Astrophysical constraints on the cold equation of state of the strongly interacting matter

TL;DR

This work addresses constraining the EOS of cold, dense, strongly interacting matter using neutron-star observations. It combines a hadronic EOS at low density, a quark–meson EOS at high density, and a polynomial energy-density interpolation, with the transition governed by $\bar{\rho}$ and $\Gamma$, and anchors to the pQCD point at $\mu_{\mathrm{QCD}}=2.6$ GeV, exploring about $10^4$ EOSs via Bayesian inference. The strongest constraints arise from the maximum neutron-star mass, the tidal deformability from GW170817, and, to a lesser extent, NICER radius measurements, with the hard bound $M_{\max}\ge M_{\min}=2.22\,M_\odot$ and the tidal bound $\tilde{\Lambda}<720$ (or $70<\Lambda_{1.4}<580$) guiding the analysis. The results favor a broad hadron–quark crossover around $\bar{\rho}\approx(4.5)\rho_0$, with typical transition width $\Gamma\approx(2.6$–$3.1)\rho_0$ and vector coupling $g_v\approx4$–$6$, yielding $R_{1.4}\approx12.3$–$12.7$ km and relatively large $\Lambda_{1.4}$. These findings illustrate how multi-messenger data tightly constrain the dense-matter EOS and highlight future directions, including incorporating strangeness and clarifying the origin of large $\Lambda_{1.4}$ preferences.

Abstract

At present, the only experimental access to the properties of cold, dense strongly interacting matter is provided by astrophysical observations. Neutron stars are the only known systems in the Universe that reach densities several times higher than normal nuclear density at nearly zero temperature, making them unique laboratories for studying dense matter. Since most neutron-star observables are sensitive to the equation of state (EOS), observational data place stringent constraints on the EOS of strongly interacting matter. In this work, we investigate constraints arising from the mass of the heaviest observed neutron star (a black widow pulsar), perturbative QCD calculations at asymptotically high densities, NICER mass-radius measurements, and the tidal deformability inferred from the binary neutron star merger GW170817. We parametrize the EOS and allow its parameters to vary freely, using observational data to constrain the admissible parameter space. We find that neutron-star observations significantly restrict the EOS of dense strongly interacting matter. While NICER has already provided measurements for five pulsars, the associated uncertainties remain relatively large. In contrast, the existence of very massive neutron stars and constraints on the tidal deformability emerge as particularly powerful probes of the EOS.

Figures (6)

• Figure 1: The presumed structure of the phase diagram of strongly interacting matter.
• Figure 3: The EOS curves coloured by their likelihood are shown when applied the minimal mass and pQCD constraints with the GW condition (left upper figure); the GW and NICER conditions (right upper figure); the GW, NICER and the HESS conditions (left lower figure); GW, NICER, and the mass gap conditions (right lower figure). The most probable parameter set is indicated in each panel.
• Figure 4: The individual $M(R)$ curves coloured by their likelihood are shown when applied the minimal mass and pQCD constraints with the GW condition (left upper figure); the GW and NICER conditions (right upper figure); the GW, NICER and the Hess conditions (left lower figure); GW, NICER, and the mass gap conditions (right lower figure).
• Figure 5: The probability distribution of $R_{1.4}$ (radius for $1.4\,M_\odot$) for the cases of Fig. \ref{['fig:pQCD_BlWi-EOS']}
• Figure 6: The probability distribution in the $q$ (mass ratio) and $\tilde{\Lambda}$ (tidal deformability) plane. In the upper left panel we only prescribe the minimal mass and the pQCD constraint, in the upper right figure we add the GW condition, while in the bottom panel the NICER conditions are applied, too. The black line indicates the result of the LIGO–Virgo analysis of Ref. LIGOScientific:2018hze.