Nutational resonances, transitional precession, and precession-averaged evolution in binary black-hole systems

In the post-Newtonian (PN) regime, the timescale on which the spins of binary black holes precess is much shorter than the radiation-reaction timescale on which the black holes inspiral to smaller separations. On the precession timescale, the angle between the total and orbital angular momenta oscillates with nutation period $\tau$, during which the orbital angular momentum precesses about the total angular momentum by an angle $\alpha$. This defines two distinct frequencies that vary on the radiation-reaction timescale: the nutation frequency $\omega \equiv 2\pi/\tau$ and the precession frequency $\Omega \equiv \alpha/\tau$. We use analytic solutions for generic spin precession at 2PN order to derive Fourier series for the total and orbital angular momenta in which each term is a sinusoid with frequency $\Omega - n\omega$ for integer $n$. As black holes inspiral, they can pass through nutational resonances ($\Omega = n\omega$) at which the total angular momentum tilts. We derive an approximate expression for this tilt angle and show that it is usually less than $10^{-3}$ radians for nutational resonances at binary separations $r > 10M$. The large tilts occurring during transitional precession (near zero total angular momentum) are a consequence of such states being approximate $n=0$ nutational resonances. Our new Fourier series for the total and orbital angular momenta converge rapidly with $n$ providing an intuitive and computationally efficient approach to understanding generic precession that may facilitate future calculations of gravitational waveforms in the PN regime.Comment: 18 pages, 9 figures, version published in PR

Earthquake recurrence as a record breaking process

Extending the central concept of recurrence times for a point process to recurrent events in space-time allows us to characterize seismicity as a record breaking process using only spatiotemporal relations among events. Linking record breaking events with edges between nodes in a graph generates a complex dynamical network isolated from any length, time or magnitude scales set by the observer. For Southern California, the network of recurrences reveals new statistical features of seismicity with robust scaling laws. The rupture length and its scaling with magnitude emerges as a generic measure for distance between recurrent events. Further, the relative separations for subsequent records in space (or time) form a hierarchy with unexpected scaling properties

Wide binaries as a critical test of Classical Gravity

Modified gravity scenarios where a change of regime appears at acceleration scales $a<a_{0}$ have been proposed. Since for $1 M_{\odot}$ systems the acceleration drops below $a_{0}$ at scales of around 7000 AU, a statistical survey of wide binaries with relative velocities and separations reaching $10^{4}$ AU and beyond should prove useful to the above debate. We apply the proposed test to the best currently available data. Results show a constant upper limit to the relative velocities in wide binaries which is independent of separation for over three orders of magnitude, in analogy with galactic flat rotation curves in the same $a<a_{0}$ acceleration regime. Our results are suggestive of a breakdown of Kepler's third law beyond $a \approx a_{0}$ scales, in accordance with generic predictions of modified gravity theories designed not to require any dark matter at galactic scales and beyond.Comment: accepted for publication in EPJ

Dynamics of black holes in de Sitter spacetimes

Nonlinear dynamics in cosmological backgrounds has the potential to teach us immensely about our Universe, and also to serve as prototype for nonlinear processes in generic curved spacetimes. Here we report on dynamical evolutions of black holes in asymptotically de Sitter spacetimes. We focus on the head-on collision of equal mass binaries and for the first time compare analytical and perturbative methods with full blown nonlinear simulations. Our results include an accurate determination of the merger/scatter transition (consequence of an expanding background) for small mass binaries and a test of the cosmic censorship conjecture, for large mass binaries. We observe that, even starting from small separations, black holes in large mass binaries eventually lose causal contact, in agreement with the conjecture

High-contrast imaging at small separation: impact of the optical configuration of two deformable mirrors on dark holes

The direct detection and characterization of exoplanets will be a major scientific driver over the next decade, involving the development of very large telescopes and requires high-contrast imaging close to the optical axis. Some complex techniques have been developed to improve the performance at small separations (coronagraphy, wavefront shaping, etc). In this paper, we study some of the fundamental limitations of high contrast at the instrument design level, for cases that use a combination of a coronagraph and two deformable mirrors for wavefront shaping. In particular, we focus on small-separation point-source imaging (around 1 $\lambda$/D). First, we analytically or semi-analytically analysing the impact of several instrument design parameters: actuator number, deformable mirror locations and optic aberrations (level and frequency distribution). Second, we develop in-depth Monte Carlo simulation to compare the performance of dark hole correction using a generic test-bed model to test the Fresnel propagation of multiple randomly generated optics static phase errors. We demonstrate that imaging at small separations requires large setup and small dark hole size. The performance is sensitive to the optic aberration amount and spatial frequencies distribution but shows a weak dependence on actuator number or setup architecture when the dark hole is sufficiently small (from 1 to $\lesssim$ 5 $\lambda$/D).Comment: 13 pages, 18 figure