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In the near future, projects like Laser Interferometer Space Antenna (LISA) and pulsar timing arrays are expected to detect gravitational waves from mergers between supermassive black holes, and it is crucial to precisely model the underlying merger populations now to maximize what we can learn from this new data. Here, we characterize expected high-redshift (z > 2) black hole mergers using the very large volume Astrid cosmological simulation, which uses a range of seed masses to probe down to low-mass black holes (BHs), and directly incorporates dynamical friction so as to accurately model the dynamical processes that bring black holes to the galaxy centre where binary formation and coalescence will occur. The black hole populations in Astrid include black holes down to $\sim 10^{4.5} \, \mathrm{M}_\odot$, and remain broadly consistent with the TNG simulations at scales $\gt 10^6 \, \mathrm{M}_\odot$ (the seed mass used in TNG). By resolving lower mass black holes, the overall merger rate is ∼5× higher than in TNG. However, incorporating dynamical friction delays mergers compared to a recentring scheme, reducing the high-z merger rate mass-matched mergers by a factor of ∼2×. We also calculate the expected LISA signal-to-noise values, and show that the distribution peaks at high SNR (>100), emphasizing the importance of implementing a seed mass well below LISA’s peak sensitivity ($\sim 10^6 \, \mathrm{M}_\odot$) to resolve the majority of LISA’s gravitational wave detections.

We examine the dual [both black hole (BH) active] and offset (one BH active and in distinct galaxies) active galactic nucleus (AGN) population (comprising ∼ 2000 pairs at $0.5\, \text{kpc}\lesssim \Delta r\lt 30\, \text{kpc}$) at z = 2 ∼ 3 in the ASTRID simulation covering (360 cMpc)3. The dual (offset) AGN make up 3.0(0.5) per cent of all AGN at z = 2. The dual fraction is roughly constant while the offset fraction increases by a factor of 10 from z = 4 ∼ 2. Compared with the full AGN population, duals are characterized by low MBH/M* ratios, high specific star formation rates (sSFR) of $\sim 1\, \text{Gyr}^{-1}$, and high Eddington ratios (∼0.05, double that of single AGN). Dual AGNs are formed in major galaxy mergers (typically involving $M_\text{halo}\lt 10^{13}\, M_\odot$), with simular-mass BHs. At small separations (when host galaxies are in the late phase of the merger), duals become 2 ∼ 8 times brighter (albeit more obscured) than at larger separations. 80  per cent of the bright, close duals would merge within $\sim 500\, \text{Myr}$. Notably, the initially less-massive BHs in duals frequently become the brighter AGN during galaxy mergers. In offset AGN, the active BH is typically ≳ 10 times more massive than its non-active counterpart and than most BHs in duals. Offsets are predominantly formed in minor galaxy mergers with the active BH residing in the centre of massive haloes ($M_\text{ halo}\sim 10^{13-14}\, \mathrm{M}_\odot$). In these deep potentials, gas stripping is common and the secondary quickly deactivates. The stripping also leads to inefficient orbital decay amongst offsets, which stall at $\Delta r\sim 5\, \text{kpc}$ for a few hundred Myrs.

The launch of space-based gravitational-wave (GW) detectors (e.g. Laser Interferometry Space Antenna; LISA) and current and upcoming Pulsar Timing Arrays will extend the GW window to low frequencies, opening new investigations into dynamical processes involving massive black hole binaries (MBHBs) and their mergers across cosmic time. MBHBs are expected to be among the primary sources for the upcoming low-frequency (10−4–10−1 Hz) window probed by LISA. It is important to investigate the expected supermassive BH merger rates and associated signals, to determine how potential LISA events are affected by physics included in current models. To study this, we post-process the large population of MBHBs in the Illustris simulation to account for dynamical friction time delays associated with BH infall/inspiral. We show that merger delays associated with binary evolution have the potential to decrease the expected merger rates, with $M_{\rm {BH}}\ \gt\ 10^6\ \mathrm{M}_\odot$ MBHBs (the lowest mass in Illustris) decreasing from ∼3 to ∼0.1 yr−1, and shifting the merger peak from z ∼2 to ∼1.25. During this time, we estimate that accretion grows the total merging mass by as much as 7x the original mass. Importantly, however, dynamical friction-associated delays (which shift the mergers toward lower redshift and higher masses) lead to a stronger signal/strain for the emitted GWs in the LISA band, increasing mean frequency from 10−3.1 to 10−3.4–10−4.0 Hz, and mean strain from 10−17.2 to 10−16.3–10−15.3. Finally, we show that after including a merger delay and associated MBH growth, mergers still tend to lie on the typical MBH–M* relation, but with an increased likelihood of an undermassive BH.

We examine massive black hole (MBH) mergers and their associated gravitational wave signals from the large-volume cosmological simulation Astrid . Astrid includes galaxy formation and black hole models recently updated with an MBH seed population between 3 × 104h−1M⊙ and 3 × 105h−1M⊙ and a sub-grid dynamical friction (DF) model to follow the MBH dynamics down to 1.5 ckpc h−1. We calculate the initial eccentricities of MBH orbits directly from the simulation at kpc-scales, and find orbital eccentricities above 0.7 for most MBH pairs before the numerical merger. After approximating unresolved evolution on scales below ${\sim 200\, \text{pc}}$, we find that the in-simulation DF on large scales accounts for more than half of the total orbital decay time ($\sim 500\, \text{Myr}$) due to DF. The binary hardening time is an order of magnitude longer than the DF time, especially for the seed-mass binaries (MBH < 2Mseed). As a result, only $\lesssim 20{{\rm per \,cent}}$ of seed MBH pairs merge at z > 3 after considering both unresolved DF evolution and binary hardening. These z > 3 seed-mass mergers are hosted in a biased population of galaxies with the highest stellar masses of $\gt 10^9\, {\rm M}_\odot$. With the higher initial eccentricity prediction from Astrid , we estimate an expected merger rate of 0.3−0.7 per year from the z > 3 MBH population. This is a factor of ∼7 higher than the prediction using the circular orbit assumption. The Laser Interferometer Space Antenna events are expected at a similar rate, and comprise $\gtrsim 60\,{\rm{per\,cent}}$ seed-seed mergers, $\sim 30\,{\rm{per\,cent}}$ involving only one seed-mass MBH, and $\sim 10\,{\rm{per\,cent}}$ mergers of non-seed MBHs.

A population of supermassive black hole (SMBH) binaries is expected to generate a stochastic gravitational wave background (SGWB) in the pulsar timing array (PTA) frequency range of 10−9 to $10^{-7}\, {\rm Hz}$. Detection of this signal is a current observational goal and so predictions of its characteristics are of significant interest. In this work, we use SMBH binary mergers from the MassiveBlackII simulation to estimate the characteristic strain of the stochastic background. We examine both a gravitational wave (GW) driven model of binary evolution and a model which also includes the effects of stellar scattering and a circumbinary gas disc. Results are consistent with PTA upper limits and similar to estimates in the literature. The characteristic strain at a reference frequency of $1\, {\rm yr}^{-1}$ is found to be $A_{\rm {yr}^{-1}}= 6.9 \times 10^{-16}$ and $A_{\rm {yr}^{-1}}= 6.4 \times 10^{-16}$ in the GW-driven and stellar scattering/gas disc cases, respectively. Using the latter approach, our models show that the SGWB is mildly suppressed compared to the purely GW-driven model as frequency decreases inside the PTA frequency band.

In this work, we establish and test methods for implementing dynamical friction (DF) for massive black hole pairs that form in large volume cosmological hydrodynamical simulations that include galaxy formation and black hole growth. We verify our models and parameters both for individual black hole dynamics and for the black hole population in cosmological volumes. Using our model of DF from collisionless particles, black holes can effectively sink close to the galaxy centre, provided that the black hole’s dynamical mass is at least twice that of the lowest mass resolution particles in the simulation. Gas drag also plays a role in assisting the black holes’ orbital decay, but it is typically less effective than that from collisionless particles, especially after the first billion years of the black hole’s evolution. DF from gas becomes less than $1{{\ \rm per\ cent}}$ of DF from collisionless particles for BH masses >107 M⊙. Using our best DF model, we calculate the merger rate down to z = 1.1 using an Lbox = 35 Mpc h−1 simulation box. We predict ∼2 mergers per year for z > 1.1 peaking at z ∼ 2. These merger rates are within the range obtained in previous work using similar resolution hydrodynamical simulations. We show that the rate is enhanced by factor of ∼2 when DF is taken into account in the simulations compared to the no-DF run. This is due to ${\gt}40{{\ \rm per\ cent}}$ more black holes reaching the centre of their host halo when DF is added.