2021MNRAS.507.3362T

Recent gravitational wave (GW) observations by LIGO/Virgo show evidence for hierarchical mergers, where the merging BHs are the remnants of previous BH merger events. These events may carry important clues about the astrophysical host environments of the GW sources. In this paper, we present the distributions of the effective spin parameter (χ_eff), the precession spin parameter (χ_p), and the chirp mass (m_chirp) expected in hierarchical mergers. Under a wide range of assumptions, hierarchical mergers produce (i) a monotonic increase of the average of the typical total spin for merging binaries, which we characterize with {bar}χ_typ≡χ_eff²+χ_p²)^1/2, up to roughly the maximum m_chirp among first-generation (1g) BHs, and (ii) a plateau at {bar}χ_typ∼0.6 at higher m_chirp. We suggest that the maximum mass and typical spin magnitudes for 1g BHs can be estimated from {bar}χ_typ as a function of m_chirp. The GW data observed in LIGO/Virgo O1-O3a prefers an increase in {bar}χ_typ at low m_chirp, which is consistent with the growth of the BH spin magnitude by hierarchical mergers at ∼2σ confidence. A Bayesian analysis using the χ_eff, χ_p, and m_chirp distributions suggests that 1g BHs have the maximum mass of ∼15-30 M_☉ if the majority of mergers are of high-generation BHs (not among 1g-1g BHs), which is consistent with mergers in active galactic nucleus discs and/or nuclear star clusters, while if mergers mainly originate from globular clusters, 1g BHs are favoured to have non-zero spin magnitudes of ∼0.3. We also forecast that signatures for hierarchical mergers in the {bar}χ_typ distribution can be confidently recovered once the number of GW events increases to >= O(100).