Interacting Binaries with Eccentric Orbits. III. Orbital Evolution due to Direct Impact and Self-Accretion

The rapid circularization and synchronization of the stellar components in an eccentric binary system at the onset of Roche lobe overflow (RLO) is a fundamental assumption common to all binary stellar evolution and population synthesis codes, even though the validity of this assumption is questionable both theoretically and observationally. Here we calculate the evolution of the orbital elements of an eccentric binary through the direct three-body integration of a massive particle ejected through the inner Lagrangian point of the donor star at periastron. The trajectory of this particle leads to three possible outcomes: direct accretion (DA) onto the companion star within a single orbit, self-accretion (SA) back onto the donor star within a single orbit, or a quasi-periodic orbit around the companion star. We calculate the secular evolution of the binary orbit in the first two cases and conclude that DA can increase or decrease the orbital semi-major axis and eccentricity, while SA always decreases the orbital both orbital elements. In cases where mass overflow contributes to circularizing the orbit, circularization can set in on timescales as short as a few per cent of the mass transfer timescale. In cases where mass overflow increases the eccentricity, the orbital evolution is governed by competition between mass overflow and tidal torques. In the absence of tidal torques, mass overflow resulting in DI can lead to substantially subsynchronously rotating donor stars. Contrary to common assumptions, DI furthermore does not always provide a strong sink of orbital angular momentum in close mass-transferring binaries; in fact we instead find that a significant part can be returned to the orbit during the particle orbit. The formulation presented here can be combined with stellar and binary evolution codes to generate a better picture of the evolution of eccentric, RLO binary star systems.Comment: 15 pages, 10 figures, Accepted for publication in Ap

Stellar Collisions and the Interior Structure of Blue Stragglers

Collisions of main sequence stars occur frequently in dense star clusters. In open and globular clusters, these collisions produce merger remnants that may be observed as blue stragglers. Detailed theoretical models of this process require lengthy hydrodynamic computations in three dimensions. However, a less computationally expensive approach, which we present here, is to approximate the merger process (including shock heating, hydrodynamic mixing, mass ejection, and angular momentum transfer) with simple algorithms based on conservation laws and a basic qualitative understanding of the hydrodynamics. These algorithms have been fine tuned through comparisons with the results of our previous hydrodynamic simulations. We find that the thermodynamic and chemical composition profiles of our simple models agree very well with those from recent SPH (smoothed particle hydrodynamics) calculations of stellar collisions, and the subsequent stellar evolution of our simple models also matches closely that of the more accurate hydrodynamic models. Our algorithms have been implemented in an easy to use software package, which we are making publicly available (see http://vassun.vassar.edu/~lombardi/mmas/). This software could be used in combination with realistic dynamical simulations of star clusters that must take into account stellar collisions.Comment: This revised version has 37 pages, 13 figures, 4 tables; submitted to ApJ; for associated software package, see http://vassun.vassar.edu/~lombardi/mmas/ This revised version presents additional comparisons with SPH results and slightly improved merger recipe

A Spectroscopic Analysis of Blue Stragglers, Horizontal Branch and Turn-Off Stars in Four Globular Clusters

We present a spectroscopic analysis of HST/STIS and FOS low- and intermediate-resolution spectroscopy of 55 stars (turn-off stars, horizontal branch stars and blue stragglers) in four globular clusters (47 Tucanae, M3, NGC6752, and NGC6397). Stars were analyzed with non-Local Thermodynamic Equilibrium model atmospheres, and values for their effective temperatures and gravities and some rotation rates were obtained. Using photometric fluxes, we also obtained radii, luminosities and spectroscopic masses.Comment: 71 pages, 28 figures. Electronic figures only in the published versio

Probing Electron-Capture Supernovae: X-Ray Binaries in Starbursts

Presenting population models of high-mass X-ray binaries (HMXBs) formed after bursts of star formation, we investigate the effect of electron-capture supernovae (ECS) of massive ONeMg white dwarfs and the hypothesis that ECS events are associated with typically low supernova kicks imparted to the nascent neutron stars. We identify an interesting ECS bump in the time evolution of HMXB numbers; this bump is caused by significantly increased production of wind-fed HMXBs 20-60 Myr post starburst. The amplitude and age extent of the ECS bump depend on the strength of ECS kicks and the mass range of ECS progenitors. We also find that ECS-HMXBs form through a specific evolutionary channel that is expected to lead to binaries with Be donors in wide orbits. These characteristics, along with their sensitivity to ECS properties, provide us with an intriguing opportunity to probe ECS physics and progenitors through studies of starbursts of different ages. Specifically, the case of the Small Magellanic Cloud, with a significant observed population of Be HMXBs and starburst activity 30-60 Myr ago, arises as a promising laboratory for understanding the role of electron-capture supernovae in neutron star formation.Comment: 5 pages, 3 figures, Published by ApJ in 07/0

Interacting Binaries with Eccentric Orbits. Secular Orbital Evolution Due To Conservative Mass Transfer

We investigate the secular evolution of the orbital semi-major axis and eccentricity due to mass transfer in eccentric binaries, assuming conservation of total system mass and orbital angular momentum. Assuming a delta function mass transfer rate centered at periastron, we find rates of secular change of the orbital semi-major axis and eccentricity which are linearly proportional to the magnitude of the mass transfer rate at periastron. The rates can be positive as well as negative, so that the semi-major axis and eccentricity can increase as well as decrease in time. Adopting a delta-function mass-transfer rate of 10^{-9} M_\sun {\rm yr}^{-1} at periastron yields orbital evolution timescales ranging from a few Myr to a Hubble time or more, depending on the binary mass ratio and orbital eccentricity. Comparison with orbital evolution timescales due to dissipative tides furthermore shows that tides cannot, in all cases, circularize the orbit rapidly enough to justify the often adopted assumption of instantaneous circularization at the onset of mass transfer. The formalism presented can be incorporated in binary evolution and population synthesis codes to create a self-consistent treatment of mass transfer in eccentric binaries.Comment: 16 pages, 8 figures, Accepted by The Astrophysical Journa

Equipotential Surfaces and Lagrangian points in Non-synchronous, Eccentric Binary and Planetary Systems

We investigate the existence and properties of equipotential surfaces and Lagrangian points in non-synchronous, eccentric binary star and planetary systems under the assumption of quasi-static equilibrium. We adopt a binary potential that accounts for non-synchronous rotation and eccentric orbits, and calculate the positions of the Lagrangian points as functions of the mass ratio, the degree of asynchronism, the orbital eccentricity, and the position of the stars or planets in their relative orbit. We find that the geometry of the equipotential surfaces may facilitate non-conservative mass transfer in non-synchronous, eccentric binary star and planetary systems, especially if the component stars or planets are rotating super-synchronously at the periastron of their relative orbit. We also calculate the volume-equivalent radius of the Roche lobe as a function of the four parameters mentioned above. Contrary to common practice, we find that replacing the radius of a circular orbit in the fitting formula of Eggleton (1983) with the instantaneous distance between the components of eccentric binary or planetary systems does not always lead to a good approximation to the volume-equivalent radius of the Roche-lobe. We therefore provide generalized analytic fitting formulae for the volume-equivalent Roche lobe radius appropriate for non-synchronous, eccentric binary star and planetary systems. These formulae are accurate to better than 1% throughout the relevant 2-dimensional parameter space that covers a dynamic range of 16 and 6 orders of magnitude in the two dimensions.Comment: 12 pages, 10 figures, 2 Tables, Accepted by the Astrophysical Journa

The Effect of Starburst Metallicity on Bright X-Ray Binary Formation Pathways

We investigate the characteristics of young ( 1e36 erg/s) High-Mass X-ray Binaries (HMXBs) and find the population to be strongly metallicity-dependent. We separate the model populations among two distinct formation pathways: (1) systems undergoing active Roche Lobe Overflow (RLO), and (2) wind accretion systems with donors in the (super)giant (SG) stage, which we find to dominate the HMXB population. We find metallicity to primarily affect the number of systems which move through each formation pathway, rather than the observable parameters of systems which move through each individual pathway. We discuss the most important model parameters affecting the HMXB population at both low and high metallicities. Using these results, we show that (1) the population of ultra-luminous X-Ray sources can be consistently described by very bright HMXBs which undergo stable Roche Lobe overflow with mild super-Eddington accretion and (2) the HMXB population of the bright starburst galaxy NGC~1569 is likely dominated by one extremely metal-poor starburst cluster.Comment: 12 pages, 10 figures, Accepted by Ap

Tidally-Induced Apsidal Precession in Double White Dwarfs: a new mass measurement tool with LISA

Galactic interacting double white dwarfs (DWD) are guaranteed gravitational wave (GW) sources for the GW detector LISA, with more than 10^4 binaries expected to be detected over the mission's lifetime. Part of this population is expected to be eccentric, and here we investigate the potential for constraining the white dwarf (WD) properties through apsidal precession in these binaries. We analyze the tidal, rotational, and general relativistic contributions to apsidal precession by using detailed He WD models, where the evolution of the star's interior is followed throughout the cooling phase. In agreement with previous studies of zero-temperature WDs, we find that apsidal precession in eccentric DWDs can lead to a detectable shift in the emitted GW signal when binaries with cool (old) components are considered. This shift increases significantly for hot (young) WDs. We find that apsidal motion in hot (cool) DWDs is dominated by tides at orbital frequencies above ~10^{-4}Hz (10^{- 3}$Hz). The analysis of apsidal precession in these sources while ignoring the tidal component would lead to an extreme bias in the mass determination, and could lead us to misidentify WDs as neutron stars or black holes. We use the detailed WD models to show that for older, cold WDs, there is a unique relationship that ties the radius and apsidal precession constant to the WD masses, therefore allowing tides to be used as a tool to constrain the source masses.Comment: 23 pages, 7 figures, revised to match accepted ApJ versio

Elliptical motions of stars in close binary systems

Motions of stars in close binary systems with a conservative mass exchange are examined. It is shown that Paczynski-Huang model widely used now for obtaining the semi-major axis variation of a relative stars orbit is incorrect, because it brings about large mistakes. A new model suitable for elliptical orbits of stars is proposed. Both of reactive and attractive forces between stars and a substance of the flowing jet are taken into account. A possibility of a mass exchange at presence of accretion disk is considere