How do binary black holes form?

Unravelling binary physics

We are making progress in understanding how two black holes can come together and merge.

On the 14th September 2015, Advanced LIGO (Laser Interferometer Gravitational-wave Observatory) detected gravitational waves from the collision of a pair of black holes, dubbed GW150914. Since then, Advanced LIGO has been joined by Advanced Virgo. Together, Advanced LIGO and Virgo observed GW170817, gravitational waves from the inspiral and merger of a pair of neutron stars. This event was subsequently observed across the electromagnetic spectrum, including as a gamma ray burst and kilonova. At the end of their first two observing runs, Advanced LIGO and Virgo had totalled up 10 binary black hole mergers and one binary neutron star merger. Their third observing run finished in March 2020.

These observations confirmed a major prediction of Albert Einstein's 1915 general theory of relativity and opened an unprecedented new window onto the cosmos. However, we still do not know how such pairs of merging black holes and neutron stars form.

In order for black holes to merge within the age of the Universe by emitting gravitational waves, they must start out close together by astronomical standards, no more than about a fifth of the distance between the Earth and the Sun for the heaviest LIGO sources. However, massive stars, which are the progenitors of the black holes that LIGO observes, expand to be much larger than this in the course of their evolution. The key challenge, then, is how to fit such large stars within a very small orbit. Several possible scenarios have been proposed to address this.

We use COMPAS to investigate massive binary evolution and constrain it with a range of observational data sets. Our code is publicly available at

Selected Papers

Summaries and data releases of papers which directly use COMPAS

Note: The data used in some of the COMPAS papers has been made available to the public.
For access, please see our Zenodo page, or check the appropriate paper below.

For a complete list of COMPAS papers, see our ADS library

Uncertainty Quantification of a Computer Model for Binary Black Hole Formation

Lin et al. 2021

Authors: Luyao Lin, Derek Bingham, Floor Broekgaarden, Ilya Mandel
arXiv: 2106.01552

In this paper, a fast and parallelizable method based on Gaussian Processes (GPs) is introduced to emulate computer models that simulate the formation of binary black holes (BBHs) through the evolution of pairs of massive stars. Two obstacles that arise in this application are the a priori unknown conditions of BBH formation and the large scale of the simulation data. We address them by proposing a local emulator which combines a GP classifier and a GP regression model. The resulting emulator can also be utilized in planning future computer simulations through a proposed criterion for sequential design. By propagating uncertainties of simulation input through the emulator, we are able to obtain the distribution of BBH properties under the distribution of physical parameters.

Impact of Massive Binary Star and Cosmic Evolution on Gravitational Wave Observations I: Black Hole - Neutron Star Mergers

Broekgaarden et al. 2021

Authors: Floor S. Broekgaarden, Edo Berger, Coenraad J. Neijssel, Alejandro Vigna-Gómez, Debatri Chattopadhyay, Simon Stevenson, Martyna Chruslinska, Stephen Justham, Selma E. de Mink, Ilya Mandel
arXiv: 2103.02608

Mergers of black hole-neutron star (BHNS) binaries are expected to be observed by gravitational wave (GW) detectors in the coming years. Such observations will 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 present binary population synthesis of isolated BHNS systems in order to predict 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 in our assumptions for the metallicity-specific star formation rate density, and characterize their relative impacts on our predictions. We predict intrinsic local BHNS merger rates in the range R^0_m ≈ 4–830 Gpc−3 yr−1 and detected rates in the range Rdet ≈ 1–180 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 impact the predicted merger rates by order O (10). We also present predictions for the GW detected BHNS merger properties and find that all 420 model variations predict that . 5% of the BHNS mergers have BH masses 𝑚BH & 18 M, total masses 𝑚tot & 20 M, chirp masses Mc & 5.5 M, mass ratios 𝑞f & 12 or 𝑞f . 2. Moreover, we find that massive NSs with 𝑚NS > 2 M are expected to be commonly detected in BHNS mergers in almost all our model variations. Finally, a wide range of ∼ 0%–70% 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.

Wind mass-loss rates of stripped stars inferred from Cygnus X-1

Neijssel et al. 2021

Authors: Coenraad J. Neijssel, Serena Vinciguerra, Alejandro Vigna-Gomez, Ryosuke Hirai, James C. A. Miller-Jones, Arash Bahramian, Thomas J. Maccarone, Ilya Mandel
arXiv: 2102.09092

Recent observations of the high-mass X-ray binary Cygnus X-1 have shown that both the companion star (41 solar masses) and the black hole (21 solar masses) are more massive than previously estimated. Furthermore, the black hole appears to be nearly maximally spinning. Here we present a possible formation channel for the Cygnus X-1 system that matches the observed system properties. In this formation channel, we find that the orbital parameters of Cygnus X-1, combined with the observed metallicity of the companion, imply a significant reduction in mass loss through winds relative to commonly used prescriptions for stripped stars.

Cygnus X-1 contains a 21–solar mass black hole—Implications for massive star winds

Miller-Jones et al. 2021

Authors: James C.A. Miller-Jones, Arash Bahramian, Jerome A. Orosz, Ilya Mandel, Lijun Gou, Thomas J. Maccarone, Coenraad J. Neijssel, Xueshan Zhao, Janusz Ziółkowski, Mark J. Reid (10), Phil Uttley (11), Xueying Zheng, Do-Young Byun (12,13), Richard Dodson (14), Victoria Grinberg (15), Taehyun Jung (12,13), Jeong-Sook Kim (12), Benito Marcote (16), Sera Markoff (11,17), María J. Rioja (14,18,19), Anthony P. Rushton (20,21), David M. Russell (22), Gregory R. Sivakoff (23), Alexandra J. Tetarenko (24), Valeriu Tudose (25), Joern Wilms
arXiv: 2102.09091

The evolution of massive stars is influenced by the mass lost to stellar winds over their lifetimes. These winds limit the masses of the stellar remnants (such as black holes) that the stars ultimately produce. We use radio astrometry to refine the distance to the black hole X-ray binary Cygnus X-1, which we find to be 2.22+0.18 −0.17 kiloparsecs. When combined with previous optical data, this implies a black hole mass of 21.2±2.2 solar masses, higher than previous measurements. The formation of such a high-mass black hole in a high-metallicity system constrains wind mass loss from massive stars.

Modelling Neutron Star-Black Hole Binaries: Future Pulsar Surveys and Gravitational Wave Detectors

Chattopadhyay et al. 2020

Authors: D. Chattopadhyay, S. Stevenson, J. R. Hurley, M. Bailes, F. Broekgaarden
arXiv: 2011.13503

Binaries comprised of a neutron star (NS) and a black hole (BH) have so far eluded observations as pulsars and with gravitational waves (GWs). We model the formation and evolution of these NS+BH binaries including pulsar evolution using the binary population synthesis code COMPAS. We predict the presence of a total of 50-1300 binaries containing a pulsar and a BH (PSR+BHs) in the Galactic field. We find the population observable by the next-generation of radio telescopes, represented by the SKA and MeerKAT, current (LIGO/Virgo) and future (LISA) GW detectors. We conclude that the SKA will observe 1-60 PSR+BHs, with 0-4 binaries containing millisecond pulsars. MeerKAT is expected to observe 0-30 PSR+BH systems. Future radio detections of NS+BHs will constrain uncertain binary evolution processes such as BH natal kicks. We show that systems in which the NS formed first (NSBH) can be distinguished from those where the BH formed first (BHNS) by their pulsar and binary properties. We find 40% of the LIGO/Virgo observed NS+BHs from a Milky-Way like field population will have a chirp mass ≥3.0 M⊙. We estimate the spin distributions of NS+BHs with two models for the spins of BHs. The remnants of BHNS mergers will have a spin of ∼0.4, whilst NSBH merger remnants can have a spin of ∼0.6 or ∼0.9 depending on the model for BH spins. We estimate that approximately 25-930 PSR+BHs will be radio alive whilst emitting GWs in the LISA frequency band, raising the possibility of joint observation by the SKA and LISA.

Massive Stellar Triples Leading to Sequential Binary Black-Hole Mergers in the Field

Vigna-Gomez et al. 2020

Authors: A. Vigna-Gomez, S. Toonen, E. Ramirez-Ruiz, N. Leigh, J. Riley, C. Haster
arXiv: 2010.13669

Stellar triples with massive stellar components are common, and can lead to sequential binary black-hole mergers. Here, we outline the evolution towards these sequential mergers, and explore these events in the context of gravitational-wave astronomy and the pair-instability mass gap. We find that binary black-hole mergers in the pair-instability mass gap can be of triple origin and therefore are not exclusively formed in dense dynamical environments. We discuss the sequential merger scenario in the context of the most massive gravitational-wave sources detected to date: GW170729 and GW190521. We propose that the progenitor of GW170729 is a low-metallicity field triple. We support the premise that GW190521 could not have been formed in the field. We conclude that triple stellar evolution is fundamental in the understanding of gravitational-wave sources, and likely, other energetic transientsas well.

Chemically Homogeneous Evolution: A rapid population synthesis approach

Riley et al. 2020

Authors: J. Riley, I. Mandel, P. Marchant, E. Butler, K. Nathaniel, C. Neijssel, S. Shortt, A. Vigna-Gomez
arXiv: 2010.00002

We explore chemically homogeneous evolution (CHE) as a formation channel for massive merging binary black holes (BBHs). We develop methods to include CHE in a rapid binary population synthesis code, Compact Object Mergers: Population Astrophysics and Statistics (COMPAS), which combines realistic models of binary evolution with cosmological models of the star-formation history of the Universe. For the first time, we simultaneously explore conventional isolated binary star evolution under the same set of assumptions. This approach allows us to constrain population properties and make simultaneous predictions about the gravitational-wave detection rates of BBH mergers for the CHE and conventional formation channels. The overall mass distribution of detectable BBHs is consistent with existing gravitational-wave observations. We find that the CHE channel may yield up to ~70% of all gravitational-wave detections of BBH mergers coming from isolated binary evolution.

Binary population synthesis with probabilistic remnant mass and kick prescriptions

Mandel et al. 2020

Authors: I. Mandel, B. Muller, J. Riley, S. E. de Mink, A. Vigna-Gomez, D. Chattopadhyay
arXiv: 2007.03890

We report on the impact of a probabilistic prescription for compact remnant masses and spins on massive binary population synthesis. We find that this prescription populates the putative mass gap between neutron stars and black holes with low-mass black holes. However, evolutionary effects reduce the number of X-ray binary candidates with low-mass black holes, consistent with the dearth of such systems in the observed sample. We further find that this prescription is consistent with the formation of heavier binary neutron stars such as GW190425, but over-predicts the masses of Galactic double neutron stars. The revised natal kicks, particularly increased ultra-stripped supernova kicks, do not directly explain the observed Galactic double neutron star orbital period--eccentricity distribution. Finally, this prescription allows for the formation of systems similar to the recently discovered extreme mass ratio binary GW190814, but only if we allow for the survival of binaries in which the common envelope is initiated by a donor crossing the Hertzsprung gap, contrary to our standard model.

Simple recipes for compact remnant masses and natal kicks

Mandel & Muller 2020

Authors: I. Mandel, B. Muller
arXiv: 2006.08360

Based on recent results from three-dimensional supernova simulations and semianalytical parametrised models, we develop analytical prescriptions for the dependence of the mass of neutron stars and black holes and the natal kicks, if any, on the presupernova carbon-oxygen core and helium shell masses. Our recipes are probabilistic rather than deterministic in order to account for the intrinsic stochasticity of stellar evolution and supernovae. We anticipate that these recipes will be particularly useful for rapid population synthesis, and we illustrate their application to distributions of remnant masses and kicks for a population of single stars.

Polluting the pair-instability mass gap for binary black holes through super-Eddington accretion in isolated binaries

van Son et al. 2020

Authors: L.A.C. van Son, S. E. de Mink, F. S. Broekgaarden, M. Renzo, S. Justham, E. Laplace, J. Moran-Fraile, D. D. Hendriks, R. Farmer
arXiv: 2004.05187

The theory for single stellar evolution predicts a gap in the mass distribution of black holes (BHs) between approximately 45--130\Msun, the so-called ``the pair-instability mass gap". We examine whether BHs can pollute the gap after accreting from a stellar companion. To this end, we simulate the evolution of isolated binaries using a population synthesis code, where we allow for super-Eddington accretion. Under our most extreme assumptions, we find that at most about 2\% of all merging binary BH systems contains a BH with a mass in the pair-instability mass gap, and we find that less than 0.5\% of the merging systems has a total mass larger than 90\Msun. We find no merging binary BH systems with a total mass exceeding 100\Msun. We compare our results to predictions from several dynamical pathways to pair-instability mass gap events and discuss the distinguishable features. We conclude that the classical isolated binary formation scenario will not significantly contribute to the pollution of the pair-instability mass gap. The robustness of the predicted mass gap for the isolated binary channel is promising for the prospective of placing constraints on (i) the relative contribution of different formation channels, (ii) the physics of the progenitors including nuclear reaction rates, and (iii), tentatively, the Hubble parameter.

Be X-ray binaries in the SMC as (I) indicators of mass transfer efficiency

Vinciguerra et al. 2020

Authors: Serena Vinciguerra, Coenraad J. Neijssel, Alejandro Vigna-Gomez, Ilya Mandel, Philipp Podsiadlowski, Thomas J. Maccarone, Matt Nicholl, Samuel Kingdon, Alice Perry, Francesco Salemi
arXiv: 2003.00195

Be X-ray binaries (BeXRBs) consist of rapidly rotating Be stars with neutron star companions accreting from the circumstellar emission disk. We compare the observed population of BeXRBs in the Small Magellanic Cloud with simulated populations of BeXRB-like systems produced with the COMPAS population synthesis code. We focus on the apparently higher minimal mass of Be stars in BeXRBs than in the Be population at large. Assuming that BeXRBs experienced only dynamically stable mass transfer, their mass distribution suggests that at least ~30% of the mass donated by the progenitor of the neutron star is typically accreted by the B-star companion. We expect these results to affect predictions for the population of double compact object mergers. A convolution of the simulated BeXRB population with the star formation history of the Small Magellanic Cloud shows that the excess of BeXRBs is most likely explained by this galaxy's burst of star formation approximately 25-40 Myr ago, rather than by its low metallicity.

Modelling Double Neutron Stars: Radio and Gravitational Waves

Chattopadhyay et al. 2020

Authors: Debatri Chattopadhyay, Simon Stevenson, Jarrod R. Hurley, Luca J. Rossi, Chris Flynn
arXiv: 1912.02415

We have implemented prescriptions for modelling pulsars in the rapid binary population synthesis code COMPAS. We perform a detailed analysis of the double neutron star (DNS) population, accounting for radio survey selection effects. The surface magnetic field decay timescale (~1000 Myr) and mass scale (~0.02 solar masses) are the dominant uncertainties in our model. Mass accretion during common envelope evolution plays a non-trivial role in recycling pulsars. We find a best-fit model that is in broad agreement with the observed Galactic DNS population. Though the pulsar parameters (period and period derivative) are strongly biased by radio selection effects, the observed orbital parameters (orbital period and eccentricity) closely represent the intrinsic distributions. The number of radio observable DNSs in the Milky Way at present is ~2500 in our model, only ~10% of the predicted total number of DNSs in the galaxy. Using our model calibrated to the Galactic DNS population, we make predictions for DNS mergers observed in gravitational waves. The DNS chirp mass distribution varies from ~1.2 to ~2.1 solar masses and median is obtained to be 1.14 solar masses. The expected effective spin chi_eff for isolated DNSs is less than approximately 0.03 from our model. We predict that ~34% of the current Galactic isolated DNSs will merge within a Hubble time, and have a median total mass of 2.7 solar masses. Finally, we discuss implications for fast radio bursts and post-merger remnant gravitational-waves.

Common-Envelope Episodes that lead to Double Neutron Star formation

Vigna-Gomez et al. 2020

Authors: Alejandro Vigna-Gomez, Morgan MacLeod, Coenraad J. Neijssel, Floor S. Broekgaarden, Stephen Justham, George Howitt, Selma E. de Mink, Ilya Mandel
arXiv: 2001.09829

Close Double Neutron Stars (DNSs) have been observed as Galactic radio pulsars, while their mergers have been detected as gamma-ray bursts and gravitational-wave sources. They are believed to have experienced at least one common-envelope episode (CEE) during their evolution prior to DNS formation. In the last decades there have been numerous efforts to understand the details of the common-envelope phase, but its computational modelling remains challenging. We present and discuss the properties of the donor and the binary at the onset of the Roche-lobe overflow (RLOF) leading to these CEEs as predicted by rapid binary population synthesis models. These properties can be used as initial conditions for detailed simulations of the common-envelope phase. There are three distinctive populations, classified by the evolutionary stage of the donor at the moment of the onset of the RLOF: giant donors with fully-convective envelopes, cool donors with partially-convective envelopes, and hot donors with radiative envelopes. We also estimate that, for standard assumptions, tides would not circularise a large fraction of these systems by the onset of RLOF. This makes the study and understanding of eccentric mass transferring systems relevant for DNS populations.

Luminous Red Novae: population models and future prospects

Howitt et al. 2019

Authors: George Howitt, Simon Stevenson, Alejandro Vigna-Gomez, Stephen Justham, Natasha Ivanova, Tyrone E. Woods, Coenraad J. Neijssel, Ilya Mandel
arXiv: 1912.07771

A class of optical transients known as Luminous Red Novae (LRNe) have recently been associated with mass ejections from binary stars undergoing common-envelope evolution. We use the population synthesis code COMPAS to explore the impact of a range of assumptions about the physics of common-envelope evolution on the properties of LRNe. In particular, we investigate the influence of various models for the energetics of LRNe on the expected event rate and light curve characteristics, and compare with the existing sample. We find that the Galactic rate of LRNe is ~0.2-1 per year in agreement with the observed rate. In our models, the luminosity function of Galactic LRNe covers multiple decades in luminosity and is dominated by signals from stellar mergers, consistent with observational constraints from iPTF and the Galactic sample of LRNe. We discuss how observations of the brightest LRNe may provide indirect evidence for the existence of massive (>40 solar mass) red supergiants. Such LRNe could be markers along the evolutionary pathway leading to the formation of double compact objects. We make predictions for the population of LRNe observable in future transient surveys with the Large Synoptic Survey Telescope and the Zwicky Transient Facility. In all plausible circumstances, we predict a selection-limited observable population dominated by bright, long-duration events caused by common envelope ejections. We show that the Large Synoptic Survey Telescope will observe 20--750 LRNe per year, quickly constraining the luminosity function of LRNe and probing the physics of common-envelope events.

Detecting Double Neutron Stars with LISA

Lau et al. 2019

Authors: Lau, M. Y. M., Mandel, I., Vigna-Gomez, A., Neijssel, C., Stevenson, S., Sesana, A.
arXiv: 1910.12422 [astro-ph.HE]

We estimate the properties of the double neutron star (DNS) population that will be observable by the planned space-based interferometer LISA. By following the gravitational radiation driven evolution of DNSs generated from rapid population synthesis of massive binary stars, we estimate that around 35 DNSs will accumulate a signal-to-noise ratio above 8 over a four-year LISA mission. The observed population mainly comprises Galactic DNSs (94 per cent), but detections in the LMC (5 per cent) and SMC (1 per cent) may also be expected. The median orbital frequency of detected DNSs is expected to be 0.8 mHz, and many of them will be eccentric (median eccentricity of 0.11). The orbital properties will provide insights into DNS progenitors and formation channels. LISA is expected to localise these DNSs to a typical angular resolution of 2∘, with best-constrained sources localised to a few arcminutes. These localisations may allow neutron star natal kick magnitudes to be constrained through the Galactic distribution of DNSs, and make it possible to follow up the sources with radio pulsar searches. However, LISA is also expected to resolve ∼104 Galactic double white dwarfs, many of which may have binary parameters that resemble DNSs; we discuss how the combined measurement of binary eccentricity, chirp mass, and sky location may aid the identification of a DNS. We expect the best-constrained DNSs to have eccentricities known to a few parts in a thousand, chirp masses measured to better than 1 per cent fractional uncertainty, and sky localisation at the level of a few arcminutes.

The Impact of Pair-Instability Mass Loss on the Binary Black Hole Mass Distribution

Stevenson et al. 2019

Authors: Stevenson, S., Sampson, M., Powell, J., Vigna-Gomez, A., Neijssel, C., Szecsi, D., Mandel, I.
arXiv: 1904.02821 [astro-ph.HE]

A population of binary black hole mergers has now been observed in gravitational waves by Advanced LIGO and Virgo. The masses of these black holes appear to show evidence for a pile-up between $30$--$45$\,\Msol{} and a cut-off above $\sim 45$\,\Msol. One possible explanation for such a pile-up and subsequent cut-off are pulsational pair-instability supernovae (PPISNe) and pair-instability supernovae (PISNe) in massive stars. We investigate the plausibility of this explanation in the context of isolated massive binaries. We study a population of massive binaries using the rapid population synthesis software COMPAS, incorporating models for PPISNe and PISNe. Our models predict a maximum black hole mass of $40$\,\Msol{}. We expect $\sim 0.5$--$4$\% of all binary black hole mergers at redshift z = 0 will include at least one component that went through a PPISN (with mass $30$--$40$\,\Msol{}), constituting $\sim 5$--$25$\% of binary black hole mergers observed during the first two observing runs of Advanced LIGO and Virgo. Empirical models based on fitting the gravitational-wave mass measurements to a combination of a power law and a Gaussian find a fraction too large to be associated with PPISNe in our models. The rates of PPISNe and PISNe track the low metallicity star formation rate, increasing out to redshift $z = 2$. These predictions may be tested both with future gravitational-wave observations and with observations of superluminous supernovae.

The Effect of the Metallicity-Specific Star Formation History on Double Compact Object Mergers

Neijssel et al. 2019

Authors: Neijssel, C., Vigna-Gomez, A., Stevenson, S., Barrett, J., Gaebel, S., Broekgaarden, F., de Mink, S., Szecsi, D., Vinciguerra, S., Mandel, I.
arXiv: 1906.08136 [astro-ph.HE]

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 catalog 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×(1+z)2.77/(1+((1+z)/2.9)4.7)M⊙ Mpc−3 yr−1. Intriguingly, this default model predicts that 80\% 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.

The Origin of Spin in Binary Black Holes: Predicting the Distributions of the Main Observables of Advanced LIGO

Bavera et al. 2019

Authors: Bavera, S., Fragos, T., Qin, Y., Zapartas, E., Neijssel, C., Mandel, I., Batta, A., Gaebel, S., Kimball, C., Steveson, S.
arXiv: 1906.12257 [astro-ph.HE]

We study the formation of coalescing binary black holes via the evolution of isolated field binaries that go through the common envelope phase in order to obtain the combined distributions of the main observables of Advanced LIGO. We use a hybrid technique that combines the parametric binary population synthesis code COMPAS with detailed binary evolution simulations performed with the MESA code. We then convolve our binary evolution calculations with the redshift- and metallicity-dependent star-formation rate and the selection effects of gravitational-wave detectors to obtain predictions of observable properties. By assuming efficient angular momentum transport, we are able to present a model capable of predicting simultaneously the three main gravitational-wave observables: the effective inspiral spin parameter χeff, the chirp mass Mchirp and the cosmological redshift of merger zmerger. We find an excellent agreement between our model and the ten events from the first two advanced detector observing runs. We make predictions for the third observing run O3 and for Advanced LIGO design sensitivity. We expect 59% of events with χeff<0.1, while the remaining 41% of events with χeff≥0.1 are split into 9% with Mchirp<15 M⊙ and 32% with Mchirp≥15 M⊙. In conclusion, the favorable comparison of the existing LIGO/Virgo observations with our model predictions gives support to the idea that the majority, if not all of the observed mergers, originate from the evolution of isolated binaries. The first-born black hole has negligible spin because it lost its envelope after it expanded to become a giant star, while the spin of the second-born black hole is determined by the tidal spin up of its naked helium star progenitor by the first-born black hole companion after the binary finished the common-envelope phase.

STROOPWAFEL: Simulating Rare Outcomes from Astrophysical Populations with Applications to Gravitational-Wave Sources

Broekgaarden et al. 2019

Authors: Broekgaarden, F., Justham, S., de Mink, S., Gair, J., Mandel, I., Stevenson, S., Barrett, J., Vigna-Gomez, A., Neijssel, C.
arXiv: 1905.00910 [astro-ph.HE]
Data Release:

Gravitational-wave observations of double compact object (DCO) mergers are providing new insights into the physics of massive stars and the evolution of binary systems. Making the most of expected near-future observations for understanding stellar physics will rely on comparisons with binary population synthesis models. However, the vast majority of simulated binaries never produce DCOs, which makes calculating such populations computationally inefficient. We present an importance sampling algorithm, STROOPWAFEL, that improves the computational efficiency of population studies of rare events, by focusing the simulation around regions of the initial parameter space found to produce outputs of interest. We implement the algorithm in the binary population synthesis code COMPAS, and compare the efficiency of our implementation to the standard method of Monte Carlo sampling from the birth probability distributions. STROOPWAFEL finds $\sim$25-200 times more DCO mergers than the standard sampling method with the same simulation size, and so speeds up simulations by up to two orders of magnitude. Finding more DCO mergers automatically maps the parameter space with far higher resolution than when using the traditional sampling. This increase in efficiency also leads to a decrease of a factor $\sim$3-10 in statistical sampling uncertainty for the predictions from the simulations. This is particularly notable for the distribution functions of observable quantities such as the black hole and neutron star chirp mass distribution, including in the tails of the distribution functions where predictions using standard sampling can be dominated by sampling noise.

Explosions Driven by the Coalescence of a Compact Object with the Core of a Massive-Star Companion Inside a Common Envelope: Circumstellar Properties, Light Curves, and Population Statistics

Schroeder et al. 2019

Schroeder, S., MacLeod, M., Loeb, A., Vigna-Gomez, A., Mandel, I.
arXiv: 1906.04189 [astro-ph.HE]

We model explosions driven by the coalescence of a black hole or neutron star with the core of its massive-star companion. Upon entering a common envelope phase, a compact object may spiral all the way to the core. The concurrent release of energy is likely to be deposited into the surrounding common envelope, powering a merger-driven explosion. We use hydrodynamic models of binary coalescence to model the common envelope density distribution at the time of coalescence. We find toroidal profiles of material, concentrated in the binary's equatorial plane and extending to many times the massive star's original radius. We use the spherically-averaged properties of this circumstellar material (CSM) to estimate the emergent light curves that result from the interaction between the blast wave and the CSM. We find that typical merger-driven explosions are brightened by up to three magnitudes by CSM interaction. From population synthesis models we discover that the brightest merger-driven explosions, MV∼−18 to −19, are those involving black holes because they have the most massive and extended CSM. Black hole coalescence events are also common; they represent about 50% of all merger-driven explosions and approximately 0.3% of the core-collapse rate. Merger-driven explosions offer a window into the highly-uncertain physics of common envelope interactions in binary systems by probing the properties of systems that merge rather than eject their envelopes.

On the Formation History of Galactic Double Neutron Stars

Vigna-Gomez et al. 2018

Authors: Vigna-Gomez, A., Neijssel, C., Stevenson, S., Barrett, J., Belczynski, K., Justham, S., de Mink, S., Muller, B., Podsiadlowski, P., Benzo, M., Szecsi, D., Mandel, I.
Journal: MNRAS
arXiv: 1805.07974 [astro-ph.HE]

Double neutron stars (DNSs) have been observed as Galactic radio pulsars, and the recent discovery of gravitational waves from the DNS merger GW170817 adds to the known DNS population. We perform rapid population synthesis of massive binary stars and discuss model predictions, including DNS formation rates, mass distributions, and delay time distributions. We vary assumptions and parameters of physical processes such as mass transfer stability criteria, supernova natal kick distributions, remnant mass prescriptions, and common-envelope energetics. We compute the likelihood of observing the orbital period-eccentricity distribution of the Galactic DNS population under each of our population synthesis models, allowing us to quantitatively compare the models. We find that mass transfer from a stripped post-helium-burning secondary (case BB) on to a neutron star is most likely dynamically stable. We also find that a natal kick distribution composed of both low (Maxwellian σ =30 km s^{-1}) and high (σ =265 km s^{-1}) components is preferred over a single high-kick component. We conclude that the observed DNS mass distribution can place strong constraints on model assumptions.

Accuracy of Inference on the Physics of Binary Evolution from Gravitational-Wave Observations

Barrett et al. 2018

Authors: Barrett, J. W., Gaebel, S. M., Neijssel, C. J., Vigna-Gómez, A., Stevenson, S., Berry, C. P. L., Farr, W. M. & Mandel, I.
Journal: MNRAS
arXiv: 1711.06287 [astro-ph.HE]

Gravitational waves give us a unique insight into the properties of binary black holes. The information from gravitational waves should help us figure out how these black holes form—in this paper we investigate exactly how accurately we will be able to determine details of binary evolution. We consider populations of binary black holes simulated using COMPAS, and how sensitive the distribution of chirp masses and merger rate (which will be measured through gravitational waves) are to changes in the input physics. In particular, we consider four of the most uncertain parameters: the supernova kick (σkick), the common-envelope efficiency (αCE), and the mass loss rates during the Wolf–Rayet and luminous blue variable phases (fWR and fLBV). We quantify the information we can gain from observations using the Fisher matrix, which includes correlations between parameters. The plot above shows (fractional) measurement uncertainties for many realisations of the binary black hole population after 1000 observations (the uncertainties scale inversely with the square root of the number of observations). We find that we can distinguish populations which differ by just a few percent in these parameters! The measurements are much better when adding in the chirp masses as well as the rates, so perhaps adding in more information from gravitational-wave (or other complementary) observations will improve things even further.

Exploring the Parameter Space of Compact Binary Population Synthesis

Barrett et al. 2017

Authors: Barrett, J., Mandel, I., Neijssel, C., Stevenson, S., Vigna-Gomez, A.
Journal: Proceedings of the International Astronomical Union
arXiv: 1704.03781 [astro-ph.HE]

As we enter the era of gravitational wave astronomy, we are beginning to collect observations which will enable us to explore aspects of astrophysics of massive stellar binaries which were previously beyond reach. In this paper we describe COMPAS (Compact Object Mergers: Population Astrophysics and Statistics), a new platform to allow us to deepen our understanding of isolated binary evolution and the formation of gravitational-wave sources. We describe the computational challenges associated with their exploration, and present preliminary results on overcoming them using Gaussian process regression as a simulation emulation technique.

Formation of the First Three Gravitational-Wave Observations through Isolated Binary Evolution

Stevenson et al. 2017a

Authors: Stevenson, S., Vigna-Gomez, A., Mandel, I., Barrett, J., Neijssel, C., Perkins, D., de Mink., S. Journal: Nature
arXiv: 1704.01352 [astro-ph.HE]
Data Release:

Figure 1 from Stevenson et al., Nature Communications 8, 14906 (2017) updated to include GW170104

In a paper published in Nature Communications, we have have shown that all three observed events can be formed via the same formation channel: isolated binary evolution via a common-envelope phase. In this channel, two massive progenitor stars start out at quite wide separations. The stars interact as they expand, engaging in several episodes of mass transfer. The latest of these is typically a common envelope - a very rapid, dynamically unstable mass transfer that envelops both stellar cores in a dense cloud of hydrogen gas. Ejecting this gas from the system takes energy away from the orbit. This brings the two stars sufficiently close together for gravitational-wave emission to be efficient, right at the time when they are small enough that such closeness will no longer put them into contact. The whole process takes a few million years to form two black holes, with a possible subsequent delay of billions of years before the black holes merge and form a single black hole.

The simulations have also helped the team to understand the typical properties of the stars that can go on to form such pairs of merging black holes and the environments where this can happen.