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Register a new userBayesian Inference of the Symmetry Energy of Super-Dense Neutron-Rich Matter from Future Radius Measurements of Massive Neutron Stars
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Using an explicitly isospin-dependent parametric Equation of State (EOS) for the core of neutron stars (NSs) within the Bayesian statistical approach, we infer the EOS parameters of super-dense neutron-rich nuclear matter from three sets of imagined mass-radius correlation data representing typical predictions by various nuclear many-body theories, i.e, the radius stays the same, decreases or increases with increasing NS mass within $pm 15%$ between 1.4 M$_{odot}$ and 2.0 M$_{odot}$. The corresponding average density increases quickly, slowly or slightly decreases as the NS mass increases from 1.4 M$_{odot}$ to 2.0 M$_{odot}$. Using the posterior probability distribution functions (PDFs) of EOS parameters inferred from GW170817 and NICER radius data for canonical NSs as references, we investigate how future radius measurements of massive NS will improve our knowledge about the EOS of super-dense neutron-rich nuclear matter, especially its symmetry energy term, compared to what people have already learned from analyzing the GW170817 and NICER data. While the EOS of symmetric nuclear matter (SNM) inferred from the three data sets are approximately the same, the corresponding high-density symmetry energies at densities above about $2rho_0$ are very different, indicating that the radii of massive NSs carry reliable information about the high-density behavior of nuclear symmetry energy with little influence from the remaining uncertainties of the SNM EOS.
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We analyze observations of eight quiescent low-mass X-ray binaries in globular clusters and combine them to determine the neutron star mass-radius curve and the equation of state of dense matter. We determine the effect that several uncertainties may have on our results, including uncertainties in the distance, the atmosphere composition, the neutron star maximum mass, the neutron star mass distribution, the possible presence of a hotspot on the neutron star surface, and the prior choice for the equation of state of dense matter. We find that the radius of a 1.4 solar mass neutron star is most likely from 10 to 14 km and that tighter constraints are only possible with stronger assumptions about the nature of the neutron stars, the systematics of the observations, or the nature of dense matter. Strong phase transitions are preferred over other models and interpretations of the data with a Bayes factor of 8 or more, and in this case, the radius is likely smaller than 12 km. However, radii larger than 12 km are preferred if the neutron stars have uneven temperature distributions.
[Purpose:] We infer the posterior probability distribution functions (PDFs) and correlations of nine parameters characterizing the EOS of dense neutron-rich matter encapsulating a first-order hadron-quark phase transition from the radius data of canonical NSs reported by LIGO/VIRGO, NICER and Chandra Collaborations. We also infer the quark matter (QM) mass fraction and its radius in a 1.4 M$_{odot}$ NS and predict their values in more massive NSs. [Method:] Meta-modelings are used to generate both hadronic and QM EOSs in the Markov-Chain Monte Carlo sampling process within the Bayesian statistical framework. An explicitly isospin-dependent parametric EOS for the $npemu$ matter in NSs at $beta$ equilibrium is connected through the Maxwell construction to the QM EOS described by the constant speed of sound (CSS) model of Alford, Han and Prakash. [Results:] (1) The most probable values of the hadron-quark transition density $rho_t/rho_0$ and the relative energy density jump there $Deep/ep_t$ are $rho_t/rho_0=1.6^{+1.2}_{-0.4}$ and $Deep/ep_t=0.4^{+0.20}_{-0.15}$ at 68% confidence level, respectively. The corresponding probability distribution of QM fraction in a 1.4 M$_{odot}$ NS peaks around 0.9 in a 10 km sphere. Strongly correlated to the PDFs of $rho_t$ and $Deep/ep_t$, the PDF of the QM speed of sound squared $cQMsq/c^2$ peaks at $0.95^{+0.05}_{-0.35}$, and the total probability of being less than 1/3 is very small. (2) The correlations between PDFs of hadronic and QM EOS parameters are very weak. [Conclusions:] The available astrophysical data considered together with all known EOS constraints from theories and terrestrial nuclear experiments prefer the formation of a large volume of QM even in canonical NSs.
We present a Bayesian analysis to constrain the equation of state of dense nucleonic matter by exploiting the available data from symmetric nuclear matter at saturation and from observations of compact X-ray sources and from the gravitational wave event GW170817. For the first time, such analysis is performed by using a class of models, the relativistic mean field models, which allow to consistently construct an equation of state in a wide range of densities, isospin asymmetries and temperatures. The selected class of models contains five nuclear physics empirical parameters at saturation for which we construct the joint posterior distributions. By exploring different types of priors, we find that the equations of state with the largest evidence are the ones featuring a strong reduction of the effective mass of the nucleons in dense matter which can be interpreted as an indication of a phase transition to a chiral symmetry restored phase. Those equations of state in turn predict $R_{1.4} sim 12$ km. Finally, we present a preliminary investigation on the effect of including $Lambda$ hyperons showing that they appear in stars more massive than about $1.6 M_{odot}$ and lead to radii larger than about $R_{1.4} sim 14$ km. Within the model here explored, the formation of such particles provide a poor agreement with the constraints from GW170817.
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