A Bayesian Approach Study of Hybrid Neutron Stars

TL;DR

The paper addresses whether deconfined quark matter can exist inside neutron stars by jointly modeling hadronic and quark phases and constraining the onset of a hadron-quark phase transition with Bayesian inference using observational data on masses, radii, and tidal deformabilities. The authors employ relativistic mean-field hadronic EoS (NL3$^{*}\omega\rho$ and EL3$\omega\rho$, with/without hyperons) and a vector MIT bag quark model under a Maxwell construction, inferring the bag constant $B^{1/4}$, vector coupling $G_v$, and Dirac-sea term $b_4$. They find that a first-order transition can occur below $2\ n_{0}$ for the studied hadronic parameterizations, allowing hybrid stars with large quark cores (often $\gtrsim80\%$ of the stellar radius) that are consistent with current NICER and GW170817 constraints. The results show that both two- and three-parameter vMIT fits yield similar mass-radius and tidal-deformability predictions, with the densest transitions shifting when enforcing a lower density onset, and the hyperon case generally remaining viable though subtly altering transition thresholds. Overall, the work demonstrates that hybrid-star configurations with sizable quark cores remain compatible with present astrophysical data and provides a quantified Bayesian framework for testing the hadron-quark transition in dense matter.

Abstract

In this work, we explore how astronomical observations (specifically measurements of masses, radii, and tidal deformabilities) can constrain the presence of quark matter inside neutron stars, namely the phase transition from nuclear matter to deconfined quark matter. Our approach employs Bayesian analysis to study this phenomenon. Hadronic matter is modeled using the relativistic mean-field (RMF) approximation, for which we have selected two parameter sets: \(NL3^{*}ωρ\), representing hadronic matter with nucleons only, and $EL3ωρ$ with nucleons only and $EL3ωρY$, which includes hyperons. On the other hand deconfined quark matter is modeled using the vector-MIT bag model. For our purpose, the phase transition is implemented using the Maxwell construction. Bayesian inference is performed by tuning three parameters: the bag constant (i.e. $B^{1/4}$), the vector coupling constant \(\left(G_{v}\right)\), and the Dirac sea contribution ($b_{4}$). We found that a phase transition could exist at densities below \(2.0\,n_{0}\) for both the $EL3ωρ- EL3ωρY $ and $NL3^{*}ωρ$ parametrizations. As a consequence, our results also indicate that a hybrid neutron star could have a large quark core that comprises more than \(80\%\) of its size.

Figures (24)

• Figure 1: The results for the inference on two vMIT parameters with H2(0.25, 153.51).
• Figure 2: The case for three vMIT parameters with H3(0.26, 153.47,0.98).
• Figure 3: The plot shows the EoSs for the parameter set $EL3\omega\rho$ and vMIT with two and three parameters, along with their corresponding hybrid star, H2(0.25, 153.51) and H3(0.26, 153.47, 0.98). We also indicate the phases as HP for the hadron phase and QP for the quark phase.
• Figure 4: The left plot shows the mass-radius diagram for the vMIT inference values for the parameter set $EL3\omega\rho$ set. The right plot the results for $\Lambda$ against $M_{\odot}$.
• Figure 5: The approximately universal relation for both $\Upsilon -\Lambda$ and $\Upsilon-C$Saes:2021fzr.