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Abstract:

We analyse the heating of stellar discs by non axisymmetric structures and giant molecular clouds (GMCs) in N-body simulations of growing disc galaxies. The analysis resolves long-standing discrepancies between models and data by demonstrating the importance of distinguishing between measured age-velocity dispersion relations (AVRs) and the heating histories of the stars that make up the AVR. We fit both AVRs and heating histories with formulae ∝ tβ and determine the exponents β bar R and β bar z derived from in-plane and vertical AVRs and βR and βz from heating histories. Values of βz are in almost all simulations larger than values of βbarz , wheras values of βR are similar to or mildly larger than values of β bar R. Moreover, values of βz (β bar z) are generally larger than values of βR (β bar R). The dominant cause of these relations is the decline over the life of the disc in importance of GMCs as heating agents relative to spiral structure and the bar. We examine how age errors and biases in solar neighbourhood surveys in uence the measured AVR: they tend to decrease β values by smearing out ages and thus measured dispersions. We compare AVRs and velocity ellipsoid shapes σz/σR from simulations to Solar-neighbourhood data. We conclude that for the expected disc mass and dark halo structure, combined GMC and spiral/bar heating can explain the AVR of the Galactic thin disc. Strong departures of the disc mass or the dark halo structure from expectation spoil fits to the data.

Abstract:

According to Muñoz-Gutiérrez et al. the orbit of comet 1P/Halley is chaotic with a surprisingly small Lyapunov time-scale of order its orbital period. In this work we analyse the origin of chaos in Halley's orbit and the growth of perturbations, in order to get a better understanding of this unusually short time-scale. We perform N-body simulations to model Halley's orbit in the Solar system and measure the separation between neighbouring trajectories. To be able to interpret the numerical results, we use a semi-analytical map to demonstrate different growth modes, i.e. linear, oscillatory or exponential, and transitions between these modes. We find the Lyapunov time-scale of Halley's orbit to be of order 300 yr, which is significantly longer than previous estimates in the literature. This discrepancy could be due to the different methods used to measure the Lyapunov time-scale. A surprising result is that next to Jupiter, also encounters with Venus contribute to the exponential growth in the next 3000 yr. Finally, we note an interesting application of the sub-linear, oscillatory growth mode to an ensemble of bodies moving through the Solar system. Whereas in the absence of encounters with a third body the ensemble spreads out linearly in time, the accumulation of weak encounters can increase the lifetime of such systems due to the oscillatory behaviour.

Abstract:

© 2016. The American Astronomical Society. All rights reserved.. The dynamical formation of stellar-mass black hole-black hole binaries has long been a promising source of gravitational waves for the Laser Interferometer Gravitational-Wave Observatory (LIGO). Mass segregation, gravitational focusing, and multibody dynamical interactions naturally increase the interaction rate between the most massive black holes in dense stellar systems, eventually leading them to merge. We find that dynamical interactions, particularly three-body binary formation, enhance the merger rate of black hole binaries with total mass M tot roughly as ∝Mtotβ, with β ≳ 4. We find that this relation holds mostly independently of the initial mass function, but the exact value depends on the degree of mass segregation. The detection rate of such massive black hole binaries is only further enhanced by LIGO's greater sensitivity to massive black hole binaries with M tot ≲ 80 . We find that for power-law BH mass functions dN/dM ∝ M -α with α ≤ 2, LIGO is most likely to detect black hole binaries with a mass twice that of the maximum initial black hole mass and a mass ratio near one. Repeated mergers of black holes inside the cluster result in about ∼5% of mergers being observed between two and three times the maximum initial black hole mass. Using these relations, one may be able to invert the observed distribution to the initial mass function with multiple detections of merging black hole binaries.