  In August 2017, the first detection of a binary neutron star merger,
GW170817, made it possible to study neutron stars in compact binary systems
using gravitational waves. Despite being the loudest gravitational wave event
detected to date (in terms of signal-to-noise ratio), it was not possible to
unequivocally determine that GW170817 was caused by the merger of two neutron
stars instead of two black holes from the gravitational-wave data alone. That
distinction was primarily due to the accompanying electromagnetic counterpart.
This raises the question: under what circumstances can gravitational-wave data
alone, in the absence of an electromagnetic signal, be used to distinguish
between different types of mergers? Here, we study whether a neutron star-black
hole binary merger can be distinguished from a binary black hole merger using
gravitational-wave data alone. We build on earlier results using chiral
effective field theory to explore whether the data from LIGO and Virgo, LIGO
A+, LIGO Voyager, the Einstein Telescope, or Cosmic Explorer could lead to such
a distinction. The results suggest that the present LIGO-Virgo detector network
will most likely be unable to distinguish between these systems even with the
planned near-term upgrades. However, given an event with favorable parameters,
third-generation instruments such as Cosmic Explorer will be capable of making
this distinction. This result further strengthens the science case for
third-generation detectors.
