=$3.8\pm0.4$, [M/H]=$-1.1\pm0.2$, $v$sin$i$=$50\pm5$ km/s, L/L$_{\odot}$=21$^{+21}_{-11}$. Thus, for the first time we report the existence of a metal poor, intermediate-mass PMS pulsating star. Ground-based and satellite data are used to derive the spectral energy distribution of CoRoT\,102699796 extending from the optical to mid-infrared wavelengths. The SED shows a significant IR excess at wavelengths greater than $\sim5 \mu$. We conclude that CoRoT\,102699796 is a young Herbig Ae (F1Ve) star with a transitional disk, likely associated to the HII region [FT96]213.1-2.2. The pulsation frequencies have been interpreted in the light of the non-radial pulsation theory, using the LOSC code in conjunction with static and rotational evolutionary tracks. A minimization algorithm was used to find the best-fit model with M=1.84 M$_{\odot}$, T$_{\rm eff}$=6900 K which imply an isochronal age of t$\sim$2.5 Myr. This result is based on the interpretation of the detected frequencies as $g$-modes of low-moderate $n$-value. To our knowledge, this is the first time that such modes are identified in a intermediate-mass PMS pulsating star. Since CoRoT\,102699796 lies in the region of the HR diagram where the $\delta$ Sct and $\gamma$ Dor instability strips intersect, we argue that the observed pulsation characteristics are intermediate between these classes of variables, i.e. CoRoT\,102699796 is likely the first PMS hybrid $\gamma$ Dor-$\delta$ Sct pulsator ever studied.Comment: 13 pages, 7 figures. Accepted for publication in Monthly Notices of the RA

New Rotation Periods in the Open Cluster NGC 1039 (M 34), and a Derivation of its Gyrochronology Age

Employing photometric rotation periods for solar-type stars in NGC 1039 [M 34], a young, nearby open cluster, we use its mass-dependent rotation period distribution to derive the cluster's age in a distance independent way, i.e., the so-called gyrochronology method. We present an analysis of 55 new rotation periods,using light curves derived from differential photometry, for solar type stars in M 34. We also exploit the results of a recently-completed, standardized, homogeneous BVIc CCD survey of the cluster in order to establish photometric cluster membership and assign B-V colours to each photometric variable. We describe a methodology for establishing the gyrochronology age for an ensemble of solar-type stars. Empirical relations between rotation period, photometric colour and stellar age (gyrochronology) are used to determine the age of M 34. Based on its position in a colour-period diagram, each M 34 member is designated as being either a solid-body rotator (interface or I-star), a differentially rotating star (convective or C-star) or an object which is in some transitory state in between the two (gap or g-star). Fitting the period and photometric colour of each I-sequence star in the cluster, we derive the cluster's mean gyrochronology age. 47/55 of the photometric variables lie along the loci of the cluster main sequence in V/B-V and V/V-I space. We are further able to confirm kinematic membership of the cluster for half of the periodic variables [21/55], employing results from an on-going radial velocity survey of the cluster. For each cluster member identified as an I-sequence object in the colour-period diagram, we derive its individual gyrochronology age, where the mean gyro age of M 34 is found to be 193 +/- 9 Myr, formally consistent (within the errors) with that derived using several distance-dependent, photometric isochrone methods (250 +/- 67 Myr).Comment: accepted for publication in Astronomy & Astrophysic

YREC: The Yale Rotating Stellar Evolution Code

The stellar evolution code YREC is outlined with emphasis on its applications to helio- and asteroseismology. The procedure for calculating calibrated solar and stellar models is described. Other features of the code such as a non-local treatment of convective core overshoot, and the implementation of a parametrized description of turbulence in stellar models, are considered in some detail. The code has been extensively used for other astrophysical applications, some of which are briefly mentioned at the end of the paper.Comment: 10 pages, 2 figures, ApSS accepte

The Evolution of Compact Binary Star Systems

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within the frequency band of ground-based detectors, while compact binaries of WDs are important sources of GWs at lower frequencies to be covered by space interferometers (LISA). Major uncertainties in the current understanding of properties of NSs and BHs most relevant to the GW studies are discussed, including the treatment of the natal kicks which compact stellar remnants acquire during the core collapse of massive stars and the common envelope phase of binary evolution. We discuss the coalescence rates of binary NSs and BHs and prospects for their detections, the formation and evolution of binary WDs and their observational manifestations. Special attention is given to AM CVn-stars -- compact binaries in which the Roche lobe is filled by another WD or a low-mass partially degenerate helium-star, as these stars are thought to be the best LISA verification binary GW sources.Comment: 105 pages, 18 figure