[en] Stellar evolution models predict the existence of a gap in the black hole mass spectrum from ∼55 M _⊙–120 M _⊙ due to pair-instability supernovae (PISNe). We investigate the possible existence of such an “upper” mass gap in the second gravitational-wave transient catalog (GWTC-2) by hierarchically modeling the astrophysical distribution of black hole masses. We extend the Truncated and Powerlaw+Peak mass distribution families to allow for an explicit gap in the mass distribution, and apply the extended models to GWTC-2. We find that with the Truncated model there is mild evidence favoring an upper mass gap with log Bayes Factor $\mathrm{l}\mathrm{n}\mathcal{B}=2.79$, inferring the lower and upper bounds at ${56.12}_{-<!--\; ???\; -->4.38}^{+7.54}{M}_{\odot <!--\; ???\; -->}$ and ${103.74}_{-<!--\; ???\; -->6.32}^{+17.01}{M}_{\odot <!--\; ???\; -->}$ respectively. When using the Powerlaw+Peak model, we find no preference for the gap. When imposing tighter priors on the gap bounds centered on the expected PISNe gap bounds, the log Bayes factors in favor of a gap mildly increase. These results are however contingent on the parameter inference for the most massive binary, GW190521, for which follow-up analyses showed the source may be an intermediate mass ratio merger that has component masses straddling the gap. Using the GW190521 posterior samples from the analysis in Nitz & Capano (2021), we find an increase in Bayes factors in favor of the gap. However, the overall conclusions are unchanged: there is no preference for a gap when using the Powerlaw+Peak model. This work paves the way for constraining the physics of pair-instability and pulsational pair-instability supernovae and high-mass black hole formation.

[en] The inspiral and merger of two black holes produces a remnant black hole with mass and spin determined by the properties of its parent black holes. Using the inferred population properties of component black holes from the first two and a half observing runs of Advanced LIGO and Virgo, we calculate the population properties of the leftover remnant black holes. By integrating their rate of formation over the age of the universe, we estimate the number density of remnant black holes today. Using simple prescriptions for the cosmic star formation rate and black hole inspiral delay times, we determine the number density of this leftover black hole population to be ${660}_{-<!--\; ???\; -->240}^{+440}{\mathrm{M}\mathrm{p}\mathrm{c}}^{-<!--\; ???\; -->3}$, corresponding to ∼60,000 black hole remnants per Milky Way–equivalent galaxy. The mass spectrum of these remnants starts at ∼10 M _⊙ and can be approximated by a decreasing exponential with characteristic length ∼15 M _⊙, the final spin distribution is sharply peaked at χ _f ∼ 0.7, and the kick velocities range from tens to thousands of kilometers per second. These kick velocities suggest that globular clusters and nuclear star clusters may retain up to $3_{-<!--\; ???\; -->2}^{+3}\mathrm{\%<!--\; \%\; -->}$ and ${46}_{-<!--\; ???\; -->15}^{+17}\mathrm{\%<!--\; \%\; -->}$ of their remnant black holes, respectively, while young star clusters would only retain a few tenths of a percent. The estimates in this work assume that none of the remnants participate in subsequent hierarchical mergers. If hierarchical mergers occur, the overall number density would drop accordingly and the remnant mass distribution shape would evolve over time. This population of leftover black holes is an inescapable result from gravitational-wave observations of binary black hole mergers.

[en] Among the most eagerly anticipated opportunities made possible by Advanced LIGO/Virgo are multimessenger observations of compact mergers. Optical counterparts may be short-lived so rapid characterization of gravitational wave (GW) events is paramount for discovering electromagnetic signatures. One way to meet the demand for rapid GW parameter estimation is to trade off accuracy for speed, using waveform models with simplified treatment of the compact objects’ spin. We report on the systematic errors in GW parameter estimation suffered when using different spin approximations to recover generic signals. Component mass measurements can be biased by $><!--\; >\; -->5\mathrm{\sigma <!--\; ??\; -->}$ using simple-precession waveforms and in excess of $20\mathrm{\sigma <!--\; ??\; -->}$ when non-spinning templates are employed. This suggests that electromagnetic observing campaigns should not take a strict approach to selecting which LIGO/Virgo candidates warrant follow-up observations based on low-latency mass estimates. For sky localization, we find that searched areas are up to a factor of $\sim <!--\; ???\; -->2$ larger for non-spinning analyses, and are systematically larger for any of the simplified waveforms considered in our analysis. Distance biases for the non-precessing waveforms can be in excess of 100% and are largest when the spin angular momenta are in the orbital plane of the binary. We confirm that spin-aligned waveforms should be used for low-latency parameter estimation at the minimum. Including simple precession, though more computationally costly, mitigates biases except for signals with extreme precession effects. Our results shine a spotlight on the critical need for development of computationally inexpensive precessing waveforms and/or massively parallel algorithms for parameter estimation.

[en] One proposed formation channel for stellar mass black holes (BHs) is through hierarchical mergers of smaller BHs. Repeated mergers between comparable mass BHs leave an imprint on the spin of the resulting BH since the final BH spin is largely determined by the orbital angular momentum of the binary. We find that for stellar mass BHs forming hierarchically the distribution of spin magnitudes is universal, with a peak at $a\sim <!--\; ???\; -->0.7$ and little support below $a\sim <!--\; ???\; -->0.5$. We show that the spin distribution is robust against changes to the mass ratio of the merging binaries, the initial spin distribution of the first generation of BHs, and the number of merger generations. While we assume an isotropic distribution of initial spin directions, spins that are preferentially aligned or antialigned do not qualitatively change our results. We also consider a “cluster catastrophe” model for BH formation in which we allow for mergers of arbitrary mass ratios and show that this scenario predicts a unique spin distribution that is similar to the universal distribution derived for major majors. We explore the ability of spin measurements from ground-based gravitational-wave (GW) detectors to constrain hierarchical merger scenarios. We apply a hierarchical Bayesian mixture model to mock GW data and argue that the fraction of BHs that formed through hierarchical mergers will be constrained with $\mathcal{O}(100)$ LIGO binary black hole detections, while with $\mathcal{O}(10)$ detections we could falsify a model in which all component BHs form hierarchically.

[en] Inspirals and mergers of black hole (BH) and/or neutron star (NS) binaries are expected to be abundant sources for ground-based gravitational-wave (GW) detectors. We assess the capabilities of Advanced LIGO and Virgo to measure component masses using inspiral waveform models including spin-precession effects using a large ensemble of GW sources randomly oriented and distributed uniformly in volume. For 1000 sources this yields signal-to-noise ratios between 7 and 200. We make quantitative predictions for how well LIGO and Virgo will distinguish between BHs and NSs and appraise the prospect of using LIGO/Virgo (LV) observations to definitively confirm, or reject, the existence of a putative “mass gap” between NSs ($m⩽<!--\; ???\; -->3M_{\odot <!--\; ???\; -->}$) and BHs ($m⩾<!--\; ???\; -->5M_{\odot <!--\; ???\; -->}$). We find sources with the smaller mass component satisfying $m_2\lesssim <!--\; ???\; -->1.5M_{\odot <!--\; ???\; -->}$ to be unambiguously identified as containing at least one NS, while systems with $m_2\gtrsim <!--\; ???\; -->6M_{\odot <!--\; ???\; -->}$ will be confirmed binary BHs. Binary BHs with $m_2<<!--\; <\; -->5M_{\odot <!--\; ???\; -->}$ (i.e., in the gap) cannot generically be distinguished from NSBH binaries. High-mass NSs ($2<<!--\; <\; -->m<<!--\; <\; -->3M_{\odot <!--\; ???\; -->}$) are often consistent with low-mass BHs ($m<<!--\; <\; -->5M_{\odot <!--\; ???\; -->}$), posing a challenge for determining the maximum NS mass from LV observations alone. Individual sources will seldom be measured well enough to confirm objects in the mass gap and statistical inferences drawn from the detected population will be strongly dependent on the underlying distribution. If nature happens to provide a mass distribution with the populations relatively cleanly separated in chirp mass space, as some population synthesis models suggest, then NSs and BHs will be more easily distinguishable.

[en] We study the evolution of the binary black hole (BBH) mass distribution across cosmic time. The second gravitational-wave transient catalog (GWTC-2) from LIGO/Virgo contains BBH events out to redshifts z ∼ 1, with component masses in the range ∼5–80 M _⊙. In this catalog, the biggest BBHs, with m ₁ ≳ 45 M _⊙, are only found at the highest redshifts, z ≳ 0.4. We ask whether the absence of high-mass observations at low redshift indicates that the mass distribution evolves: the biggest BBHs only merge at high redshift, and cease merging at low redshift. Modeling the BBH primary-mass spectrum as a power law with a sharp maximum mass cutoff (Truncated model), we find that the cutoff increases with redshift (> 99.9% credibility). An abrupt cutoff in the mass spectrum is expected from (pulsational) pair-instability supernova simulations; however, GWTC-2 is only consistent with a Truncated mass model if the location of the cutoff increases from ${45}_{-<!--\; ???\; -->5}^{+13}{M}_{\odot <!--\; ???\; -->}$ at z < 0.4 to ${80}_{-<!--\; ???\; -->13}^{+16}{M}_{\odot <!--\; ???\; -->}$ at z > 0.4. Alternatively, if the primary-mass spectrum has a break in the power law (Broken Power Law) at ${38}_{-<!--\; ???\; -->8}^{+15}{M}_{\odot <!--\; ???\; -->}$, rather than a sharp cutoff, the data are consistent with a nonevolving mass distribution. In this case, the overall rate of mergers, at all masses, increases with redshift. Future observations will distinguish between a sharp mass cutoff that evolves with redshift and a nonevolving mass distribution with a gradual taper, such as a Broken Power Law. After ∼100 BBH merger observations, a continued absence of high-mass, low-redshift events would provide a clear signature that the mass distribution evolves with redshift.

[en] Advanced ground-based gravitational-wave (GW) detectors begin operation imminently. Their intended goal is not only to make the first direct detection of GWs, but also to make inferences about the source systems. Binary neutron-star mergers are among the most promising sources. We investigate the performance of the parameter-estimation (PE) pipeline that will be used during the first observing run of the Advanced Laser Interferometer Gravitational-wave Observatory (aLIGO) in 2015: we concentrate on the ability to reconstruct the source location on the sky, but also consider the ability to measure masses and the distance. Accurate, rapid sky localization is necessary to alert electromagnetic (EM) observatories so that they can perform follow-up searches for counterpart transient events. We consider PE accuracy in the presence of non-stationary, non-Gaussian noise. We find that the character of the noise makes negligible difference to the PE performance at a given signal-to-noise ratio. The source luminosity distance can only be poorly constrained, since the median 90% (50%) credible interval scaled with respect to the true distance is 0.85 (0.38). However, the chirp mass is well measured. Our chirp-mass estimates are subject to systematic error because we used gravitational-waveform templates without component spin to carry out inference on signals with moderate spins, but the total error is typically less than ${10}^{-<!--\; ???\; -->3}{M}_{\odot <!--\; ???\; -->}$. The median 90% (50%) credible region for sky localization is $\sim <!--\; ???\; -->600{\mathrm{d}\mathrm{e}\mathrm{g}}^2$ ($\sim <!--\; ???\; -->150{\mathrm{d}\mathrm{e}\mathrm{g}}^2$), with 3% (30%) of detected events localized within $100{\mathrm{d}\mathrm{e}\mathrm{g}}^2.$ Early aLIGO, with only two detectors, will have a sky-localization accuracy for binary neutron stars of hundreds of square degrees; this makes EM follow-up challenging, but not impossible.

[en] We anticipate the first direct detections of gravitational waves (GWs) with Advanced LIGO and Virgo later this decade. Though this groundbreaking technical achievement will be its own reward, a still greater prize could be observations of compact binary mergers in both gravitational and electromagnetic channels simultaneously. During Advanced LIGO and Virgo's first two years of operation, 2015 through 2016, we expect the global GW detector array to improve in sensitivity and livetime and expand from two to three detectors. We model the detection rate and the sky localization accuracy for binary neutron star (BNS) mergers across this transition. We have analyzed a large, astrophysically motivated source population using real-time detection and sky localization codes and higher-latency parameter estimation codes that have been expressly built for operation in the Advanced LIGO/Virgo era. We show that for most BNS events, the rapid sky localization, available about a minute after a detection, is as accurate as the full parameter estimation. We demonstrate that Advanced Virgo will play an important role in sky localization, even though it is anticipated to come online with only one-third as much sensitivity as the Advanced LIGO detectors. We find that the median 90% confidence region shrinks from ∼500 deg² in 2015 to ∼200 deg² in 2016. A few distinct scenarios for the first LIGO/Virgo detections emerge from our simulations.

[en] Inspiraling binary neutron stars (BNSs) are expected to be one of the most significant sources of gravitational-wave signals for the new generation of advanced ground-based detectors. We investigate how well we could hope to measure properties of these binaries using the Advanced LIGO detectors, which began operation in September 2015. We study an astrophysically motivated population of sources (binary components with masses $1.2M_{\odot <!--\; ???\; -->}\text{--}1.6M_{\odot <!--\; ???\; -->}$ and spins of less than 0.05) using the full LIGO analysis pipeline. While this simulated population covers the observed range of potential BNS sources, we do not exclude the possibility of sources with parameters outside these ranges; given the existing uncertainty in distributions of mass and spin, it is critical that analyses account for the full range of possible mass and spin configurations. We find that conservative prior assumptions on neutron-star mass and spin lead to average fractional uncertainties in component masses of ∼16%, with little constraint on spins (the median 90% upper limit on the spin of the more massive component is ∼0.7). Stronger prior constraints on neutron-star spins can further constrain mass estimates but only marginally. However, we find that the sky position and luminosity distance for these sources are not influenced by the inclusion of spin; therefore, if LIGO detects a low-spin population of BNS sources, less computationally expensive results calculated neglecting spin will be sufficient for guiding electromagnetic follow-up.

[en] The Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) discovered gravitational waves (GWs) from a binary black hole merger in 2015 September and may soon observe signals from neutron star mergers. There is considerable interest in searching for their faint and rapidly fading electromagnetic (EM) counterparts, though GW position uncertainties are as coarse as hundreds of square degrees. Because LIGO’s sensitivity to binary neutron stars is limited to the local universe, the area on the sky that must be searched could be reduced by weighting positions by mass, luminosity, or star formation in nearby galaxies. Since GW observations provide information about luminosity distance, combining the reconstructed volume with positions and redshifts of galaxies could reduce the area even more dramatically. A key missing ingredient has been a rapid GW parameter estimation algorithm that reconstructs the full distribution of sky location and distance. We demonstrate the first such algorithm, which takes under a minute, fast enough to enable immediate EM follow-up. By combining the three-dimensional posterior with a galaxy catalog, we can reduce the number of galaxies that could conceivably host the event by a factor of 1.4, the total exposure time for the Swift X-ray Telescope by a factor of 2, the total exposure time for a synoptic optical survey by a factor of 2, and the total exposure time for a narrow-field optical telescope by a factor of 3. This encourages us to suggest a new role for small field of view optical instruments in performing targeted searches of the most massive galaxies within the reconstructed volumes.