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Updated universal relations for tidal deformabilities of neutron stars from phenomenological equations of state
High Energy Astrophysical Phenomena · Submitted 22 Dec 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that the new fits yield a NS radius that is smaller by about 500 meters.
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The abstract, sentence by sentence
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 compactnesses. We show that waveform models that neglect higher-than-leading-order tidal deformations of the NSs accumulate as much as $3.5$ radians of dephasing from $20\,{\rm Hz}$ to merger. We also perform a full Bayesian parameter estimation of the GW170817 data, and we compare the NS radius constraints produced using universal relations from the literature and the updated fits we propose here. We find that the new fits yield a NS radius that is smaller by about 500 meters. This difference is less than the statistical uncertainty on the radius at the signal-to-noise-ratio of GW170817, but it is significantly larger than the precision anticipated for next-generation detectors.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | background 1.00 | 0.05 | 0.06 | asserted 1.00 |
| s1 | Here, we validate and recalibrate these universal relations using a large set of almost 2 million phenomenological EOSs that are consistent with current observations. | contribution 0.51 | 0.96 | 0.06 | asserted 0.99 |
| s2 | In doing so, we extend universal relations to a larger region of the EOS parameter space, most notably to softer EOSs and larger compactnesses. | contribution 0.96 | 0.93 | 0.11 | asserted 1.00 |
| s3 | We show that waveform models that neglect higher-than-leading-order tidal deformations of the NSs accumulate as much as $3.5$ radians of dephasing from $20\,{\rm Hz}$ to merger. | result 1.00 | 0.86 | 0.12 | asserted 1.00 |
| s4 | We also perform a full Bayesian parameter estimation of the GW170817 data, and we compare the NS radius constraints produced using universal relations from the literature and the updated fits we propose here. | method 0.81 | 0.97 | 0.08 | asserted 0.97 |
| s5 | We find that the new fits yield a NS radius that is smaller by about 500 meters. | result 1.00 | 0.97 | 0.28 | asserted 1.00 |
| s6 | This difference is less than the statistical uncertainty on the radius at the signal-to-noise-ratio of GW170817, but it is significantly larger than the precision anticipated for next-generation detectors. | interpretation 0.97 | 0.90 | 0.22 | asserted 1.00 |
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The paper
Original abstract
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 compactnesses. We show that waveform models that neglect higher-than-leading-order tidal deformations of the NSs accumulate as much as $3.5$ radians of dephasing from $20\,{\rm Hz}$ to merger. We also perform a full Bayesian parameter estimation of the GW170817 data, and we compare the NS radius constraints produced using universal relations from the literature and the updated fits we propose here. We find that the new fits yield a NS radius that is smaller by about 500 meters. This difference is less than the statistical uncertainty on the radius at the signal-to-noise-ratio of GW170817, but it is significantly larger than the precision anticipated for next-generation detectors.
Human review
References
How the literature uses it
18 arXiv papers cite this in 34 sentences
Papers citing it · 24 sentences without a confident label
Uses its method or tool 2 papers
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The mass of both NSs was set to $1.4$, while we also utilized the quasi-universal relation of Ref. [ref] between the compactness $C$ and $Λ$, in order to determine the individual radii of NSs given a fixed value for $Λ̃$.
Observability of dynamical tides in merging eccentric neutron star binaries · Implications for the equation of state · 0.86
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Two EOSs have been constructed by randomly selecting piecewise polytropic indices from [ref] marked here as PP2 and PP5.
Systematic errors due to quasi-universal relations in binary neutron stars and their correction for unbiased model selection · Equations of state simulated · 0.85
Uses its data or values 1 paper
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Note that, in both cases, $ℓ> 2$ multipolar tidal parameters are estimated via the fits from Ref. [ref] .
Analytically improved and numerical-relativity informed effective-one-body model for coalescing binary neutron stars · Effect of the analytical information · 0.89
Compares with it 3 papers
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The residuals remain below $∼10%$ for many EOS models and over a wide range of $Λ_s;$ the fits of [ref] have smaller residuals than those of [ref] but can still be as large as 25% when the tidal deformabilities are small, corresponding to heavier neutron stars and/or softer EOSs.
Systematic errors due to quasi-universal relations in binary neutron stars and their correction for unbiased model selection · Universal relation between tidal deformabilities of a pair of neutron stars · 0.90
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Finally, Fig. [ref] shows the tidal deformability as a function of the compactness $C=M/R$ of the 1F posterior and of the two branches of the 2F posterior, and compare them with the quasi-universal $C$–$Λ$ relation [ref] , shown as the purple band.
Is the coexistence of strange quark stars and hadronic stars favored by astrophysical data? A Bayesian analysis · Compact star properties · 0.97
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In Fig. [ref], we compare our results to a recent study by [ref] .
$f$-mode oscillations of compact stars with realistic equations of state in dynamical spacetime · Compactness - Tidal deformability universal relations · 1.00
Cites it as background 2 papers
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EOS-insensitive relations are heavily used in GW astronomy with BNSs in order to either reduce the matter's degrees of freedom in waveform modeling or connect spectral features to the NS equilibria and mass-radius diagram [ref] .
Pre/post-merger consistency test for gravitational signals from binary neutron star mergers · Introduction · 0.97
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Applications of qURs include obtaining constraints on NS quantities [ref] , breaking degeneracies in GW parameter estimation [ref] , measuring the Hubble constant [ref] , and performing direct measurements of the relations themselves [ref] .
Investigating the impact of quasi-universal relations on neutron star constraints in third-generation detectors · Introduction · 0.85
What it cites · 73 sentences without a confident label
Uses the method or tool of 10 papers
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We use a variation of the piecewise polytropic interpolation scheme developed by [ref] .
Constraints on a phenomenologically parameterized neutron-star equation of state · EOS Parameterization · 1.00
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We utilize the publicly available code described in [ref] and [ref] to solve the TOV equation.
Gravitational waves from pulsations of neutron stars described by realistic Equations of State · MCMC Algorithm · 1.00
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We utilize the publicly available code described in [ref] and [ref] to solve the TOV equation.
Relativistic tidal properties of neutron stars · MCMC Algorithm · 1.00
Uses data or values from 5 papers
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We use the parameters of the fit by [ref] as the initial parameter values for our fit.
Measuring the neutron star tidal deformability with equation-of-state-independent relations and gravitational waves · Binary Relation · 0.89
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The upper limit on $Λ_2$ is the 90%-credible upper bound derived in the LIGO/VIRGO analysis of GW170817 [ref] .
GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral · MCMC Algorithm · 0.99
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[ref] originally analyzed the $Λ_a$-$Λ_s$ relation using a set of theoretical EOSs with an average effective polytropic index of $n̅ = 0.743$.
Binary Love Relations · Binary Relation · 0.84
Compares with 7 papers
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In Fig. [ref], we compare the the 68%, 95%, and 99.7% relative errors of the radii recovered using the fits in this work to those recovered using the fits by [ref] and [ref] .
Measuring the neutron star tidal deformability with equation-of-state-independent relations and gravitational waves · Binary Relation · 1.00
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In Fig. [ref], we compare the the 68%, 95%, and 99.7% relative errors of the radii recovered using the fits in this work to those recovered using the fits by [ref] and [ref] .
Equation-of-state-independent relations in neutron stars · Binary Relation · 1.00
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In Fig. [ref] we report the marginalized one-dimensional posteriors for the reduced tidal parameter and the NS radius for the original run of [ref] that used the Yagi relations (red inline) and for the one performed here with the new quasiuniversal relations (black inline).
Waveform systematics in the gravitational-wave inference of tidal parameters and equation of state from binary neutron star signals · Application to waveform modeling and PE · 0.98
Cites as support 5 papers
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The specific choice of the low-density crust EOS does not significantly determine the bulk physical properties of the NS [ref]
Constraints on a phenomenologically parameterized neutron-star equation of state · EOS Parameterization · 0.99
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The specific choice of the low-density crust EOS does not significantly determine the bulk physical properties of the NS [ref]
New constraints on radii and tidal deformabilities of neutron stars from GW170817 · EOS Parameterization · 0.99
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However, [ref] have shown that the effects of discontinuities in $c_s$ on the bulk properties of a NS are negligible.
Speed of sound constraints from tidal deformability of neutron stars · EOS Parameterization · 0.99
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