  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.
