Self-bound hybrid stars with strong phase transitions can relieve major compact star observation tensions

A recent observational study has set a constraint on the maximum mass of neutron stars (NSs), specifically focusing on PSR J0952-0607 and the compact star remnant HESS J1731-347, particularly within the low-mass regime. In our recent study, Ref. 1 , we developed an energy density functional named NITR, which successfully produced the mass limit of the aforementioned pulsar but did not fully meet other observational constraints, such as those from NICER+XMM and GW170817. In this study, we introduce a new EDF named “NITR-I”, which not only reproduces the mass limit of PSR J0952-0607 but also aligns its canonical radius with NICER+XMM data, and its canonical dimensionless tidal deformability is consistent with the GW170817 event, thereby demonstrating the robustness of our model. The low-mass constraint associated with HESS J1731-347 suggests various possible compositions for the NS. The NITR-I model alone does not satisfy the HESS J1731-347 constraint; thus, we explore the possibility of incorporating dark matter (DM) inside the NS to meet this constraint. This approach proves successful when a specific value of Fermi momentum is considered. We also examine the impact of DM with varying Fermi momentum on different NS properties, such as tidal deformability and nonradial f-mode oscillation, using various relativistic mean-field (RMF) models. For the NITR-I EOS, the f-mode frequency is about 2.15[Formula: see text]kHz at 1.4 [Formula: see text] when [Formula: see text][Formula: see text]GeV, and it slightly increases to around 2.32[Formula: see text]kHz with [Formula: see text][Formula: see text]GeV. This increase in frequency due to DM suggests a possible reduction in tidal deformability, indicating that neutron stars with higher DM content are less susceptible to deformation by tidal forces which could be detectable in gravitational wave signals from neutron star mergers. Finally, we explore various universal relations (URs) for DM-admixed NSs, such as the relation between compactness and tidal deformability, the f-mode frequency and tidal deformability, and estimate the canonical values corresponding to both compactness and f-mode frequency using the GW170817 data.

Finite size effects in a neutron star merger are manifested, at leading\norder, through the tidal deformabilities (Lambdas) of the stars. If strong\nfirst-order phase transitions do not exist within neutron stars, both neutron\nstars are described by the same equation of state, and their Lambdas are highly\ncorrelated through their masses even if the equation of state is unknown. If,\nhowever, a strong phase transition exists between the central densities of the\ntwo stars, so that the more massive star has a phase transition and the least\nmassive star does not, this correlation will be weakened. In all cases, a\nminimum Lambda for each neutron star mass is imposed by causality, and a less\nconservative limit is imposed by the unitary gas constraint, both of which we\ncompute. In order to make the best use of gravitational wave data from mergers,\nit is important to include the correlations relating the Lambdas and the masses\nas well as lower limits to the Lambdas as a function of mass. Focusing on the\ncase without strong phase transitions, and for mergers where the chirp mass\nM_chirp<1.4M_sun, which is the case for all observed double neutron star\nsystems where a total mass has been accurately measured, we show that the\ndimensionless Lambdas satisfy Lambda_1/Lambda_2= q^6, where q=M_2/M_1 is the\nbinary mass ratio; $M$ is mass of each star, respectively. Moreover, they are\nbounded by q^{n_-}>Lambda_1/Lambda_2> q^{n_{0+}+qn_{1+}}, where\nn_-<n_{0+}+qn_{1+}; the parameters depend only on M_chirp, which is accurately\ndetermined from the gravitational-wave signal. We also provide analytic\nexpressions for the wider bounds that exist in the case of a strong phase\ntransition. We argue that bounded ranges for Lambda_1/Lambda_2, tuned to\nM_chirp, together with lower bounds to Lambda(M), will be more useful in\ngravitational waveform modeling than other suggested approaches.\n

Context. Using parametric equations of state (relativistic polytropes and a simple quark bag model) to model dense-matter phase transitions, we study global, measurable astrophysical parameters of compact stars such as their allowed radii and tidal deformabilities. We also investigate the influence of stiffness of matter before the onset of the phase transitions on the parameters of the possible exotic dense phase. Aims. The aim of our study is to compare the parameter space of the dense matter equation of state permitting phase transitions to a sub-space compatible with current observational constraints such as the maximum observable mass, tidal deformabilities of neutron star mergers, radii of configurations before the onset of the phase transition, and to give predictions for future observations. Methods. We studied solutions of the Tolman-Oppenheimer-Volkoff equations for a flexible set of parametric equations of state, constructed using a realistic description of neutron-star crust (up to the nuclear saturation density), and relativistic polytropes connected by a density-jump phase transition to a simple bag model description of deconfined quark matter. Results. In order to be consistent with recent observations of massive neutron stars, a compact star with a strong high-mass phase transition cannot have a radius smaller than 12 km in the range of masses 1.2 − 1.6 M⊙. We also compare tidal deformabilities of stars with weak and strong phase transitions with the results of the GW170817 neutron star merger. Specifically, we study characteristic phase transition features in the Λ1 − Λ2 relation, and estimate the deviations of our results from the approximate formulæ for Λ∼ − R (M1) and Λ-compactness proposed in the literature. We find constraints on the hybrid equations of state to produce stable neutron stars on the twin branch. For the exemplary equations of state most of the high-mass twins occur for the minimum values of the density jump λ = 1.33 − 1.54; corresponding values of the square of the speed of sound are α = 0.7 − 0.37. We compare results with observations of gravitational waves and with the theoretical causal limit and find that the minimum radius of a twin branch is between 9.5 and 10.5 km, and depends on the phase transition baryon density. For these solutions the phase transition occurs below 0.56 fm−3.

The composition of neutron stars at the extreme densities reached in their cores is currently unknown. Besides nuclear matter of normal neutrons and protons, the cores of neutron stars might harbor exotic matter such as deconfined quarks. In this paper we study strong hadron-quark phase transitions in the context of gravitational wave observations of inspiraling neutron stars. We consider upcoming detections of neutron star coalescences and model the neutron star equations of state with phase transitions through the Constant-Speed-of-Sound parametrization. We use the fact that neutron star binaries with one or more hadron-quark hybrid stars can exhibit qualitatively different tidal properties than binaries with hadronic stars of the same mass, and hierarchically model the masses and tidal properties of simulated populations of binary neutron star inspiral signals. We explore the parameter space of phase transitions and discuss under which conditions future observations of binary neutron star inspirals can identify this effect and constrain its properties, in particular the threshold density at which the transition happens and the strength of the transition. We find that if the detected population of binary neutron stars contains both hadronic and hybrid stars, the onset mass and strength of a sufficiently strong phase transition can be constrained with 50-100 detections. If the detected neutron stars are exclusively hadronic or hybrid, then it is possible to place lower or upper limits on the transition density and strength.

We investigate 22 hadronic equations of state that incorporate the possibility of heavy baryon formation at sufficiently high densities, with the aim of establishing quasi-universal relations for both slowly and rapidly rotating neutron stars. The selected equations of state satisfy current observational constraints, such as those from NICER and GW170817. Our fitting results yield relations between various macroscopic quantities that are approximately independent of the underlying equation of state, with typical deviations on the order of 𝒪(10%) for neutron stars containing heavy baryonic degrees of freedom. The approximately universal I-Love-Q relations for slowly rotating neutron stars and the I-C-Q relations for rapidly rotating configurations are further extended to encompass very low-mass neutron stars, such as the central compact object in HESS J1731-347. To explore the influence of phase transitions on these relations, we construct an additional set of 100 hybrid equations of state, accounting for various features of the hadron-quark deconfinement transition. The macroscopic properties — such as masses, radii, and tidal deformabilities — of the resulting hybrid stars are found to be consistent with recent astrophysical observations. We further extend our analysis to establish quasi-universal relations for compact stars with more general core compositions, including nucleonic, heavy baryonic including entire baryon octet, and deconfined quark degrees of freedom. The possibility of the appearance of deconfined quark matter inside the core of low-mass neutron stars cannot be excluded from our EoS dataset. To this end, we derive relations among various macroscopic quantities using a comprehensive set consisting of 22 hadronic and 100 hybrid equations of state. Our results demonstrate that both the I-Love-Q relation for slowly rotating stars and the I-C-Q relation for rapidly rotating compact stars remain approximately universal. We observe that diverse core compositions degrade the quasi-universal behaviour, introducing variability of up to ≲ 𝒪(20%). These results highlight the robustness and limitations of universal relations when extended to compact stars with diverse internal compositions and rotational profiles.

In agreement with the constantly increasing gravitational wave events, new aspects of the internal structure of compact stars can be considered. A scenario in which a first order transition takes place inside these stars is of particular interest as it can lead, under conditions, to a third gravitationally stable branch (besides white dwarfs and neutron stars), the twin stars. The new branch yields stars with the same mass as normal compact stars but quite different radii. In the present work, we focus on hybrid stars undergone a hadron to quark phase transition near their core and how this new stable configuration arises. Emphasis is to be given on the aspects of the phase transition and its parametrization in two different ways, namely with Maxwell and Gibbs construction. We systematically study the gravitational mass, the radius, and the tidal deformability, and we compare them with the predictions of the recent observation by LIGO/VIRGO collaboration, the GW170817 event, along with the mass and radius limits, suggesting possible robust constraints. Moreover, we extent the study in order to include rotation effects on the twin stars configurations. The recent discovery of the fast rotating supermassive pulsar PSR J0952-0607 triggered the effort to constrain the equation of state and moreover to examine possible predictions related to the phase transition in dense nuclear matter. We pay special attention to relate the PSR J0952-0607 pulsar properties with the twin stars predictions and mainly to explore the possibility that the existence of such a massive object would rule out the existence of twin stars. Finally, we discuss the constraints on the radius and mass of the recently observed compact object within the supernova remnant HESS J1731-347. The estimations implies that this object is either the lightest neutron star known, or a star with a more exotic equation of state.

Once further confirmed in future analyses, the radius and mass measurement of HESS J1731-347 with and will be among the lightest and smallest compact objects ever detected. This raises many questions about its nature and opens up the window for different theories to explain such a measurement. In this article, we use the information from Doroshenko et al. on the mass, radius, and surface temperature together with the multimessenger observations of neutron stars to investigate the possibility that HESS J1731-347 is one of the lightest observed neutron star, a strange quark star, a hybrid star with an early deconfinement phase transition, or a dark matter–admixed neutron star. The nucleonic and quark matter are modeled within realistic equation of states (EOSs) with a self-consistent calculation of the pairing gaps in quark matter. By performing the joint analysis of the thermal evolution and mass–radius constraint, we find evidence that within a 1σ confidence level, HESS J1731-347 is consistent with the neutron star scenario with the soft EOS as well as with a strange and hybrid star with the early deconfinement phase transition with a strong quark pairing and neutron star admixed with dark matter.

We explore the implications of a strong first-order phase transition region in the dense matter equation of state in the interiors of rotating neutron stars, and the resulting creation of two disjoint families of neutron-star configurations (the so-called high-mass twins). We numerically obtained rotating, axisymmetric, and stationary stellar configurations in the framework of general relativity, and studied their global parameters and stability. The instability induced by the equation of state divides stable neutron star configurations into two disjoint families: neutron stars (second family) and hybrid stars (third family), with an overlapping region in mass, the high-mass twin-star region. These two regions are divided by an instability strip. Its existence has interesting astrophysical consequences for rotating neutron stars. We note that it provides a natural explanation for the rotational frequency cutoff in the observed distribution of neutron star spins, and for the apparent lack of back-bending in pulsar timing. It also straightforwardly enables a substantial energy release in a mini-collapse to another neutron-star configuration (core quake), or to a black hole.

We study current bounds on strong first-order phase transitions (PTs) along the equation of state (EOS) of dense strongly interacting matter in neutron stars, under the simplifying assumption that on either side of the PT, the EOS can be approximated by a simple polytropic form. We construct a large ensemble of possible EOSs of this form, anchor them to chiral effective field theory calculations at nuclear density and perturbative Quantum Chromodynamics at high densities, and subject them to astrophysical constraints from high-mass pulsars and gravitational-wave observations. Within this setup, we find that a PT permits neutron-star solutions with larger radii, but only if the transition begins below twice nuclear saturation density. We also identify a large parameter space of allowed PTs currently unexplored by numerical-relativity studies. Additionally, we locate a small region of parameter space allowing twin-star solutions, though we find them to only marginally pass the current astrophysical constraints. Finally, we find that sizeable cores of high-density matter beyond the PT may be located in the centers of some stable neutron stars, primarily those with larger masses.

Electromagnetic (EM) observations and gravitational wave (GW) measurements enable us to determine the mass and radius of neutron stars (NSs) and their tidal deformability, respectively. These parameters offer valuable insights into the properties of dense matter in NSs. In this study, the vector-interaction-enhanced bag model (vBag model) is employed to investigate strange and hybrid stars’ properties. The parameters of the vBag model are constrained using multi-messenger observations, revealing that strange stars are incompatible with current observations. In contrast, hybrid stars can exhibit a substantial mixed phase region and a thin hadronic shell. Furthermore, we present the frequencies and damping time of fundamental mode (f-mode) oscillations of hybrid stars and test their universal relations with compactness and tidal deformability. The findings indicate that the presence of mixed phase components leads to larger frequencies and shorter damping time of the f-mode oscillation of hybrid stars, and the softer equation of state (EoS) affects this behavior more significantly. The universal relations of hybrid stars in the vBag model can be described by fourth-order/seventh-order polynomials, which do not break the previous results.

A class of hybrid compact star equations of state is investigated that joins by a Maxwell construction a low-density phase of hadronic matter, modeled by a relativistic meanfield approach with excluded nucleon volume, with a high-density phase of color superconducting two-flavor quark matter, described within a nonlocal covariant chiral quark model. We find the conditions on the vector meson coupling in the quark model under which a stable branch of hybrid compact stars occurs in the cases with and without diquark condensation. We show that these hybrid stars do not form a third family disconnected from the second family of ordinary neutron stars unless additional (de)confining effects are introduced with a density-dependent bag pressure. A suitably chosen density dependence of the vector meson coupling assures that at the same time the $2~$M$_\odot$ maximum mass constraint is fulfilled on the hybrid star branch. A twofold interpolation method is realized which implements both, the density dependence of a confining bag pressure at the onset of the hadron-to-quark matter transition as well as the stiffening of quark matter at higher densities by a density-dependent vector meson coupling. For three parametrizations of this class of hybrid equation of state the properties of corresponding compact star sequences are presented, including mass twins of neutron and hybrid stars at 2.00, 1.39 and 1.20 $M_\odot$, respectively. The sensitivity of the hybrid equation of state and the corresponding compact star sequences to variations of the interpolation parameters at the 10% level is investigated and it is found that the feature of third family solutions for compact stars is robust against such a variation. This advanced description of hybrid star matter allows to interpret GW170817 as a merger not only of two neutron stars but also of a neutron star with a hybrid star or of two hybrid stars.

At supranuclear densities, explored in the core of neutron stars, a strong phase transition from hadronic matter to more exotic forms of matter might be present. To test this hypothesis, binary neutron-star mergers offer a unique possibility to probe matter at densities that we can not create in any existing terrestrial experiment. In this work, we show that, if present, strong phase transitions can have a measurable imprint on the binary neutron-star coalescence and the emitted gravitational-wave signal. We construct a new parameterization of the supranuclear equation of state that allows us to test for the existence of a strong phase transition and extract its characteristic properties purely from the gravitational-wave signal of the inspiraling neutron stars. We test our approach using a Bayesian inference study simulating 600 signals with three different equations of state and find that for current gravitational-wave detector networks already twelve events might be sufficient to verify the presence of a strong phase transition. Finally, we use our methodology to analyze GW170817 and GW190425, but do not find any indication that a strong phase transition is present at densities probed during the inspiral.

Gravitational wave (GW) detections of binary neutron star inspirals will be crucial for constraining the dense matter equation of state (EOS). We demonstrate a new degeneracy in the mapping from tidal deformability data to the EOS, which occurs for models with strong phase transitions. We find that there exists a new family of EOS with phase transitions that set in at different densities and that predict neutron star radii that differ by up to ∼500 m but that produce nearly identical tidal deformabilities for all neutron star masses. Next-generation GW detectors and advances in nuclear theory may be needed to resolve this degeneracy.

Taking on a new perspective of the electroweak phase transition, we investigate in detail the role played by the depth of the electroweak minimum ("vacuum energy difference"). We find a strong correlation between the vacuum energy difference and the strength of the phase transition. This correlation only breaks down if a negative eigenvalue develops upon thermal corrections in the squared scalar mass matrix in the broken vacuum before the critical temperature. As a result the scalar fields slide across field space toward the symmetric vacuum, often causing a significantly weakened phase transition. Phenomenological constraints are found to strongly disfavour such sliding scalar scenarios. For several popular models, we suggest numerical bounds that guarantee a strong first order electroweak phase transition. The zero temperature phenomenology can then be studied in these parameter regions without the need for any finite temperature calculations. For almost all non-supersymmetric models with phenomenologically viable parameter points, we find a strong phase transition is guaranteed if the vacuum energy difference is greater than $-8.8\times 10^7$~\text{GeV}$^4$. For the GNMSSM, we guarantee a strong phase transition for phenomenologically viable parameter points if the vacuum energy difference is greater than $-6.9\times 10^7$~\text{GeV}$^4$. Alternatively, we capture more of the parameter space exhibiting a strong phase transition if we impose a simultaneous bound on the vacuum energy difference and the singlet mass.

Neutron stars are born when massive stars run out of their nuclear fuel and undergo gravitational collapse. Neutron stars belong to the most compact objects in the observable Universe. Macroscopic properties of neutron stars like their masses and radii are sensitive to the microscopic properties of the nuclear equation of state of dense matter. The equation of state is determined by the strong interaction among the constituents. The underlying theory is quantum chromodynamics that is, however, highly non-perturbative in the physics regime relevant for neutron stars. Moreover, neutron stars provide an interplay between nuclear physics and astrophysics. Astrophysical observations like the detection of 2 solar mass neutron stars have a major impact on the equation of state. Radii are, however, inherently difficult to measure due to systematic uncertainties. Other observables like the moment of inertia or the tidal deformability present promising alternatives. The double neutron star system PSR J0737-3039 constitutes an outstanding system as it provides the prospect of a moment of inertia measurement for the first time. A new era stated with the pioneering observation of gravitational waves from a binary neutron star merger. The analysis of the gravitational wave signal of GW170817 provides a range for the tidal deformability of typical neutron stars. Moreover, the current NICER mission will provide simultaneous mass-radius measurements. In this thesis, we use state-of-the-art chiral effective field theory interactions to describe the equation of state at nuclear densities. In the high-density regime beyond nuclear saturation density, we use different extrapolation approaches. First, we utilize the established ansatz of piecewise polytropic equations of state which provides a direct parametrization. However, piecewise polytropic equations of state possess unphysical behavior such as discontinuities in the speed of sound. Second, we use a physically motivated parametrization of the speed of sound inside the neutron star from which we derive the equation of state. Both methods allow us to probe the equation of state over a large range of densities. We further impose general constraints on the equation of state such as the requirement of causality at all densities and the support of at least 2 solar mass neutron stars. From the equations of state compatible with the constraints, we determine diverse neutron star observables. We begin with non-rotating neutron stars and focus on their masses and radii. We study correlations among properties of the equation of state at nuclear densities and observables of typical neutron stars. Moreover, we explore the impact of hypothetical, simultaneous measurements of masses and radii of neutron stars on the equation of state. Applying both simple compatibility cuts and the framework of Bayesian statistics, we investigate the sensitivity of the inference on the chosen parametrization of the equation of state. We extend then our considerations to slowly rotating neutron stars and study the moment of inertia. Assuming hypothetical moment of inertia measurements, we determine constraints for the radius of neutron stars and thus the equation of state. In addition, we extend our considerations of isolated neutron stars to binary neutron star systems. In particular, we treat the tidal field of the companion as a small perturbation. This allows us to determine the tidal deformability. By applying higher orders in the metric perturbation, we calculate the quadrupole moment of neutron stars. Although the structure of neutron stars is sensitive to the equation of state, relations between the moment of inertia, the tidal deformability, and the quadrupole moment are remarkably insensitive. We investigate the properties of neutron stars in binary systems and ultimately confront the results of our models with the gravitational wave constraints from a binary neutron star merger.