Direct Measurement of the Accretion Disk Formed in Prompt Collapse Mergers with Future Gravitational-Wave Observatories

The production site of heavy r-process elements, such as Gold and Uranium, is uncertain. Neutron star mergers are the only astrophysical phenomenon in which we have witnessed their formation. However, the amount of heavy elements resulting from the merger remains poorly constrained, mainly due to uncertainties on the mass and angular momentum of the disk formed in the merger remnant. Matter accretion from the disk is also thought to power gamma ray-bursts. We discover from numerical relativity simulations that the accretion disk influences the ringdown gravitational-wave signal produced by binaries that promptly collapse to black-hole at merger. We propose a method to \emph{directly} measure the mass of the accretion disk left during black hole formation in binary mergers using observatories such as the Einstein Telescope or Cosmic Explorer with a relative error of 10\% for binaries at a distance of up to 30~Mpc, corresponding to an event rate of 0.001 to 0.25 events per year.