The Hosts and Mass Distribution Function of the Most Massive Black Holes: Implications for the nHz Gravitational Wave Background
Abstract
We use the core-radius, rγ, of a galaxy's central core along with a volume-limited sample of brightest cluster galaxies (BCG) to determine the z=0 mass distribution function of the most massive super-massive black holes (SMBH). We recover a MBH−rγ relationship between the SMBH mass, MBH, and rγ of form MBH ≈1.3×1010 (rγ/kpc) M⊙, with σ= 0.25±0.03 dex scatter in MBH. We derive a core distribution function (CDF), based on HST and DLS images of the BCGs. The CDF falls steeply as N(rγ)∼ rγ−3 for rγ>0.50 kpc. Only ∼5% of BCGs have rγ>1 kpc. Combining the CDF and MBH − rγ relationship yields the BH mass distribution function (MDF). For MBH ≥ 7×109 M⊙ (the mean MBH at rγ=0.50 kpc) we derive: log(dN(MBH)/(dMBH/1010 M⊙) [Mpc−3])=(−3.05±0.42) log(MBH/1010M⊙) − 5.11 (+0.41, −0.36). Cores with rγ≥ 0.50 kpc are found almost exclusively in BCGs, implying that SMBHs with MBH ≥7×109 M⊙ may also be exclusive to BCGs. Core-radius correlates with α, a parameter that characterizes the growth of BCG envelopes by mergers, suggesting that the most massive SMBHs grew in tandem with their BCG hosts. The BH MDF embodies a significant population of SMBH with MBH >7×109 M⊙. When combined with the Liepold & Ma (2024) BH MDF to account for SMBH with MBH < 7×109 M⊙, it can comfortably explain the nHz gravitational wave background.
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BibTeX
@misc{postman2026hosts,
title = {{The Hosts and Mass Distribution Function of the Most Massive Black Holes: Implications for the nHz Gravitational Wave Background}},
author = {Marc Postman and Tod R. Lauer and Daniel J. D'Orazio and Bellamy Bailey},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33162},
eprint = {2610.33162},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33162},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Hosts and Mass Distribution Function of the Most Massive Black Holes: Implications for the nHz Gravitational Wave Background
AU - Marc Postman
AU - Tod R. Lauer
AU - Daniel J. D'Orazio
AU - Bellamy Bailey
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.33162
UR - https://arxiv.org/abs/2610.33162
AB - We use the core-radius, r_γ, of a galaxy's central core along with a volume-limited sample of brightest cluster galaxies (BCG) to determine the z=0 mass distribution function of the most massive super-massive black holes (SMBH). We recover a M_BH−r_γ relationship between the SMBH mass, M_BH, and r_γ of form M_BH ≈1.3×10^10 (r_γ/kpc) M_⊙, with σ= 0.25±0.03 dex scatter in M_BH. We derive a core distribution function (CDF), based on HST and DLS images of the BCGs. The CDF falls steeply as N(r_γ)∼ r_γ^−3 for r_γ>0.50 kpc. Only ∼5% of BCGs have r_γ>1 kpc. Combining the CDF and M_BH − r_γ relationship yields the BH mass distribution function (MDF). For M_BH ≥ 7×10^9 M_⊙ (the mean M_BH at r_γ=0.50 kpc) we derive: log(dN(M_BH)/(dM_BH/10^10 M_⊙) [Mpc^−3])=(−3.05±0.42) log(M_BH/10^10M_⊙) − 5.11 (+0.41, −0.36). Cores with r_γ≥ 0.50 kpc are found almost exclusively in BCGs, implying that SMBHs with M_BH ≥7×10^9 M_⊙ may also be exclusive to BCGs. Core-radius correlates with α, a parameter that characterizes the growth of BCG envelopes by mergers, suggesting that the most massive SMBHs grew in tandem with their BCG hosts. The BH MDF embodies a significant population of SMBH with M_BH >7×10^9 M_⊙. When combined with the Liepold & Ma (2024) BH MDF to account for SMBH with M_BH < 7×10^9 M_⊙, it can comfortably explain the nHz gravitational wave background.
ER -