Abstract

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 kiloparsec scales all the way to coalescence using a semi-analytic model developed in our previous work. We find that for the 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 an MBH coalescence rate ≲0.45 yr−1 and a LISA detection rate ≲0.34 yr−1. Most LISA detections should originate from 106 to 106.8 M ⊙ MBHs in gas-rich galaxies at redshifts 1.6 ≤ z ≤ 2.4 and have a characteristic signal-to-noise ratio S/N ∼100. We however find a dramatic reduction in the coalescence and detection rates, as well as the average S/N, 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−1), and the LISA detection rate is reduced by 94% (to 0.02 yr−1), whereas the average S/N is ∼10. We emphasize that our model provides a conservative estimate of the LISA detection rates, due to the limited MBH mass range in TNG50-3, consistent with other works in the literature that draw their MBH pairs from cosmological simulations.

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