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

Eccentric double white dwarfs as LISA sources in globular clusters

We consider the formation of double white dwarfs (DWDs) through dynamical interactions in globular clusters. Such interactions can give rise to eccentric DWDs, in contrast to the exclusively circular population expected to form in the Galactic disk. We show that for a 5-year Laser Interferometer Space Antenna (LISA) mission and distances as far as the Large Magellanic Cloud, multiple harmonics from eccentric DWDs can be detected at a signal-to-noise ratio higher than 8 for at least a handful of eccentric DWDs, given their formation rate and typical lifetimes estimated from current cluster simulations. Consequently the association of eccentricity with stellar-mass LISA sources does not uniquely involve neutron stars, as is usually assumed. Due to the difficulty of detecting (eccentric) DWDs with present and planned electromagnetic observatories, LISA could provide unique dynamical identifications of these systems in globular clusters.Comment: Published in ApJ 665, L5

The Divine Clockwork: Bohr's correspondence principle and Nelson's stochastic mechanics for the atomic elliptic state

We consider the Bohr correspondence limit of the Schrodinger wave function for an atomic elliptic state. We analyse this limit in the context of Nelson's stochastic mechanics, exposing an underlying deterministic dynamical system in which trajectories converge to Keplerian motion on an ellipse. This solves the long standing problem of obtaining Kepler's laws of planetary motion in a quantum mechanical setting. In this quantum mechanical setting, local mild instabilities occur in the Kelperian orbit for eccentricities greater than 1/\sqrt{2} which do not occur classically.Comment: 42 pages, 18 figures, with typos corrected, updated abstract and updated section 6.

Single-shot readout of electron spin states in a quantum dot using spin-dependent tunnel rates

We present a method for reading out the spin state of electrons in a quantum dot that is robust against charge noise and can be used even when the electron temperature exceeds the energy splitting between the states. The spin states are first correlated to different charge states using a spin dependence of the tunnel rates. A subsequent fast measurement of the charge on the dot then reveals the original spin state. We experimentally demonstrate the method by performing read-out of the two-electron spin states, achieving a single-shot visibility of more than 80%. We find very long triplet-to-singlet relaxation times (up to several milliseconds), with a strong dependence on in-plane magnetic field.Comment: 4 pages, 4 figure

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

The impact of reduction of doublet well spacing on the Net Present Value and the life time of fluvial Hot Sedimentary Aquifer doublets

This paper evaluates the impact of reduction of doublet well spacing, below the current West Netherlands Basin standard of 1000 to 1500 m, on the Net Present Value (NPV) and the life time of fluvial Hot Sedimentary Aquifer (HSA) doublets. First, a sensitivity analysis is used to show the possible advantage of such reduction on the NPV. The parameter value ranges are derived from West Netherlands Basin HSA doublet examples. The results indicate that a reduction of well spacing from 1400 to 1000 m could already influence NPV by up to 15%. This effect would be larger in more marginally economic HSA doublets compared to the West Netherlands Basin base case scenario. The possibility to reduce well spacing is supported by finite element production simulations, utilizing detailed facies architecture models. Furthermore, our results underline the necessity of detailed facies architecture models to assess the potential and risks of HSA doublets. This factor significantly affects doublet life time and net energy production of the doublet

Rigorous results on the local equilibrium kinetics of a protein folding model

A local equilibrium approach for the kinetics of a simplified protein folding model, whose equilibrium thermodynamics is exactly solvable, was developed in [M. Zamparo and A. Pelizzola, Phys. Rev. Lett. 97, 068106 (2006)]. Important properties of this approach are (i) the free energy decreases with time, (ii) the exact equilibrium is recovered in the infinite time limit, (iii) the equilibration rate is an upper bound of the exact one and (iv) computational complexity is polynomial in the number of variables. Moreover, (v) this method is equivalent to another approximate approach to the kinetics: the path probability method. In this paper we give detailed rigorous proofs for the above results.Comment: 25 pages, RevTeX 4, to be published in JSTA