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arXiv · 2610.28680

A Unified Model for the Gravitational Wave Background and Quasar Luminosity Functions

Cayenne Matt·Kayhan Gültekin·Ryan Hickox
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Abstract

The supermassive black hole mass function (BHMF) is a necessary ingredient in our understanding of how BHs grow and evolve with their host galaxies. Estimations of the BHMF based on observations of local BHs, quasars, and gravitational wave data yield inconsistent results, leading to large uncertainties in, e.g., BH accretion and seeding models. The nanohertz gravitational wave background (GWB) has been a powerful tool to provide constraints on the BHMF across cosmic time. We take posterior BHMFs that describe the GWB and fit them to bolometric quasar luminosity functions (QLF) across $0.2 \leq z \leq 6.2$ to constrain the Eddington ratio distribution function (ERDF). Compared to a fiducial BHMF, based on galaxy and a local black hole mass scaling relation, the BHMFs that match the GWB can reproduce the observed QLFs with lower Eddington fractions and without requiring significant super-Eddington accretion. We use a double power-law form of the ERDF and find that the fits using the GWB-inferred BHMF have systematically lower break-points and marginally steeper slopes in the high-Eddington fraction portion of the function. Furthermore, the best-fit QLFs using the GWB-inferred BHMFs provide better fits to the high-luminosity end of the QLF data than the fiducial model. For both models the ERDF shows significant redshift evolution of the break-point which reaches a maximum around $z \sim 2$. Overall, our prescription can produce realistic QLFs from BHMFs and our GWB-based model is consistent with electromagnetic and gravitational wave data sets.

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Cayenne Matt, Kayhan Gültekin, Ryan Hickox. 2026-10-19. A Unified Model for the Gravitational Wave Background and Quasar Luminosity Functions. https://arxiv.org/abs/2610.28680

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