Search for Eccentric Binary Black Hole Mergers with Advanced LIGO and Advanced Virgo during Their First and Second Observing Runs

When formed through dynamical interactions, stellar-mass binary black holes (BBHs) may retain eccentric orbits (e > 0.1 at 10 Hz) detectable by ground-based gravitational-wave detectors. Eccentricity can therefore be used to differentiate dynamically formed binaries from isolated BBH mergers. Current template-based gravitational-wave searches do not use waveform models associated with eccentric orbits, rendering the search less efficient for eccentric binary systems. Here we present the results of a search for BBH mergers that inspiral in eccentric orbits using data from the first and second observing runs (O1 and O2) of Advanced LIGO and Advanced Virgo. We carried out the search with the coherent WaveBurst algorithm, which uses minimal assumptions on the signal morphology and does not rely on binary waveform templates. We show that it is sensitive to binary mergers with a detection range that is weakly dependent on eccentricity for all bound systems. Our search did not identify any new binary merger candidates. We interpret these results in light of eccentric binary formation models. We rule out formation channels with rates ⪆100 Gpc-3 yr-1 for e > 0.1, assuming a black hole mass spectrum with a power-law index ≲2

Scalar field self-force effects on orbits about a Schwarzschild black hole

For a particle of mass mu and scalar charge q, we compute the effects of the scalar field self-force upon circular orbits, upon slightly eccentric orbits and upon the innermost stable circular orbit of a Schwarzschild black hole of mass M. For circular orbits the self force is outward and causes the angular frequency at a given radius to decrease. For slightly eccentric orbits the self force decreases the rate of the precession of the orbit. The effect of the self force moves the radius of the innermost stable circular orbit inward by 0.122701 q^2/mu, and it increases the angular frequency of the ISCO by the fraction 0.0291657 q^2/mu M.Comment: 15 pages, 8 figure

On the origin of eccentricities among extrasolar planets

Most observed extrasolar planets have masses similar to, but orbits very different from, the gas giants of our solar system. Many are much closer to their parent stars than would have been expected and their orbits are often rather eccentric. We show that some of these planets might have formed in systems much like our solar system, i.e. in systems where the gas giants were originally on orbits with a semi-major axis of several au, but where the masses of the gas giants were all rather similar. If such a system is perturbed by another star, strong planet-planet interactions follow, causing the ejection of several planets while leaving those remaining on much tighter and more eccentric orbits. The eccentricity distribution of these perturbed systems is very similar to that of the observed extrasolar planets with semi-major axis between 1 and 6 au.Comment: Accepted for publication in MNRAS Letter

Dynamics of Black Hole Pairs II: Spherical Orbits and the Homoclinic Limit of Zoom-Whirliness

Spinning black hole pairs exhibit a range of complicated dynamical behaviors. An interest in eccentric and zoom-whirl orbits has ironically inspired the focus of this paper: the constant radius orbits. When black hole spins are misaligned, the constant radius orbits are not circles but rather lie on the surface of a sphere and have acquired the name "spherical orbits". The spherical orbits are significant as they energetically frame the distribution of all orbits. In addition, each unstable spherical orbit is asymptotically approached by an orbit that whirls an infinite number of times, known as a homoclinic orbit. A homoclinic trajectory is an infinite whirl limit of the zoom-whirl spectrum and has a further significance as the separatrix between inspiral and plunge for eccentric orbits. We work in the context of two spinning black holes of comparable mass as described in the 3PN Hamiltonian with spin-orbit coupling included. As such, the results could provide a testing ground of the accuracy of the PN expansion. Further, the spherical orbits could provide useful initial data for numerical relativity. Finally, we comment that the spinning black hole pairs should give way to chaos around the homoclinic orbit when spin-spin coupling is incorporated.Comment: 16 pages, several figure

The influence of general-relativity effects, dynamical tides and collisions on planet-planet scattering close to the star

Planet--Planet scattering is an efficient and robust dynamical mechanism for producing eccentric exoplanets. Coupled to tidal interactions with the central star, it can also explain close--in giant planets on circularized and potentially misaligned orbits. We explore scattering events occurring close to the star and test if they can reproduce the main features of the observed orbital distribution of giant exoplanets on tight orbits.In our modeling we exploit a numerical integration code based on the Hermite algorithm and including the effects of general relativity, dynamical tides and two--body collisions.We find that P--P scattering events occurring in systems with three giant planets initially moving on circular orbits close to their star produce a population of planets similar to the presently observed one, including eccentric and misaligned close--in planets. The contribution of tides and general relativity is relevant in determining the final outcome of the chaotic phase. Even if two--body collisions dominate the chaotic evolution of three planets in crossing orbits close to their star, the final distribution shows a significant number of planets on eccentric orbits. The highly misaligned close--in giant planets are instead produced by systems where the initial semi--major axis of the inner planet was around 0.2 au or beyond.Comment: Accepted for publication on A&

Gravitational radiation reaction in compact binary systems: Contribution of the quadrupole-monopole interaction

The radiation reaction in compact spinning binaries on eccentric orbits due to the quadrupole-monopole interaction is studied. This contribution is of second post-Newtonian order. As result of the precession of spins the magnitude $L$ of the orbital angular momentum is not conserved. Therefore a proper characterization of the perturbed radial motion is provided by the energy $E$ and angular average $\bar{L}$. As powerful computing tools, the generalized true and eccentric anomaly parametrizations are introduced. Then the secular losses in energy and magnitude of orbital angular momentum together with the secular evolution of the relative orientations of the orbital angular momentum and spins are found for eccentric orbits by use of the residue theorem. The circular orbit limit of the energy loss agrees with Poisson's earlier result.Comment: accepted for publication in Phys. Rev.

Single Close Encounters Do Not Make Eccentric Planetary Orbits

The recent discovery of a planet in an orbit with eccentricity $e = 0.63 \pm 0.08$ around the Solar-type star 16 Cyg B, together with earlier discoveries of other planets in orbits of significant eccentricity, raises the question of the origin of these orbits, so unlike the nearly circular orbits of our Solar system. In this paper I consider close encounters between two planets, each initially in a nearly circular orbit (but with sufficient eccentricity to permit the encounter). Such encounters are described by a two-body approximation, in which the effect of the attracting star is neglected, and by the approximation that their separation vector follows a nearly parabolic path. A single encounter cannot produce the present state of these systems, in which one planet is in an eccentric orbit and the other has apparently been lost. Even if the requirement that the second planet be lost is dropped, nearly circular orbits cannot scatter into eccentric ones.Comment: 9 pp., 1 figure, te