Neutron stars can accumulate asymmetric dark matter (ADM) in their interiors,
which affects the neutron star's measurable properties and makes compact
objects prime targets to search for ADM. In this work, we use Bayesian
inference to explore potential neutron star mass-radius measurements, from
current and future x-ray telescopes, to constrain the bosonic ADM parameters
for the case where bosonic ADM has accumulated in the neutron star interior. We
find that the current uncertainties in the baryonic equation of state do not
allow for constraints on the ADM parameter space to be made. However, we also
find that ADM cannot be excluded and the inclusion of bosonic ADM in neutron
star cores relaxes the constraints on the baryonic equation of state space. If
the baryonic equation of state were more tightly constrained independent of
ADM, we find that statements about the ADM parameter space could be made. In
particular, we find that the high bosonic ADM particle mass ($m_\chi$) and low
effective self-interaction strength ($g_\chi/m_\phi)$ regime is disfavored due
to the observationally and theoretically motivated constraint that neutron
stars must have at least a mass of $1 \, \mathrm{M_\odot}$. However, within the
remaining parameter space, $m_\chi$ and $g_\chi/m_\phi$ are individually
unconstrained. On the other hand, the ADM mass-fraction, i.e., the fraction of
ADM mass inside the neutron star, can be constrained by such neutron star
measurements.
