Bayesian Inference of Dense Matter Equation of State within Relativistic Mean Field Models Using Astrophysical Measurements

Abstract

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, observations of compact X-ray sources, and the gravitational wave event GW170817. For the first time, such an analysis is performed by using a class of models, the relativistic mean field models, that allow one 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 ∼ 12 km. Finally, we present a preliminary investigation of the effect of including Λ hyperons, showing that they appear in stars more massive than about 1.6 M ⊙ and lead to radii larger than about R 1.4 ∼ 14 km. Within the model explored here, the formation of such particles provides poor agreement with the constraints from GW170817.

Studying the parameters of the extended σ-ω model for neutron star matter

“…For instance [9], presents an exhaustive study using the MPP approach to cover the phase space of EoS parameters by imposing constraints on the lower bound of the maximum neutron star mass and tidal deformability values. Later on, the mass-radius measurement of PSR J0030+0451 by NICER would help to provide tighter constraints on the resulting EoS regions, see [31][32][33][34][35][36][37][38][39][40] where different considerations and constrains, for example different Bayesian priors, have been taken into account. Most importantly, the EoS study parameters considered here have been studied in a few other Bayesian works that consider different EoS models, as is the case of Miller et al [32] that use the MPP EoS parameterization to study the impact of laboratory measured the symmetry energy on the compact star EoS, below nuclear saturation densities.…”

A Bayesian Analysis on Neutron Stars within Relativistic Mean Field Models

“…In this respect, a further analysis using density dependent couplings models would be valuable [32,33]. Another important extension of this work, partially studied in [4], is the inclusion of heavier baryons such as hyperons and deltas since their possible formation in the core of neutron stars has been confirmed by a number of theoretical studies; see, e.g., [34][35][36][37][38][39]. Finally, the possibility of a strong first order phase transition to quark matter, in the twin star scenario [40][41][42][43][44] or the two-families scenario [45][46][47][48][49], should also be studied within a Bayesian approach with the aim of comparing the "evidence" (or Bayes factor) of the standard one-family scenario and the scenarios of disconnected mass-radius relations [50,51].…”

“…Since the seminal paper [3], a huge effort has been put in trying to infer the properties of the EoS of neutron stars by using astrophysical data. There are several different approaches, see [4] for a complete list, which make use of several different parametrizations of the EoS: e.g., piecewise-polytropic, constant speed of sound EoSs, Taylor expansion around the nuclear matter point, etc. In [4], a relativistic mean field model parametrization has been adopted which is based on the non linear Walecka model proposed in [5,6].…”

“…There are several different approaches, see [4] for a complete list, which make use of several different parametrizations of the EoS: e.g., piecewise-polytropic, constant speed of sound EoSs, Taylor expansion around the nuclear matter point, etc. In [4], a relativistic mean field model parametrization has been adopted which is based on the non linear Walecka model proposed in [5,6]. The main result that we review and further analyze in this contribution is the possibility of obtaining mass-radius relations which are qualitatively very similar to the ones obtained when considering hybrid stars i.e., neutron stars in which, at some density in the inner core, a phase transition to quark matter occurs.…”

The possibility of twin star solutions in a model based on lattice QCD thermodynamics

“…Such a phase transition can be discovered astrophysically in the properties of compact stars and their corresponding mass-radius relations from the Tolman-Oppenheimer-Volkoff equation (TOV) [8,9], tidal deformability [10], as well as dynamical observables from the binary mergers of neutron stars as in the GW170817 event [3,11]. New methods, such as machine learning [12,13] and Bayesian analysis [14][15][16] are being developed in order to directly extract the equation of state (EoS) from available data.…”