Table 1.
Overview of population hyperparameters and prior choices.
| Parameter | Definition | Injected value | Prior range |
|---|---|---|---|
| Cosmological parameters (flat ΛCDM) | |||
| H0 | Hubble parameter [km s−1 Mpc−1] | 67.7 | U(10, 200) |
| Ωm | Matter density parameter | 0.3065 | U(0, 1) |
| Rate evolution (Madau-rate) | |||
| γ | Evolution slope for z < zp | 4.56 | U(0, 12) |
| κ | Evolution slope for z > zp | 2.86 | U(0, 6) |
| zp | Redshift of peak rate | 2.47 | U(0, 4) |
| R0 | Local merger rate [Gpc−3 yr−1] | 20 | U(0, 100) |
| Mass function parameters (PowerLaw + Peak) | |||
| α | Power-law index of primary mass | 3.78 | U(1.5, 12) |
| β | Power-law index of secondary mass | 0.81 | U(−4, 12) |
| δm | Smoothing parameter [M⊙] | 4.8 | U(0, 10) |
| mmin | Minimum source mass [M⊙] | 4.98 | U(2, 10) |
| mmax | Maximum source mass [M⊙] | 112.5 | U(50, 200) |
| μg | Mean of the Gaussian peak [M⊙] | 32.27 | U(20, 50) |
| σg | Width of the Gaussian peak [M⊙] | 3.88 | U(0.4, 10) |
| λg | Fraction of events in the Gaussian peak | 0.03 | U(0, 1) |
| Mass function parameters (Multi + peak) | |||
| α | Power-law index of primary mass | U(1.5, 12) | |
| β | Power-law index of secondary mass | U(−4, 12) | |
| mmin | Minimum source mass [M⊙] | U(2, 10) | |
| mmax | Maximum source mass [M⊙] | U(50, 200) | |
| δm | Smoothing parameter [M⊙] | U(0, 10) | |
| μg, low | Mean of the lower Gaussian peak [M⊙] | U(7, 12) | |
| μg, high | Mean of the higher Gaussian peak [M⊙] | U(20, 50) | |
| σg, low | Width of the lower Gaussian peak [M⊙] | U(0.4, 5) | |
| σg, high | Width of the higher Gaussian peak [M⊙] | U(0.4, 10) | |
| λg | Fraction of events in the peaks | U(0, 1) | |
| λg, low | Fraction of events in the lower peak | U(0, 1) | |
Notes. U(⋅) represents a uniform distribution. The POWER LAW + PEAK (PLP) model is used only for the simulations in Sect. 4, while the MULTI + PEAK model is used for the analysis of O3 data in Sect. 5. The priors used on cosmological parameters and rate evolution parameters are the same for the simulation and real data cases. For the simulation case, we also report the injected value. The rate parameters, mass model parameters and H0 are chosen to be consistent with the posterior distributions from Abbott et al. (2023b) while Ωm is set by Ade et al. (2016).
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