ESA and NASA are moving forward with plans to launch LISA around 2034. With data from the Illustris cosmological simulation, we provide analysis of LISA detection rates accompanied by characterization of the merging massive black hole population. Massive black holes of total mass ∼ 10 5 − 10 10 M are the focus of this study. We evolve Illustris massive black hole mergers, which form at separations on the order of the simulation resolution (∼kpc scales), through coalescence with two different treatments for the binary massive black hole evolutionary process. The coalescence times of the population, as well as physical properties of the black holes, form a statistical basis for each evolutionary treatment. From these bases, we Monte Carlo synthesize many realizations of the merging massive black hole population to build mock LISA detection catalogs. We analyze how our massive black hole binary evolutionary models affect detection rates and the associated parameter distributions measured by LISA. With our models, we find massive black hole binary detection rates with LISA of ∼ 0.5 − 1 yr −1 for massive black holes with masses greater than 10 5 M . This should be treated as a lower limit primarily because our massive black hole sample does not include masses below 10 5 M , which may significantly add to the observed rate. We suggest reasons why we predict lower detection rates compared to much of the literature.

The gravitational-wave astronomical revolution began in 2015 with LIGO's observation of the coalescence of two stellar-mass black holes. Over the coming decades, ground-based detectors like LIGO will extend their reach, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will enable gravitational-wave observations of the massive black holes in galactic centres. Between LISA and groundbased observatories lies the unexplored decihertz gravitational-wave frequency band. Here, we propose a Decihertz Observatory to cover this band, and complement observations made by other gravitational-wave observatories. The decihertz band is uniquely suited to observation of intermediate-mass (∼ 10 2-10 4 M) black holes, which may form the missing link between stellar-mass and massive black holes, offering a unique opportunity to measure their properties. Decihertz observations will be able to detect stellar-mass binaries days to years before they merge and are observed by ground-based detectors, providing early warning of nearby binary neutron star mergers, and enabling measurements of the eccentricity of binary black holes, providing revealing insights into their formation. Observing decihertz gravitational-waves also opens the possibility of testing fundamental physics in a new laboratory, permitting unique tests of general relativity and the Standard Model of particle physics. Overall, a Decihertz Observatory will answer key questions about how black holes form and evolve across cosmic time, open new avenues for multimessenger astronomy, and advance our understanding of gravitation, particle physics and cosmology.

The dynamical processing of black holes in the dense cores of globular clusters (GCs), makes them efficient factories for producing binary black holes (BBHs). Here we explore the population of BBHs that form dynamically in GCs and may be observable at mHz frequencies or higher with the future space-based gravitational-wave observatory, LISA. We use our Monte Carlo stellar dynamics code, which includes gravitational radiation reaction effects for all BH encounters. By creating a representative local universe of GCs, we show that up to dozens of these systems may be resolvable by LISA. Approximately one third of these binaries will have measurable eccentricities (e > 10 −3 ) in the LISA band and a small number ( 5) may evolve from the LISA band to the LIGO band during the LISA mission.

The future space mission LISA will observe a wealth of gravitational-wave sources at millihertz frequencies. Of these, the extreme-mass-ratio inspirals of compact objects into massive black holes are the only sources that combine the challenges of strong-field complexity with that of long-lived signals. Such signals are found and characterized by comparing them against a large number of accurate waveform templates during data analysis, but the rapid generation of templates is hindered by computing the ∼10 3 -10 5 harmonic modes in a fully relativistic waveform. We use order-reduction and deep-learning techniques to derive a global fit for the ≈4000 modes in the special case of an eccentric Schwarzschild orbit, and implement the fit in a complete waveform framework with hardware acceleration. Our highfidelity waveforms can be generated in under 1 s, and achieve a mismatch of ≲5 × 10 −4 against reference waveforms that take ≳10 4 times longer. This marks the first time that analysis-length waveforms with full harmonic content can be produced on timescales useful for direct implementation in LISA analysis algorithms.

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