The composition of the neutron star is one of the most fundamental and long-standing problems in nuclear- and astro-physics. The known properties of nuclear matter, together with the astronomical observations, impose the stringent and interconnected constraints on the theoretical descriptions. In this work, by using the most general quantum hadrodynamics model including and in addition to nucleons, and performing a Bayesian joint analysis of experimental nuclear matter data and astrophysical observations, we point out that the nuclear matter made of only hadrons can provide a unified description of nuclear matter properties and astrophysical observations at -level. In addition, we find that the existence of interaction naturally leads to a peak structure in the speed of sound at times saturation density which results to a small size intermediate mass neutron star and the upper bound mass . What we find here indicate that the sequential measurement of neutron star mass and radius by the next generation facilities, especially that of the intermediate mass neutron stars, is crucial for distinguishing the pure nucleonic stars from the hybrid ones.

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