Spin-Orbit Misalignment of Merging Black-Hole Binaries with Tertiary Companions

We study the effect of external companion on the orbital and spin evolution of merging black-hole (BH) binaries. An sufficiently close by and inclined companion can excite Lidov-Kozai (LK) eccentricity oscillations in the binary, thereby shortening its merger time. During such LK-enhanced orbital decay, the spin axis of the BH generally exhibits chaotic evolution, leading to a wide range ($0^\circ$-$180^\circ$) of final spin-orbit misalignment angle from an initially aligned configuration. For systems that do not experience eccentricity excitation, only modest ($\lesssim 20^\circ$) spin-orbit misalignment can be produced, and we derive an analytic expression for the final misalignment using the principle of adiabatic invariance. The spin-orbit misalignment directly impacts the gravitational waveform, and can be used to constrain the formation scenarios of BH binaries and dynamical influences of external companions.Comment: Published in ApJ

Suppression of extreme orbital evolution in triple systems with short range forces

The Lidov-Kozai (LK) mechanism plays an important role in the secular evolution of many hierarchical triple systems. The standard LK mechanism consists of large-amplitude oscillations in eccentricity and inclination of a binary subject to the quadrupole potential from an outer perturber. Recent work has shown that when the octupole terms are included in the potential, the inner binary can reach more extreme eccentricities as well as undergo orientation flips. It is known that pericenter precessions due to short-range effects, such as General Relativity and tidal and rotational distortions, can limit the growth of eccentricity and even suppress standard (quadrupolar) LK oscillations, but their effect on the octupole-level LK mechanism has not been fully explored. In this paper, we systematically study how these short-range forces affect the extreme orbital behaviour found in octupole LK cycles. In general, the influence of the octupole potential is confined to a range of initial mutual inclinations Itot centered around 90deg (when the inner binary mass ratio is <<1), with this range expanding with increasing octupole strength. We find that, while the short-range forces do not change the width and location of this "window of influence", they impose a strict upper limit on the maximum achievable eccentricity. This limiting eccentricity can be calculated analytically, and its value holds even for strong octupole potential and for the general case of three comparable masses. Short-range forces also affect orbital flips, progressively reducing the range of Itot within which flips are possible as the intensity of these forces increases.Comment: 20 pages,15 figures, updated to match version published on MNRA

Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution

Convolutional neural networks have recently demonstrated high-quality reconstruction for single-image super-resolution. In this paper, we propose the Laplacian Pyramid Super-Resolution Network (LapSRN) to progressively reconstruct the sub-band residuals of high-resolution images. At each pyramid level, our model takes coarse-resolution feature maps as input, predicts the high-frequency residuals, and uses transposed convolutions for upsampling to the finer level. Our method does not require the bicubic interpolation as the pre-processing step and thus dramatically reduces the computational complexity. We train the proposed LapSRN with deep supervision using a robust Charbonnier loss function and achieve high-quality reconstruction. Furthermore, our network generates multi-scale predictions in one feed-forward pass through the progressive reconstruction, thereby facilitates resource-aware applications. Extensive quantitative and qualitative evaluations on benchmark datasets show that the proposed algorithm performs favorably against the state-of-the-art methods in terms of speed and accuracy.Comment: This work is accepted in CVPR 2017. The code and datasets are available on http://vllab.ucmerced.edu/wlai24/LapSRN