Exploring the small mass ratio binary black hole merger via Zeno's dichotomy approach

We perform a sequence of binary black hole simulations with increasingly small mass ratios, reaching to a 128:1 binary that displays 13 orbits before merger. Based on a detailed convergence study of the $q=m_1\mathrm{/}{m}_2=1\mathrm{/}15$ nonspinning case, we apply additional mesh refinements levels around the smaller hole horizon to reach successively the $q=1\mathrm{/}32$, $q=1\mathrm{/}64$, and $q=1\mathrm{/}128$ cases. Roughly a linear computational resources scaling with $1\mathrm{/}q$ is observed on 8-nodes simulations. We compute the remnant properties of the merger: final mass, spin, and recoil velocity, finding precise consistency between horizon and radiation measures. We also compute the gravitational waveforms: its peak frequency, amplitude, and luminosity. We compare those values with predictions of the corresponding phenomenological formulas, reproducing the particle limit within 2%, and we then use the new results to improve their fitting coefficients.