  Massive black hole (MBH) coalescences are powerful sources of low-frequency
gravitational waves. To study these events in the cosmological context we need
to trace the large-scale structure and cosmic evolution of a statistical
population of galaxies, from dim dwarfs to bright galaxies. To cover such a
large range of galaxy masses, we analyse two complementary simulations:
Horizon-AGN with a large volume and low resolution which tracks the high-mass
(> 1e7 Msun) MBH population, and NewHorizon with a smaller volume but higher
resolution that traces the low-mass (< 1e7 Msun) MBH population. While
Horizon-AGN can be used to estimate the rate of inspirals for Pulsar Timing
Arrays, NewHorizon can investigate MBH mergers in a statistical sample of dwarf
galaxies for LISA, which is sensitive to low-mass MBHs. We use the same method
to analyse the two simulations, post-processing MBH dynamics to account for
time delays mostly determined by dynamical friction and stellar hardening. In
both simulations, MBHs typically merge long after the galaxies do, so that the
galaxy morphology at the time of the MBH merger is no longer determined by the
galaxy merger from which the MBH merger originated. These time delays cause a
loss of high-z MBH coalescences, shifting the peak of the MBH merger rate to
z~1-2. This study shows how tracking MBH mergers in low-mass galaxies is
crucial to probing the MBH merger rate for LISA and investigate the properties
of the host galaxies.
