The sound speed and core of massive compact stars: A manifestation of hadron-quark duality

When baryon-quark continuity is formulated in terms of a topology change without invoking explicit QCD degrees of freedom at a density higher than twice the nuclear matter density $n_0$ the core of massive compact stars can be described in terms of fractionally charged particles, behaving neither like pure baryons nor deconfined quarks. Hidden symmetries, both local gauge and pseudo-conformal (or broken scale), lead to the pseudo-conformal (PC) sound velocity $v_{pcs}^2/c^2approx 1/3$ at $gsim 3n_0$ in compact stars. We argue these symmetries are emergent from strong nuclear correlations and conjecture that they reflect hidden symmetries in QCD proper exposed by nuclear correlations. We establish a possible link between the quenching of $g_A$ in superallowed Gamow-Teller transitions in nuclei and the precocious onset at $ngsim 3n_0$ of the PC sound velocity predicted at the dilaton limit fixed point. We propose that bringing in explicit quark degrees of freedom as is done in terms of the quarkyonic and other hybrid hadron-quark structure and our topology-change strategy represent the hadron-quark duality formulated in terms of the Cheshire-Cat mechanism~cite{CC} for the smooth cross-over between hadrons and quarks. Confrontation with currently available experimental observations is discussed to support this notion.