Merging Rates of Compact Binaries in Galaxies: Perspectives for Gravitational Wave Detections

Abstract

We investigate the merging rates of compact binaries in galaxies, and the related detection rate of gravitational wave (GW) events with AdvLIGO/Virgo and with the Einstein Telescope. To this purpose, we rely on three basic ingredients: (i) the redshift-dependent galaxy statistics provided by the latest determination of the star formation rate functions from UV+far-IR/(sub)millimeter/radio data; (ii) star formation and chemical enrichment histories for individual galaxies, modeled on the basis of observations; (iii) compact remnant mass distribution and prescriptions for merging of compact binaries from stellar evolution simulations. We present results for the intrinsic birthrate of compact remnants, the merging rates of compact binaries, GW detection rates and GW counts, attempting to differentiate the outcomes among BH-BH, NS-NS, and BH-NS mergers, and to estimate their occurrence in disk and spheroidal host galaxies. We compare our approach with the one based on cosmic SFR density and cosmic metallicity, exploited by many literature studies; the merging rates from the two approaches are in agreement within the overall astrophysical uncertainties. We also investigate the effects of galaxy-scale strong gravitational lensing of GW in enhancing the rate of detectable events toward high-redshift. Finally, we discuss the contribution of undetected GW emission from compact binary mergers to the stochastic background.

Growth of Supermassive Black Hole Seeds in ETG Star-forming Progenitors: Multiple Merging of Stellar Compact Remnants via Gaseous Dynamical Friction and Gravitational-wave Emission

“…The event rate density increases quite rapidly from the local Universe toward high redshift, features a peak around z ≈ 2.5 and then declines steeply. This result is compared with the analogous quantity for the merging of binary compact remnants (e.g., stellar BH-BH) in galaxies, as computed in Boco et al (2019). The similarity in the redshift evolution of the event rates for the two processes is easily understood since eventually they are both proportional to the birthrate of compact remnants, which is illustrated in the inset.…”

“…However, two occurrences mitigate the effect. First, most of remnants relevant to the growth of the BH seed are formed and migrate to the center within a few 10 7 yr, when the average gas metallicity amounts to Z /10 (e.g., Pantoni et al 2019;Boco et al 2019); in these conditions, most of the remnants are formed by direct collapse without undergoing a SN explosions (e.g., Spera et al 2015;Spera & Mapelli 2017). Second, even if the SN explodes, it can efficiently sweep up material during the energy-conserving expansion phase, out to a radius R SN ∼ 5 t pc where E 51 ≡ E SN /10 51 erg is the energy of a SN explosion, n 2 ≡ n/10 2 cm −3 is the average gas density and t 4 ≡ t/10 4 yr the time since the explosion (e.g., Ostriker & McKee 1988;Mo et al 2010); however, once formed the remnant will move in the gaseous medium at a typical velocity of σ 200 ≡ σ/200 km s −1 and thus will travel a distance R rem ∼ 2 σ 200 t 4 pc, implying that most of the gas mass swept up by the remnant is replaced after 10 5 yr.…”

“…the quantity dp/dm • represents the probability distribution of producing a compact remnant of mass m • given the initial star mass m and a metallicity Z. Following Boco et al (2019) this probability distribution is taken to be a lognormal dp The contribution to the hole growth from gaseous dynamical friction (blue solid lines) and from disk accretion with Eddington ratio λ = 1 (red solid lines) is highlighted; for comparison, evolutionary tracks due to pure disk accretion with λ = 1 (dashed black line) and λ = 3 (dotted black line) are also illustrated. Right panel: the same is shown for a typical ETG progenitor located at z ∼ 2 and featuring SFR ψ ∼ 300 M yr −1 ; we illustrate the evolution when including dynamical friction and disk accretion with λ = 1 (solid lines) or λ = 0.3 (dot-dashed lines), and that for pure disk accretion with λ = 1 (dashed lines).…”

“…1 and 3.1). Finally, an integration over the possible values of the SFR ψ is performed, by weighting with the galaxy SFR functions dN/dV dψ at cosmic time t z ; these galaxy statistics have been determined observationally over a wide range of SFRs ψ ∼ 10 − 3000 M yr −1 and redshifts z ∼ 0 − 8 thanks the combination of deep UV/near-IR/far-IR/submm/radio surveys (see Mancuso et al 2016a,b;Lapi et al 2017;Boco et al 2019, their Fig. 1).…”

“…The overall event rate for the process of BH seed formation by gaseous dynamical friction considered here is generally higher by factors 3 − 10 than that for the merging of BH-BH binaries; however, one must caveat that the overall normalization of the latter curve is uncertain since it depends on several assumptions regarding complex processes of stellar astrophysics and binary evolution (e.g., binary fraction, common envelope development/survival, supernova kicks, mass transfers, etc. ), and has been actually set by comparison with the current AdvLIGO/Virgo measurements in the local Universe (see Abbott et al 2019;Boco et al 2019).…”