We report the observation of a gravitational-wave signal produced by the coalescence of two stellar-mass black holes. The signal, GW151226, was observed by the twin detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) on December 26, 2015 at 03:38:53 UTC. The signal was initially identified within 70 s by an online matched-filter search targeting binary coalescences. Subsequent off-line analyses recovered GW151226 with a network signal-to-noise ratio of 13 and a significance greater than 5σ. The signal persisted in the LIGO frequency band for approximately 1 s, increasing in frequency and amplitude over about 55 cycles from 35 to 450 Hz, and reached a peak gravitational strain of 3.4 −0.04 . All uncertainties define a 90% credible interval. This second gravitational-wave observation provides improved constraints on stellar populations and on deviations from general relativity.

In this paper, we study the strong gravitational lensing of gravitational waves (GWs) from a statistical perspective, with particular focus on the high frequency GWs from stellar binary black hole coalescences. These are most promising targets for groundbased detectors such as Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) and the proposed Einstein Telescope (ET) and can be safely treated under the geometrical optics limit for GW propagation. We perform a thorough calculation of the lensing rate, by taking account of effects caused by the ellipticity of lensing galaxies, lens environments, and magnification bias. We find that in certain GW source rate scenarios, we should be able to observe strongly lensed GW events once per year (∼ 1 yr −1 ) in the aLIGO survey at its design sensitivity; for the proposed ET survey, the rate could be as high as ∼ 80 yr −1 . These results depend on the estimate of GW source abundance, and hence can be correspondingly modified with an improvement in our understanding of the merger rate of stellar binary black holes. We also compute the fraction of four-image lens systems in each survey, predicting it to be ∼ 30 per cent for the aLIGO survey and ∼ 6 per cent for the ET survey. Finally, we evaluate the possibility of missing some images due to the finite survey duration, by presenting the probability distribution of lensing time delays. We predict that this selection bias will be insignificant in future GW surveys, as most of the lens systems (∼ 90 per cent) will have time delays less than ∼ 1 month, which will be far shorter than survey durations.

Understanding the host galaxy properties of stellar binary black hole (SBBH) mergers is important for revealing the origin of the SBBH gravitational-wave sources detected by advanced LIGO and helpful for identifying their electromagnetic counterparts. Here we present a comprehensive analysis of the host galaxy properties of SBBHs by implementing semi-analytical recipes for SBBH formation and merger into cosmological galaxy formation model. If the time delay between SBBH formation and merger ranges from < ∼ Gyr to the Hubble time, SBBH mergers at redshift z < ∼ 0.3 occur preferentially in big galaxies with stellar mass M * > ∼ 2 × 10 10 M ⊙ and metallicities Z peaking at ∼ 0.6Z ⊙ . However, the host galaxy stellar mass distribution of heavy SBBH mergers (M •• > ∼ 50M ⊙ ) is bimodal with one peak at ∼ 10 9 M ⊙ and the other peak at ∼ 2 × 10 10 M ⊙ . The contribution fraction from host galaxies with Z < ∼ 0.2Z ⊙ to heavy mergers is much larger than that to less heavy mergers. If SBBHs were formed in the early universe (e.g., z > 6), their mergers detected at z < ∼ 0.3 occur preferentially in even more massive galaxies with M * > 3 × 10 10 M ⊙ and in galaxies with metallicities mostly > ∼ 0.2Z ⊙ and peaking at Z ∼ 0.6Z ⊙ , due to later cosmic assembly and enrichment of their host galaxies. SBBH mergers at z < ∼ 0.3 mainly occur in spiral galaxies, but the fraction of SBBH mergers occur in elliptical galaxies can be significant if those SBBHs were formed in the early universe; and about two thirds of those mergers occur in the central galaxies of dark matter halos. We also present results on the host galaxy properties of SBBH mergers at higher redshift.