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 posteriorprobability distributions of the EoS parameters, using which we infer the posterior distribution for the radius and the mass of the two neutron stars of GW170817. The constraints we set on the radii are tighter than previous bounds.
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…
We present predictions for neutron star tidal deformabilities obtained from a Bayesian analysis of the nuclear equation of state, assuming a minimal model at high-density that neglects the possibility of phase transitions. The Bayesian posterior probability distribution is constructed from priors obtained from microscopic many-body theory based on realistic two- and three-body nuclear forces, while the likelihood functions incorporate empirical information about the equation of state from nuclear experiments. The neutron star crust equation of state is constructed from the liquid drop model, a…
We confront observational data from gravitational wave event GW170817 with microscopic modeling of the cold neutron star equation of state. We develop and employ a Bayesian statistical framework that enables us to implement constraints on the equation of state from laboratory measurements of nuclei and state-of-the-art chiral effective field theory methods. The energy density functionals constructed from the posterior probability distributions are then used to compute consistently the neutron star equation of state from the outer crust to the inner core, assuming a composition consisting of pr…
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）
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 …
We perform a systematic assessment of models for the equation of state (EOS) of dense matter in the context of recent neutron star mass and radius measurements to obtain a broad picture of the structure of neutron stars. We demonstrate that currently available neutron star mass and radius measurements provide strong constraints on moments of inertia, tidal deformabilities, and crust thicknesses. A measurement of the moment of inertia of PSR J0737-3039A with 10% error, without any other information from observations, will constrain the EOS over a range of densities to within 50%$-$60%. We find …
In this work we study the outcomes related to dimensionless tidal deformability $(Λ)$ obtained through a relativistic mean-field (RMF) hadronic model including short-range correlations (SRC) and dark matter (DM) content [Phys. Rev. D 105, 023008 (2022)]. As a dark particle candidate, we use the lightest neutralino interacting with nucleons through the Higgs boson exchange. In particular, we test the model against the constraints regarding the observation of gravitational waves from the binary neutron star merger GW170817 event provided by LIGO and Virgo collaboration (LVC). We show that $Λ$ de…
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…
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…
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…
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…
We compute the tidal deformabilities for neutron star merger for equations of state with a strong first order phase transition producing a new separate branch in the mass-radius diagram. A case is found where all three possible pairs of combinations between these two neutron star branches are present for the total mass of $M=2.7M_\odot$ of the observed merger event GW170817. It is demonstrated that the plot of the two tidal deformabilities $Λ_1$ and $Λ_2$ of the binary neutron star can show up to three separate branches. We propose that the future detections of neutron star merger events with …
The neutron star tidal deformability is a critical parameter which determines the pre-merger gravitational-wave signal in a neutron star merger. In this article, we show how neutron star tidal deformabilities behave in the presence of one or two sharp phase transition(s). We characterize how the tidal deformability changes when the properties of these phase transitions are modified in dense matter equation of state (EoS). Sharp phase transitions lead to the smallest possible tidal deformabilities and also induce discontinuities in the relation between tidal deformability and gravitational mass…
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 …
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…
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 …
Recent experimental and ab initio theory investigations of the 208Pb neutron skin thickness are sufficiently precise to inform the neutron star equation of state. In particular, the strong correlation between the 208Pb neutron skin thickness and the pressure of neutron matter at normal nuclear densities leads to modified predictions for the radii, tidal deformabilities, and moments of inertia of typical 1.4 solar-mass neutron stars. In the present work, we study the relative impact of these recent analyses of the 208Pb neutron skin thickness on bulk properties of neutron stars within a Bayesia…
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…
Based on the distribution of tidal deformabilities and component masses of binary neutron star merger GW170817, the parametric equation of states (EOS) are employed to probe the nuclear symmetry energy and the properties of neutron star. To obtain a proper distribution of the parameters of the EOS that is consistent with the observation, Bayesian analysis is used and the constraints of causality and maximum mass are considered. From this analysis, it is found that the symmetry energy at twice the saturation density of nuclear matter can be constrained within $E_{sym}(2{ρ_{0}})$ = $34.5^{+20.5}…
We study the interface effects of quark-hadron mixed phase in compact stars. The properties of nuclear matter are obtained based on the relativistic-mean-field model. For the quark phase, we adopt perturbation model with running quark masses and coupling constant. At certain choices of parameter sets, it is found that varying the quark-hadron interface tension will have sizable effects on the radii ($ΔR \approx 600$ m) and tidal deformabilities ($ΔΛ/Λ\approx 50\%$) of hybrid stars. These provide possibilities for us to constrain the quark-hadron interface tension with future gravitational wave…
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…
Much effort is devoted to measuring the nuclear symmetry energy through neutron star (NS) and nuclear observables. Since matter in the NS core may be non-hadronic, observables like radii and tidal deformability may not provide reliable constraints on properties of nucleonic matter. We demonstrate that coincident timing of a resonant shattering flare (RSF) and gravitational wave signal during binary NS inspiral probes the crust-core transition region and provides constraints on the symmetry energy comparable to terrestrial nuclear experiments. We show that nuclear masses, RSFs and measurements …
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…
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）
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…
Constraints set on key parameters of the nuclear matter equation of state (EoS) by the values of the tidal deformability, inferred from GW170817, are examined by using a diverse set of relativistic and non-relativistic mean field models. These models are consistent with bulk properties of finite nuclei as well as with the observed lower bound on the maximum mass of neutron star $\sim 2 ~ {\rm M}_\odot$. The tidal deformability shows a strong correlation with specific linear combinations of the isoscalar and isovector nuclear matter parameters associated with the EoS. Such correlations suggest …
Observations of gravitational waves from neutron star mergers open up novel directions for exploring fundamental physics: they offer the first access to the structure of objects with a non-negligible contribution from vacuum energy to their total mass. The presence of such vacuum energy in the inner cores of neutron stars occurs in new QCD phases at large densities, with the vacuum energy appearing in the equation of state for a new phase. This in turn leads to a change in the internal structure of neutron stars and influences their tidal deformabilities which are measurable in the chirp signa…
Universal relations between the quasinormal modes of neutron stars and magnetic tidal deformability
Kochi University（高知大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心（iTHEMS））；University of Tübingen（蒂宾根大学）
We estimate the accuracy in the measurement of the tidal Love number of a supermassive compact object through the detection of an extreme mass ratio inspiral~(EMRI) by the future LISA mission. A nonzero Love number would be a smoking gun for departures from the classical black hole prediction of General Relativity. We find that an EMRI detection by LISA could set constraints on the tidal Love number of a spinning central object with dimensionless spin $\hat a=0.9$ ($\hat a=0.99$) which are approximately four (six) orders of magnitude more stringent than what achievable with current ground-base…
Stars that pass close to the supermassive black holes located in the center of galaxies can be violently disrupted by tidal forces, leading to flares that are observed as bright transient events in sky surveys. The rate for these events to occur depends on the black hole spins, which in turn can be affected by ultra-light bosons due to superradiance. We perform a detailed analysis of these effects and show that searches for stellar tidal disruptions have a significant potential to uncover the existence of ultra-light bosons. In particular, we find that upcoming stellar tidal disruption rate me…
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…
We revisit asteroseismology with quadrupolar wI modes and present universal relationships for its fundamental and first overtone. In contrast to relationships proposed in the literature, our universal relationships are capable of including slow stable hybrid stars that appear when considering slow sharp hadron-quark phase transitions. We show that, if the frequency and damping time of the fundamental mode of a given pulsating object are measured, its mass, radius, and dimensionless tidal deformability can be inferred. Moreover, we show that the errors of such estimates are smaller than a few p…
The increasing richness of data related to cold dense matter, from laboratory experiments to neutron-star observations, requires a framework for constraining the properties of such matter that makes use of all relevant information. Here, we present a rigorous but practical Bayesian approach that can include diverse evidence, such as nuclear data and the inferred masses, radii, tidal deformabilities, moments of inertia, and gravitational binding energies of neutron stars. We emphasize that the full posterior probability distributions of measurements should be used rather than, as is common, imp…
Tidal disruption of stars by massive black holes produce transient accretion flows that flare at optical, UV, and X-ray wavelengths. At late times, these accretion flows may launch relativistic jets that can be detected through the interaction of the jet with the dense interstellar medium of the galaxy. We present an upper limit for the flux density of a radio counterpart to a tidal disruption event detected by GALEX that is a factor of 6 below theoretical predictions. We also examine existing radio surveys for transients with a time scale of 1 year and use these to set a $2 σ$ upper limit on …
We inspect the possibility that neutron star interiors are a mixture of ordinary matter and mirror dark matter. This is a scenario that can be naturally envisaged according to well studied accretion mechanisms, including the Bondi-Hoyle one. We show that the inclusion of mirror dark matter in neutron star models lowers the maximum neutron star mass for a given equation of state, and that it decreases the tidal deformability of a given neutron star. These general features imply that, given an equation of state, one can constrain the maximum viable amount of mirror dark matter in neutron stars i…
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…
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 ``…
We develop a Bayesian analysis method for selecting the most probable equation of state under a set of constraints from compact star physics, which now include the tidal deformability from GW170817. We apply this method for the first time to a two-parameter family of hybrid equations of state that is based on realistic models for the hadronic phase (KVORcut02) and the quark matter phase (SFM$α$) which produce a third family of hybrid stars in the mass-radius diagram. One parameter ($α$) characterizes the screening of the string tension in the string-flip model of quark matter while the other (…
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.
We compute the mass, radius and tidal deformability of stars containing phase transitions from hadronic to quark phase(s). These quantities are computed for three types of hadronic envelopes: purely nuclear, hyperonic, and $Δ$-resonance--hyperon admixed matter. We consider either a single first-order phase transition to a quark phase with a maximally stiff equation of state (EOS) or two sequential first-order phase transitions mimicking a transition from hadronic to a quark matter phase followed by a second phase transition to another quark phase. We explore the parameter space which produces …
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…
