Neutron - mirror neutron mixing and neutron stars

The oscillation of neutrons $n$ into mirror neutrons $n'$, their mass degenerate partners from dark mirror sector, can have interesting implications for neutron stars: an ordinary neutron star could gradually transform into a mixed star consisting in part of mirror dark matter. Mixed stars can be detectable as twin partners of ordinary neutron stars: namely, there can exist compact stars with the same masses but having different radii. For a given equation of state (identical between the ordinary and mirror components), the mass and radius of a mixed star depend on the proportion between the ordinary and mirror components in its interior which in turn depends on its age. If $50 \% - 50\%$ proportion between two fractions can be reached asymptotically in time, then the maximum mass of such "maximally mixed stars" should be $\sqrt2$ times smaller than that of ordinary neutron star while the stars exceeding a critical mass value $M^{\rm max}_{NS}/\sqrt2$ should collapse in black holes after certain time. We evaluate the evolution time and discuss the implications of $n-n'$ transition for the pulsar observations as well as for the gravitational waves from the neutron star mergers and associated electromagnetic signals.
Comment: 18 pages, 6 figures