On the detectability of massive black hole merger eventsby LISA

Abstract: The launch of space based gravitational wave (GW) detectors (e.g. Laser Interferometry Space Antenna; LISA) and current and upcoming Pulsar Timing Arrays (PTAs) 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 MBH 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 $M_{\rm{BH}} > 10^6 M_\odot$ MBHBs (the lowest mass in Illustris) decreasing from $\sim 3$ yr$^{-1}$ to $\sim 0.1 $yr$^{-1}$, and shifting the merger peak from z $\sim 2$ to $\sim 1.25$. During this time, we estimate that accretion grows the total merging mass by as much as 7x from 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 $M_{\rm{BH}}$ growth, mergers still tend to lie on the typical $M_{\rm{BH}}-M_*$ relation, but with an increased likelihood of an undermassive black hole.