Probing the incompressibility of nuclear matter at ultra-high density through the prompt collapse of asymmetric neutron star binaries

Using 250 neutron star merger simulations with microphysics, we explore for the first time the role of nuclear incompressibility in the prompt collapse threshold for binaries with different mass ratios. We demonstrate that observations of prompt collapse thresholds, either from binaries with two different mass ratios or with one mass ratio but combined with the knowledge of the maximum neutron star mass or compactness, will constrain the incompressibility at the maximum neutron star density, $K_{\rm max}$, to within tens of percent. This, otherwise inaccessible, measure of $K_{\rm max}$ can potentially reveal the presence of hyperons or quarks inside neutron stars.