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The existence of massive compact stars $(Mgtrsim 2.1 M_{odot})$ implies that the conformal limit of the speed of sound $c_s^2=1/3$ is violated if those stars have a crust of ordinary nuclear matter. Here we show that, if the most massive objects are strange quark stars, i.e. stars entirely composed of quarks, the conformal limit can be respected while observational limits on those objects are also satisfied. By using astrophysical data associated with those massive stars, derived from electromagnetic and gravitational wave signals, we show, within a Bayesian analysis framework and by adopting a constant speed of sound equation of state, that the posterior distribution of $c_s^2$ is peaked around 0.3, and the maximum mass of the most probable equation of state is $sim 2.13 M_{odot}$. We discuss which new data would require a violation of the conformal limit even when considering strange quark stars, in particular we analyze the possibility that the maximum mass of compact stars is larger than $2.5M_{odot}$, as it would be if the secondary component of GW190814 is a compact star and not a black hole. Finally, we discuss how the new data for PSR J0740+6620 obtained by the NICER collaboration compare with our analysis (not based on them) and with other possible interpretations.
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We analyse the phenomenological implications of the two-families scenario on the merger of compact stars. That scenario is based on the coexistence of both hadronic stars and strange quark stars. After discussing the classification of the possible mergers, we turn to detailed numerical simulations of the merger of two hadronic stars, i.e., first family stars in which delta resonances and hyperons are present, and we show results for the threshold mass of such binaries, for the mass dynamically ejected and the mass of the disk surrounding the post-merger object. We compare these results with those obtained within the one-family scenario and we conclude that relevant signatures of the two-families scenario can be suggested, in particular: the possibility of a rapid collapse to a black hole for masses even smaller than the ones associated to GW170817; during the first milliseconds, oscillations of the postmerger remnant at frequencies higher than the ones obtained in the one-family scenario; a large value of the mass dynamically ejected and a small mass of the disk, for binaries of low total mass. Finally, based on a population synthesis analysis, we present estimates of the number of mergers for: two hadronic stars; hadronic star - strange quark star; two strange quark stars. We show that for unequal mass systems and intermediate values of the total mass, the merger of a hadronic star and a strange quark star is very likely (GW170817 has a possible interpretation into this category of mergers). On the other hand, mergers of two strange quark stars are strongly suppressed.
It is usually thought that a single equation of state (EoS) model correctly represents cores of all compact stars. Here we emphasize that two families of compact stars, viz., neutron stars and strange stars, can coexist in nature, and that neutron stars can get converted to strange stars through the nucleation process of quark matter in the stellar center. From our fully general relativistic numerical computations of the structures of fast-spinning compact stars, known as millisecond pulsars, we find that such a stellar conversion causes a simultaneous spin-up and decrease in gravitational mass of these stars. This is a new type of millisecond pulsar evolution through a new mechanism, which gives rise to relatively lower mass compact stars with higher spin rates. This could have implication for the observed mass and spin distributions of millisecond pulsars. Such a stellar conversion can also rescue some massive, spin-supported millisecond pulsars from collapsing into black holes. Besides, we extend the concept of critical mass $M_{rm cr}$ for the neutron star sequence (Berezhiani et al. 2003; Bombaci et al. 2004) to the case of fast-spinning neutron stars, and point out that neutron star EoS models cannot be ruled out by the stellar mass measurement alone. Finally, we emphasize the additional complexity for constraining EoS models, for example, by stellar radius measurements using X-ray observations, if two families of compact stars coexist.
We calculate the speed of sound $c_s$ in an ideal gas of resonances whose mass spectrum is assumed to have the Hagedorn form $rho(m) sim m^{-a}exp{bm}$, which leads to singular behavior at the critical temperature $T_c = 1/b$. With $a = 4$ the pressure and the energy density remain finite at $T_c$, while the specific heat diverges there. As a function of the temperature the corresponding speed of sound initially increases similarly to that of an ideal pion gas until near $T_c$ where the resonance effects dominate causing $c_s$ to vanish as $(T_c - T)^{1/4}$. In order to compare this result to the physical resonance gas models, we introduce an upper cut-off M in the resonance mass integration. Although the truncated form still decreases somewhat in the region around $T_c$, the actual critical behavior in these models is no longer present.
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.
We review theoretical developments in studies of dense matter and its phase structure of relevance to compact stars. Observational data on compact stars, which can constrain the properties of dense matter, are presented critically and interpreted.
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