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Register a new userThe time delay distribution and formation metallicity of LIGO-Virgos binary black holes
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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.
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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 $sim5$--$80,M_odot$. 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.
The distribution of effective spin $chi_{rm eff}$, a parameter that encodes the degree of spin-orbit alignment in a binary system, has been widely regarded as a robust discriminator between the isolated and dynamical formation pathways for merging binary black holes. Until the recent release of the GWTC-2 catalog, such tests have yielded inconclusive results due to the small number of events with measurable nonzero spins. In this work, we study the $chi_{rm eff}$ distribution of the binary black holes detected in the LIGO-Virgo O1-O3a observing runs. Our focus is on the degree to which the $chi_{rm eff}$ distribution is symmetric about $chi_{rm eff} = 0$ and whether the data provides support for a population of negative-$chi_{rm eff}$ systems. We find that the $chi_{rm eff}$ distribution is asymmetric at 95% credibility, with an excess of aligned-spin binary systems ($chi_{rm eff}>0$) over anti-aligned ones. Moreover, we find that there is no evidence for negative-$chi_{rm eff}$ systems in the current population of binary black holes. Thus, based solely on the $chi_{rm eff}$ distribution, dynamical formation is disfavored as being responsible for the entirety of the observed merging binary black holes, while isolated formation remains viable. We also study the mass distribution of the current binary black hole population, confirming that a single truncated power law distribution in the primary source-frame mass, $m_1^{rm src}$, fails to describe the observations. Instead, we find that the preferred models have a steep feature at $m_1^{rm src} sim 40 ,rm M_odot$ consistent with a step and an extended, shallow tail to high masses.
We show how LIGO is expected to detect coalescing binary black holes at $z>1$, that are lensed by the intervening galaxy population. Gravitational magnification, $mu$, strengthens gravitational wave signals by $sqrt{mu}$, without altering their frequencies, which if unrecognised leads to an underestimate of the event redshift and hence an overestimate of the binary mass. High magnifications can be reached for coalescing binaries because the region of intense gravitational wave emission during coalescence is so small ($sim$100km), permitting very close projections between lensing caustics and gravitational-wave events. Our simulations incorporate accurate waveforms convolved with the LIGO power spectral density. Importantly, we include the detection dependence on sky position and orbital orientation, which for the LIGO configuration translates into a wide spread in observed redshifts and chirp masses. Currently we estimate a detectable rate of lensed events rateEarly{}, that rises to rateDesign{}, at LIGOs design sensitivity limit, depending on the high redshift rate of black hole coalescence.
We introduce a semi-parametric model for the primary mass distribution of binary black holes (BBHs) observed with gravitational waves (GWs) that applies a cubic-spline perturbation to a power law. We apply this model to the 46 BBHs included in the second gravitational wave transient catalog (GWTC-2). The spline perturbation model recovers a consistent primary mass distribution with previous results, corroborating the existence of a peak at $35,M_odot$ ($>97%$ credibility) found with the textsc{Powerlaw+Peak} model. The peak could be the result pulsational pair-instability supernovae (PPISNe). The spline perturbation model finds potential signs of additional features in the primary mass distribution at lower masses similar to those previously reported by Tiwari and Fairhurst (2021). However, with fluctuations due to small number statistics, the simpler textsc{Powerlaw+Peak} and textsc{BrokenPowerlaw} models are both still perfectly consistent with observations. Our semi-parametric approach serves as a way to bridge the gap between parametric and non-parametric models to more accurately measure the BBH mass distribution. With larger catalogs we will be able to use this model to resolve possible additional features that could be used to perform cosmological measurements, and will build on our understanding of BBH formation, stellar evolution and nuclear astrophysics.
All ten LIGO/Virgo binary black hole (BH-BH) coalescences reported from the O1/O2 runs have near zero effective spins. There are only three potential explanations of this fact. If the BH spin magnitudes are large then (i) either both BH spin vectors must be nearly in the orbital plane or (ii) the spin angular momenta of the BHs must be oppositely directed and similar in magnitude. Or, (iii) the BH spin magnitudes are small. We test the third hypothesis within the framework of the classical isolated binary evolution scenario of the BH-BH merger formation. We test three models of angular momentum transport in massive stars: a mildly efficient transport by meridional currents (as employed in the Geneva code), an efficient transport by the Tayler-Spruit magnetic dynamo (as implemented in the MESA code), and a very-efficient transport (as proposed by Fuller et al.) to calculate natal BH spins. We allow for binary evolution to increase the BH spins through accretion and account for the potential spin-up of stars through tidal interactions. Additionally, we update the calculations of the stellar-origin BH masses, include revisions to the history of star formation and to the chemical evolution across cosmic time. We find that we can match simultaneously the observed BH-BH merger rate density, BH masses, and effective spins. Models with efficient angular momentum transport are favored. The updated stellar-mass weighted gas-phase metallicity evolution now used in our models appears to be a key in better reproducing the LIGO/Virgo merger rate estimate. Mass losses during the pair-instability pulsation supernova phase are likely overestimated if the merger GW170729 hosts a BH more massive than 50 Msun. We also estimate rate of BH-NS mergers from recent LIGO/Virgo observations. Our updated models of BH-BH, BH-NS and NS-NS mergers are now publicly available at www.syntheticuniverse.org.
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