Letter to the Editor Possible third family of compact stars more dense than neutron stars

The work of J. A. Wheeler in the mid 1960’s showed that for smooth equations of state no stable stellar configurations with central densities above that corresponding to the limiting mass of ‘neutron stars’ (in the generic sense including hybrids) were stable. Accordingly, there has been no reason to expect that a stable degenerate family of stars with higher density than the known white dwarfs and neutron stars might exist. Nevertheless, we have found a class of equations of state that describe a first order phase transition and are insufficiently smooth to obey the conditional theorem of Wheeler. We identify the attributes that give rise to a third family of stable dense stars, discuss how such a higher density family of stars could be formed in nature, and how the promising new exploration of oscillations in the X-ray brightness of accreting neutron stars might provide a means of identifying them.