Massive Black Hole Mergers with Orbital Information: Predictions from the ASTRID Simulation

Abstract: 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 a MBH seed population between $3\times 10^4M_{\odot}/h$ and $3\times 10^5M_{\odot}/h$ and a sub-grid dynamical friction (DF) model to follow the MBH dynamics down to $1.5\;\text{ckpc}/h$. We calculate 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 ($\sim 500\,\text{Myrs}$) due to DF. The binary hardening time is an order of magnitude longer than the DF time, especially for the seed-mass binaries ($M_\text{BH}<2M_\text{seed}$). As a result, only $\lesssim20\%$ 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 $>10^9\,M_\odot$. 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 $\sim 7$ higher than the prediction using the circular orbit assumption. The LISA events are expected at a similar rate, and comprise $\gtrsim 60\%$ seed-seed mergers, $\sim 30\%$ involving only one seed-mass MBH, and $\sim 10\%$ mergers of non-seed MBHs.