Divergence in mass ratio distributions between low-mass and high-mass coalescing binary black holes

The first successful detection of a gravitational-wave (GW) signal from a coalescing binary black hole (BBH) on 2015 September 14 (Abbott et al., 2016) has brought about the era of GW astronomy. Very recently, the LIGO-Virgo-KAGRA Collaborations (LVKC) reported the second part of the GW events detected in the third observing run (O3) (The LIGO Scientific Collaboration et al., 2021a), and to date, nearly 100 detections have been reported (Abbott et al., 2019a, 2021a; The LIGO Scientific Collaboration et al., 2021b, a). The number of detections may even reach 1000 once the GW detector network is observing in its design sensitivity (Abbott et al., 2018). However, the origins of these compact objects remain uncertain. Several evolutionary channels have been proposed (see Refs. Mapelli, 2020; Gerosa & Fishbach, 2021, for recent reviews), including, for instance, the isolated binary evolution and dynamical capture. These formation channels will leave an imprint on the properties of the compact binary population (Taylor & Gerosa, 2018; Arca Sedda & Benacquista, 2019). Therefore, studying the rapidly increasing population of GW events enables us to investigate how compact binaries form. Various studies that employed some analytical models (e.g., Talbot & Thrane, 2017; Abbott et al., 2019b, 2021b; The LIGO Scientific Collaboration et al., 2021c) or some nonparametric approaches (e.g., Li et al., 2021b; Tiwari & Fairhurst, 2021; Tiwari, 2022) were carried out, and some formation / evolutionary processes of the compact binaries are being revealed (e.g., Wang et al., 2021b; Kimball et al., 2021; Galaudage et al., 2021; Safarzadeh & Wysocki, 2021; Baxter et al., 2021; Tang et al., 2021; Mapelli et al., 2022; Li et al., 2021a; Wang et al., 2021a).

The mass ratio may also carry some information about the formation and evolution mechanism of the BBHs. For instance, Fishbach & Holz (2020) found that the two objects in the merging BBHs are more likely to be of comparable mass rather than randomly paired, consistent with the predictions of some formation channels (Dominik et al., 2015; Amaro-Seoane & Chen, 2016; Rodriguez et al., 2016; Mandel & de Mink, 2016; Marchant et al., 2016; Mandel & Farmer, 2022). In particular, Mandel & de Mink (2016) (see also (de Mink & Mandel, 2016; Marchant et al., 2016)) proposed a route toward merging massive BHs, i.e., the chemically homogeneous evolution, such that BBHs that form through it are expected to be most likely equal-mass components because the binary systems were in contact (shared mass) on the main sequence, before disengaging during subsequent phases of the chemically homogeneous evolution. The traditional isolated evolution channel, i.e., the common-envelope evolution, is also predicted to produce BBHs with comparable mass components. Anyhow, the chemically homogeneous evolution can only produce massive binaries with a total BH mass above $\sim 55M_{\odot}$ (Mandel & de Mink, 2016; Marchant et al., 2016), which exceeds the majority of the mass range for the common-envelope evolution, and the common-envelope evolution preference for equal-mass systems is less extreme than that by the chemically homogeneous evolution. Additionally, the dynamical assembly, such as in globular clusters and nuclear star clusters, may also have a strong preference for symmetric masses (see, e.g., Rodriguez et al., 2016; Banerjee, 2017; Antonini et al., 2019; Zevin et al., 2021, and their references), and in such channels heavier BHs are more likely to merge (see Mandel & Farmer, 2022, for a recent review). Therefore, the mass ratio distribution of BHs may be dependent on the primary mass.

In this Letter, we perform a hierarchical Bayesian inference to explore the features of the mass ratio distribution in the BBH populations. The work is organized as follows: In Section 2, we introduce the data and the models used for inference, and in Section 3, we present the results. We make our conclusion and discussion in Section 4.

In this section, we display the results obtained using the methods described in Section 2. All the results shown here are marginalized over the hyperparameters of the spin distribution. We firstly compare all the models by the Bayes factors, as summarized in Table 2. Model II provides us with an overall picture ²²2Note that the lower bound of $\sigma_{\rm q}$ in the higher-mass range can still be smaller than that in the range of 30-40 $M_{\odot}$. of how the mass ratio distribution varies with the primary mass, as is shown in Fig. 2. We find nontrivial Bayes factors between Model II (with $\sigma_{\rm knot}$=0.5 or $\sigma_{\rm knot}$=1 ) and invariable half-Gaussianmodel. Additionally, the Bayes factors are still significantly positive when we change the primary mass model or exclude the asymmetric event GW190412. So, we conclude that an invariable mass ratio distribution in the whole mass range is disfavored. The mass ratio distribution should vary with primary mass, which indicates that the BBHs in the different mass ranges may have different evolutionary processes.

Model I divides the BBHs into two mass ranges (low and high) at $m_{\rm cut}$, where the mass ratio distributions have two different widths, $\sigma_{\rm q}^{\rm low}$ and $\sigma_{\rm q}^{\rm high}$. We obtained $m_{\rm cut}=29.3^{+5.7}_{-4.0}M_{\odot}$ (90% credible interval), and the value slightly shifts to a smaller value of $27.4^{+10.2}_{-5.5}M_{\odot}$ if we leave out GW190412 from the analysis. We find that the BBHs in the high-mass range (i.e., with $m_{1}>m_{\rm cut}$) have a more preference for equal masses than those in the low-mass range (i.e., with $m_{1}<m_{\rm cut}$) at a $97.6\%$ credible level, as shown in Fig. 3 (a), and the credibility becomes $86.7\%$ in the absence of GW190412. To find out the influence of the primary mass model, we also perform the inferences with the Broken PowerLaw model (Abbott et al., 2021b) instead of the PowerLaw Peak (Eq. (2.2)); then the conclusion remains unchanged, and the credibility even rises to $99.7\%$, though $m_{\rm cut}$ slightly shift to lower values, as shown in Fig. 3 (b). As shown in Fig. 2 that $\sigma_{\rm q}$ may wiggle in the lower-mass range ($m_{1}<m_{\rm cut}$). To find out whether there are actually additional features, We use an extended Model I (see the Appendix A) for analysis. Our results suggest that none of the perturbations are statistically significant enough to declare an additional structure as shown in Fig. 6.

The Bayes factors between Model III and the invariable half-Gaussian mass ratio distribution model as summarized in Tab. 2, provide milder evidence that the BBHs with $m_{1}$ in the Gaussian component have a mass ratio distribution different from that of the other mass range, as shown in Fig. 4 (a). The width of the mass ratio distribution of BBHs in the Gaussian component ($\sigma_{\rm q}^{\rm G}$) is smaller than that in the power-law component ($\sigma_{\rm q}^{\rm PL}$) at $95.4\%$ credibility (see Fig. 4 (b)); such a feature is also present in Fig. 2 as well as Fig. 1, where the BBHs with $m_{1}\sim 35M_{\odot}$ have a stronger preference for being equal-mass systems. When we exclude GW190412 from the analysis, $\sigma_{\rm q}^{\rm PL}-\sigma_{\rm q}^{\rm G}$ is still positive, though $\sigma_{\rm q}^{\rm PL}$ shifts to a smaller value. Note that the Gaussian component is almost in the high-mass range for the results obtained by Model II, and we find no evidence that Model III is more preferred than Model I. Therefore, whether the BBHs with primary masses in the Gaussian component have a mass ratio distribution different from the more massive BBHs is inconclusive.

We have investigated the population of BBHs with some parameterized / semiparameterized models to adequately address some potential features in the mass ratio distribution. With the current coalescing BBH sample (The LIGO Scientific Collaboration et al., 2021a), we first conclude that the mass ratio distribution is not invariable in the whole mass range but varies with the primary mass. This feature may support the fact that the BBHs observed by LIGO/Virgo/KAGRA may come from not only one evolution process. Then we conclude that BBHs in the higher-mass range are more likely to be equal-mass systems than those in the lower-mass range, and the demarcation point $m_{\rm cut}$ may lie between $25M_{\odot}$ and $30M_{\odot}$. Consequently, we predict that asymmetric events are more likely to emerge in the lower-mass range. Note that we have excluded GW190814 in our analysis, and our conclusion will be strengthened if we include GW190814, which is potentially located in the lower-mass range. However, from the current observations, we cannot conclude yet whether or not there are additional structures or not in the lower-mass range (see the Appendix A for the details of the analysis). In addition to the common-envelope evolution, some formation and evolution channels that have a stronger preference for producing symmetric BBHs, such as chemically homogeneous evolution (de Mink & Mandel, 2016; Marchant et al., 2016) and dynamical assembly (Rodriguez et al., 2016; Banerjee, 2017; Antonini et al., 2019), have been proposed. BBHs from chemically homogeneous evolution are expected to have total masses above $55M_{\odot}$; meanwhile, for the dynamical assembly in the nuclear star clusters, the heavier BHs are more likely to merge (Mandel & Farmer, 2022). Therefore, our finding that BBHs in the higher-mass range are more likely to be of equal mass is in concert with the predictions resulting from these formation channels.

We also find that the BBHs with primary masses in the Gaussian component may have a stronger preference for equal mass than the BBHs in the power-law component. This feature in the mass ratio distribution may be associated with the pulsational pair-instability supernovae (PPISNe) (Woosley & Heger, 2015; Belczynski et al., 2016), because the nearly symmetric systems may be the built up of the high-mass BHs created from PPISNe. Additionally, as mentioned above, the chemically homogeneous evolution and the dynamical assembly can also contribute to the nearly symmetric systems in the Gaussian component. However, currently, we find no evidence that the BBHs in the Gaussian component are more symmetric than those in the higher-mass range, as described above.

We have qualitatively proven that the mass ratio distribution varies with the primary mass in the surveyed mass range, where the asymmetric systems are more likely to emerge in the lower mass range, and the BBHs are more symmetric in the higher-mass range. The parameterized / semiparameterized models considered here are still limited and may not be able to describe the BBH populations completely (Mandel & Broekgaarden, 2022). For example, it would be beneficial to construct a mass-dependent spin model together with the mass ratio distribution, and we leave this for future work. Meanwhile, the BBH sample is expected to increase rapidly in the near future (Abbott et al., 2018). Therefore, with a significantly extended sample, besides better characterizing the mass ratio distribution in the whole mass range, new structures may be revealed in the mass spectrum and distribution of spin properties of BBHs, shedding new light onto the BBH formation channels.