We derive the first constraints on the time delay distribution of binary black hole (BBH) mergers using the LIGO-Virgo Gravitational-Wave Transient Catalog GWTC-2. Assuming that the progenitor formation rate follows the star formation rate (SFR), the
data favor that $43$--$100%$ of mergers have delay times $<4.5$ Gyr (90% credibility). Adopting a model for the metallicity evolution, we derive joint constraints for the metallicity-dependence of the BBH formation efficiency and the distribution of time delays between formation and merger. Short time delays are favored regardless of the assumed metallicity dependence, although the preference for short delays weakens as we consider stricter low-metallicity thresholds for BBH formation. For a $p(tau) propto tau^{-1}$ time delay distribution and a progenitor formation rate that follows the SFR without metallicity dependence, we find that $tau_mathrm{min}<2.2$ Gyr, whereas considering only the low-metallicity $Z < 0.3,Z_odot$ SFR, $tau_mathrm{min} < 3.0$ Gyr (90% credibility). Alternatively, if we assume long time delays, the progenitor formation rate must peak at higher redshifts than the SFR. For example, for a $p(tau) propto tau^{-1}$ time delay distribution with $tau_mathrm{min} = 4$ Gyr, the inferred progenitor rate peaks at $z > 3.9$ (90% credibility). Finally, we explore whether the inferred formation rate and time delay distribution vary with BBH mass.
We review theoretical findings, astrophysical modeling, and current gravitational-wave evidence of hierarchical stellar-mass black-hole mergers. While most of the compact binary mergers detected by LIGO and Virgo are expected to consist of first-gene
ration black holes formed from the collapse of stars, others might instead be of second (or higher) generation, containing the remnants of previous black-hole mergers. Such a subpopulation of hierarchically assembled black holes presents distinctive gravitational-wave signatures, namely higher masses, possibly within the pair-instability mass gap, and dimensionless spins clustered at the characteristic value of $sim$0.7. In order to produce hierarchical mergers, astrophysical environments need to overcome the relativistic recoils imparted to black-hole merger remnants, a condition which prefers hosts with escape speeds $gtrsim$ 100 km/s. Promising locations for efficient production of hierarchical mergers include nuclear star clusters and accretion disks surrounding active galactic nuclei, though environments that are less efficient at retaining merger products such as globular clusters may still contribute significantly to the detectable population of repeated mergers. While GW190521 is the single most promising hierarchical-merger candidate to date, constraints coming from large population analyses are becoming increasingly more powerful.
The recent report of an association of the gravitational-wave (GW) binary black hole (BBH) merger GW190521 with a flare in the Active Galactic Nuclei (AGN) J124942.3+344929 has generated tremendous excitement. However, GW190521 has one of the largest
localization volumes amongst all of the GW events detected so far. The 90% localization volume likely contains $7,400$ unobscured AGN brighter than $g leq 20.5$ AB mag, and it results in a $gtrsim 70%$ probability of chance coincidence for an AGN flare consistent with the GW event. We present a Bayesian formalism to estimate the confidence of an AGN association by analyzing a population of BBH events with dedicated follow-up observations. Depending on the fraction of BBH arising from AGNs, counterpart searches of $mathcal{O}(1)-mathcal{O}(100)$ GW events are needed to establish a confident association, and more than an order of magnitude more for searches without followup (i.e, using only the locations of AGNs and GW events). Follow-up campaigns of the top $sim 5%$ (based on volume localization and binary mass) of BBH events with total rest frame mass $ge 50~M_odot$ are expected to establish a confident association during the next LIGO/Virgo/KAGRA observing run (O4), as long as the true value of the fraction of BBH giving rise to AGN flares is $>0.1$. Our formalism allows us to jointly infer cosmological parameters from a sample of BBH events that include chance coincidence flares. Until the confidence of AGN associations is established, the probability of chance coincidence must be taken into account to avoid biasing astrophysical and cosmological constraints.
Gravitational waves (GWs) directly measure the luminosity distance to the merger, which, when combined with an independent measurement of the sources redshift, provides a novel probe of cosmology. The proposed next generation of ground-based GW detec
tors, Einstein Telescope and Cosmic Explorer, will detect tens of thousands of binary neutron stars (BNSs) out to cosmological distances ($z>2$), beyond the peak of the star formation rate (SFR), or cosmic noon. At these distances, it will be challenging to measure the sources redshifts by observing electromagnetic (EM) counterparts or statistically marginalizing over a galaxy catalog. In the absence of an EM counterpart or galaxy catalog, Ding et al. showed that theoretical priors on the merger redshift distribution can be used to infer parameters in a $w$CDM cosmology. We argue that in the BNS case, the redshift distribution will be measured by independent observations of short gamma ray bursts (GRBs), kilonovae, and known BNS host galaxies. We show that, in addition to measuring the background cosmology, this method can constrain the effects of dark energy on modified GW propagation. We consider the simple case in which the BNS rate is textit{a priori} known to follow the SFR. If the SFR is perfectly known, $mathcal{O}(10,000)$ events (to be expected within a year of observation with Cosmic Explorer) would yield a sub-tenth percent measurement of the combination $H_0^{2.8}Omega_M$. Fixing $H_0$ and $Omega_M$, this method may enable a 5% measurement of the dark energy equation of state parameter. Fixing the background cosmology and probing modified GW propagation, the running of the Planck mass parameter $c_M$ may be measured to $pm0.02$. Although realistically, the redshift evolution of the merger rate will be uncertain, prior knowledge of the peak redshift will provide valuable information for standard siren analyses.
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 $z sim 1$, with component masses in the range $s
im5$--$80,M_odot$. In this catalog, the biggest black holes, with $m_1 gtrsim 45,M_odot$, are only found at the highest redshifts, $z gtrsim 0.4$. We ask whether the absence of high-mass BBH observations at low redshift indicates that the astrophysical BBH mass distribution evolves: the biggest BBHs only merge at high redshift, and cease merging at low redshift. Alternatively, this feature might be explained by gravitational-wave selection effects. 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 $45^{+13}_{-5},M_odot$ at $z < 0.4$ to $80^{+16}_{-13},M_odot$ at $z > 0.4$. Alternatively, if the primary mass spectrum has a break in the power law (Broken power law) at ${38^{+15}_{-8},M_odot}$, rather than a sharp cutoff, the data are consistent with a non-evolving mass distribution. In this case, the overall rate of mergers, at all masses, increases with increasing redshift. Future observations will confidently distinguish between a sharp maximum mass cutoff that evolves with redshift and a non-evolving mass distribution with a gradual taper, such as a Broken power law. After $sim 100$ BBH merger observations, a continued absence of high-mass, low-redshift events would provide a clear signature that the mass distribution evolves with redshift.
Models for black hole (BH) formation from stellar evolution robustly predict the existence of a pair-instability supernova (PISN) mass gap in the range $sim50$ to $sim120$ solar masses. This theoretical prediction is supported by the binary black hol
es (BBHs) of LIGO/Virgos first two observing runs, whose component masses are well-fit by a power law with a maximum mass cutoff at $m_mathrm{max}=40.8^{+11.8}_{-4.4},M_odot$. Meanwhile, the BBH event GW190521 has a reported primary mass of $m_1=85^{+21}_{-14},M_odot$, firmly above the inferred $m_mathrm{max}$, and secondary mass $m_2=66^{+17}_{-18},M_odot$. Rather than concluding that both components of GW190521 belong to a new population of mass-gap BHs, we explore the conservative scenario in which GW190521s secondary mass belongs to the previously-observed population of BHs. We replace the default priors on $m_1$ and $m_2$, which assume that BH detector-frame masses are uniformly distributed, with this population-informed prior on $m_2$, finding $m_2<48,M_odot$ at 90% credibility. Moreover, because the total mass of the system is better constrained than the individual masses, the population prior on $m_2$ automatically increases the inferred $m_1$ to sit emph{above} the gap (39% for $m_1 > 120,M_odot$, or 25% probability for $m_1>130,M_odot$). As long as the prior odds for a double-mass-gap BBH are smaller than $sim 1:15$, it is more likely that GW190521 straddles the pair-instability gap. We argue that GW190521 may be the first example of a straddling binary black hole, composed of a conventional stellar mass BH and a BH from the ``far side of the PISN mass gap.
Gravitational-wave detectors have opened a new window through which we can observe black holes (BHs) and neutron stars (NSs). Analyzing the 11 detections from LIGO/Virgos first gravitational-wave catalog, GWTC-1, we investigate whether the power-law
fit to the BH mass spectrum can also accommodate the binary neutron star (BNS) event GW170817, or whether we require an additional feature, such as a mass gap, in between the NS and BH populations. We find that with respect to the power-law fit to binary black hole (BBH) masses, GW170817 is an outlier at the 0.13% level, suggesting a distinction between NS and BH masses. A single power-law fit across the entire mass range is in mild tension with: (a) the detection of one source in the BNS mass range ($sim 1$--$2.5 ,M_odot$), (b) the absence of detections in the mass-gap range ($sim 2.5$--$5 ,M_odot$), and (c) the detection of 10 sources in the BBH mass range ($gtrsim 5 ,M_odot$). Instead, the data favor models with a feature between NS and BH masses, including a mass gap (Bayes factor of 4.6) and a break in the power law, with a steeper slope at NS masses compared to BH masses (91% credibility). We estimate the merger rates of compact binaries based on our fit to the global mass distribution, finding $mathcal{R}_mathrm{BNS} = 871^{+3015}_{-805} mathrm{Gpc}^{-3} mathrm{yr}^{-1}$ and $mathcal{R}_mathrm{BBH} = 47.5^{+57.9}_{-28.8} mathrm{Gpc}^{-3} mathrm{yr}^{-1}$. We conclude that, even in the absence of any prior knowledge of the difference between NSs and BHs, the gravitational-wave data alone already suggest two distinct populations of compact objects.
Gravitational waves produced from the merger of binary neutron stars (BNSs) are accompanied by electromagnetic counterparts, making it possible to identify the associated host galaxy. We explore how properties of the host galaxies relate to the astro
physical processes leading to the mergers. It is thought that the BNS merger rate within a galaxy at a given epoch depends primarily on the galaxys star-formation history as well as the underlying merger time-delay distribution of the binary systems. The stellar history of a galaxy, meanwhile, depends on the cosmological evolution of the galaxy through time, and is tied to the growth of structure in the Universe. We study the hosts of BNS mergers in the context of structure formation by populating the Universe Machine simulations with gravitational-wave events~ according to a simple time-delay model. We find that different time-delay distributions predict different properties of the associated host galaxies, including the distributions of stellar mass, star-formation rate, halo mass, and local and large-scale clustering of hosts. BNSs that merge today with short delay times prefer to be in hosts that have high star-formation rates, while those with long delay times live in dense regions within massive halos that have low star formation. We show that with ${mathcal O}(10)$ events from current gravitational-wave detector networks, it is possible to make preliminary distinctions between formation channels which trace stellar mass, halo mass, or star-formation rate. We also find that strategies to follow up gravitational-wave events with electromagnetic telescopes can be significantly optimized using the clustering properties of their hosts.
Simultaneous measurements of distance and redshift can be used to constrain the expansion history of the universe and associated cosmological parameters. Merging binary black hole (BBH) systems are standard sirens---their gravitational waveform provi
des direct information about the luminosity distance to the source. Because gravity is scale-free, there is a perfect degeneracy between the source masses and redshift; some non-gravitational information is necessary to break the degeneracy and determine the redshift of the source. Here we suggest that the pair instability supernova (PISN) process, thought to be the source of the observed upper-limit on the black hole (BH) mass in merging BBH systems at $sim 45 , M_odot$, imprints a mass scale in the population of BBH mergers and permits a measurement of the redshift-luminosity-distance relation with these sources. We simulate five years of BBH detections in the Advanced LIGO and Virgo detectors with realistic assumptions about the BBH merger rate, a mass distribution incorporating a smooth PISN cutoff, and measurement uncertainty. We show that after one year of operation at design sensitivity (circa 2021) the BBH population can constrain $H(z)$ to $6.1%$ at a pivot redshift $z simeq 0.8$. After five years (circa 2025) the constraint improves to $2.9%$. This measurement relies only on general relativity and the presence of a cutoff mass scale that is approximately fixed or calibrated across cosmic time; it is independent of any distance ladder or cosmological model. Observations by future ``third-generation gravitational wave detectors, which can see BBH mergers throughout the universe, would permit sub-percent cosmographical measurements to $z gtrsim 4$ within one month of observation.
