  We point out that the very existence of a "horizontal branch" in the
mass-radius characteristics for neutron stars indicates a strong first-order
phase transition and thus supports the existence of a critical endpoint (CEP)
of first order phase transitions in the QCD phase diagram. This branch would
sample a sequence of hybrid stars with quark matter core, leading to the
endpoint of stable compact star configurations with the highest possible baryon
densities. Since we know of the existence of compact stars with $2M_\odot$,
this hypothetical branch has to lie in the vicinity of this mass value, if it
exists. We report here a correlation between the maximal radius of the
horizontal branch and the pressure at the onset of hadron-to-quark matter phase
transition which is likely to be a universal quantity of utmost relevance to
the upcoming experiments with heavy-ion collisions at NICA and FAIR.
