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Massive Black Hole Binaries from the TNG50-3 Simulation: I. Coalescence and LISA Detection Rates

We evaluate the cosmological coalescence and detection rates for massive black hole (MBH) binaries targeted by the gravitational wave observatory Laser Interferometer Space Antenna (LISA). Our calculation starts with a population of gravitationally unbound MBH pairs, drawn from the TNG50-3 cosmological simulation, and follows their orbital evolution from kpc scales all the way to coalescence using a semi-analytic model developed in our previous work. We find that for a majority of MBH pairs that coalesce within a Hubble time dynamical friction is the most important mechanism that determines their coalescence rate. Our model predicts a MBH coalescence rate < 0.45/ yr and a LISA detection rate < 0.34/ yr. Most LISA detections should originate from 10^6 - 10^6.8 solar masses MBHs in gas-rich galaxies at redshifts 1.6 < z < 2.4, and have a characteristic signal to noise ratio SNR ~ 100. We however find a dramatic reduction in the coalescence and detection rates, as well as the average SNR, if the effects of radiative feedback from accreting MBHs are taken into account. In this case, the MBH coalescence rate is reduced by 78% (to < 0.1/ yr), and the LISA detection rate is reduced by 94% (to 0.02/ yr), whereas the average SNR is ~ 10. We emphasize that our model provides a lower limit on the LISA detection rate, consistent with other works in the literature that draw their MBH pairs from cosmological simulations.