Basic observational signatures of Pop III BBH mergers for the 18 models listed in Table 2. Column 1: model name. Columns 2: all-sky merger rate |$\dot{\mathcal {N}}$| (equation 24) for all mergers within |$z\lt 1$|. Column 3: fraction |$\mathcal {F}_{\rm NSC}$| of all-sky merger rate contributed by NSC mergers for |$z\lt 1$|. Column 4: fraction |$\mathcal {F}_{\rm PopIII}$| of all-sky merger rate of BBH mergers contributed by Pop III stars for |$z\lt 1$|. Column 5: all-sky merger rate |$\dot{\mathcal {N}}_{\rm IMBH}$| of Pop III BBHs with at least one IMBH (i.e. |$m_{1}\gt 100\ \rm M_\odot$|) for |$z\lt 1$|. Columns 6–9: same as Columns 2–5 but for |$z\lt 20$|. Columns 10 and 11: peak value |$\Omega _{\rm GW}^{\rm peak}$| and location |$\nu _{\rm peak}$| of the SGWB energy spectrum from Pop III BBH mergers. Column 12: maximum ratio |$f_{\rm SGWB}^{\rm PopIII}$| between the SGWB produced by Pop III BBH mergers and the conservative prediction of the SGWB from Pop I/II and PBH mergers by Bavera et al. (2022). Given the optimistic results for the total SGWB inferred from GWTC-3 events (Abbott et al. 2023a) as the reference, the maximum contribution of Pop III BBH mergers to the total SGWB is approximately |$f_{\rm SGWB}^{\rm PopIII}/5$|.
| Model . | |$\dot{\mathcal {N}}\ [\rm yr^{-1}]$| . | |$\mathcal {F}_{\rm NSC}$| . | |$\mathcal {F}_{\rm PopIII}$| . | |$\dot{\mathcal {N}}_{\rm IMBH}$| . | |$\dot{\mathcal {N}}\ [\rm yr^{-1}]$| . | |$\mathcal {F}_{\rm NSC}$| . | |$\mathcal {F}_{\rm PopIII}$| . | |$\dot{\mathcal {N}}_{\rm IMBH}$| . | |$\Omega _{\rm GW}^{\rm peak}$| . | |$\nu _{\rm peak}$| . | |$f_{\rm SGWB}^{\rm PopIII}$| . |
|---|---|---|---|---|---|---|---|---|---|---|---|
| . | |$(z\lt 1)$| . | |$(z\lt 1)$| . | |$(z\lt 1)$| . | |$(z\lt 1)$| . | |$(z\lt 20)$| . | |$(z\lt 20)$| . | |$(z\lt 20)$| . | |$(z\lt 20)$| . | |$[10^{-12}]$| . | [Hz] . | . |
| LOG1_obs | 8.95 | 41.6% | 0.423% | 1.34 | 650 | 4.75% | 2.93% | 11.6 | 10.4 | 14 | 13.5% |
| TOP1_obs | 4.87 | 63% | 0.231% | 2.18 | 264 | 8.41% | 1.21% | 16.2 | 13.8 | 12.6 | 18.7% |
| KRO1_obs | 21.2 | 30.9% | 0.998% | 0.304 | 1400 | 3.35% | 6.12% | 2.56 | 11.8 | 105 | 9.05% |
| LOG5_obs | 10.1 | 91.9% | 0.476% | 5.35 | 151 | 54% | 0.697% | 48.3 | 28.7 | 13.1 | 40.6% |
| TOP5_obs | 10.6 | 96% | 0.499% | 8.53 | 117 | 70.4% | 0.539% | 70.7 | 44.8 | 12.6 | 64.8% |
| KRO5_obs | 10.5 | 88.9% | 0.494% | 1.19 | 174 | 44.3% | 0.799% | 11.2 | 10.8 | 92.8 | 11.7% |
| LOG1_full | 13.4 | 62.4% | 0.631% | 2.8 | 707 | 12.7% | 3.17% | 32.5 | 17.6 | 13.1 | 26.4% |
| TOP1_full | 8.1 | 78.7% | 0.383% | 4.33 | 309 | 21.9% | 1.41% | 48.2 | 24.6 | 11.6 | 39.2% |
| KRO1_full | 28.2 | 50.2% | 1.32% | 0.615 | 1490 | 9.56% | 6.48% | 6.91 | 16.7 | 98.6 | 13% |
| LOG5_full | 20.7 | 96.2% | 0.973% | 10.9 | 310 | 77.7% | 1.42% | 140 | 50.4 | 11.6 | 83.6% |
| TOP5_full | 20.7 | 98.2% | 0.974% | 16.7 | 279 | 87.7% | 1.28% | 207 | 78.9 | 11.2 | 134% |
| KRO5_full | 21 | 94.7% | 0.988% | 2.38 | 320 | 69.9% | 1.46% | 30 | 19.3 | 83.9 | 23.3% |
| LOG1_low | 8 | 33.9% | 0.379% | 1.08 | 626 | 1.05% | 2.82% | 2.76 | 11 | 14.8 | 13.3% |
| TOP1_low | 4.02 | 54.9% | 0.191% | 1.61 | 248 | 2.3% | 1.14% | 4.32 | 14.7 | 14.5 | 17.9% |
| KRO1_low | 19 | 21.6% | 0.893% | 0.235 | 1370 | 0.66% | 5.97% | 0.56 | 10.7 | 116 | 8.37% |
| LOG5_low | 8 | 89.7% | 0.378% | 4.47 | 87.4 | 20.2% | 0.404% | 11.7 | 33.2 | 14.5 | 40.3% |
| TOP5_low | 8.22 | 95.1% | 0.389% | 6.81 | 54.8 | 36.9% | 0.253% | 17.9 | 52.3 | 14.2 | 64.1% |
| KRO5_low | 7.26 | 83.9% | 0.343% | 0.945 | 110 | 12.2% | 0.508% | 2.44 | 9.47 | 101 | 10.5% |
| Model . | |$\dot{\mathcal {N}}\ [\rm yr^{-1}]$| . | |$\mathcal {F}_{\rm NSC}$| . | |$\mathcal {F}_{\rm PopIII}$| . | |$\dot{\mathcal {N}}_{\rm IMBH}$| . | |$\dot{\mathcal {N}}\ [\rm yr^{-1}]$| . | |$\mathcal {F}_{\rm NSC}$| . | |$\mathcal {F}_{\rm PopIII}$| . | |$\dot{\mathcal {N}}_{\rm IMBH}$| . | |$\Omega _{\rm GW}^{\rm peak}$| . | |$\nu _{\rm peak}$| . | |$f_{\rm SGWB}^{\rm PopIII}$| . |
|---|---|---|---|---|---|---|---|---|---|---|---|
| . | |$(z\lt 1)$| . | |$(z\lt 1)$| . | |$(z\lt 1)$| . | |$(z\lt 1)$| . | |$(z\lt 20)$| . | |$(z\lt 20)$| . | |$(z\lt 20)$| . | |$(z\lt 20)$| . | |$[10^{-12}]$| . | [Hz] . | . |
| LOG1_obs | 8.95 | 41.6% | 0.423% | 1.34 | 650 | 4.75% | 2.93% | 11.6 | 10.4 | 14 | 13.5% |
| TOP1_obs | 4.87 | 63% | 0.231% | 2.18 | 264 | 8.41% | 1.21% | 16.2 | 13.8 | 12.6 | 18.7% |
| KRO1_obs | 21.2 | 30.9% | 0.998% | 0.304 | 1400 | 3.35% | 6.12% | 2.56 | 11.8 | 105 | 9.05% |
| LOG5_obs | 10.1 | 91.9% | 0.476% | 5.35 | 151 | 54% | 0.697% | 48.3 | 28.7 | 13.1 | 40.6% |
| TOP5_obs | 10.6 | 96% | 0.499% | 8.53 | 117 | 70.4% | 0.539% | 70.7 | 44.8 | 12.6 | 64.8% |
| KRO5_obs | 10.5 | 88.9% | 0.494% | 1.19 | 174 | 44.3% | 0.799% | 11.2 | 10.8 | 92.8 | 11.7% |
| LOG1_full | 13.4 | 62.4% | 0.631% | 2.8 | 707 | 12.7% | 3.17% | 32.5 | 17.6 | 13.1 | 26.4% |
| TOP1_full | 8.1 | 78.7% | 0.383% | 4.33 | 309 | 21.9% | 1.41% | 48.2 | 24.6 | 11.6 | 39.2% |
| KRO1_full | 28.2 | 50.2% | 1.32% | 0.615 | 1490 | 9.56% | 6.48% | 6.91 | 16.7 | 98.6 | 13% |
| LOG5_full | 20.7 | 96.2% | 0.973% | 10.9 | 310 | 77.7% | 1.42% | 140 | 50.4 | 11.6 | 83.6% |
| TOP5_full | 20.7 | 98.2% | 0.974% | 16.7 | 279 | 87.7% | 1.28% | 207 | 78.9 | 11.2 | 134% |
| KRO5_full | 21 | 94.7% | 0.988% | 2.38 | 320 | 69.9% | 1.46% | 30 | 19.3 | 83.9 | 23.3% |
| LOG1_low | 8 | 33.9% | 0.379% | 1.08 | 626 | 1.05% | 2.82% | 2.76 | 11 | 14.8 | 13.3% |
| TOP1_low | 4.02 | 54.9% | 0.191% | 1.61 | 248 | 2.3% | 1.14% | 4.32 | 14.7 | 14.5 | 17.9% |
| KRO1_low | 19 | 21.6% | 0.893% | 0.235 | 1370 | 0.66% | 5.97% | 0.56 | 10.7 | 116 | 8.37% |
| LOG5_low | 8 | 89.7% | 0.378% | 4.47 | 87.4 | 20.2% | 0.404% | 11.7 | 33.2 | 14.5 | 40.3% |
| TOP5_low | 8.22 | 95.1% | 0.389% | 6.81 | 54.8 | 36.9% | 0.253% | 17.9 | 52.3 | 14.2 | 64.1% |
| KRO5_low | 7.26 | 83.9% | 0.343% | 0.945 | 110 | 12.2% | 0.508% | 2.44 | 9.47 | 101 | 10.5% |
Basic observational signatures of Pop III BBH mergers for the 18 models listed in Table 2. Column 1: model name. Columns 2: all-sky merger rate |$\dot{\mathcal {N}}$| (equation 24) for all mergers within |$z\lt 1$|. Column 3: fraction |$\mathcal {F}_{\rm NSC}$| of all-sky merger rate contributed by NSC mergers for |$z\lt 1$|. Column 4: fraction |$\mathcal {F}_{\rm PopIII}$| of all-sky merger rate of BBH mergers contributed by Pop III stars for |$z\lt 1$|. Column 5: all-sky merger rate |$\dot{\mathcal {N}}_{\rm IMBH}$| of Pop III BBHs with at least one IMBH (i.e. |$m_{1}\gt 100\ \rm M_\odot$|) for |$z\lt 1$|. Columns 6–9: same as Columns 2–5 but for |$z\lt 20$|. Columns 10 and 11: peak value |$\Omega _{\rm GW}^{\rm peak}$| and location |$\nu _{\rm peak}$| of the SGWB energy spectrum from Pop III BBH mergers. Column 12: maximum ratio |$f_{\rm SGWB}^{\rm PopIII}$| between the SGWB produced by Pop III BBH mergers and the conservative prediction of the SGWB from Pop I/II and PBH mergers by Bavera et al. (2022). Given the optimistic results for the total SGWB inferred from GWTC-3 events (Abbott et al. 2023a) as the reference, the maximum contribution of Pop III BBH mergers to the total SGWB is approximately |$f_{\rm SGWB}^{\rm PopIII}/5$|.
| Model . | |$\dot{\mathcal {N}}\ [\rm yr^{-1}]$| . | |$\mathcal {F}_{\rm NSC}$| . | |$\mathcal {F}_{\rm PopIII}$| . | |$\dot{\mathcal {N}}_{\rm IMBH}$| . | |$\dot{\mathcal {N}}\ [\rm yr^{-1}]$| . | |$\mathcal {F}_{\rm NSC}$| . | |$\mathcal {F}_{\rm PopIII}$| . | |$\dot{\mathcal {N}}_{\rm IMBH}$| . | |$\Omega _{\rm GW}^{\rm peak}$| . | |$\nu _{\rm peak}$| . | |$f_{\rm SGWB}^{\rm PopIII}$| . |
|---|---|---|---|---|---|---|---|---|---|---|---|
| . | |$(z\lt 1)$| . | |$(z\lt 1)$| . | |$(z\lt 1)$| . | |$(z\lt 1)$| . | |$(z\lt 20)$| . | |$(z\lt 20)$| . | |$(z\lt 20)$| . | |$(z\lt 20)$| . | |$[10^{-12}]$| . | [Hz] . | . |
| LOG1_obs | 8.95 | 41.6% | 0.423% | 1.34 | 650 | 4.75% | 2.93% | 11.6 | 10.4 | 14 | 13.5% |
| TOP1_obs | 4.87 | 63% | 0.231% | 2.18 | 264 | 8.41% | 1.21% | 16.2 | 13.8 | 12.6 | 18.7% |
| KRO1_obs | 21.2 | 30.9% | 0.998% | 0.304 | 1400 | 3.35% | 6.12% | 2.56 | 11.8 | 105 | 9.05% |
| LOG5_obs | 10.1 | 91.9% | 0.476% | 5.35 | 151 | 54% | 0.697% | 48.3 | 28.7 | 13.1 | 40.6% |
| TOP5_obs | 10.6 | 96% | 0.499% | 8.53 | 117 | 70.4% | 0.539% | 70.7 | 44.8 | 12.6 | 64.8% |
| KRO5_obs | 10.5 | 88.9% | 0.494% | 1.19 | 174 | 44.3% | 0.799% | 11.2 | 10.8 | 92.8 | 11.7% |
| LOG1_full | 13.4 | 62.4% | 0.631% | 2.8 | 707 | 12.7% | 3.17% | 32.5 | 17.6 | 13.1 | 26.4% |
| TOP1_full | 8.1 | 78.7% | 0.383% | 4.33 | 309 | 21.9% | 1.41% | 48.2 | 24.6 | 11.6 | 39.2% |
| KRO1_full | 28.2 | 50.2% | 1.32% | 0.615 | 1490 | 9.56% | 6.48% | 6.91 | 16.7 | 98.6 | 13% |
| LOG5_full | 20.7 | 96.2% | 0.973% | 10.9 | 310 | 77.7% | 1.42% | 140 | 50.4 | 11.6 | 83.6% |
| TOP5_full | 20.7 | 98.2% | 0.974% | 16.7 | 279 | 87.7% | 1.28% | 207 | 78.9 | 11.2 | 134% |
| KRO5_full | 21 | 94.7% | 0.988% | 2.38 | 320 | 69.9% | 1.46% | 30 | 19.3 | 83.9 | 23.3% |
| LOG1_low | 8 | 33.9% | 0.379% | 1.08 | 626 | 1.05% | 2.82% | 2.76 | 11 | 14.8 | 13.3% |
| TOP1_low | 4.02 | 54.9% | 0.191% | 1.61 | 248 | 2.3% | 1.14% | 4.32 | 14.7 | 14.5 | 17.9% |
| KRO1_low | 19 | 21.6% | 0.893% | 0.235 | 1370 | 0.66% | 5.97% | 0.56 | 10.7 | 116 | 8.37% |
| LOG5_low | 8 | 89.7% | 0.378% | 4.47 | 87.4 | 20.2% | 0.404% | 11.7 | 33.2 | 14.5 | 40.3% |
| TOP5_low | 8.22 | 95.1% | 0.389% | 6.81 | 54.8 | 36.9% | 0.253% | 17.9 | 52.3 | 14.2 | 64.1% |
| KRO5_low | 7.26 | 83.9% | 0.343% | 0.945 | 110 | 12.2% | 0.508% | 2.44 | 9.47 | 101 | 10.5% |
| Model . | |$\dot{\mathcal {N}}\ [\rm yr^{-1}]$| . | |$\mathcal {F}_{\rm NSC}$| . | |$\mathcal {F}_{\rm PopIII}$| . | |$\dot{\mathcal {N}}_{\rm IMBH}$| . | |$\dot{\mathcal {N}}\ [\rm yr^{-1}]$| . | |$\mathcal {F}_{\rm NSC}$| . | |$\mathcal {F}_{\rm PopIII}$| . | |$\dot{\mathcal {N}}_{\rm IMBH}$| . | |$\Omega _{\rm GW}^{\rm peak}$| . | |$\nu _{\rm peak}$| . | |$f_{\rm SGWB}^{\rm PopIII}$| . |
|---|---|---|---|---|---|---|---|---|---|---|---|
| . | |$(z\lt 1)$| . | |$(z\lt 1)$| . | |$(z\lt 1)$| . | |$(z\lt 1)$| . | |$(z\lt 20)$| . | |$(z\lt 20)$| . | |$(z\lt 20)$| . | |$(z\lt 20)$| . | |$[10^{-12}]$| . | [Hz] . | . |
| LOG1_obs | 8.95 | 41.6% | 0.423% | 1.34 | 650 | 4.75% | 2.93% | 11.6 | 10.4 | 14 | 13.5% |
| TOP1_obs | 4.87 | 63% | 0.231% | 2.18 | 264 | 8.41% | 1.21% | 16.2 | 13.8 | 12.6 | 18.7% |
| KRO1_obs | 21.2 | 30.9% | 0.998% | 0.304 | 1400 | 3.35% | 6.12% | 2.56 | 11.8 | 105 | 9.05% |
| LOG5_obs | 10.1 | 91.9% | 0.476% | 5.35 | 151 | 54% | 0.697% | 48.3 | 28.7 | 13.1 | 40.6% |
| TOP5_obs | 10.6 | 96% | 0.499% | 8.53 | 117 | 70.4% | 0.539% | 70.7 | 44.8 | 12.6 | 64.8% |
| KRO5_obs | 10.5 | 88.9% | 0.494% | 1.19 | 174 | 44.3% | 0.799% | 11.2 | 10.8 | 92.8 | 11.7% |
| LOG1_full | 13.4 | 62.4% | 0.631% | 2.8 | 707 | 12.7% | 3.17% | 32.5 | 17.6 | 13.1 | 26.4% |
| TOP1_full | 8.1 | 78.7% | 0.383% | 4.33 | 309 | 21.9% | 1.41% | 48.2 | 24.6 | 11.6 | 39.2% |
| KRO1_full | 28.2 | 50.2% | 1.32% | 0.615 | 1490 | 9.56% | 6.48% | 6.91 | 16.7 | 98.6 | 13% |
| LOG5_full | 20.7 | 96.2% | 0.973% | 10.9 | 310 | 77.7% | 1.42% | 140 | 50.4 | 11.6 | 83.6% |
| TOP5_full | 20.7 | 98.2% | 0.974% | 16.7 | 279 | 87.7% | 1.28% | 207 | 78.9 | 11.2 | 134% |
| KRO5_full | 21 | 94.7% | 0.988% | 2.38 | 320 | 69.9% | 1.46% | 30 | 19.3 | 83.9 | 23.3% |
| LOG1_low | 8 | 33.9% | 0.379% | 1.08 | 626 | 1.05% | 2.82% | 2.76 | 11 | 14.8 | 13.3% |
| TOP1_low | 4.02 | 54.9% | 0.191% | 1.61 | 248 | 2.3% | 1.14% | 4.32 | 14.7 | 14.5 | 17.9% |
| KRO1_low | 19 | 21.6% | 0.893% | 0.235 | 1370 | 0.66% | 5.97% | 0.56 | 10.7 | 116 | 8.37% |
| LOG5_low | 8 | 89.7% | 0.378% | 4.47 | 87.4 | 20.2% | 0.404% | 11.7 | 33.2 | 14.5 | 40.3% |
| TOP5_low | 8.22 | 95.1% | 0.389% | 6.81 | 54.8 | 36.9% | 0.253% | 17.9 | 52.3 | 14.2 | 64.1% |
| KRO5_low | 7.26 | 83.9% | 0.343% | 0.945 | 110 | 12.2% | 0.508% | 2.44 | 9.47 | 101 | 10.5% |
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