# Gravitational Wave Sources from Pop III Stars are Preferentially Located within the Cores of their Host Galaxies

Fabio Pacucci, Abraham Loeb, Stefania Salvadori

► To cite this version:

Fabio Pacucci, Abraham Loeb, Stefania Salvadori. Gravitational Wave Sources from Pop III Stars are Preferentially Located within the Cores of their Host Galaxies. Monthly Notices of the Royal Astronomical Society, 2017, 471 (1), pp.L72-L76. 10.1093/mnrasl/slx111. hal-01645593

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# Gravitational wave sources from Pop III stars are preferentially located within the cores of their host Galaxies

Fabio Pacucci,<fnref n="1" />* Abraham Loeb<fnref n="2" /> and Stefania Salvadori<fnref n="3" />,<fnref n="4" />,<fnref n="5" />

Accepted 2017 June 30. Received 2017 June 29; in original form 2017 May 12

## ABSTRACT

The detection of gravitational waves (GWs) generated by merging black holes has recently opened up a new observational window into the Universe. The mass of the black holes in the first and third Laser Interferometer Gravitational Wave Observatory (LIGO) detections (36–29 M⊙ and 32–19 M⊙) suggests low-metallicity stars as their most likely progenitors. Based on high-resolution N-body simulations, coupled with state-of-the-art metal enrichment models, we find that the remnants of Pop III stars are preferentially located within the cores of galaxies. The probability of a GW signal to be generated by Pop III stars reaches ~90 per cent at ~0.5 kpc from the galaxy centre, compared to a benchmark value of ~5 per cent outside the core. The predicted merger rates inside bulges is ~60 × $\beta_{\text{III}}$ Gpc$^{-3}$ yr$^{-1}$ ($\beta_{\text{III}}$ is the Pop III binarity fraction). To match the 90 per cent credible range of LIGO merger rates, we obtain: 0.03 < $\beta_{\text{III}}$ < 0.88. Future advances in GW observatories and the discovery of possible electromagnetic counterparts could allow the localization of such sources within their host galaxies. The preferential concentration of GW events within the bulge of galaxies would then provide an indirect proof for the existence of Pop III stars.

**Key words:** black hole physics – gravitational waves – stars: Population III – galaxies: bulges – dark ages, reionization, first stars – early Universe.

## 1 INTRODUCTION

The first detection of gravitational waves (GWs) by the Laser Interferometer Gravitational Wave Observatory (LIGO) has marked the birth of GW astronomy. The event GW150914 (Abbott et al. 2016a) originated from the merger of a binary black hole (BBH) system with masses ~36 and ~29 M⊙ at a redshift $z \sim 0.1$, corresponding to a luminosity distance of ~410 Mpc. This discovery was followed by a second (Abbott et al. 2016b) and a third detection (The LIGO Scientific Collaboration et al. 2017), the latter one with inferred source-frame masses of ~32 and ~19 M⊙ at $z \sim 0.2$. Current predictions (Abbott et al. 2016d) indicate that GW events will be detected regularly with the additional GW detectors (e.g. VIRGO and KAGRA) at a rate of several per month up to $z \sim 1$. Overall, the inferred merger rate is 2–200 Gpc$^{-3}$ yr$^{-1}$.

The opening of a new observational window would enable a revolution in our understanding of the Universe. From an astrophysical point of view (Abbott et al. 2016c), the detection provides direct evidence for the existence of BBHs with comparable mass components.

This type of BBHs have been predicted in two main types of formation channels, involving isolated stellar binaries in galactic fields or dynamical interactions in dense stellar environments (Belczynski et al. 2016; Rodriguez, Chatterjee & Rasio 2016). Moreover, a high-mass (>$\sim$25 M⊙) stellar progenitor favors a low-metallicity formation environment ($<\sim$0.5 Z⊙; see e.g. Eldridge & Stanway 2016). Extremely low metallicity ($Z < 10^{-4}$ Z⊙) leads to the formation of high-mass stars because: (i) the process of gas fragmentation is less efficient and results in proto-stellar clouds that are ~10 times more massive than in the presence of dust and metals and (ii) the accretion of gas on to the proto-stellar cores is more efficient (Abel, Bryan & Norman 2002; Bromm, Coppi & Larson 2002; Omukai & Palla 2001).

The low redshift of the event GW150914 ($z \sim 0.1$) and the low metallicity of the stellar progenitors of the BBH suggest two main formation scenarios for this source. The BBH could have formed in the local Universe, possibly in a low-mass galaxy with a low metal content (Belczynski et al. 2016). Another possible formation channel is in globular clusters (Rodriguez et al. 2016; Zevin et al. 2017). This formation channel implies that the BBH underwent a prompt merger, on a time-scale much shorter than the Hubble time. Alternatively, the progenitors of the BBH could have formed in the

<footnote n="1">¹Department of Physics, Yale University, New Haven, CT 06511, USA</footnote>

<footnote n="2">²Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA</footnote>

<footnote n="3">³Dipartimento di Fisica e Astronomia, Università di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italy</footnote>

<footnote n="4">⁴INAF/Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy</footnote>

<footnote n="5">⁵GEPI, Observatoire de Paris, PSL Research University, CNRS, Place Jule Janssen, F-92190 Meudon, France</footnote>

<footnote>* E-mail: fabio.pacucci@yale.edu</footnote>
early Universe, possibly from Pop III stars (see e.g. Belczynski, Bulik & Rudak 2004). The first population of stars has not been observed so far (see Sobral et al. 2015; Natarajan et al. 2017; Pacucci et al. 2017) and large uncertainties remain about their physical properties. Current theories (Barkana & Loeb 2001; Bromm 2013; Loeb & Furlanetto 2013) suggest that Pop III stars are characterized by: (i) very low metallicities (~$10^{-4}$–$10^{-6}$ Z⊙) and (ii) large masses ($\gtrsim 10$ M⊙). The formation of the BBH progenitors at high redshifts from Pop III stars would imply a time delay between formation and merger of $\gtrsim 10$ Gyr. Pop III stars are therefore natural candidates for the progenitors of massive BBHs. For instance, Kinugawa et al. (2014) pointed out that the detection of GW signals from BBHs with masses $\gtrsim 10$ M⊙ would strongly indicate that these sources preferentially originated from Pop III stars. Hartwig et al. (2016) estimated the contribution of Pop III stars to the intrinsic merger rate density: owing to their higher masses, the remnants of Pop III stars produce strong GW signals, even if their contribution in number is small and most of them would occur at high z.

In this Letter, we propose an independent way to assess if the component of BBHs, detected through GWs, originated from Pop III stars. Employing a data-constrained chemical evolution model coupled with high-resolution *N*-body simulations, we study the location of Pop III star remnants in a galaxy like the Milky Way (MW) and its high-z progenitors. Due to the hierarchical build-up of structures, we expect these old and massive black hole relics to be preferentially found inside the bulge of galaxies. Previously, Gao et al. (2010) employed the Aquarius simulation to show that half of Pop III remnants should be localized within ~30 kpc h⁻¹ of galactic centres. Here, we aim at improving this result, tracking the location of Pop III remnants interior to the galactic bulge (≤3 kpc). The localization of GW sources by future observations would therefore allow to test their Pop III origin. Such spatial localization of GW events is currently out of reach. For instance, Nissanke, Kasliwal & Georgieva (2013) stated that with an array of new detectors it will be possible to reach an accuracy in the spatial localization up to ~6 square degrees. This would allow the localization of a GW event within the dimension of a typical galactic bulge (~5 kpc) only for a few galaxies in the local Universe. This situation would change if GW events had electromagnetic (EM) counterparts. The *Fermi* satellite reported the detection of a transient signal at photon energies $\gtrsim 50$ keV that lasted ~1 s and appeared 0.4 s after GW150914 (Connaughton et al. 2016), encompassing ~75 per cent of the probability sky map associated with the LIGO event. Similarly, the satellite AGILE might have detected a high-energy (~MeV) EM counterpart associated with GW170104 (Verrecchia et al. 2017). While the merging of the components of an isolated BBH generates no EM counterpart, other physical situations exist in which the GW is associated with an EM signal. For instance, the merging BBHs may be orbiting inside the disc of a supermassive black hole (Kocsis, Haiman & Menou 2008), inducing a tidal disruption event (see also Murase et al. 2016; Perna, Lazzati & Giacomazzo 2016). Moreover, the collapse of the massive star forming an inner binary in a dumbbell configuration could appear as a supernova explosion or a GRB (Loeb 2016; Fedrow et al. 2017). The identification of EM counterparts of GW signals would allow a precise localization of the source.

## 2 METHODS

We start by describing the properties of the simulations employed along with the general assumptions for Pop III stars.

### 2.1 *N*-body simulation and chemical evolution

We employed a data-constrained chemical evolution model designed to study the first stellar generations combined with *N*-body simulations of MW analogues to localize Pop III remnants within the scale of the MW bulge, ~3.5 kpc (Ness et al. 2013).

While the most important features of the *N*-body simulation are reported here, more details can be found in Scannapieco et al. (2006) and Salvadori et al. (2010a). These papers simulated a MW analogue with the GCD+ code (Kawata & Gibson 2003) using a multiresolution technique to achieve high resolution. The initial conditions are set up at z = 56 using GRAFIC2 (Bertschinger 2001). The highest resolution region in the full simulation is a sphere with a radius four times larger than the virial radius of the MW analogue at z = 0. The dark matter particles mass and spatial resolution are, respectively, 7.8 × $10^5$ M⊙ and ~0.5 kpc. The total mass of stars contained in the MW disc and used to calibrate the simulation is ~4 × $10^{10}$ M⊙. The virial mass and radius of the MW analogue, containing about $10^6$ particles, are consistent with observational estimates $M_{vir} = 10^{12}$ M⊙, $R_{vir} = 258$ kpc (Battaglia et al. 2005).

While the resolution of this *N*-body simulation is not the highest currently available, the chemical evolution model is unrivaled in studying the metal enrichment of Pop III and Pop I/II stellar populations down to the present day. The star formation and metal enrichment history of the MW is studied by using a model that self-consistently follows the formation of Pop III and PopI/II stars and that is calibrated to reproduce the observed properties of the MW (Salvadori et al. 2010a). Combined with the *N*-body simulation, the model naturally reproduces the age-metallicity relation, along with the properties of metal-poor stars, including the metallicity distribution functions and spatial distributions. Furthermore, it matches the properties of higher-z galaxies (Salvadori, Dayal & Ferrara 2010b). So far, no other simulations can simultaneously account for these observations. Hence, even if we are unable to resolve the main formation sites of Pop III stars (i.e. the mini-haloes), we are able to localize with great accuracy the descendants of Pop III stars, i.e. the extremely low metallicity Pop II stars. For this reason, the method we employ here is perfectly suitable for pinpointing the location of Pop III stars in the MW and its progenitors.

### 2.2 General assumptions for Pop III remnants

Regarding the properties of Pop III stars, we make educated guesses or parametrize the unknown properties. For instance, the initial mass function (IMF) for Pop III stars is predicted to be different from the IMF of local stars. In the simulations, we employ different Pop III IMFs (see Section 4 for details) and check that the radial distribution of Pop III stars is nearly independent on these choices. Moreover, not all binaries can produce LIGO sources (Christian & Loeb 2017), since they need to have suitable initial masses and separations (see Section 4). Also the binarity fraction of Pop III stars could be different from the one of local systems. A qualitative constraint on its value can be derived by matching our predictions with the LIGO merger rate (see Section 5).

## 3 LOCATION OF POP III REMNANTS WITHIN THEIR HOST GALAXY

Next we analyse the spatial distribution of Pop III stellar remnants for the MW analogue and for some of its progenitors at different halo masses and redshifts (see Table 1).
<table><caption>**Table 1.** Details of the MW analogue and its progenitors (P). $M_{DM}$ is the dark matter mass, $M_*$ is the stellar mass and $z$ is the redshift.</caption><thead><tr><th>Galaxy identifier</th><th><i>M</i><sub>DM</sub> (M<sub>☉</sub>)</th><th><i>M</i><sub>*</sub> (M<sub>☉</sub>)</th><th><i>z</i></th></tr></thead><tbody><tr><td>MW</td><td>7.7 × 10<sup>11</sup></td><td>6.0 × 10<sup>10</sup></td><td>0</td></tr><tr><td>P1</td><td>1.5 × 10<sup>11</sup></td><td>5.0 × 10<sup>9</sup></td><td>3</td></tr><tr><td>P2</td><td>7.0 × 10<sup>9</sup></td><td>1.0 × 10<sup>8</sup></td><td>3</td></tr></tbody></table>

### 3.1 Pop III remnants in a Milky Way-like galaxy

Fig. 1 compares the spatial distributions of Pop III and of Pop I/II stars in the simulation of the MW analogue. The kernel density estimation (left-hand panel) suggests that the distribution of Pop III remnants is highly concentrated near the centre. Each contour corresponds to 10 per cent of the components of each population. We find that ~80 per cent of Pop III stars are located within ~3 kpc from the galactic centre. This is confirmed by the probability distribution function (PDF, right-hand panel) for the distance from the centre on the galactic plane. The radial distribution of the two stellar components is significantly different, as the FWHM suggest: ~3 kpc for Pop III stars and ~8 kpc for Pop I/II stars. Fig. 2 shows the stellar densities for both populations: the radial distribution of Pop III remnants is steeper, $\rho_*(\text{Pop III}) \propto r^{-5/2}$, than the radial distribution of normal stars, $\rho_*(\text{Pop I/II}) \propto r^{-3/2}$. Thus, at increasing radial distances Pop III remnants are rarer:

$$ \frac{\rho_{*}(\text{Pop III})}{\rho_{*}(\text{Pop I/II})} \sim r^{-1}. \qquad (1) $$

Similar radial profiles are found for smaller galactic systems, such as P1 and P2 in Table 1. This is illustrated in Fig. 3.

### 4 MODELING THE PROBABILITY OF OBSERVING A GW SIGNAL FROM POP III STARS

Employing our N-body simulations, we compute the probability that GW signals generated by BBHs originated from Pop III stars. We name this probability $P_{\text{III,GW}}(r)$ and we calculate it as a function

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Radial density profiles of the stellar density of Pop III remnants and Pop I/II stars in the MW analogue, up to $r \sim 13$ kpc from the Galactic centre. Both distributions roughly follow power laws: at increasing radial distances Pop III remnants become rarer. The total mass of stars contained in the MW disc and used to calibrate the simulation is $\sim 4 \times 10^{10} M_{\odot}$.</figcaption></figure>

of the galactocentric distance $r$. Formally, the probability $P_{\text{III,GW}}(r)$ is the product of three terms.

The first term, $P_{\text{III}}(r)$, is the probability of having a Pop III remnant at $r$ out of the entire sample of stars: $P_{\text{III}}(r) = N_*(\text{Pop III})/N_*(\text{total})$, see Fig. 3 for examples of $P_{\text{III}}(r)$.

The second term, $P_{\text{bin}}$, is the probability of having binary systems. This probability takes into account both the scenario in which a BBH is formed from binary stars and the scenario in which the black holes form separately and then become gravitationally bound. The binarity probability depends on several factors and have been extensively studied for Pop I/II stars. Instead, there are large uncertainties in the extrapolation to the binarity probability of Pop III stars. Here, we parametrize it with a constant value, independent of mass: $P_{\text{bin,III}} = \beta_{\text{III}}$. Assuming that GW events are generated by Pop III stars in galactic bulges, we derive in Section 5 an estimate

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Left-hand panel: kernel density estimate of the stellar distribution of Pop I/II (red) and Pop III (blue) stars. Each contour adds 10 per cent of the corresponding population. Right-hand panel: probability distribution function for the radial position in the galactic plane of a MW analogue. The full widths at half-maximum (FWHM) of each distribution is marked by a vertical line. About 80 per cent of Pop III stars are located within the inner ~3 kpc, while FWHM for Pop I/II stars is ~8 kpc.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 3. Probabilities that a GW signal is generated by remnants of binary Pop III stars, as a function of the galactocentric distance. Points are the probabilities for the MW analogue assuming $\beta_{III} = \beta_{III, high} = 0.88$ and $M_{c, III} = 10 M_{\odot}$ (orange) or $M_{c, III} = 20 M_{\odot}$ (red). The probability of a GW signal to be generated by Pop III stars is strongly enhanced within the core, reaching ~90 per cent at ~0.5 kpc from the centre, compared to a benchmark value of ~5 per cent outside the core. Best-fitting lines show instead the probability $P_{III}(r)$, i.e. not taking into account the binarity fraction and the IMFs, for the smaller galactic units, of $10^8 M_{\odot}$ and $5 \times 10^9 M_{\odot}$. Vertical dashed lines show the extent of the bulges in the three galaxies.</figcaption></figure>

of the parameter $\beta_{III}$ by matching our predicted GW rate with the LIGO statistics, requiring that $\beta_{III} \le 1$.

The third term, $P_{III}(M_1, M_2)$, is the probability that the progenitor stars end up with remnants of the correct masses to produce a given GW event, such as GW150914 or GW170104. This probability depends on a large number of parameters and is generally impossible to calculate from first principles. The mass ratio distribution, the orbital separation, the mass exchange between companions and the natal kicks after supernova events can only be incorporated by complicated population synthesis models (Eldridge & Stanway 2016). The use of these models goes beyond the scope of this Letter. An improvement in our knowledge of mass ratios could occur in the near future from large surveys, such as GAIA. Mashian & Loeb (2017) predict that up to ~3 × 10⁵ astrometric binaries hosting black holes and stellar companions brighter than GAIA’s detection threshold should be discovered with ~5σ sensitivity. Whereas calculating the mass distribution of normal Pop I/II stars is feasible, the IMF for Pop III stars is poorly constrained. Hence, we make the simplifying assumption that $P_{III}(M_1, M_2)$ depends only on the IMFs of the two populations of stars. In other words, we assume that it depends only on their respective probability of forming stars above a given mass threshold, e.g. $M_{min} = 20 M_{\odot}$. In fact, the mass range for LIGO-detected BBHs so far is 7–36 $M_{\odot}$, and the initial stellar mass needs to be significantly higher than these values. The characteristic mass of Pop III stars is predicted to be larger than the mass of local stars, and so they are more prone to having the minimum mass necessary to form BBH sources of LIGO signals. With this assumption we are neglecting all the complications that can only be accounted for by population synthesis models. We use the following IMF for the two stellar populations, with a Salpeter exponent and a low-mass cut-off $M_c$ that depends on the stellar population:

$$ \Phi(m) \propto m^{-2.35} \exp\left(-\frac{M_c}{m}\right), \qquad (2) $$

where $m$ is in solar units. For Pop III stars, we assume $M_{c, III} = 10–20 M_{\odot}$, while for Pop I/II stars $M_{c, I/II} = 0.35 M_{\odot}$. With $M_{c, III} = 20 M_{\odot}$, we find that Pop III stars are ~700 times more common in the mass range >$M_{min}$ than Pop I/II stars. Instead, with $M_{c, III} = 10 M_{\odot}$, the factor is ~200.

The final expression for $P_{III,GW}(r)$ is:

$$ P_{III,GW}(r) = P_{III}(r) \times P_{bin,III} \times P(M_1, M_2). \qquad (3) $$

Given our assumptions, the only term that directly depends on position is the first one.

## 5 CONSTRAINTS ON BINARITY AND RADIAL PROBABILITIES

We are now at a position to constrain the binarity probability of Pop III stars given the inferred LIGO merger rate and then compute the overall probability that a GW signal event localized in the bulge of a MW analogue originated from Pop III remnants.

The LIGO detection statistics (Abbott et al. 2016d) imply a 90 per cent credible range of merger rates $R$ between 2 and 53 Gpc⁻³ yr⁻¹. In general, $R$ is computed as follows:

$$ R = \rho_G \times N_{BBH} \times P, \qquad (4) $$

where $\rho_G$ is the number density of galaxies in the local Universe, $N_{BBH}$ is the average number of BBHs in a MW-mass galaxy and $P$ is the average merger rate. We assume $\rho_G \sim 2 \times 10^{-3}$ Mpc⁻³ (Conselice et al. 2016) and $P = 10^{-9}$ yr⁻¹ (from the distribution of merging times in Rodriguez et al. 2016 for BBHs in globular clusters). A comment on the latter value is warranted. The PDF of semimajor axes in binary orbits for Pop III stars is largely unconstrained. Here, we make the educated guess that the PDF should not significantly vary between Pop III and Pop I/II stars (Sana et al. 2012). Thus, it is also reasonable to employ the distribution of merging times for Pop I/II stars. Moreover, the number of binaries within the bulge of our MW analogue is $N_{BBH} = 3 \times 10^4 \times \beta_{III}$ (with $\beta_{III}$ the binarity probability for Pop III stars). We therefore obtain: $R = 60 \times \beta_{III}$ Gpc⁻³ yr⁻¹. From the LIGO predicted rate we obtain upper and lower limits for the Pop III binarity probability of $\beta_{III, high} = 0.88$ and $\beta_{III, low} = 0.03$. Stacy & Bromm (2013) find an overall binarity fraction of 35 per cent, which is in the middle of our range. The estimated binarity fraction of Pop III stars is large and somewhat compatible with observations of massive stars in the Milky Way, indicating that about 45–75 per cent of O-type stars have spectroscopic binary companions. This is also consistent with the fact that primordial stars are predicted to form preferentially in multiple systems (see e.g. Greif et al. 2012; Stacy, Bromm & Lee 2016).

The probability $P_{III,GW}(r)$ that a GW signal is generated by remnants of binary Pop III stars is shown in Fig. 3 for a MW analogue. In the calculation, we assumed $\beta_{III} = \beta_{III, high} = 0.88$ and different values of the characteristic mass in the Pop III IMF: $M_{c, III} = 10 M_{\odot}$ and $M_{c, III} = 20 M_{\odot}$. The probability that a GW signal is generated by Pop III stars is enhanced in all cases within the core of the MW analogue. In particular, for $M_{c, III} = 20 M_{\odot}$ the probability reaches ~90 per cent at ~0.5 kpc from the centre, compared to a benchmark value of ~5 per cent outside the galactic core. Similarly, in the $M_{c, III} = 10 M_{\odot}$ case, the peak probability inside the core is ~35 per cent, with a benchmark value of ~2 per cent. Also, note that for $M_{c, III} \sim 30 M_{\odot}$ the probability reaches ~100 per cent inside the galactic core.
## 6 DISCUSSION AND CONCLUSIONS

The masses of the two merging black holes in the first LIGO detection suggest that their most likely progenitors are massive low-metallicity stars. The BBH could have formed in the local Universe, possibly in a galaxy with a low content of metals, and then merged. Alternatively, the progenitors of the BBH formed in the early Universe, possibly as Pop III stars, and then merged on a Hubble timescale. By using high-resolution N-body simulations of MW-like and smaller galaxies, coupled with a state-of-the-art metal enrichment model, we suggest that the remnants of Pop III stars should be preferentially found within the bulges of galaxies, i.e. ~3 kpc from the centre of a MW-like galaxy. We predict a merger rate for GW events generated by Pop III stars inside bulges in the local Universe ($z \ll 1$) of ~60 $\times \beta_{III} \text{Gpc}^{-3} \text{yr}^{-1}$, where $\beta_{III}$ is the binarity probability of Pop III stars. By matching with the LIGO merger rate, we derive lower and upper limits of $0.03 < \beta_{III} < 0.88$. By using $\beta_{III} = 0.88$ and a Salpeter-like IMF with a variable low-mass cut-off $M_{c, III}$ for Pop III stars, we predict that the probability for observing GW signals generated by Pop III stars is strongly enhanced in the core of their host galaxies. In particular, in the case $M_{c, III} = 20 \text{ M}_\odot$, the probability reaches ~90 per cent at ~0.5 kpc from the galactic centre, compared to a benchmark value of ~5 per cent outside it.

A GW signal from within the bulge of galaxies could also originate from BBHs formed in globular clusters and slowly drifting towards the core (Rodriguez et al. 2016). Globular clusters can produce a significant population of massive BBHs that merge in the local Universe, with a merger rate of ~5 $\text{Gpc}^{-3} \text{yr}^{-1}$, with ~80 per cent of sources having total masses in the range 32–64 $\text{M}_\odot$. They drift towards the centre of their galaxy, but the dynamical friction time to reach the innermost ~3 kpc is very long. Since only a fraction $\lesssim 10^{-3}$ of BBHs generated in globular clusters would be found inside the innermost core of the galaxy, the merger rate inside the bulge would be ~0.005 $\beta \text{Gpc}^{-3} \text{yr}^{-1}$, unable to match the LIGO merger rate. We conclude that the Pop III channel is still the preferential one for generating GW events in galactic bulges.

While most Pop III stars are within the core of the galaxy, their total number is small with respect to the Pop I/II stars, whose population had a much longer fraction of the Hubble time to form. Nonetheless, the IMF of Pop III stars is skewed towards more massive stars. It is then up to ~700 times more likely to have a Pop III binary star with the right masses to produce GW signal like the first or the third LIGO detections than in the case of Pop I/II stars.

Despite the large uncertainties regarding the physical properties (or even the existence) of Pop III stars, there is one robust conclusion that can be drawn. If the first population of massive ($M_* \gg 10 \text{ M}_\odot$) and metal-free ($Z \ll 10^{-4} \text{Z}_\odot$) stars exists, then we predict that GW signals generated by their BBHs are preferentially ($P_{\text{III,GW}} \sim 90$ per cent) located within the inner core of galaxies. If the GW signals detected so far by LIGO are indeed generated by Pop III remnants, we predict in addition that their binarity probability is within the range $0.03 < \beta_{III} < 0.88$.

The localization of a GW in the core of a galaxy would not by itself pinpoint its origin as Pop III remnants. Nonetheless, the future build-up of a solid statistics of GW events and the possible localization of a large fraction of them within the core of galaxies, coupled with considerations about their masses, could clearly provide an indirect probe of Pop III stars.

## ACKNOWLEDGEMENTS

FP acknowledges the Chandra grant no. AR6-17017B and NASA-ADAP grant no. MA160009 and is grateful to Charles Bailyn, Frank van den Bosch and Daisuke Kawata. SS was supported by the

European Commission through a Marie Curie Fellowship (project PRIMORDIAL, no. 700907). This work was supported in part by the Black Hole Initiative at Harvard University, which is funded by a grant from the John Templeton Foundation.

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