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Investigating the I-Love-Q and w-mode Universal Relations Using Piecewise Polytropes
High Energy Astrophysical Phenomena · Submitted 6 Oct 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We also propose new empirical relations between $I$, $\lambda$, $Q$, and the complex frequency $\omega=\omega_R+i\omega_I$ of the fundamental axial $w$-mode, and find that they are comparably tight to the I-Love-Q correlations.
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The abstract, sentence by sentence
Neutron stars are expected to have a tight relation between their moment of inertia ($I$), tidal deformability ($\lambda$, which is related to the Love number), and rotational mass quadrupole moment ($Q$) that is nearly independent of the unknown equation of state (EoS) of cold dense matter. These and similar relations are often called "universal", and they have been used for various applications including analysis of gravitational wave data. We extend these studies using piecewise polytropic representations of dense matter, including for so-called twin stars that have a second branch of stability at high central densities. The second-branch relations are less tight, by a factor of $\sim 3$, than the relations found in the first stable branch. We find that the relations on both branches become tighter when we increase the lower limit to the maximum mass for the EoS under consideration. We also propose new empirical relations between $I$, $\lambda$, $Q$, and the complex frequency $\omega=\omega_R+i\omega_I$ of the fundamental axial $w$-mode, and find that they are comparably tight to the I-Love-Q correlations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Neutron stars are expected to have a tight relation between their moment of inertia ($I$), tidal deformability ($\lambda$, which is related to the Love number), and rotational mass quadrupole moment ($Q$) that is nearly independent of the unknown equation of state (EoS) of cold dense matter. | background 1.00 | 0.06 | 0.09 | hedged possibility 0.89 |
| s1 | These and similar relations are often called "universal", and they have been used for various applications including analysis of gravitational wave data. | background 1.00 | 0.04 | 0.02 | asserted 0.98 |
| s2 | We extend these studies using piecewise polytropic representations of dense matter, including for so-called twin stars that have a second branch of stability at high central densities. | contribution 0.62 | 0.87 | 0.05 | asserted 0.95 |
| s3 | The second-branch relations are less tight, by a factor of $\sim 3$, than the relations found in the first stable branch. | result 1.00 | 0.85 | 0.20 | asserted 1.00 |
| s4 | We find that the relations on both branches become tighter when we increase the lower limit to the maximum mass for the EoS under consideration. | result 1.00 | 0.96 | 0.12 | asserted 1.00 |
| s5 | We also propose new empirical relations between $I$, $\lambda$, $Q$, and the complex frequency $\omega=\omega_R+i\omega_I$ of the fundamental axial $w$-mode, and find that they are comparably tight to the I-Love-Q correlations. | result 0.64 | 0.96 | 0.36 | asserted 1.00 |
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The paper
Original abstract
Neutron stars are expected to have a tight relation between their moment of inertia ($I$), tidal deformability ($\lambda$, which is related to the Love number), and rotational mass quadrupole moment ($Q$) that is nearly independent of the unknown equation of state (EoS) of cold dense matter. These and similar relations are often called "universal", and they have been used for various applications including analysis of gravitational wave data. We extend these studies using piecewise polytropic representations of dense matter, including for so-called twin stars that have a second branch of stability at high central densities. The second-branch relations are less tight, by a factor of $\sim 3$, than the relations found in the first stable branch. We find that the relations on both branches become tighter when we increase the lower limit to the maximum mass for the EoS under consideration. We also propose new empirical relations between $I$, $\lambda$, $Q$, and the complex frequency $\omega=\omega_R+i\omega_I$ of the fundamental axial $w$-mode, and find that they are comparably tight to the I-Love-Q correlations.
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References
How the literature uses it
7 arXiv papers cite this in 11 sentences
Papers citing it · 6 sentences without a confident label
Compares with it 1 paper
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For the piecewise-polytrope model, this is qualitatively similar to the findings of Ref. [ref] .
Assessing equation of state-independent relations for neutron stars with nonparametric models · Discussion · 0.99
Cites it as background 4 papers
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Universal relationships for axial (and polar) $w$-modes of NSs, strange quark stars and also HSs, have been proposed in the literature (see, for example Refs. [ref] ).
Breaking of universal relationships of axial wI-modes in hybrid stars: rapid and slow hadron-quark conversion scenarios · Results · 0.88
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See Refs. [ref] for a discussion of the tidal deformability in the presence of first-order phase transitions and twin stars [ref] .
Extreme Matter meets Extreme Gravity: Ultra-heavy neutron stars with crossovers and first-order phase transitions · From disconnected twins to unstable sequences through bumps in the speed of sound · 0.97
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For a partial list on universal relations in several contexts, such as alternative theories of gravity, rapidly rotating compact stars, including exotic matter and the mass etc., see e.g. [ref] and references therein.
Universal relations for non-rotating objects made of dark energy · Introduction · 1.00
What it cites · 35 sentences without a confident label
Uses the method or tool of 6 papers
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Here, to compute the $w$-mode frequencies, we follow the numerical scheme of [ref] .
Reconstruction of the neutron star equation of state from $w$-quasinormal modes spectra with a piecewise polytropic meshing and refinement method · Methods · 1.00
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To compute $λ≡2/3G^-1R^5k_2$ (where $G$ is Newton's constant, $R$ is the circumferential radius, and $k_2$ is the $l=2$ electric tidal Love number, or apsidal constant) we follow [ref] , as amended in the erratum [ref] .
Tidal Love numbers of neutron stars · Methods · 0.99
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Once we have computed $I$, $λ$, $Q$, and the $w$-mode frequencies for each of our neutron stars, we follow [ref] in fitting a fourth-order polynomial to our values: [equation] where $c_0i, c_1i$ etc. are our fitting coefficients, we take $log_10Q̅$ as our independent variable $X$, and $Y_i$ is $log_10I̅$, $log_10λ̅$, or the real or imaginary part of the $w$-mode frequency.
I-Love-Q Relations in Neutron Stars and their Applications to Astrophysics, Gravitational Waves and Fundamental Physics · Methods · 0.99
Compares with 1 paper
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We have 497,220 stars in our first-branch set; this compares with 27,440 in [ref] (all of which are first-branch stars).
Reconstruction of the neutron star equation of state from $w$-quasinormal modes spectra with a piecewise polytropic meshing and refinement method · Methods · 0.99
Cites as background 34 papers
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Later work explored the effect of rescaling the $w$-mode frequencies with the square root of the central pressure [ref] , and correlations of the rescaled frequencies with $λ$ [ref] .
Phenomenological Relations for Axial Quasi-normal Modes of Neutron Stars with Realistic Equations of State · Methods · 0.98
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Later work explored the effect of rescaling the $w$-mode frequencies with the square root of the central pressure [ref] , and correlations of the rescaled frequencies with $λ$ [ref] .
Reconstruction of the neutron star equation of state from $w$-quasinormal modes spectra with a piecewise polytropic meshing and refinement method · Methods · 0.98
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Previous work has demonstrated that $f$-mode frequencies correlate well with the inverse square root of $I̅$ [ref] .
Fundamental oscillation modes of neutron stars: validity of universal relations · Correlations with $w$-mode frequencies · 0.80
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