How Neutron Star Observations Point Towards Exotic Matter: Existing Explanations and a Prospective Proposal

TL;DR

The paper addresses the tension between neutron-star observational constraints and dense-matter EOS by proposing slow-conversion, first-order hadron–quark phase transitions that yield slow stable hybrid stars (SSHS). It develops a model-independent framework using a three-piece generalized polytropic hadronic EOS with a BPS-BBP crust and explores quark matter with MIT Bag, CSS, and a novel non-CSS speed-of-sound parametrization, analyzing stability via radial oscillations. The results suggest SSHS can satisfy multiple constraints (including $M \approx 2 M_\odot$ and GW170817 tidal data) but require unusually stiff quark matter ($c_s^2 \sim 0.8$–$0.9$) and careful parameter tuning; some configurations (notably crust-inclusive CQQ) fail certain tidal constraints, while non-CSS helps with pQCD alignment but can shorten SSHS branches. The work positions SSHS as a competitive exotic-core scenario among others (two-family, DM-admixed NSs, QQ-HS) and outlines observational tests, such as gravitational-wave asteroseismology and precise tidal deformability measurements, to decisively probe the presence and nature of HQ phase transitions in NS interiors.

Abstract

Multi-messenger astronomical observations of neutron stars, together with more precise calculations and constraints coming from dense matter microphysics, are generating tension with regard to equations of state models used to describe neutron star cores. Assuming an abrupt first-order phase transition with a slow conversion speed between phases, we propose different slow stable hybrid star configurations aiming to reconcile all current constraints simultaneously; within this framework, we also introduce a novel non-CSS parametrization to the quark matter equation of state and discuss its strengths and limitations. We analyze our model results in conjunction with a review of other relevant theoretical possibilities existing in the literature. We found that modern neutron star observations seem to favor the existence of some type of exotic matter in the neutron star cores; in particular, our slow stable hybrid star scenario remains a proposal capable of satisfying these constraints. However, due both to the existing skepticism regarding some of the adopted hypotheses in most extreme neutron star measurements and to the precise adjustment needed for the equation-of-state parameters, significant tension and open questions remain.

Figures (6)

• Figure S1: $P$-$\varepsilon$ (top panel) and $c_s^2$-$\varepsilon$ (bottom panel) relationships of the hybrid EOSs selected for the CSS ($\beta=0$) analysis. In both panels, the star marks represent the maximum energy density value reached
• Figure S2: $M$-$R$ relationship of the of the hybrid EOSs selected for the CSS ($\beta=0$) analysis. For all sets, we present only stable configurations, considering the slow conversion scenario; configurations beyond the maximum mass, up to the terminal one (star marks), belong to the SSHS branch. We also show astrophysical constraints from the $\sim$2 $M_\odot$ pulsars Demorest:2010sdmAntoniadis:2013ampArzoumanian:2018tnyCromartie:2020rsdFonseca:2021rfa, NICER pulsars Miller:2019pjmRiley2019anvMiller:2021troRiley:2021anvSalmi:2024anvChoudhury2024anvMauviard:2025anv, GW170817 Abbott:2017oogAbbott:2018gmo and GW190425 Abbott:2020goo events, the black widow PSR J0952-0607 Romani:2022pjt, HESS J1731-347 Doroshenko:2022asl, and XTE J1814-338 Kini:2024ctp. The upper horizontal dotted area is the region excluded by Shibata:2019ctb, $M_\textrm{max} \leq 2.3~M_\odot$. The gray area in the right bottom corner indicates the TOV integration of the $\chi$EFT EOS constraint (along with a BPS-BBP crust for lower densities); as already mentioned, this constraint does not apply to compact objects containing quark matter at such masses. The shaded region in the upper left corner indicates the causality forbidden zone.
• Figure S3: $\Lambda$-$M$ relationship of the of the hybrid EOSs selected for the CSS ($\beta=0$) analysis. For all sets we present only stable configurations, considering the slow conversion scenario; configurations beyond the maximum mass, up to the terminal one at the end of the curve, belong to the SSHS branch. We also show the constraint obtained from the analysis of the multimessenger event with gravitational waves GW170817 Abbott:2018gmo. The CQQ cases, although satisfying the $M$-$R$ constraint for GW170817 (see Figure \ref{['fig:mraio_beta0']}), does not satisfy the $\Lambda$ one. All the other selected EOSs satisfy it trough the totally stable branch.
• Figure S4: $P$-$\varepsilon$ (top panel) and $c_s^2$-$\varepsilon$ (bottom panel) relationships of the hybrid EOSs selected for the non-CSS ($\beta \neq 0$) analysis. In both panels, the star marks represent the maximum energy density value reached at the center of the terminal SSHS configuration. Top panel: colored regions and dashed segment details are in caption of Figure \ref{['fig:peps_beta0']}. Except for the $\beta$ parameter (detailed in the legend for each curve), the shared parameters for all curves are $P_t = 400$ MeV/fm$^3$, $\Delta \varepsilon = 2500$ MeV/fm$^3$, $c_t^2 = 1.0$. The increasing $\beta$ value helps to satisfy the pQCD constraint. Bottom panel: each EOS indicates the abrupt phase transition with the empty gap between vertical dashed segments in each curve. The horizontal dashed black line indicates the conformal limit value, $c_L^2 = 1/3$, and the vertical pink dashed line indicates the beginning of the pQCD region. After the phase transition all EOSs begins with same value $c_s^2 = 1.0$ and, depending on the $\beta$ value, decrease exponentially with different rapidity approaching the conformal limit. The $\beta=0.4$ and $\beta=0.7$ cases decrease enough to almost reach this limit well before the beginning of the pQCD region.
• Figure S5: $M$-$R$ relationship of the of the hybrid EOSs selected for the non-CSS ($\beta \neq 0$) analysis. For all sets we present only stable configurations, considering the slow conversion scenario, these being the configurations after the maximum mass one up to the terminal one (star marks) of the SSHS branch. Colored regions constraints are detailed in Figure \ref{['fig:mraio_beta0']}. Except for the $\beta$ parameter (detailed in the legend for each curve), the shared parameters for all curves are $P_t = 400$ MeV/fm$^3$, $\Delta \varepsilon = 2500$ MeV/fm$^3$, and $c_t^2 = 1.0$. The increasing $\beta$ value, while helping satisfy the pQCD constraint, reduces the possibility of meeting the XTE J1814-338 constraint.