Generating ultra-compact neutron stars with bosonic dark matter

In this work we investigate the properties of neutron stars admixed with selfinteracting scalar bosonic dark matter. The dark matter interaction is described by a generalized $\phi^n$ power-law potential. We perform a stability analysis of these two-fluid objects by studying the onset of the unstable radial modes. We find ultra-compact neutron star-dark matter configurations where the neutron star matter is confined to a core radius of values below $7$ km which is unreachable for pure neutron stars. The total gravitational maximum mass of these ultra-compact configurations can have values of $3.4 \, M_\odot$. With our general ansatz of the power-law potential we show that the compactness of these solutions can be extreme, i.e. the compactness is $C = 1/3$ or even larger, making them compact enough to have a light-ring mimicking black holes. These ultra-compact objects are stable and possess a dark matter halo while having a hadronic matter core. With the addition of dark matter to neutron stars recent unusual mass-radius measurements of compact stars can be explained. We conclude that apparently contradictory measurements of neutron star masses and radii could be not only an indication of the presence of dark matter around a the hadronic matter core which is stabilized by the gravitational potential of dark matter but could also serve to disentangle the selfinteraction strength of dark matter. Our work points to a stiff equation of state for the dark matter fluid, rather than a soft one.