Black Hole-neutron Star Binaries Research Articles

Dissecting the properties of neutron star\u2013black hole mergers originating in dense star clusters

The detection of gravitational waves emitted during a neutron star–black hole merger and the associated electromagnetic counterpart will provide a wealth of information about stellar evolution nuclear matter, and general relativity. While the theoretical framework about neutron star–black hole binaries formed in isolation is well established, the picture is loosely constrained for those forming via dynamical interactions. Here, we use N-body simulations to show that mergers forming in globular and nuclear clusters could display distinctive marks compared to isolated mergers, namely larger masses, heavier black holes, and the tendency to have no associated electromagnetic counterpart. These features could represent a useful tool to interpreting forthcoming observations. In the local Universe, gravitational waves emitted from dynamical mergers could be unraveled by detectors sensitive in the decihertz frequency band, while those occurring at the distance range of Andromeda and the Virgo Cluster could be accessible to lower-frequency detectors like LISA.

On the Possibility of GW190425 Being a Black Hole–Neutron Star Binary Merger

Abstract We argue that the kilonova/macronova associated with the gravitational-wave event GW190425 could have been bright enough to be detected if it was caused by the merger of a low-mass black hole (BH) and a neutron star (NS). Although tidal disruption occurs for such a low-mass BH is generally expected, the masses of the dynamical ejecta are limited to ≲10−3 M ⊙, which is consistent with previous work in the literature. The remnant disk could be as massive as 0.05–0.1 M ⊙, and the disk outflow of ∼0.01–0.03 M ⊙ is likely to be driven by viscous or magnetohydrodynamic effects. The disk outflow may not be neutron-rich enough to synthesize an abundance of lanthanide elements, even in the absence of strong neutrino emitter, if the ejection is driven on the viscous timescale of ≳0.3 s. If this is the case, the opacity of the disk outflow is kept moderate, and a kilonova/macronova at the distance of GW190425 reaches a detectable brightness of 20–21 mag at 1 day after merger for most viewing angles. If some disk activity ejects the mass within ∼0.1 s, instead, lanthanide-rich outflows would be launched and the detection of emission becomes challenging. Future possible detections of kilonovae/macronovae from GW190425-like systems will disfavor the prompt collapse of binary NSs and a non-disruptive low-mass BH–NS binary associated with a small NS radius, whose mass ejection is negligible. The host-galaxy distance will constrain the viewing angle and deliver further information about the mass ejection.

On the Rate of Neutron Star Binary Mergers from Globular Clusters

Abstract The first detection of gravitational waves from a neutron star–neutron star (NS–NS) merger, GW170817, and the increasing number of observations of short gamma-ray bursts have greatly motivated studies of the origins of NS–NS and neutron star–black hole (NS–BH) binaries. We calculate the merger rates of NS–NS and NS–BH binaries from globular clusters (GCs) using realistic GC simulations with the CMC Cluster Catalog. We use a large sample of models with a range of initial numbers of stars, metallicities, virial radii, and galactocentric distances, representative of the present-day Milky Way GCs, to quantify the inspiral times and volumetric merger rates as a function of redshift, both inside and ejected from clusters. We find that over the complete lifetime of most GCs, stellar BHs dominate the cluster cores and prevent the mass segregation of NSs, thereby reducing the dynamical interaction rates of NSs so that at most a few NS binary mergers are ever produced. We estimate the merger rate in the local universe to be ∼0.02 Gpc−3 yr−1 for both NS–NS and NS–BH binaries, or a total of ∼0.04 Gpc−3 yr−1 for both populations. These rates are about 5 orders of magnitude below the current empirical merger rate from the Laser Interferometer Gravitational-Wave Observatory/Virgo. We conclude that dynamical interactions in GCs do not play a significant role in enhancing the NS–NS and NS–BH merger rates.

Mass and star formation rate of the host galaxies of compact binary mergers across cosmic time

ABSTRACT We investigate the properties of the host galaxies of compact binary mergers across cosmic time, by means of population-synthesis simulations combined with galaxy catalogues from the eagle suite. We analyse the merger rate per galaxy of binary neutron stars (BNSs), black hole–neutron star binaries (BHNSs), and binary black holes (BBHs) from redshift zero up to six. The binary merger rate per galaxy strongly correlates with the stellar mass of the host galaxy at any redshift considered here. This correlation is significantly steeper for BNSs than for both BHNSs and BBHs. Moreover, we find that the merger rate per galaxy depends also on host galaxy’s star formation rate (SFR) and metallicity. We derive a robust fitting formula that relates the merger rate per galaxy with galaxy’s SFR, stellar mass, and metallicity at different redshifts. The typical masses of the host galaxies increase significantly as redshift decreases, as a consequence of the interplay between delay time distribution of compact binaries and cosmic assembly of galaxies. Finally, we study the evolution of the merger rate density with redshift. At low redshift (z ≤ 0.1) early-type galaxies give a larger contribution to the merger rate density than late-type galaxies. This trend reverts at z ≥ 1.

Possible Electromagnetic Phenomena during the Coalescence of Neutron Star–Black Hole Binary Systems

Possible models for the generation of electromagnetic (EM) radiation during the coalescence of neutron star-black hole binaries are considered. The mass of the remnant disk around the black hole during the coalescence of neutron stars and black holes is calculated by taking into account the equation of state for neutron stars and the rotation of the binary components before the coalescence. The parameters of binary systems before the coalescence (the mass ratio, the component rotation, the neutron star magnetic field) are calculated by the population synthesis method. The derived mass of the remnant disk around the black hole after the coalescence is used to estimate the kinetic energy of the relativistic jet launched by the Blandford-Znajek mechanism. A disk mass of more than $\sim 0.05 M_\odot$ required for the formation of short gamma-ray bursts is shown to be obtained in no more than 1-10\% of the coalescences (depending on the equation of state). Less efficient common envelopes (a large parameter $\alpha_{CE}$) lead to a noticeably larger percentage of events with astrophysically interesting EM energy release. For binaries with a large mass ratio, in which a magnetized neutron star is not subjected to tidal disruption before the coalescence, the possibility of the formation of an electrically charged rotating black hole (Wald charge) is considered and estimates of the maximum EM power released by such a black hole after the coalescence are made. The conversion of the emitted gravitational waves into electromagnetic ones in the relativistic lepton plasma generated in coalescing pulsar-black hole binaries at the pre-coalescence stage is discussed.

Merger and Mass Ejection of Neutron Star Binaries

Mergers of binary neutron stars and black hole–neutron star binaries are among the most promising sources for ground-based gravitational-wave (GW) detectors and are also high-energy astrophysical phenomena, as illustrated by the observations of GWs and electromagnetic (EM) waves in the event of GW170817. Mergers of these neutron star binaries are also the most promising sites for r-process nucleosynthesis. Numerical simulation in full general relativity (numerical relativity) is a unique approach to the theoretical prediction of the merger process, GWs emitted, mass ejection process, and resulting EM emission. We summarize the current understanding of the processes of neutron star mergers and subsequent mass ejection based on the results of the latest numerical-relativity simulations. We emphasize that the predictions of the numerical-relativity simulations agree broadly with the optical and IR observations of GW170817.

The host galaxies of double compact objects across cosmic time

ABSTRACT We explore the host galaxies of compact-object binaries (black hole–black hole binaries, BHBs; neutron star–black hole binaries, NSBHs; double–neutron stars; DNSs) across cosmic time, by means of population-synthesis simulations combined with the Illustris cosmological simulation. At high redshift (z ≳ 4), the host galaxies of BHBs, NSBHs, and DNSs are very similar and are predominantly low-mass galaxies (stellar mass M < 1011 M⊙). If z ≳ 4, most compact objects form and merge in the same galaxy, with a short delay time. At low redshift (z ≤ 2), the host galaxy populations of DNSs differ significantly from the host galaxies of both BHBs and NSBHs. DNSs merging at low redshift tend to form and merge in the same galaxy, with relatively short delay time. The stellar mass of DNS hosts peaks around ∼1010–1011 M⊙. In contrast, BHBs and NSBHs merging at low redshift tend to form in rather small galaxies at high redshift and then to merge in larger galaxies with long delay times. This difference between DNSs and black hole binaries is a consequence of their profoundly different metallicity dependence.

Black Hole and Neutron Star Binary Mergers in Triple Systems. II. Merger Eccentricity and Spin–Orbit Misalignment

Abstract We study the dynamical signatures of black hole (BH) and neutron star (NS) binary mergers via Lidov–Kozai oscillations induced by tertiary companions in hierarchical triple systems. For each type of binary (BH–BH and BH–NS), we explore a wide range of binary/triple parameters that lead to binary mergers and determine the distributions of merger time T m, eccentricity (e m), and spin–orbit misalignment angle ( ) when the binary enters the LIGO/VIRGO band (10 Hz). We use the double-averaged (over both orbits) and single-averaged (over the inner orbit) secular equations, as well as N-body integration, to evolve systems with different hierarchy levels, including the leading-order post-Newtonian effect, de Sitter spin–orbit coupling, and gravitational radiation. We find that for merging BH–BH binaries with comparable masses, about 7% have e m > 0.1 and 0.7% have e m > 0.9. The majority of the mergers have significant eccentricities in the LISA band. The BH spin evolution and the final spin–orbit misalignment are correlated with the orbital evolution and e m. Mergers with negligible e m (≲10−3) have a distribution of that peaks around 90° (and thus favoring a projected binary spin parameter χ eff ∼ 0), while mergers with larger e m have more isotropic spin–orbit misalignments. For typical BH–NS binaries, strong octupole effects lead to more mergers with nonnegligible e m (with ∼18% of the mergers having e m > 0.1 and 2.5% having e m > 0.9), and the final BH spin axis tends to be randomly oriented. Measurements or constraints on eccentric mergers and from LIGO/VIRGO and LISA would provide useful diagnostics on the dynamical formation of merging BH or NS binaries in triples. The recently detected BH merger events may implicate such dynamical formation channel.

Numerical simulations of neutron star-black hole binaries in the near-equal-mass regime

Simulations of neutron star-black hole (NSBH) binaries generally consider black holes with masses in the range $(5-10)M_\odot$, where we expect to find most stellar mass black holes. The existence of lower mass black holes, however, cannot be theoretically ruled out. Low-mass black holes in binary systems with a neutron star companion could mimic neutron star-neutron (NSNS) binaries, as they power similar gravitational wave (GW) and electromagnetic (EM) signals. To understand the differences and similarities between NSNS mergers and low-mass NSBH mergers, numerical simulations are required. Here, we perform a set of simulations of low-mass NSBH mergers, including systems compatible with GW170817. Our simulations use a composition and temperature dependent equation of state (DD2) and approximate neutrino transport, but no magnetic fields. We find that low-mass NSBH mergers produce remnant disks significantly less massive than previously expected, and consistent with the post-merger outflow mass inferred from GW170817 for moderately asymmetric mass ratio. The dynamical ejecta produced by systems compatible with GW170817 is negligible except if the mass ratio and black hole spin are at the edge of the allowed parameter space. That dynamical ejecta is cold, neutron-rich, and surprisingly slow for ejecta produced during the tidal disruption of a neutron star : $v\sim (0.1-0.15)c$. We also find that the final mass of the remnant black hole is consistent with existing analytical predictions, while the final spin of that black hole is noticeably larger than expected -- up to $\chi_{\rm BH}=0.84$ for our equal mass case.

Host galaxies of merging compact objects: mass, star formation rate, metallicity, and colours

Characterizing the properties of the host galaxies of merging compact objects provides essential clues to interpret current and future gravitational-wave detections. Here, we investigate the stellar mass, star formation rate (SFR), metallicity and colours of the host galaxies of merging compact objects in the local Universe, by combining the results of MOBSE population-synthesis models together with galaxy catalogs from the EAGLE simulation. We predict that the stellar mass of the host galaxy is an excellent tracer of the merger rate per galaxy ${\rm n}_{\rm GW}$ of double neutron stars (DNSs), double black holes (DBHs) and black hole-neutron star binaries (BHNSs). We find a significant correlation also between ${\rm n}_{\rm GW}$ and SFR. As a consequence, ${\rm n}_{\rm GW}$ correlates also with the $r-$band luminosity and with the $g-r$ colour of the host galaxies. Interestingly, $\gtrsim{}60$ %, $\gtrsim{}64$ % and $\gtrsim{}73$ % of all the DNSs, BHNSs and DBHs merging in the local Universe lie in early-type galaxies, such as NGC 4993. We predict a local DNS merger rate density of $\sim{}238~{\rm Gpc}^{-3}~{\rm yr}~^{-1}$ and a DNS merger rate $\sim{}16-121$ Myr$^{-1}$ for Milky Way-like galaxies. Thus, our results are consistent with both the DNS merger rate inferred from GW170817 and the one inferred from Galactic DNSs.

Unbiased Cosmic Opacity Constraints from Standard Sirens and Candles

Abstract The observation of Type Ia supernovae (SNe Ia) plays an essential role in probing the expansion history of the universe. But the possible presence of cosmic opacity can degrade the quality of SNe Ia. The gravitational-wave (GW) standard sirens, produced by the coalescence of double neutron stars and black hole–neutron star binaries, provide an independent way to measure the distances of GW sources, which are not affected by cosmic opacity. In this paper, we first propose that combining the GW observations of third-generation GW detectors with SN Ia data in similar redshift ranges offers a novel and model-independent method to constrain cosmic opacity. Through Monte Carlo simulations, we find that one can constrain the cosmic opacity parameter κ with an accuracy of σ κ ∼ 0.046 by comparing the distances from 100 simulated GW events and 1048 current Pantheon SNe Ia. The uncertainty of κ can be further reduced to ∼0.026 if 800 GW events are considered. We also demonstrate that combining 2000 simulated SNe Ia and 1000 simulated GW events could result in much severer constraints on the transparent universe, for which κ = 0.0000 ± 0.0044. Compared to previous opacity constraints involving distances from other cosmic probes, our method using GW standard sirens and SN Ia standard candles at least achieves competitive results.

The properties of merging black holes and neutron stars across cosmic time

The next generation ground-based gravitational wave interferometers will possibly observe mergers of binary black holes (BBHs) and binary neutron stars (BNSs) to redshift $z\gtrsim{}10$ and $z\gtrsim{}2$, respectively. Here, we characterize the properties of merging BBHs, BNSs and neutron star-black hole binaries across cosmic time, by means of population-synthesis simulations combined with the Illustris cosmological simulation. We find that the mass of merging compact objects does not depend (or depends very mildly) on the merger redshift. Even the mass distribution of black holes depends only mildly on redshift, because BBHs originating from metal-poor progenitors ($Z\leq{}4\times{}10^{-3}$) dominate the entire population of merging BBHs across cosmic time. For a common-envelope efficiency $\alpha{}\ge{}3$, the main difference between the mass distribution of BBHs merging in the last Gyr and that of BBHs merging more than 11 Gyr ago is that there is an excess of heavy merging black holes ($20-35$ M$_\odot$) in the last Gyr. This excess is explained by the longer delay time of massive BBHs.

Mergers of black hole–neutron star binaries and rates of associated electromagnetic counterparts

Black hole-neutron star (BHNS) binaries are amongst promising candidates for the joint detection of electromagnetic (EM) signals with gravitational waves (GWs) and are expected to be detected in the near future. Here we study the effect of the BHNS binary parameters on the merger ejecta properties and associated EM signals. We estimate the remnant disk and unbound ejecta masses for BH mass and spin distributions motivated from the observations of transient low-mass X-ray binaries (LMXBs) and specific NS equation of state (EoS). The amount of r-process elements synthesised in BHNS mergers is estimated to be a factor of $\sim 10^{2}-10^{4}$ smaller than BNS mergers, due to the smaller dynamical ejecta and merger rates for the former. We compute the EM luminosities and light curves for the early- and late-time emissions from the ultra-relativistic jet, sub-relativistic dynamical ejecta and wind, and the mildly-relativistic cocoon for typical ejecta parameters. We then evaluate the low-latency EM follow-up rates of the GW triggers in terms of the GW detection rate $\dot{N}_{GW}$ for current telescope sensitivities and typical BHNS binary parameters to find that most of the EM counterparts are detectable for high BH spin, small BH mass and stiffer NS EoS when NS disruption is significant. Based on the relative detection rates for given binary parameters, we find the ease of EM follow-up to be: ejecta afterglow $>$ cocoon afterglow $\gtrsim$ jet prompt $>$ ejecta macronova $>$ cocoon prompt $>$ jet afterglow $>>$ wind macronova $>>$ wind afterglow.

Gravitational waveforms from spectral Einstein code simulations: Neutron star-neutron star and low-mass black hole-neutron star binaries

Gravitational waveforms from numerical simulations are a critical tool to test and analytically calibrate the waveform models used to study the properties of merging compact objects. In this paper, we present a series of high-accuracy waveforms produced with the SpEC code for systems involving at least one neutron star. We provide for the first time waveforms with sub-radian accuracy over more than twenty cycles for low-mass black hole-neutron star binaries, including binaries with non-spinning objects, and binaries with rapidly spinning neutron stars that maximize the impact on the gravitational wave signal of the near-resonant growth of the fundamental excitation mode of the neutron star (f-mode). We also provide for the first time with SpEC a high-accuracy neutron star-neutron star waveform. These waveforms are made publicly available as part of the SxS catalogue. We compare our results to analytical waveform models currently implemented in data analysis pipelines. For most simulations, the models lie outside of the predicted numerical errors in the last few orbits before merger, but do not show systematic deviations from the numerical results: comparing different models appears to provide reasonable estimates of the modeling errors. The sole exception is the equal-mass simulation using a rapidly counter-rotating neutron star to maximize the impact of the excitation of the f-mode, for which all models perform poorly. This is however expected, as even the single model that takes f-mode excitation into account ignores the significant impact of the neutron star spin on the f-mode excitation frequency.

Multimessenger Probes of High-energy Sources

Multimessenger observations may hold the key to learn about the most energetic sources in the universe. The recent construction of large scale observatories opened new possibilities in testing non thermal cosmic processes with alternative probes, such as high energy neutrinos and gravitational waves. We propose to combine information from gravitational wave detections, neutrino observations and electromagnetic signals to obtain a comprehensive picture of some of the most extreme cosmic processes. Gravitational waves are indicative of source dynamics, such as the formation, evolution and interaction of compact objects. These compact objects can play an important role in astrophysical particle acceleration, and are interesting candidates for neutrino and in general high-energy astroparticle studies. In particular we will concentrate on the most promising gravitational wave emitter sources: compact stellar remnants. The merger of binary black holes, binary neutron stars or black hole-neutron star binaries are abundant gravitational wave sources and will likely make up the majority of detections. However, stellar core collapse with rapidly rotating core may also be significant gravitational wave emitter, while slower rotating cores may be detectable only at closer distances. The joint detection of gravitational waves and neutrinos from these sources will probe the physics of the sources and will be a smoking gun of the presence of hadrons in these objects which is still an open question. Conversely, the non-detection of neutrinos or gravitational waves from these sources will be fundamental to constrain the hadronic content.

Jet launching from binary black hole-neutron star mergers: Dependence on black hole spin, binary mass ratio, and magnetic field orientation

Black hole-neutron star (BHNS) mergers are one of the most promising targets for multimessenger astronomy. Using general relativistic magnetohydrodynamic simulations of BHNS undergoing merger we showed that a magnetically--driven jet can be launched by the remnant if the NS is endowed with a dipole B field extending from the interior into the exterior as in a radio pulsar. These self-consistent studies considered a BHNS system with mass ratio $q=3:1$, BH spin $a/M_{BH}=0.75$ aligned with the total orbital angular momentum (OAM), and a NS that is irrotational, threaded by an aligned B field, and modeled by an $\Gamma$--law equation of state with $\Gamma=2$. Here, as a crucial step in establishing BHNS systems as viable progenitors of central engines that power short gamma--ray bursts (sGRBs) and thereby solidify their role as multimessenger sources, we survey different BHNS configurations that differ in BH spin ($a/M_{BH} =-0.5,\,0,\,0.5,\,0.75$), in the mass ratio ($q=3:1$ and $q=5:1$), and in the orientation of the B field (aligned and tilted by $90^\circ$ with respect to the OAM). We find that by $\Delta t\sim 3500M-4000M \sim 88(M_{NS}/1.4M_\odot){\rm ms}-100(M_{NS}/1.4M_\odot)\rm ms$ after the peak gravitational wave signal a jet is launched in the cases where the initial BH spin is $a/M_{BH}= 0.5$ or $0.75$. The lifetime of the jets[$\Delta t\sim 0.5(M_{NS}/1.4M_\odot){\rm s-0.7}(M_{NS}/1.4M_\odot)\rm s$] and their Poynting luminosities [$L_{jet}\sim 10^{51\pm 1}\rm erg/s$] are consistent with sGRBs, as well as with the Blandford--Znajek mechanism. By the time we terminate our simulations, we do not observe either an outflow or a large-scale B field collimation in the other configurations we simulate. These results suggest that future multimessenger detections from BHNSs are more likely produced by binaries with highly spinning BH companions and small tilt-angle B fields.

Model-independent Curvature Determination from Gravitational-wave Standard Sirens and Cosmic Chronometers

Abstract The detection of gravitational waves (GWs) provides a direct way to measure the luminosity distance, which enables us to probe cosmology. In this paper, we continue to expand the application of GW standard sirens in cosmology, and propose that the spatial curvature can be estimated in a model-independent way by comparing the distances from future GW sources and current cosmic-chronometer observations. We expect an electromagnetic counterpart of the GW event to give the source redshift, and simulate hundreds of GW data from the coalescence of double neutron stars and black hole–neutron star binaries using the Einstein Telescope as a reference. Our simulations show that, from 100 simulated GW events and 31 current cosmic-chronometer measurements, the error of the curvature parameter Ω K is expected to be constrained at the level of ∼0.125. If 1000 GW events were observed, the uncertainty of Ω K would be further reduced to ∼0.040. We also find that adding 50 mock H(z) data points (consisting of 81 cosmic-chronometer data points and 1000 simulated GW events) could result in a much tighter constraint on the zero cosmic curvature, for which Ω K = −0.002 ± 0.028. Compared to some actual model-independent curvature tests involving distances from other cosmic probes, this method using GW data achieves constraints with much higher precision.

Quantum gravity and BH-NS binaries

We argue that the Black Hole-Neutron Star (BH-NS) binaries are the natural astrophysical probes of quantum gravity in the context of the new era of multi-messenger astronomy. In particular, we discuss the observable effect of enhanced BH mass loss in a BH-NS binary, due to the presence of an additional length scale tied to the intrinsic noncommutativity of quantum spacetime in quantum gravity.

Measuring the Hubble Constant with Neutron Star Black Hole Mergers.

The detection of GW170817 and the identification of its host galaxy have allowed for the first standard-siren measurement of the Hubble constant, with an uncertainty of ∼14%. As more detections of binary neutron stars with redshift measurement are made, the uncertainty will shrink. The dominating factors will be the number of joint detections and the uncertainty on the luminosity distance of each event. Neutron star black hole mergers are also promising sources for advanced LIGO and Virgo. If the black hole spin induces precession of the orbital plane, the degeneracy between luminosity distance and the orbital inclination is broken, leading to a much better distance measurement. In addition, neutron star black hole sources are observable to larger distances, owing to their higher mass. Neutron star black holes could also emit electromagnetic radiation: depending on the black hole spin and on the mass ratio, the neutron star can be tidally disrupted, resulting in electromagnetic emission. We quantify the distance uncertainty for a wide range of black hole mass, spin, and orientations and find that the 1σ statistical uncertainty can be up to a factor of ∼10 better than for a nonspinning binary neutron star merger with the same signal-to-noise ratio. The better distance measurement, the larger gravitational-wave detectable volume, and the potentially bright electromagnetic emission imply that spinning black hole neutron star binaries can be the optimal standard-siren sources as long as their astrophysical rate is larger than O(10) Gpc^{-3} yr^{-1}, a value allowed by current astrophysical constraints.

The cosmic merger rate of neutron stars and black holes

Six gravitational wave detections have been reported so far, providing crucial insights on the merger rate of double compact objects. We investigate the cosmic merger rate of double neutron stars (DNSs), neutron star-black hole binaries (NSBHs) and black hole binaries (BHBs) by means of population-synthesis simulations coupled with the Illustris cosmological simulation. We have performed six different simulations, considering different assumptions for the efficiency of common envelope (CE) ejection and exploring two distributions for the supernova (SN) kicks. The current BHB merger rate derived from our simulations spans from $\sim{}150$ to $\sim{}240$ Gpc$^{-3}$ yr$^{-1}$ and is only mildly dependent on CE efficiency. In contrast, the current merger rates of DNSs (ranging from $\sim{}20$ to $\sim{}600$ Gpc$^{-3}$ yr$^{-1}$) and NSBHs (ranging from $\sim{}10$ to $\sim{}100$ Gpc$^{-3}$ yr$^{-1}$) strongly depend on the assumptions on CE and natal kicks. The merger rate of DNSs is consistent with the one inferred from the detection of GW170817 only if a high efficiency of CE ejection and low SN kicks (drawn from a Maxwellian distribution with one dimensional root mean square $\sigma{}=15$ km s$^{-1}$) are assumed.