Quantifying the evidence for primordial black holes in LIGO/Virgo gravitational-wave data Gabriele Franciolini,1, ∗ Vishal Baibhav,2 Valerio De Luca,1, 3 Ken K. Y. Ng,4, 5 Kaze W. K. Wong,2 Emanuele Berti,2 Paolo Pani,3, 6 Antonio Riotto,1 and Salvatore Vitale4, 5 1Département de Physique Théorique and Centre for Astroparticle Physics (CAP), Université de Genève, 24 quai E. Ansermet, CH-1211 Geneva, Switzerland 2Department of Physics and Astronomy, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA 3Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185, Roma, Italy 4LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 5Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 6INFN, Sezione di Roma, Piazzale Aldo Moro 2, 00185, Roma, Italy, With approximately 50 binary black hole events detected by LIGO/Virgo to date and many more expected in the next few years, gravitational-wave astronomy is shifting from individual-event analyses to population studies. We perform a hierarchical Bayesian analysis on the GWTC-2 catalog by combining several astrophysical formation models with a population of primordial black holes. We compute the Bayesian evidence for a primordial population compared to the null hypothesis, and the inferred fraction of primordial black holes in the data. We find that these quantities depend on the set of assumed astrophysical models: the evidence for primordial black holes against an astrophysical-only multichannel model is decisively favored in some scenarios, but it is significantly reduced in the presence of a dominant stable-mass-transfer isolated formation channel. The primordial channel can explain mergers in the upper mass gap such as GW190521, but (depending on the astrophysical channels we consider) a significant fraction of the events could be of primordial origin even if we neglected GW190521. The tantalizing possibility that LIGO/Virgo may have already detected black holes formed after inflation should be verified by reducing uncertainties in astrophysical and primordial formation models, and it may ultimately be confirmed by third-generation interferometers. Introduction. The latest catalog of compact bi- excess of massive BHs could be the result of hierarchical nary mergers published by the LIGO/Virgo collabora- mergers of smaller objects [10–14], the end product of tion (LVC) [1, 2] includes 39 events, most of which are the life of massive stars just below the pair-instability binary black holes (BBHs) [3]. This brings the total supernova mass gap [15–17], or it may be of primordial ori- number of BBHs reported by the LVC to date to 47 [4]. gin [18, 19]. One event in particular, GW190521 [20], chal- Additional detections have been reported by indepen- lenges traditional formation scenarios. With component +29:1 +19:3 dent groups using public data, though usually with lower masses of m1 = 90:9−17:3 M and m2 = 66:3−20:3 M , statistical significance (see e.g. [5–7]). As the number of GW190521 is the most massive BBH detected to date. observations increases, we can characterize with increasing The posterior of the primary mass has support nearly accuracy the properties of the underlying population of entirely in the pair-instability supernova mass gap, where black holes (BHs) and the relative contribution of various BHs are not expected to form from the collapse of massive BBH formation channels. stars (see [21–27] for discussions of astrophysical uncer- In their population analysis, the LVC has used phe- tainties in this prediction). nomenological models built to capture key expected fea- tures of the mass, spin, and redshift distribution of BBHs In addition to astrophysical formation channels, a tan- (e.g. a power-law mass distribution), but not the physi- talizing possibility is that a fraction of these events may arXiv:2105.03349v2 [gr-qc] 16 Jun 2021 cal mechanisms responsible for these features (e.g., mass be due to primordial BHs (PBHs) [28–31] formed from the transfer in binary evolution) [4]. The model that is pre- collapse of large overdensities in the radiation-dominated ferred by the data describes the distribution of the pri- early universe [32–35]. In this scenario, PBHs are not mary (i.e., most massive) BH in the binary as the sum clustered at formation [36–41] and primordial BBHs are as- of a power-law and a Gaussian distribution, denoted as sembled via gravitational decoupling from the Hubble flow “Power Law + Peak” in Ref. [4]. The model has several before the matter-radiation equality [42, 43] (see [44, 45] free parameters and it is preferred to a simpler power-law for reviews). PBHs in different mass ranges could con- tribute to a sizeable fraction f Ω =Ω of the function, which might suggest that multiple formation PBH ≡ PBH DM channels are at play. dark matter energy density [46], but current GW data imply an upper bound f (10−3) in the mass range Many astrophysical formation scenarios could con- PBH . O tribute to the observed population [8, 9]. The observed of interest to current GW detectors [47–66]. A differ- ent scenario predicts that PBHs may form with a broad mass distribution shaped by the QCD transition [67, 68], and could assemble dynamically in dense halos in the ∗ [email protected] late-time universe [69–71]. This, however, requires PBHs 2 to be strongly clustered to evade existing astrophysical natal spins are negligible and independent of χb. To cap- constraints on their abundance [46]. ture uncertainties in the accretion model we introduce a Overall, the data indicate that not all BBH events cut-off redshift zcut-off below which accretion is inefficient. detected so far can be explained by a single formation If zcut-off & 30, accretion is negligible in the mass range of channel, be it either astrophysical [72] or primordial [61] interest for LVC observations and PBHs retain small spins (see [62] for the most updated analysis of the PBH sce- even at low redshift, whereas zcut-off 10 would corre- ' nario). Previous work tried to infer the mixing fraction of spond to a strong accretion phase, leading to larger PBH multiple astrophysical populations [72–76] and compared masses and spins [60, 77]. Similarly to the dynamical the PBH scenario against the phenomenological LVC astrophysical channels, the PBH spin orientations with re- power-law model [61, 63, 64]. In this Letter we present a spect to the binary’s angular momentum are independent more comprehensive hierarchical Bayesian inference study and uniformly distributed on the sphere. of the GWTC-2 catalog, mixing a state-of-the-art PBH Overall, our astrophysical models depend on the hy- model [55, 77] with several astrophysical models that perparameters λABH = [αCE; χb;NCE;NSMT;NGC;NNSC], can reproduce many features of the observed population. where the number of events in each channel Ni, follow- This allows us to infer the evidence for PBHs in GW data ing Ref. [72], is assumed to be unconstrained and inde- given our present (admittedly incomplete) knowledge of pendent of αCE and χb. The PBH channel depends on 2 astrophysical formation scenarios. λPBH = [Mc; σ; fPBH; zcut-off], with NPBH fPBH [62]. ≈ Our astrophysical models come from Ref. [72], the most Data analysis. Our setup follows Refs. [62, 64] and the comprehensive attempt to date at comparing different as- inference is performed by sampling the likelihood [85] trophysical formation scenarios against LVC data. That Nobs 1 Si p (jθ λ) work considered three field formation models and two −Ndet(λ) Nobs Y X pop i p(λ d) = π(λ)e [N(λ)] j j ; dynamical formation models. Among the three field for- j i π( θi) i=1 S j=1 mation scenarios – a late-phase common envelope (CE), (1) binaries that only have stable mass transfer between the star and the already formed BH (SMT), and chemically in the space of λ = λ λ by using the Markov ABH [ PBH homogeneous evolution (CHE) – Ref. [72] found that the chain Monte Carlo software emcee [86]. In Eq. (1), Nobs dominant channels correspond to the CE and SMT sce- is the number of GW events in the catalog; N(λ) is the narios. These two channels were simulated using the number of events in the model; Ndet(λ) is the number of POSYDON framework [78, 79], which models binary evo- observable events computed by accounting for the exper- lution with the population synthesis code COSMIC [80] imental selection bias; i is the length of the posterior and uses MESA [81] for binary evolution calculations. sample of each event inS the catalog; π(θ) is the prior on The key parameters of these models are the CE efficiency the binary parameters θ used by the LVC when perform- αCE [0:2; 0:5; 1:0; 2:0; 5:0], with large values of αCE lead- ing the parameter estimation – this prior is removed to ing to2 efficient CE evolution, and the natal BH spin extract the values of the single-event likelihood, ensur- χb [0; 0:1; 0:2; 0:5]. The two dynamical models consider ing only the informative part of the event posterior is formation2 in old, metal-poor globular clusters (GC) and used and does not affect the population inference (but see in nuclear star clusters (NSC). The GC models are taken Refs. [87–90] for its impact on the interpretation of single from a grid of 96 N-body models of collisional star clusters events); and π(λ) is the prior on the hyperparameters, simulated using the cluster Monte Carlo code CMC [12]. which is assumed to be flat. The 96 models consist of four independent grids of 24 The quantity p (θ λ) is the distribution of the BBH pop j models, each with different initial spins.