We perform a statistical inference of the astrophysical population of binary black hole (BBH) mergers observed during the first two observing runs of Advanced LIGO and Advanced Virgo, including events reported in the GWTC-1 and IAS catalogs. We deriv
e a novel formalism to fully and consistently account for events of arbitrary significance. We carry out a software injection campaign to obtain a set of mock astrophysical events subject to our selection effects, and use the search background to compute the astrophysical probabilities $p_{rm astro}$ of candidate events for several phenomenological models of the BBH population. We emphasize that the values of $p_{rm astro}$ depend on both the astrophysical and background models. Finally, we combine the information from individual events to infer the rate, spin, mass, mass-ratio and redshift distributions of the mergers. The existing population does not discriminate between random spins with a spread in the effective spin parameter, and a small but nonzero fraction of events from tidally-torqued stellar progenitors. The mass distribution is consistent with one having a cutoff at $m_{rm max} = 41^{+10}_{-5},rm M_odot$, while the mass ratio favors equal masses; the mean mass ratio $bar q> 0.67$. The rate shows no significant evolution with redshift. We show that the merger rate restricted to BBHs with a primary mass between 20 and $30, rm M_odot$, and a mass ratio $q > 0.5$, and at $z sim 0.2$, is 1.5 to $5.3,{rm Gpc^{-3} yr^{-1}}$ (90% c.l.); these bounds are model independent and a factor of $sim 3$ tighter than that on the local rate of all BBH mergers, and hence are a robust constraint on all progenitor models. Including the events in our catalog increases the Fisher information about the BBH population by $sim 47%$, and tightens the constraints on population parameters.
We search for strongly lensed and multiply imaged gravitational wave signals in the second observing run of Advanced LIGO and Advanced Virgo (O2). We exploit a new source of information, the so-called Morse phase, which further mitigates the search b
ackground and constrains viable lenses. The best candidate we find is consistent with a strongly lensed signal from a massive binary black hole (BBH) merger, with three detected images consisting of the previously catalogued events GW170104 and GW170814, and a subthreshold trigger, GWC170620. Given the number of BBH events detected so far, we estimate an overall false alarm probability $sim 10^{-4}$ for the observed high degree of parameter coincidence between the three events. On the flip side, we measure the Morse phase differences which suggest a complex and atypical lens system, with at least five images including a magnified image at a local maximum of the Fermat potential. The low prior probability for multiple lensed images and the amount of fine tuning required in the lens model reduce the credibility of the lensing hypothesis. The long time delays between lensed images point toward a galaxy cluster lens with an internal velocity dispersion $sigma sim 650,{rm km/s}$, and the observed strain amplitudes imply a likely range $0.4 < z lesssim 0.7$ for the source redshift. We provide an error ellipse of $sim 16,{rm deg}^2$ for the sky location of the source together with additional specific constraints on the lens-host system, and encourage follow-up efforts to confirm or rule out any viable lens. If this is indeed a lensed event, successfully pinpointing the system would offer a unique opportunity to identify the host galaxy of a BBH merger, and even localize the source within it.
We introduce a new technique to search for gravitational wave events from compact binary mergers that produce a clear signal only in a single gravitational wave detector, and marginal signals in other detectors. Such a situation can arise when the de
tectors in a network have different sensitivities, or when sources have unfavorable sky locations or orientations. We start with a short list of loud single-detector triggers from regions of parameter space that are empirically unaffected by glitches (after applying signal-quality vetoes). For each of these triggers, we compute evidence for astrophysical origin from the rest of the detector network by coherently combining the likelihoods from all detectors and marginalizing over extrinsic geometric parameters. We report the discovery of two new binary black hole (BBH) mergers in the second observing run of Advanced LIGO and Virgo (O2), in addition to the ones that were reported in Abbott et al. (2018) and Venumadhav et al. (2019). We estimate that the two events have false alarm rates of one in 19 years (60 O2) and one in 11 years (36 O2). One of the events, GW170817A, has primary and secondary masses $m_1^{rm src} = 56_{-10}^{+16} , M_odot$ and $m_2^{rm src} = 40_{-11}^{+10} , M_odot$ in the source frame. The existence of GW170817A should be very informative about the theoretically predicted upper mass gap for stellar mass black holes. Its effective spin parameter is measured to be $chi_{rm eff} = 0.5 pm 0.2$, which is consistent with the tendency of the heavier detected BBH systems to have large and positive effective spin parameters. The other event, GWC170402, will be discussed thoroughly in future work.
Searches for gravitational waves crucially depend on exact signal processing of noisy strain data from gravitational wave detectors, which are known to exhibit significant non-Gaussian behavior. In this paper, we study two distinct non-Gaussian effec
ts in the LIGO/Virgo data which reduce the sensitivity of searches: first, variations in the noise power spectral density (PSD) on timescales of more than a few seconds; and second, loud and abrupt transient `glitches of terrestrial or instrumental origin. We derive a simple procedure to correct, at first order, the effect of the variation in the PSD on the search background. Given the knowledge of the existence of localized glitches in particular segments of data, we also develop a method to insulate statistical inference from these glitches, so as to cleanly excise them without affecting the search background in neighboring seconds. We show the importance of applying these methods on the publicly available LIGO data, and measure an increase in the detection volume of at least $15%$ from the PSD-drift correction alone, due to the improved background distribution.
Detection of templates (e.g., sources) embedded in low-number count Poisson noise is a common problem in astrophysics. Examples include source detection in X-ray images, gamma-rays, UV, neutrinos, and search for clusters of galaxies and stellar strea
ms. However, the solutions in the X-ray-related literature are sub-optimal -- in some cases by considerable factors. Using the lemma of Neyman-Pearson we derive the optimal statistics for template detection in the presence of Poisson noise. We demonstrate that this method provides higher completeness, for a fixed false-alarm probability value, compared with filtering the image with the point-spread function (PSF). In turn, we find that filtering by the PSF is better than filtering the image using the Mexican-hat wavelet (used by wavedetect). For some background levels, our method improves the sensitivity of source detection by more than a factor of two over the popular Mexican-hat wavelet filtering. This filtering technique can also be used also for fast PSF photometry and flare detection, and it is efficient, as well as straight forward to implement. We provide an implementation in MATLAB.
