  The QCD axion is a hypothetical particle motivated by the Strong CP problem
of particle physics. One of the primary ways in which its existence can be
inferred is via its function as an additional cooling channel in stars, with
some of the strongest constraints coming from the supernova observation
SN1987A. Multimessenger observations of binary neutron star mergers (such as
those of GW170817, AT2017gfo, and GRB170817A) may provide another scenario in
which such constraints could be obtained. In particular, the axion could
potentially alter the lifetime, the ejection of material, and the emitted
gravitational wave signal of the postmerger remnant. In this article, we
perform numerical relativity simulations of a binary neutron star merger,
including a phenomenological description of the nucleon-nucleon-axion
bremsstrahlung to quantify the effects of such a cooling channel on the
dynamical evolution. While our simulations show a difference in the temperature
profile of the merger remnant, the imprint of the axion via
nucleon-nucleon-axion bremsstrahlung on the emitted gravitational wave signal
and the ejecta mass is too small to improve constraints on the axion mass with
current or future planned detectors. Whilst we consider a limited number of
cases, and a simplified cooling model, these broadly represent the "best case"
scenario, thus, a more thorough investigation is unlikely to change the
conclusions, at least for this particular interaction channel.
