We investigate the impact of uncertainty in the metallicity-specific star formation rate over cosmic time on predictions of the rates and masses of double compact object mergers observable through gravitational waves. We find that this uncertainty can change the predicted detectable merger rate by more than an order of magnitude, comparable to contributions from uncertain physical assumptions regarding binary evolution, such as mass transfer efficiency or supernova kicks. We statistically compare the results produced by the COMPAS population synthesis suite against a catalogue of gravitational-wave detections from the first two Advanced LIGO and Virgo observing runs. We find that the rate and chirp mass of observed binary black hole mergers can be well matched under our default evolutionary model with a star formation metallicity spread of 0.39 dex around a mean metallicity 〈Z〉 that scales with redshift z as 〈Z〉 = 0.035 × 10−0.23z, assuming a star formation rate of $0.01 \times (1+z)^{2.77} / (1+((1+z)/2.9)^{4.7}) \, \rm {M}_\odot$ Mpc−3 yr−1. Intriguingly, this default model predicts that 80 per cent of the approximately one binary black hole merger per day that will be detectable at design sensitivity will have formed through isolated binary evolution with only dynamically stable mass transfer, i.e. without experiencing a common-envelope event.

Gravitational-wave detections are enabling measurements of the rate of coalescences of binaries composed of two compact objects—neutron stars and/or black holes. The coalescence rate of binaries containing neutron stars is further constrained by electromagnetic observations, including Galactic radio binary pulsars and short gamma-ray bursts. Meanwhile, increasingly sophisticated models of compact objects merging through a variety of evolutionary channels produce a range of theoretically predicted rates. Rapid improvements in instrument sensitivity, along with plans for new and improved surveys, make this an opportune time to summarise the existing observational and theoretical knowledge of compact-binary coalescence rates.

Compact Object Mergers: Population Astrophysics and Statistics (COMPAS; https://compas.science) is a public rapid binary population synthesis code. COMPAS generates populations of isolated stellar binaries under a set of parameterized assumptions in order to allow comparisons against observational data sets, such as those coming from gravitational-wave observations of merging compact remnants. It includes a number of tools for population processing in addition to the core binary evolution components. COMPAS is publicly available via the GitHub repository https://github.com/TeamCOMPAS/COMPAS/, and is designed to allow for flexible modifications as evolutionary models improve. This paper describes the methodology and implementation of COMPAS. It is a living document that will be updated as new features are added to COMPAS; the current document describes COMPAS v02.21.00.

Einstein Telescope (ET) is the European project for a gravitational-wave (GW) observatory of third-generation. In this paper we present a comprehensive discussion of its science objectives, providing state-of-the-art predictions for the capabilities of ET in both geometries currently under consideration, a single-site triangular configuration or two L-shaped detectors. We discuss the impact that ET will have on domains as broad and diverse as fundamental physics, cosmology, early Universe, astrophysics of compact objects, physics of matter in extreme conditions, and dynamics of stellar collapse. We discuss how the study of extreme astrophysical events will be enhanced by multi-messenger observations. We highlight the ET synergies with ground-based and space-borne GW observatories, including multi-band investigations of the same sources, improved parameter estimation, and complementary information on astrophysical or cosmological mechanisms obtained combining observations from different frequency bands. We present advancements in waveform modeling dedicated to third-generation observatories, along with open tools developed within the ET Collaboration for assessing the scientific potentials of different detector configurations. We finally discuss the data analysis challenges posed by third-generation observatories, which will enable access to large populations of sources and provide unprecedented precision.

Gravitational-wave detectors are starting to reveal the redshift evolution of the binary black hole (BBH) merger rate, R _BBH(z). We make predictions for R _BBH(z) as a function of black hole mass for systems originating from isolated binaries. To this end, we investigate correlations between the delay time and black hole mass by means of the suite of binary population synthesis simulations, COMPAS. We distinguish two channels: the common envelope (CE), and the stable Roche-lobe overflow (RLOF) channel, characterized by whether the system has experienced a common envelope or not. We find that the CE channel preferentially produces BHs with masses below about 30 M _⊙ and short delay times (t _delay ≲ 1 Gyr), while the stable RLOF channel primarily forms systems with BH masses above 30 M _⊙ and long delay times (t _delay ≳ 1 Gyr). We provide a new fit for the metallicity-dependent specific star formation rate density based on the Illustris TNG simulations, and use this to convert the delay time distributions into a prediction of R _BBH(z). This leads to a distinct redshift evolution of R _BBH(z) for high and low primary BH masses. We furthermore find that, at high redshift, R _BBH(z) is dominated by the CE channel, while at low redshift, it contains a large contribution (∼40%) from the stable RLOF channel. Our results predict that, for increasing redshifts, BBHs with component masses above 30 M _⊙ will become increasingly scarce relative to less massive BBH systems. Evidence of this distinct evolution of R _BBH(z) for different BH masses can be tested with future detectors.

Mergers of black hole–neutron star (BHNS) binaries have now been observed by gravitational wave (GW) detectors with the recent announcement of GW200105 and GW200115. Such observations not only provide confirmation that these systems exist but will also give unique insights into the death of massive stars, the evolution of binary systems and their possible association with gamma-ray bursts, r-process enrichment, and kilonovae. Here, we perform binary population synthesis of isolated BHNS systems in order to present their merger rate and characteristics for ground-based GW observatories. We present the results for 420 different model permutations that explore key uncertainties in our assumptions about massive binary star evolution (e.g. mass transfer, common-envelope evolution, supernovae), and the metallicity-specific star formation rate density, and characterize their relative impacts on our predictions. We find intrinsic local BHNS merger rates spanning |$\mathcal {R}_{\rm {m}}^0 \approx$| 4–830 |$\, \rm {Gpc}^{-3}$| |$\, \rm {yr}^{-1}$| for our full range of assumptions. This encompasses the rate inferred from recent BHNS GW detections and would yield detection rates of |$\mathcal {R}_{\rm {det}} \approx 1$|–180|$\, \rm {yr}^{-1}$| for a GW network consisting of LIGO, Virgo, and KAGRA at design sensitivity. We find that the binary evolution and metallicity-specific star formation rate density each impacts the predicted merger rates by order |$\mathcal {O}(10)$|⁠. We also present predictions for the GW-detected BHNS merger properties and find that all 420 model variations predict that |$\lesssim 5{{\ \rm per\ cent}}$| of the BHNS mergers have BH masses |$m_{\rm {BH}} \gtrsim 18\, \rm {M}_{\odot }$|⁠, total masses |$m_{\rm {tot}} \gtrsim 20\, \rm {M}_{\odot }$|⁠, chirp masses |${\mathcal {M}}_{\rm {c}} \gtrsim 5.5\, \rm {M}_{\odot }$|⁠, and mass ratios q_f ≳ 12 or q_f ≲ 2. Moreover, we find that massive NSs with |$m_{\rm {NS}} \gt 2\, \rm {M}_{\odot }$| are expected to be commonly detected in BHNS mergers in almost all our model variations. Finally, a wide range of |$\sim 0{{\ \rm per\ cent}}$| to |$70{{\ \rm per\ cent}}$| of the BHNS mergers are predicted to eject mass during the merger. Our results highlight the importance of considering variations in binary evolution and cosmological models when predicting, and eventually evaluating, populations of BHNS mergers.