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Extreme Mass Ratio Inspirals (EMRIs) are one of the key sources for future space-based gravitational wave interferometers. Measurements of EMRI gravitational waves are expected to determine the characteristics of their sources with sub-percent precision. However, their waveform generation is challenging due to the long duration of the signal and the high harmonic content. Here, we present the first ready-to-use Schwarzschild eccentric EMRI waveform implementation in the frequency domain for use with either graphics processing units (GPUs) or central processing units (CPUs). We present the overall waveform implementation and test the accuracy and performance of the frequency domain waveforms against the time domain implementation. On GPUs, the frequency domain waveform takes in median 0.044 s to generate and is twice as fast to compute as its time domain counterpart when considering massive black hole masses $\ge 2\times 10^6{\text{M}}_{\odot }$and initial eccentricitiese₀> 0.2. On CPUs, the median waveform evaluation time is 5 s, and it is five times faster in the frequency domain than in the time domain. Using a sparser frequency array can further speed up the waveform generation, reaching up to 0.3 s. This enables us to perform, for the first time, EMRI parameter inference with fully relativistic waveforms on CPUs. Future EMRI models, which encompass wider source characteristics (particularly black hole spin and generic orbit geometries), will require significantly more harmonics. Frequency domain models will be essential analysis tools for these astrophysically realistic and important signals. 

Abstract 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 ∼105 − 1010M⊙ 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 105M⊙. This should be treated as a lower limit primarily because our massive black hole sample does not include masses below 105M⊙, which may significantly add to the observed rate. We suggest reasons why we predict lower detection rates compared to much of the literature. 

Abstract Since 2015 the gravitational-wave observations of LIGO and Virgo have transformed our understanding of compact-object binaries. In the years to come, ground-based gravitational-wave observatories such as LIGO, Virgo, and their successors will increase in sensitivity, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will provide gravitational-wave observations of massive black holes binaries. Between the $$\sim 10$$ ∼ 10 –10 3 Hz band of ground-based observatories and the $$\sim 10^{-4}$$ ∼ 1 0 − 4 –10 − 1 Hz band of LISA lies the uncharted decihertz gravitational-wave band. We propose a Decihertz Observatory to study this frequency range, and to complement observations made by other detectors. Decihertz observatories are well suited to observation of intermediate-mass ( $$\sim 10^{2}$$ ∼ 1 0 2 –10 4 M ⊙ ) black holes; they will be able to detect stellar-mass binaries days to years before they merge, providing early warning of nearby binary neutron star mergers and measurements of the eccentricity of binary black holes, and they will enable new tests of general relativity and the Standard Model of particle physics. Here we summarise how a Decihertz Observatory could provide unique insights into how black holes form and evolve across cosmic time, improve prospects for both multimessenger astronomy and multiband gravitational-wave astronomy, and enable new probes of gravity, particle physics and cosmology.