Evaluating Black Hole Detectability with LISA

We conduct an analysis of the measurement abilities of distinctive LISA detector designs, examining the influence of LISA's low-frequency performance on the detection and characterization of massive black hole binaries. We are particularly interested in LISA's ability to measure massive black holes merging at frequencies near the low-frequency band edge, with masses in the range of $\sim 10^6-10^{10}M_\odot$. We examine the signal-to-noise ratio (SNR) using phenomenological waveforms for inspiral, merger, and ringdown over a wide range of massive black hole binary parameters. We employ a broad palette of possible LISA configurations with different sensitivities at low frequencies. For this analysis, we created a tool (github.com/mikekatz04/BOWIE) that evaluates the change in SNR between two parameterized situations. The shifts in SNR are computed as gains or losses as a function of binary parameters, and graphically displayed across a two dimensional grid of parameter values. We illustrate the use of this technique for both parameterized LISA mission designs, as well as for considering the influence of astrophysical parameters on gravitational wave signal models. In terms of low-frequency sensitivity, acceleration noise or armlength is found to be the most important factor in observing the largest massive black hole binaries, followed by break frequency and then spectral index. LISA's ability to probe the astrophysical population of $\sim10^7-10^9M_\odot$ black holes is greatly influenced by these aspects of its sensitivity. The importance of the constituent black hole spins is also highlighted.