Probing strange dark matter through f-mode oscillations of neutron stars with hyperons and quark matter

Context. The presence of dark matter in neutron stars is of growing interest due to its potential impact on the structure and observable properties of these objects. Among the various candidates, the hypothetical sexaquark has emerged as a promising bosonic dark matter particle, potentially forming under extreme conditions in neutron star cores. Aims. We investigate whether a hybrid neutron star model that includes hyperons, bosonic dark matter (in the form of sexaquarks), and deconfined quark matter can satisfy all current observational constraints. We particularly focus on identifying the range of sexaquark masses consistent with mass-radius measurements and the tidal deformability limit. Methods. We used the DD2Y-T model for the hadronic phase, which includes hyperons, and a nonlocal Nambu–Jona-Lasinio model for the deconfined quark phase. The phase transition was modeled as a smooth crossover using the replacement interpolation construction method. Sexaquark-baryon interactions were introduced via an effective mass shift representing repulsion. We incorporated the full set of current observational data, including NICER measurements of PSRs J0437–4715 and newly published J0614–3329 data, and performed a Bayesian analysis to constrain the sexaquark mass. Results. Our results show that the presence of the sexaquark softens the equation of state, enabling the hybrid model to satisfy both the radius and tidal deformability constraints around the canonical 1.4,M_⊙ neutron stars. We find that hybrid EOSs with a sexaquark mass around 1900 MeV are in agreement with all available constraints, including those from HESS J1731–347 and PSR J0952–0607, which represent the lowest and highest mass neutron stars observed to date. The Bayesian analysis favors a sexaquark mass range of 1885–1935 MeV, supporting the potential relevance of this exotic particle in neutron star interiors.

We investigate the behavior of the prominent non-radial fundamental f-mode oscillations of dark matter (DM) admixed strange quark stars (DMSQSs), by adopting an equation of state (EoS) developed in Ref. Sen and Guha (Mon Not R Astron Soc 517:518, 2022. https://doi.org/10.1093/mnras/stac2675), which considers the possible presence of feebly interacting DM in strange quark stars (SQSs) for the first time. Within the model, feeble interaction between fermionic DM χ and strange quark matter (SQM) is invoked via a vector new physics mediator ξ with coupling strength yξ. The pure SQM is described by the vector MIT Bag model. By varying different EoS parameters, the structural properties viz. the mass, radius and tidal deformability (Λ) of the DMSQSs are studied with respect to various astrophysical constraints. We study in detail the f-mode spectra within the Cowling approximation by obtaining the frequencies as a function of mass, compactness and Λ of the star. To the best of our knowledge, this study represents the first analysis of non-radial f-mode oscillations of DMSQSs. Our investigation indicates that the presence of DM and its interaction with SQM has great impact on the f-modes. We show that the f-mode frequencies are larger for DMSQSs, which are largely populated with massive DM fermions, compared to the SQSs. Further, we obtain a linear empirical relation between the f-modes and the average density of the star. We also find that the mass-scaled angular frequency varies universally with compactness and lnΛ for DMSQSs. Further, our studies indicate that the inclusion of DM in compact stars reduces the deviation of f-mode frequency from general relativistic to Cowling approximation.

We investigate the probable existence of dark matter in the interior of neutron stars. Despite the current state of knowledge, the observational properties of neutron stars have not definitively ruled out the possibility of dark matter. Our research endeavors to shed light on this intriguing mystery by examining how certain neutron star properties, including mass, radius, and tidal deformability, might serve as constraints for the dark matter model. In our investigation, we adopt a two-fluid approach to calculate the properties of neutron stars. For the nuclear matter equation-of-state (EOS), we employ several realistic EOS derived from the relativistic mean field model (RMF), each exhibiting varying stiffness and composition. In parallel, we look into the dark matter EOS, considering fermionic matter with repulsive interaction described by a relativistic mean field Lagrangian. A reasonable range of parameters is sampled meticulously. Our study primarily focuses on exploring correlations between the dark matter model parameters and different neutron star properties using a rich set of EOSs. Interestingly, our results reveal a promising correlation between the dark matter model parameters and stellar properties, particularly when we ignore the uncertainties in the nuclear matter EOS. However, when introducing uncertainties in the nuclear sector, the correlation weakens, suggesting that the task of conclusively constraining any particular dark matter model might be challenging using global properties alone, such as mass, radius, and tidal deformability. Notably, we find that dark-matter admixed stars tend to have higher central baryonic density, potentially allowing for non-nucleonic degrees of freedom or direct Urca processes in stars with lower masses. There is also a tantalizing hint regarding the detection of stars with the same mass but different surface temperatures, which may indicate the presence of dark matter. With our robust and extensive dataset, we delve deeper and demonstrate that even in the presence of dark matter, the semiuniversal C-Love relation remains intact. This captivating finding adds another layer of complexity to the interplay between dark matter and neutron star properties. Published by the American Physical Society 2024

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.

Because of their extreme densities and consequently, gravitational potential, compact objects such as neutron stars can prove to be excellent captors of dark matter particles. Considering purely gravitational interactions between dark and hadronic matter, we construct dark matter admixed stars composed of two-fluid matter subject to current astrophysical constraints on maximum mass and tidal deformability. We choose a wide range of parameters to construct the dark matter equation of state, and the DDME2 parameterization for the hadronic equation of state. We then examine the effect of dark matter on the stellar structure, tidal deformability and non-radial modes considering the relativistic Cowling approximation. We find the effect on p-modes is substantial, with frequencies decreasing up to the typical f-mode frequency range for most stars with a dark matter halo. The effects on the f-mode frequency are less extreme. Finally, we find the most probable values of the dark matter parameters that satisfy the observational constraints.

This work studies the influence of scalar dark matter on the structural properties of strange quark stars (SQS) within a one-fluid framework, considering Yukawa interactions between dark matter and quark matter. Contributions from perturbative QCD, Yukawa interaction between scalar dark matter and quarks, and Bose-Einstein condensation of dark matter are included in the model. We first determine the allowable range of Yukawa interaction coupling by imposing the stability condition for strange quark matter (SQM). Using this range, we derive the equation of state (EOS) for different fractions of dark matter within the total pressure of SQS. These fractions are constrained by the tidal deformability limit from GW170817. The presence of dark matter alters the EOS, leading to changes in the mass–radius relationship, tidal deformability, and stability of SQS. We demonstrate that increasing the mass of dark matter softens the EOS, whereas higher fractions of dark matter lead to stiffer EOSs. We also explore the reasons behind this behavior. Our EOSs not only describe massive objects, such as PSR J0952-0607 and PSR J2215+5135, but also satisfy the tidal deformability constraint from GW170817. These results reveal that incorporating dark matter modifies the EOS, enabling the support of higher stellar masses while maintaining consistency with observational data.

Within a minimum model for neutron stars consisting of nucleons, electrons\nand muons at $\\beta$-equilibrium using about a dozen Equation of States (EOSs)\nfrom microscopic nuclear many-body theories and 40,000 EOSs randomly generated\nusing an explicitly isospin-dependent parametric EOS model for high-density\nneutron-rich nucleonic matter within its currently known uncertainty range, we\nstudy correlations among the f-mode frequency, its damping time and the tidal\ndeformability as well as the compactness of neutron stars. Except for quark\nstars, both the f-mode frequency and damping time of canonical neutron stars\nare found to scale with the tidal deformability independent of the EOSs used.\nApplying the constraint on the tidal deformability of canonical neutron stars\n$\\Lambda_{1.4}=190^{+390}_{-120}$ extracted by the LIGO+VIRGO Collaborations\nfrom their improved analyses of the GW170817 event, the f-mode frequency and\nits damping time of canonical neutron stars are limited to 1.67 kHz - 2.18 kHz\nand 0.155 s - 0.255 s, respectively, providing a useful guidance for the\nongoing search for gravitational waves from the f-mode oscillations of isolated\nneutron stars. Moreover, assuming either or both the f-mode frequency and its\ndamping time will be measured precisely in future observations with advanced\ngravitational wave detectors, we discuss how information about the mass and/or\nradius as well as the still rather elusive nuclear symmetry energies at\nsupra-saturation densities may be extracted.\n

We study radial oscillations of hybrid neutron stars composed of hadronic external layers followed by a quark matter core. We employ a density-dependent relativistic mean-field model including hyperons and Δ baryons to describe hadronic matter, and a density-dependent quark model for quark matter. We obtain the ten lowest eigenfrequencies and the corresponding oscillation functions of N, N+Δ, N+H, and N+H+Δ equations-of-state with a phase transition to the quark matter at 1.4 and 1.8 M ⊙, focusing on the effects of a slow phase transition at the hadron-quark interface. We observe that the maximum mass is reached before the fundamental mode's frequency vanishes for slow phase transitions, suggesting that some stellar configurations with higher central densities than the maximum mass remain stable even when they undergo small radial perturbations. Future gravitational wave detectors and multi-messenger astronomy, complemented by robust microscopic models enabling exploration of various neutron star compositions, including hyperon content, are anticipated to impose precise limitations on the equation of state of baryonic matter under high-density conditions.

We propose a dark-matter (DM) admixed density-dependent equation of state where the fermionic DM interacts with the nucleons via Higgs portal. Presence of DM can hardly influence the particle distribution inside neutron star (NS) but can significantly affect the structure as well as equation of state (EOS) of NS. Introduction of DM inside NS softens the equation of state. We explored the effect of variation of DM mass and DM Fermi momentum on the NS EOS. Moreover, DM-Higgs coupling is constrained using dark matter direct detection experiments. Then, we studied cooling of normal NSs using APR and DD2 EOSs and DM admixed NSs using dark-matter modified DD2 with varying DM mass and Fermi momentum. We have done our analysis by considering different NS masses. Also DM mass and DM Fermi momentum are varied for fixed NS mass and DM-Higgs coupling. We calculated the variations of luminosity and temperature of NS with time for all EOSs considered in our work and then compared our calculations with the observed astronomical cooling data of pulsars namely Cas A, RX J0822-43, 1E 1207-52, RX J0002+62, XMMU J17328, PSR B1706-44, Vela, PSR B2334+61, PSR B0656+14, Geminga, PSR B1055-52 and RX J0720.4-3125. It is found that APR EOS agrees well with the pulsar data for lighter and medium mass NSs but cooling is very fast for heavier NS. For DM admixed DD2 EOS, it is found that for all considered NS masses, all chosen DM masses and Fermi momenta agree well with the observational data of PSR B0656+14, Geminga, Vela, PSR B1706-44 and PSR B2334+61. Cooling becomes faster as compared to normal NSs in case of increasing DM mass and Fermi momenta. It is infered from the calculations that if low mass super cold NSs are observed in future that may support the fact that heavier WIMP can be present inside neutron stars.

Constraining mirror dark matter inside neutron stars

We systematically investigate f-mode oscillations (ℓ = 2) in quarkyonic neutron stars with dark matter, employing the Cowling approximation within the framework of linearized general relativity. The relativistic mean-field approach is used to compute various macroscopic properties of neutron stars. The analysis focuses on three key free parameters in the model: transition density, QCD confinement scale, and dark matter (DM) Fermi momentum, all of which significantly affect the properties of f-mode oscillations. The inclusion of dark matter in quarkyonic equations of state leads to notable variations in f-mode frequencies. Despite these changes, several universal relations among the oscillation properties are found to hold, demonstrating their robustness in the presence of dark matter. Motivation: our model is distinct in that it incorporates quarkyonic matter composed of up and down quarks, which exists in beta equilibrium with neutron star matter, i.e., this model is a combination of the quarkyonic degrees of freedom, the E-RMF framework, and the inclusion of the Fermionic dark matter. To our knowledge, no such unique model exists in the literature. Please note that the development of the model is recently published in JCAP [1], and the present work is an application to f-mode calculations of neutron stars. Understanding the oscillation properties within such a composition provides crucial insights into the possible existence and behavior of quarkyonic matter in neutron stars. This model is a viable alternative to explain the mysterious secondary object present in the recent GW190814 multi-messenger event [2].

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.

We describe two fitting schemes that aim to represent the high-density part of realistic equations of state for numerical simulations such as neutron star oscillations. The low-density part of the equation of state is represented by an arbitrary polytropic crust, and we propose a generic procedure to stitch any desired crust to the high-density fit, which is performed to ensure continuity of the internal energy, pressure, and sound speed for barotropic equations of state that describe cold neutron stars in $\ensuremath{\beta}$ equilibrium. An extension of the fitting schemes to equations of state with an additional compositional argument is proposed. In particular we develop a formalism that ensures the existence of a $\ensuremath{\beta}$ equilibrium at low densities. An additional feature of this low-density model is that it can be, in principle, applied to any parametrization. The performance of the fits is checked on mass, radius and tidal deformability as well as on the dynamical radial oscillation frequencies. To that end, we use a pseudospectral single neutron star evolution code based on a nonconservative form of the hydrodynamical equations. A comparison to existing parametrizations is proposed, as far as possible, and to published radial frequency values in the literature. The static and dynamic quantities are well reproduced by the fitting schemes. Our results suggest that, even though the radius is very sensitive to the choice of the crust, this choice has little influence on the oscillation frequencies of a neutron star.

For a new parameterization of the modified effective chiral model, developed primarily to regulate the density content of the symmetry energy and its higher order terms, equations of state (EoSs) for hyperon-rich matter (H) and delta baryon matter (Δ) were obtained. The models were used to investigate the emission of gravitational waves (GWs) through f-mode oscillations in the corresponding neutron stars. We obtained the stellar structure, f-mode frequency and tidal deformability Λ for our models. We report that the Δ EoS is stiffer compared to the H EoS. We also analyzed the velocity of sound in these media. The corresponding mass–radius relationships were obtained and compared with various observations. We studied the dependence of f-mode frequencies on the stellar mass, redshift and tidal deformability. We employed the well known Cowling approximation to obtain the f-mode frequencies for l=2,3 and 4 modes of oscillation. We found that the f-mode frequencies of the H and Δ EoSs were almost the same in the lower mass region, while we observed a substantial difference between them in the high-mass region. We also obtained an empirical relation for the EoSs considered. The various attributes obtained for our models showed close agreement with various observational constraints from pulsars and GW events.

Dark matter (DM) continues to evade direct detection, but neutron stars (NSs) serve as natural laboratories where even a modest DM component can alter their structure. While many studies have examined DM effects on NSs, they often rely on specific choices of equations of state (EOS) models, assume isotropy, and lack a Bayesian statistical framework, limiting their predictive power. In this work, we present a Bayesian framework that couples pressure-anisotropic nuclear EOS to a self-interacting fermionic DM component, constrained by NICER and GW170817 data. Our results show that DM mass fractions up to $\ensuremath{\sim}10%$ remain consistent with current data, which softens the high-density EOS, leading to reduced stellar radii and tidal deformabilities while requiring negligible pressure anisotropy. Bayesian model comparison reveals no statistically significant preference between pure baryonic and DM-admixed NSs, indicating that DM inclusion enhances physical realism without complexity penalties. However, existing data cannot tightly constrain the DM parameters, and our empirical radius definition introduces a systematic bias toward the DM core configurations. To address this, we therefore introduce the DM radius span $\mathrm{\ensuremath{\Delta}}{R}_{\ensuremath{\chi}}\ensuremath{\equiv}{R}_{\ensuremath{\chi},\mathrm{max}}\ensuremath{-}{R}_{\ensuremath{\chi},\mathrm{min}}$ as a unified diagnostic for DM distributions. This parameter simultaneously characterizes core-halo transition features while exhibiting strong linear correlations ($\mathrm{\ensuremath{\Delta}}{R}_{\ensuremath{\chi}}<4\text{ }\text{ }\mathrm{km}$) with both DM and baryonic parameters, providing a clear avenue for future constraints. Our approach bridges current limitations and future potential in probing DM through compact star observations.