We explore in a parameterized manner a very large range of physically plausible equations of state (EOSs) for compact stars for matter that is either purely hadronic or that exhibits a phase transition. In particular, we produce two classes of EOSs with and without phase transitions, each containing one million EOSs. We then impose constraints on the maximum mass, ($M < 2.16 M_{\odot}$), and on the dimensionless tidal deformability ($\tildeΛ <800$) deduced from GW170817, together with recent suggestions of lower limits on $\tildeΛ$. Exploiting more than $10^9$ equilibrium models for each class of EOSs, we produce distribution functions of all the stellar properties and determine, among other quantities, the radius that is statistically most probable for any value of the stellar mass. In this way, we deduce that the radius of a purely hadronic neutron star with a representative mass of $1.4\,M_{\odot}$ is constrained to be $12.00\!<\!R_{1.4}/{\rm km}\!<\!13.45$ at a $2$-$σ$ confidence level, with a most likely value of $\bar{R}_{1.4}=12.39\,{\rm km}$; similarly, the smallest dimensionless tidal deformability is $\tildeΛ_{1.4}\!>\!375$, again at a $2$-$σ$ level. On the other hand, because EOSs with a phase transition allow for very compact stars on the so-called `twin-star' branch, small radii are possible with such EOSs although not probable, i.e. $8.53\!<\!R_{1.4}/{\rm km}\!<\!13.74$ and $\bar{R}_{1.4}=13.06\,{\rm km}$ at a $2$-$σ$ level, with $\tildeΛ_{1.4}\!>\!35.5$ at a $3$-$σ$ level. Finally, since these EOSs exhibit upper limits on $\tildeΛ$, the detection of a binary with total mass of $3.4\,M_{\odot}$ and $\tildeΛ_{1.7}\!>\!461$ can rule out twin-star solutions.
Using a Bayesian approach, we combine measurements of neutron star macroscopic observables obtained by astrophysical and gravitational observations, to derive joint constraints on the equation of state (EoS) of matter at supranuclear density. In our analysis we use two sets of data: (i) the masses and tidal deformabilities measured in the binary neutron star event GW170817, detected by LIGO and Virgo; (ii) the masses and stellar radii measured from observations of nuclear bursts in accreting low-mass X-ray binaries. Using two different parametrizations of the equation of state, we compute the …
We use gravitational-wave observations of the binary neutron star merger GW170817 to explore the tidal deformabilities and radii of neutron stars. We perform Bayesian parameter estimation with the source location and distance informed by electromagnetic observations. We also assume that the two stars have the same equation of state; we demonstrate that for stars with masses comparable to the component masses of GW170817, this is effectively implemented by assuming that the stars' dimensionless tidal deformabilities are determined by the binary's mass ratio $q$ by $Λ_1/Λ_2 = q^6$. We investigat…
Gravitational-wave observations in the near future may allow us to measure tidal deformabilities of neutron stars, which leads us to the understanding of physics at nuclear density. In principle, the gravitational waveform depends on various tidal parameters, which correlate strongly. Therefore, it would be useful if one can express such tidal parameters with a single parameter. Here, we report on universal relations among various $\ell$-th (dimensionless) electric, magnetic and shape tidal deformabilities in neutron stars and quark stars that do not depend sensitively on the equation of state…
One of largest uncertainties in nuclear physics is the relation between the pressure and density of supranuclear matter: the equation of state. Some of this uncertainty may be removed through future gravitational wave observations of neutron star binaries by extracting the tidal deformabilities (or Love numbers) of neutron stars. Previous studies showed that only a certain combination of the individual deformabilities of each body (chirp tidal deformability) can be measured with second-generation gravitational wave interferometers, such as Adv. LIGO, due to correlations between the individual …
Equation of state (EOS) insensitive relations, so-called universal relations, between the neutron star (NS) compactness, its multipolar tidal deformability coefficients, and between the tidal parameters for binary systems are essential to break degeneracies in gravitational wave data analysis. Here, we validate and recalibrate these universal relations using a large set of almost 2 million phenomenological EOSs that are consistent with current observations. In doing so, we extend universal relations to a larger region of the EOS parameter space, most notably to softer EOSs and larger compactne…
When in a tight binary, the mutual tidal deformations of neutron stars imprint onto observables, encoding information about their internal structure at supranuclear densities and gravity in the extreme-gravity regime. Gravitational wave observations of their late binary inspiral may serve as a tool to extract the individual tidal deformabilities, but this is made difficult by degeneracies between them in the gravitational wave model. We here resolve this problem by discovering approximately universal relations between dimensionless combinations of the individual tidal deformabilities. We show …
Finite size effects in a neutron star merger are manifested, at leading order, through the tidal deformabilities (Lambdas) of the stars. If strong first-order phase transitions do not exist within neutron stars, both neutron stars are described by the same equation of state, and their Lambdas are highly correlated through their masses even if the equation of state is unknown. If, however, a strong phase transition exists between the central densities of the two stars, so that the more massive star has a phase transition and the least massive star does not, this correlation will be weakened. In…
Neutron star equations of state with strong phase transitions may support twin stars, hybrid and hadronic stars with the same mass but different tidal deformabilities. The presence of twin stars in the population of merging neutron stars produces distinctive gaps in the joint distribution of binary tidal deformabilities and chirp masses. We analyze a simulated population of binary neutron star mergers recovered with a network of next-generation (XG) ground-based gravitational-wave detectors to determine how many observations are needed to infer, or rule out, the existence of twin stars. Using …
Tidal deformations of general-relativistic multifluid compact stars
Institute of Astronomy and Astrophysics, Université Libre de Bruxelles（布鲁塞尔自由大学天体物理与天文学研究所）；Brussels Laboratory of the Universe（布鲁塞尔宇宙实验室）；Leuven Gravity Institute, KU Leuven（荷语鲁汶大学引力研究所）
The spacetime surrounding compact objects such as neutron stars and black holes provides an excellent place to study gravity in the strong, non-linear, dynamical regime. Here, the effects of strong curvature can leave their imprint on observables which we may use to study gravity. Recently, NICER provided a mass and radius measurement of an isolated neutron star using x-rays, while LIGO/Virgo measured the tidal deformability of neutron stars through gravitational waves. These measurements can be used to test the relation between the tidal deformability and compactness of neutron stars that are…
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. 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 suc…
In this paper we present a new approach to the inverse problem for relativistic stars using the piecewise polytropic parametrization of the equation of state. The algorithm is a piecewise polytropic meshing and refinement method that reconstructs the neutron star equation of state from experimental data of the mass and the tidal Love parameter. We use an initial mesh of 65536 equations of state in a 4-volume of piecewise polytropic parameters that contains most of the candidate equations of state used today. The refinement process drives us to the reconstruction of the equation of state with a…
Gravitational wave measurements of binary neutron star coalescences offer information about the properties of the extreme matter that comprises the stars. Despite our expectation that all neutron stars in the Universe obey the same equation of state, i.e. the properties of the matter that forms them are universal, current tidal inference analyses treat the two bodies as independent. We present a method to measure the effect of tidal interactions in the gravitational wave signal -- and hence constrain the equation of state -- that assumes that the two binary components obey the same equation of…
The gravitational wave emission from the merging binary neutron star system GW170817 arrived full of tidal information which can be used to probe the fundamental ultra-dense nuclear physics residing in these stars. In previous work, we used two-dimensional correlations between nuclear matter parameters and tidal deformabilities of neutron stars applying specifically to GW170817 to derive constraints on the former. Here, we extend this analysis by finding similar correlations for varying chirp masses, the dominant determining factor in the frequency evolution of the inspiral, such that one can …
LIGO and Virgo have recently observed a number of gravitational wave (GW) signals that are fully consistent with being emitted by binary black holes described by general relativity. However, there are theoretical proposals of exotic objects that can be massive and compact enough to be easily confused with black holes. Nevertheless, these objects differ from black holes in having nonzero tidal deformabilities, which can allow one to distinguish binaries containing such objects from binary black holes using GW observations. Using full Bayesian parameter estimation, we investigate the possibility…
If a phase transition is allowed to take place in the core of a compact star, a new stable branch of equilibrium configurations can appear, providing solutions with the same mass as the purely hadronic branch and hence giving rise to twin-star configurations. We perform an extensive analysis of the features of the phase transition leading twin-star configurations and, at the same time, fulfilling the constraints coming from the maximum mass of $2M_\odot$ and the information following gravitational-wave event GW170817. In particular, we use a general equation of state for the neutron-star matte…
The thermodynamic relation between pressure and density (i.e. the equation of state) of cold supranuclear matter is critical in describing neutron stars, yet it remains one of the largest uncertainties in nuclear physics. The extraction of tidal deformabilities from the gravitational waves emitted in the coalescence of neutron star binaries, such as GW170817, is a promising tool to probe this thermodynamic relation. Equation-of-state insensitive relations between symmetric and antisymmetric combinations of individual tidal deformabilities, the so-called "binary Love relations", have proven imp…
Gravitational wave detectors in the LIGO/Virgo frequency band are able to measure the individual masses and the composite tidal deformabilities of neutron-star binary systems. This paper demonstrates that high accuracy measurements of these quantities from an ensemble of binary systems can in principle be used to determine the high density neutron-star equation of state exactly. This analysis assumes that all neutron stars have the same thermodynamically stable equation of state, but does not use simplifying approximations for the composite tidal deformability or make additional assumptions ab…
We construct new, multivariate empirical relations for measuring neutron star radii and tidal deformabilities from the dominant gravitational wave frequency in the post-merger phase of binary neutron star mergers. The relations determine neutron star radii and tidal deformabilities for specific neutron star masses with consistent accuracy and depend only on two observables: the post-merger peak frequency $f_{\rm peak}$ and the chirp mass $M_{\rm chirp}$. The former could be measured with good accuracy from gravitational waves emitted in the post-merger phase using next-generation detectors, wh…
The inverse stellar structure problem determines the equation of state of the matter in stars from a knowledge of their macroscopic observables (e.g. their masses and radii). This problem was solved in a previous paper by constructing a spectral representation of the equation of state whose stellar models match a prescribed set of macroscopic observables. This paper improves and extends that work in two significant ways: i) The method is made more robust by accounting for an unexpected feature of the enthalpy based representations of the equations of state used in this work. After making the a…
Analyses that connect astrophysical observations of neutron stars with nuclear matter properties sometimes rely on equation-of-state insensitive relations. We show that the slope of the binary Love relations (i.e.~between the tidal deformabilities of binary neutron stars) encodes the rate of change of the nuclear matter speed of sound below three times nuclear saturation density. Twin stars lead to relations that present a signature ''hill'', ''drop'', and ''swoosh'' due to the second (mass-radius) stable branch, requiring a new description of the binary love relations.
Thermodynamic Consistent Description of Compact Stars of Two Interacting Fluids: The Case of Neutron Stars with Higgs Portal Dark Matter
University of Oklahoma（俄克拉荷马大学）；Goethe Universität Frankfurt（法兰克福歌德大学）；Institute of Space Sciences, Campus UAB（空间科学研究所（UAB校区））；Institut d’Estudis Espacials de Catalunya（加泰罗尼亚空间研究学院）；Frankfurt Institute for Advanced Studies（法兰克福高等研究院）
We investigate a simple holographic model for cold and dense deconfined QCD matter consisting of three quark flavors. Varying the single free parameter of the model and utilizing a Chiral Effective Theory equation of state (EoS) for nuclear matter, we find four different compact star solutions: traditional neutron stars, strange quark stars, as well as two non-standard solutions we refer to as hybrid stars of the second and third kind (HS2 and HS3). The HS2s are composed of a nuclear matter core and a crust made of stable strange quark matter, while the HS3s have both a quark mantle and a nucl…
Properties of neutron stars in GW170817 are investigated using different equations of state (EoS) involving nucleons, $Λ$ hyperons, quarks resulting in $2M_{\odot}$ neutron stars. This calculation is performed using the same EoS for merger components and for low spin prior case. It is found from the computations of tidal deformability parameters that soft to moderately stiff equations of state are allowed by the 50$\%$ and 90$\%$ credible regions obtained from the gravitational wave observation of binary neutron star merger GW170817, whereas the stiffest hadron-quark EoS which lies above the u…
Effects of the symmetry energy slope on magnetized neutron stars
Centro Federal de Educação Tecnológica de Minas Gerais（米纳斯吉拉斯州联邦技术教育学院）；Universidade Estadual da Região Tocantina do Maranhão, UEMASUL（马拉尼昂托坎蒂纳地区州立大学）；Universidade Federal do Maranhão（马拉尼昂联邦大学）；Universidade Federal de Santa Catarina（圣卡塔琳娜联邦大学）
The recent detection of gravitational waves (GWs) from the neutron star binary inspiral GW170817 has opened a unique avenue to probe matter and fundamental interactions in previously unexplored regimes. Extracting information on neutron star matter from the observed GWs requires robust and computationally efficient theoretical waveform models. We develop an approximate frequency-domain GW phase model of a main GW signature of matter: dynamic tides associated with the neutron stars' fundamental oscillation modes ($f$-modes). We focus on nonspinning objects on circular orbits and demonstrate tha…
A New Scaling of Neutron Star Tidal Deformability for Directly Probing the Central Equation of State Parameter
Fudan University（复旦大学）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（NSFC与复旦大学上海理论核物理研究中心）；Institute of Modern Physics, Fudan University（复旦大学现代物理研究所）；East Texas A&M University（东德克萨斯农工大学）；College of Physics, East China Normal University（华东师范大学物理学院）
In this work we re-analyze the data of GW170817, the first binary neutron star (BNS) merger event, in two ways, including the parameterized equation of state (EoS) method and gravitational wave (GW) parameter estimation analysis. Three sets of data, including the combined LIGO/Virgo (HLV) data, the LIGO-Hanford (H1) data and the LIGO-Livingston (L1) data, have been analyzed, respectively. We confirm the bimodal probability distribution of the tidal deformability of GW170817 with the HLV data and resolve the different contributions of H1 and L1 detectors. Our simulation reveals a tendency of ``…
Accurate gravitational-wave (GW) signal models exist for black hole binary (BBH) and neutron-star binary (BNS) systems, which are consistent with all of the published GW observations to date. Detections of a third class of compact-binary systems, neutron-star black hole (NSBH) binaries, have not yet been confirmed, but are eagerly awaited in the near future. For NSBH systems, GW models do not exist across the viable parameter space of signals. In this work we present the frequency-domain phenomenological model, PhenomNSBH, for GWs produced by NSBH systems with mass ratios from equal-mass up to…
The tidal measurement of gravitational waves from the binary neutron star merger event GW170817 allows us to probe nuclear physics that suffers less from astrophysical systematics compared to neutron star radius measurements with electromagnetic wave observations. A recent work found strong correlation among neutron-star tidal deformabilities and certain combinations of nuclear parameters associated with the equation of state. These relations were then used to derive bounds on such parameters from GW170817 assuming that the relations and neutron star masses are known exactly. Here, we expand o…
What can we learn about the density dependence of nuclear symmetry energy $E_{\rm{sym}}(ρ)$ from precise measurements of the radius ($R_{\rm{1.4}}$) and/or tidal polarizability ($Λ_{1.4}$) of canonical neutron stars (NSs) with a mass of 1.4 M$_\odot$? With the $E_{\rm{sym}}(ρ)$ parameterized using three parameters $L$, $K_{\rm{sym}}$, and $J_{\rm{sym}}$ which have the asymptotic meaning of being respectively the slope, curvature, and skewness of symmetry energy at saturation density, we found that, while both the $R_{\rm{1.4}}$ and $Λ_{1.4}$ depend strongly on the slope $L$, the $K_{\rm{sym}}$…
Gravitational wave observations of GW170817 placed bounds on the tidal deformabilities of compact stars allowing one to probe equations of state for matter at supranuclear densities. Here we design new parametrizations for hybrid hadron-quark equations of state, that give rise to low-mass twin stars, and test them against GW170817. We find that GW170817 is consistent with the coalescence of a binary hybrid star--neutron star. We also test and find that the I-Love-Q relations for hybrid stars in the third family agree with those for purely hadronic and quark stars within $\sim 3\%$ for both slo…
Self-bound hybrid stars with strong phase transitions can relieve major compact star observation tensions
Tongji University（同济大学）；The Hong Kong University of Science and Technology（香港科技大学）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Peking University（北京大学）
Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Universidade Tecnológica Federal do Paraná（巴拉那联邦技术大学）；Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学）；Universidad Santiago de Cali（圣地亚哥德卡利大学）；Universidad Antonio Nariño（安东尼奥·纳里尼奥大学）
本文提出保守 $f(R,T)$ 引力理论，通过有效能量动量张量重构引力函数，避免了传统方法中引力依赖物质方程的局限性，推导了中子星结构方程，并利用真实 EoS 计算中子星观测特征，对比现有天体物理约束。
Binary neutron star mergers with a subsolar mass star
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；California State University Fullerton（加州州立大学富勒顿分校）
