Can Population III stars be major origins of both merging binary black holes and extremely metal poor stars?

Recently, a large number of black hole (BH) mergers have been detected by gravitational wave (GW) observations (Abbott et al., 2019, 2021; The LIGO Scientific Collaboration et al., 2021a). Many formation scenarios of such BH mergers have been suggested: isolated binary evolution of Population I/II (Pop I/II) stars (Bethe & Brown, 1998; Belczynski et al., 2007, 2016a; Mapelli et al., 2017; Eldridge et al., 2017; Ablimit & Maeda, 2018; Eldridge et al., 2019; Mapelli et al., 2019; Belczynski et al., 2020; Olejak et al., 2020; Santoliquido et al., 2021; García et al., 2021), dynamical interactions in globular clusters (Kulkarni et al., 1993; Sigurdsson & Hernquist, 1993; Portegies Zwart & McMillan, 2000; Banerjee et al., 2010; Downing et al., 2010; Tanikawa, 2013; Fujii et al., 2017; Askar et al., 2017; Park et al., 2017; Rodriguez et al., 2018; Samsing et al., 2018; Hong et al., 2020; Kimball et al., 2021; Wang et al., 2021; Anagnostou et al., 2020; Arca-Sedda et al., 2021), star clusters (Ziosi et al., 2014; Banerjee, 2017; Fishbach et al., 2017; Gerosa & Berti, 2017; Rastello et al., 2019; Kumamoto et al., 2020; Di Carlo et al., 2020; Kremer et al., 2020; Trani et al., 2021b; Fragione & Banerjee, 2021), and galactic centers (O’Leary et al., 2009; Antonini & Perets, 2012; VanLandingham et al., 2016; Bartos et al., 2017; Petrovich & Antonini, 2017; Stone et al., 2017; Hoang et al., 2018; Hamers et al., 2018; McKernan et al., 2018; Leigh et al., 2018; Yang et al., 2019; Rasskazov & Kocsis, 2019; Tagawa et al., 2020; McKernan et al., 2020; Arca Sedda, 2020; Mapelli et al., 2021; Gerosa & Fishbach, 2021; Liu & Bromm, 2021), secular evolution in multiple stellar systems (Antonini et al., 2014; Silsbee & Tremaine, 2017; Rodriguez & Antonini, 2018; Liu & Lai, 2019; Fragione & Kocsis, 2019; Hamers & Safarzadeh, 2020; Fragione et al., 2020; Britt et al., 2021; Trani et al., 2021a), hybrid channels of binary evolution and dynamical interactions (Bouffanais et al., 2021), and primordial BHs (Franciolini et al., 2021).

The first-generation metal-free (Population or Pop III) stars are typically massive ($10$–$1000~{}M_{\odot}$) (Omukai & Nishi, 1998; Abel et al., 2002; Bromm & Larson, 2004; Yoshida et al., 2008; Hosokawa et al., 2011; Stacy et al., 2011; Susa, 2013; Hirano et al., 2014), and thus leave behind BHs more efficiently than Pop I/II stars. Thus, Pop III stars can contribute to the formation of merging BHs (Kinugawa et al., 2014; Hartwig et al., 2016; Belczynski et al., 2017; Tanikawa et al., 2021b; Liu & Bromm, 2020a). Moreover, several rare GW events can be explained by Pop III stars. For example, a GW event with a $2.6$ $M_{\odot}$ compact object GW190814 (Abbott et al., 2020b) can be explained by Pop III remnant mergers (Kinugawa et al., 2021b). GW190521 with a BH in the pair instability (PI) mass gap (Abbott et al. (2020a, c); but see Fishbach & Holz (2020)) can be formed from Pop III stars (Liu & Bromm, 2020b; Kinugawa et al., 2021a; Farrell et al., 2021; Tanikawa et al., 2021a, c). Next-generation GW observatories, such as Cosmic Explorer (Reitze et al., 2019) and Einstein telescope (Punturo et al., 2010), may detect Pop III BHs more massive than $100$ $M_{\odot}$ (Belczynski et al., 2004; Hijikawa et al., 2021).

However, there is a debate whether Pop III stars are a major origin of observed BH mergers. Kinugawa et al. (2021c) have claimed that Pop III stars are a major origin of observed BH mergers with more than 20 $M_{\odot}$ (hereafter, Pop III BH merger scenario). On the other hand, Hartwig et al. (2016) (see also Tanikawa et al. (2021b); Liu et al. (2021a)) have argued that the merger rate of Pop III BHs should be much lower than observed. This debate comes from adopted Pop III formation rate. The former study has supposed the total Pop III mass in the local universe to be $\sim 10^{15}$ $M_{\odot}$ ${\rm Gpc}^{-3}$, which is the upper limit constrained by the cosmic reionization (de Souza et al., 2011; Inayoshi et al., 2016, 2021). The latter studies have chosen it as $\sim 10^{13}$ $M_{\odot}$ ${\rm Gpc}^{-3}$ obtained by theoretical studies of Pop III star formation (Magg et al., 2016; Skinner & Wise, 2020; Visbal et al., 2020). It is difficult to determine Pop III formation rate, since no Pop III star has been discovered so far (Frebel & Norris, 2015; Magg et al., 2019).

In this paper, we suggest extremely metal-poor (EMP) stars as another approach to examine if Pop III stars may be a major origin of observed BH mergers. EMP stars are thought as stars with ${\rm[Fe/H]}\lesssim-3$ and considered to form in gas clouds enriched by one or several supernovae (SNe) of Pop III stars (Audouze & Silk, 1995; Ryan et al., 1996; Cayrel et al., 2004; Frebel & Norris, 2015).¹¹1${\rm[X/Y]}=\log(n_{\rm X}/n_{\rm Y})-\log(n_{\rm X}/n_{\rm Y})_{\odot}$, where $n_{\rm X}$ and is the number density of an element X. The metal contents and elemental abundances of EMP stars are crucial to trace back the properties of Pop III stars. EMP stars can be divided into two types: carbon-normal EMP stars and carbon-rich EMP stars (or carbon-enhanced metal-poor stars, CEMP stars) (Beers & Christlieb, 2005). Carbon-normal EMP stars have elemental abundance patterns similar to the Sun. On the other hand, carbon-rich EMP stars have higher carbon abundances than the Sun (${\rm[C/Fe]}>0.7$) (Aoki et al., 2007). The abundance ratio of carbon-rich stars to carbon-normal stars increases with [Fe/H] decreasing (Beers & Christlieb, 2005; Yong et al., 2013).

The presence of the two types can be interpreted as follows. Elemental abundances of carbon-normal EMP stars can best fit with the models of successful core-collapse supernovae (CCSNe). To explain the origin of carbon-rich stars, Umeda & Nomoto (2003) have proposed a so-called faint SN model: inner layers of stellar core falls back into central compact remnants, and only outer layers containing light elements, such as carbon, are ejected. However, in their model, mass cut is a free parameter to reproduce the elemental abundance of carbon-rich stars. Fryer et al. (2012) have independently found that a considerable fraction of ejecta falls back into a proto-neutron stars in a window of progenitor mass $20$–$30~{}M_{\odot}$. Such failed supernovae (FSNe) leave behind a BH and should eject only carbon-rich outer layers. There is a firm evidence that a CEMP star is formed from the mixture of primordial gas and the ejecta of FSNe (Ito et al., 2013). These studies motivate us to define CCSNe and FSNe as the progenitors of carbon-normal and carbon-rich EMP stars, respectively. If primordial gas in dark matter minihalos (hereafter, minihalos) is enriched by carbon-normal and carbon-rich materials, the minihalos form carbon-normal and carbon-rich EMP stars, respectively. Note that there are many other scenarios of carbon-rich star formations: abundant production of carbon in supermassive rapidly rotating stars (Fryer et al., 2001; Liu et al., 2021b), enrichment of a Pop III star from asymptotic giant branch winds (Suda et al., 2004; Campbell et al., 2010), and interstellar medium accretion of gas decoupled from dust (Johnson, 2015).

The purpose of this paper is to assess the Pop III BH merger scenario, under a hypothesis that EMP stars consist of primordial gas and Pop III supernova ejecta. Here, we remark the importance of this purpose. Although many formation scenarios of BH mergers have been proposed as described above, they have not yet been critically verified, and none of them has been rejected. Moreover, several studies have suggested that binary BHs can have multiple origins (Bouffanais et al., 2021; Zevin et al., 2021; Ng et al., 2021; Hütsi et al., 2021). As the first step, we need to narrow down promising formation scenarios of BH mergers, and scrutinize these formation scenarios one by one. In particular, we focus on Pop III stars, since they can be the origin of binary BHs with $\sim 30$ $M_{\odot}$ (Kinugawa et al., 2014, 2021c), or with PI mass gap BHs (Tanikawa et al., 2021a). Among the scenarios of Pop III star origins, we pay attention to the Pop III BH merger scenario suggested by Kinugawa et al. (2014) and Kinugawa et al. (2021c). Since this scenario assumes the largest Pop III star mass in total among all the BH scenarios requiring Pop III stars, it would be easiest to get constrained. We also attribute CCSNe and FSNe to the formation of EMP stars, although there are several scenarios to explain the formation of EMP stars. This is because this EMP formation scenario can explain the abundance pattern of EMP stars (Ito et al., 2013) as described above.

The structure of this paper is as follows. In section 2, we present our method to obtain the merger rate of Pop III BHs, and the abundance ratio of carbon-rich EMP stars to carbon-normal EMP stars. In sections 3 and 4, we show our results, and summarize this paper, respectively.

In this section, we present a method to obtain the merger rate of Pop III BHs, and the abundance ratio of carbon-rich EMP stars to carbon-normal EMP stars. In section 2.1, we describe our Pop III star formation model. In section 2.2, we review our binary population synthesis model to derive the merger rate of Pop III BHs. In section 2.3, we show our EMP star formation model based on the results of binary population synthesis calculations. In section 2.4, we describe the necessary conditions satisfying GW and EMP observations.

Figure 1 shows which ($m_{\min}$, $M_{\max}$) satisfies the three necessary conditions described in section 2.4. We first focus on $M_{\max}$. We need $M_{\max}\lesssim 3\times 10^{4}$ $M_{\odot}$ in order to satisfy the first necessary condition. We also need $M_{\max}\gtrsim 10^{4}$ $M_{\odot}$. Otherwise, the second necessary condition cannot be satisfied, since the Pop III BH merger rate density is too small: $R_{20-40}<3$ ${\rm yr}^{-1}$ ${\rm Gpc}^{-3}$. This $M_{\max}$ is much larger than $M_{\max}\sim 600$ $M_{\odot}$ obtained by numerical simulations of Skinner & Wise (2020). Similar things have been already pointed out by Hartwig et al. (2016). Nevertheless, we have to note that the first necessary condition is not still violated even when the second necessary condition is satisfied.

We next focus on $m_{\min}$. We need $15\lesssim m_{\min}/M_{\odot}\lesssim 27$ in order to satisfy the third necessary condition. The allowed $M_{\max}$ becomes narrower when $m_{\min}$ deviates from $\sim 20M_{\odot}$, the boundary mass between CCSNe and FSNe. If $m_{\min}$ is too small, $f_{\rm c-rich}<0.01$, since minihalos have a large number of CCSNe, get iron elements, and cannot form carbon-rich EMP stars. If $m_{\min}$ is too large, $f_{\rm c-rich}>1$, since minihalos have a small number of CCSNe, get little iron element, and cannot form carbon-normal EMP stars.

If we relax the second necessary condition from $3\leq R_{20-40}/({\rm yr}^{-1}{\rm Gpc}^{-3})\leq 30$ to $1\leq R_{20-40}/({\rm yr}^{-1}{\rm Gpc}^{-3})\leq 100$, the allowed region becomes wider not only in the direction of $M_{\max}$, but also in the direction of $m_{\min}$. Especially, $m_{\min}=10$ $M_{\odot}$ can be allowed. Each minihalo forms a smaller amount of Pop III stars in the latter case than in the former case. Each minihalo has CCSNe at a smaller probability, and gets a smaller amount of iron elements. Thus, some of minihalos can form carbon-rich EMP stars.

In order to complement the above explanations, we demonstrate how to satisfy the three necessary conditions. Table 1 shows our choice of $(m_{\min},M_{\max})$ in advance. As the starting point, we choose $(m_{\min},M_{\max})=(10M_{\odot},600M_{\odot})$. The values of $m_{\min}$ and $M_{\max}$ are consistent with Susa et al. (2014) and Skinner & Wise (2020), respectively. Thus, these values are based on recent numerical simulations for Pop III star formations. The results are shown in Figure 2. In this case, the first and third conditions are satisfied. However, the BH merger rate is $R_{20-40}\sim 1.6\times 10^{-1}$ yr^-1 ${\rm Gpc}^{-3}$, which is much smaller than the second necessary condition. Thus, we need to change $(m_{\min},M_{\max})$ to increase $R_{20-40}$.

In order to increase $R_{20-40}$, we set $(m_{\min},M_{\max})=(10M_{\odot},15000M_{\odot})$. Figure 3 shows the results for this case. The Pop III star formation rate is $\rho_{3}\sim 5.9\times 10^{14}$ $M_{\odot}$ ${\rm Gpc}^{-3}$. This is much larger than that of Skinner & Wise (2020), however does not still violate the first necessary condition. The large $M_{\max}$ increases $R_{20-40}$ to $\sim 3.1$ ${\rm yr}^{-1}$ ${\rm Gpc}^{-3}$, consistent with the second necessary condition. On the other hand, $f_{\rm c-rich}\ll 0.01$. This is much smaller than the third necessary condition. The reason why $f_{\rm c-rich}$ decreases from the case of $(m_{\min},M_{\max})=(10M_{\odot},600M_{\odot})$ to $(10M_{\odot},15000M_{\odot})$ is as follows. In the case of $(m_{\min},M_{\max})=(10M_{\odot},15000M_{\odot})$, all the minihalos have a large number of Pop III stars with $m_{\rm zams}\lesssim 20M_{\odot}$. They have many CCSNe, and are sufficiently polluted by iron. Thus, they form only carbon-normal EMP stars after that.

In order to increase $f_{\rm c-rich}$, we adopt $(m_{\min},M_{\max})=(17M_{\odot},12000M_{\odot})$ as seen in Figure 4. In this case, the third necessary condition are satisfied as well as the first and second conditions. Since we increase $m_{\min}$, minihalos have Pop III stars with $m_{\rm zams}\lesssim 20M_{\odot}$ and CCSNe at a small probability. Then, a significant fraction of minihalos are not polluted by iron. There are no EMP stars with ${\rm[Fe/H]}\sim-6$–$-3$ in our model in contrast to the observation of EMP stars. However, this may be reconciled when we take into account inhomogeneous mixing of Pop III supernova ejecta in minihalos.

In order to assess the Pop III BH merger scenario, previous studies have focused on the secondary necessary condition. Thus, they have only pointed out that minihalos should form a larger amount of Pop III stars than predicted theoretically by a factor of more than 10. In addition to that, we find a new constraint on $m_{\min}$: $15\lesssim m_{\min}/M_{\odot}\lesssim 27$ by taking into account the third necessary condition. The allowed range $M_{\max}$ becomes narrower when $m_{\min}$ deviates from $\sim 20$ $M_{\odot}$. In other words, $m_{\min}$ should be close to the critical mass where the fate of a Pop III star transits from a CCSN to a FSN. The critical mass is $\sim 20$ $M_{\odot}$ in our adopted supernova model. Otherwise, minihalos can form only one type of carbon-rich and carbon-normal EMP stars.

We examine the Pop III BH merger scenario under the hypothesis that EMP stars consist of primordial gas and Pop III supernova ejecta. We suppose that the scenario is valid if the following three necessary conditions are satisfied. First, Pop III formation rate is $\rho_{3}\leq 10^{15}$ $M_{\odot}$ ${\rm Gpc}^{-3}$. Second, Pop III BHs merge at a rate of $3\leq R_{20-40}/({\rm yr}^{-1}{\rm Gpc}^{-3})\leq 30$. Third, EMP stars have the number ratio $0.01\leq f_{\rm c-rich}\leq 1$. In order to obtain Pop III BHs and EMP stars, we construct a simple formation model of Pop III stars, and simulate the evolution of Pop III stars by binary population synthesis technique.

We find that there is a region satisfying the three necessary conditions. The Pop III formation rate should be $\rho_{3}\gtrsim 3\times 10^{14}$ $M_{\odot}$ ${\rm Gpc}^{-3}$. This means that each minihalo should form Pop III stars with $M_{\max}\sim 10^{4}$ $M_{\odot}$, or $10^{3}-10^{4}$ $M_{\odot}$ in total. Although this formation rate does not violate the first necessary condition, it is much larger than numerically predicted by Skinner & Wise (2020). Similar things have been already pointed out by Hartwig et al. (2016).

We newly find that the minimum mass of Pop III stars should be $15\lesssim m_{\min}/M_{\odot}\lesssim 27$. If $m_{\min}/M_{\odot}\lesssim 15$ or $m_{\min}/M_{\odot}\gtrsim 27$, $f_{\rm c-rich}$ is smaller or larger than the third necessary condition, respectively. This is because each minihalo gets too much CCSNe and FSNe for $m_{\min}/M_{\odot}\lesssim 15$ and $m_{\min}/M_{\odot}\gtrsim 27$, respectively. Moreover, the allowed region becomes narrower with $m_{\min}$ deviating from $\sim 20$ $M_{\odot}$, which is the boundary mass between CCSNe and FSNe.

We compare the new constraint with $m_{\min}$ obtained from numerical simulations. Susa et al. (2014) have shown that the number of Pop III stars is sharply decreased just below $\sim 10$ $M_{\odot}$. On the other hand, in Hirano et al. (2014) (see also Hirano et al. (2015)), the number of $10$ $M_{\odot}$ Pop III stars is much smaller than that of $20$ $M_{\odot}$, which can be interpreted as $10\lesssim m_{\min}/M_{\odot}\lesssim 20$. From these numerical simulations, we can regard $10\lesssim m_{\min}/M_{\odot}\lesssim 20$, however cannot strictly determine $m_{\min}$. Thus, we do not exclude possibility of the Pop III BH merger scenario, under our assumption that EMP stars are formed from primordial gas mixed with Pop III supernova ejecta.

We have to note that recent studies have also found the formation of low-mass Pop III stars (Machida et al., 2008; Clark et al., 2011a, b; Greif et al., 2011, 2012; Machida & Doi, 2013; Susa et al., 2014; Chiaki et al., 2016). Such low-mass Pop III stars can have $\lesssim 1$ $M_{\odot}$. However, the number of such low-mass Pop III stars is much smaller than Pop III stars with $\gtrsim 10$ $M_{\odot}$. The presence of such low-mass Pop III stars can be negligible for our results.

We emphasize that the new constraint on $m_{\min}$ ($15\lesssim m_{\min}/M_{\odot}\lesssim 27$) is necessary only when we claim the Pop III BH merger scenario. Note that Pop III stars are a major origin of observed BH mergers with more than 20 $M_{\odot}$ in the Pop III BH merger scenario. In other words, Pop III stars can have $\lesssim 15$ $M_{\odot}$ stars (say $10$ $M_{\odot}$ stars or less massive stars) if we do not adopt the Pop III merger scenario. The new constraint on $m_{\min}$ can be applicable when we reconcile the Pop III BH merger scenario with $0.01\leq f_{\rm c-rich}\leq 1$.

Hereafter, we make caveats on our model. We treat $M_{\max}$ as a free parameter, while we fix $n_{\rm halo}$ as $\sim 10^{11}$ ${\rm Gpc}^{-3}$. However, $M_{\max}$ and $n_{\rm halo}$ may be anti-correlated. Skinner & Wise (2020) have performed numerical simulations to follow cosmic chemical evolution as well as Pop III star formation. Since we assume that more Pop III stars are formed than Skinner & Wise (2020) expected, Pop III’s surrounding gas should be polluted more rapidly. The pollution should stop forming Pop III stars earlier, and start forming Pop I/II stars earlier. Thus, if we assume that each minihalo yields a larger amount of Pop III stars than their results (i.e. $M_{\max}\gg 600$ $M_{\odot}$), we should decrease the number density of minihalos (i.e. $n_{\rm halo}\ll 10^{11}$ ${\rm Gpc}^{-3}$). In that case, the Pop III BH merger scenario should be difficult to be valid. In this paper, we do not take into account this, because we simply control Pop III star formation rate.

We prepare the three necessary conditions as described in section 2.4. It might be possible to add other necessary conditions. As for merging BHs, GW observations obtain not only BH masses but also BH spins. We might account for BH spins for necessary conditions. However, we do not do so. This is because the estimates of BH spins are less reliable and less constrained than BH masses (The LIGO Scientific Collaboration et al., 2021b). Thus, we adopt only BH masses for the necessary conditions. As for EMP stars, chemical elements other than carbon are also observed. Nevertheless, we do not take into account them. This is because carbon abundance is the most characteristic and most observed elements in EMP stars, and is the most sensitive to whether CCSNe or FSNe happen.

In our supernova model, Pop III stars with $m_{\rm zams}/M_{\odot}\lesssim 20$ and $\gtrsim 20$ deterministically cause CCSNe and FSNe, respectively, except that binary interactions slightly change their fates. On the other hand, recent supernova studies have suggested that stars with $m_{\rm zams}=10-30$ $M_{\odot}$ cause CCSNe stochastically (Ugliano et al., 2012; Pejcha & Thompson, 2015; Sukhbold et al., 2016; Müller et al., 2016; Sukhbold et al., 2018; Kresse et al., 2021). This may largely affect our results. However, we do not adopt such supernova models. This is because these models have not been prepared to use in binary population synthesis technique. These models tell us whether stars experience CCSNe or direct collapses to BHs, but do not include FSNe which is needed in binary population synthesis technique.

We thank organizers of the first star and first galaxy conference 2020 in Japan for giving us a good opportunity to start our collaboration. This study was supported in part by Grants-in-Aid for Scientific Research (19K03907, 20H00174, 20H01904, 21K13915) from the Japan Society for the Promotion of Science and Grants-in-Aid for Scientific Research on Innovative areas (17H06360, 18H05437, 20H04747) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.