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Constraints on the equation of state from the stability condition of neutron stars
Nuclear Theory · Submitted 25 Jun 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We found that it holds a model-independent relation between $\gamma_{\rm cr}$ and $\beta$.
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The abstract, sentence by sentence
The stellar equilibrium and collapse, including mainly white dwarfs, neutron stars and supper massive stars, is an interplay between general relativistic effects and the equation of state of nuclear matter. In the present work, we use the Chandrasekhar criterion of stellar instability by employing a large number of realistic equations of state (EoS) of neutron star matter. We mainly focus on the critical point of transition from stable to unstable configuration. This point corresponds to the maximum neutron star mass configuration. We calculate, in each case, the resulting compactness parameter, $\beta=GM/c^2R$, and the corresponding effective adiabatic index, $\gamma_{\rm cr}$. The role of the trial function $\xi(r)$ is presented and discussed in details. We found that it holds a model-independent relation between $\gamma_{\rm cr}$ and $\beta$. This statement is strongly supported by the large number of EoS and it is also corroborated by using analytical solutions of the Einstein's field equations. In addition, we present and discuss the relation between the maximum rotation rate and the adiabatic index close to the instability limit. Accurate observational measurements of the upper bound of the neutron star mass and the corresponding radius, in connection with the present predictions, may help to impose constraints on the high density part of the neutron star equation of state.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The stellar equilibrium and collapse, including mainly white dwarfs, neutron stars and supper massive stars, is an interplay between general relativistic effects and the equation of state of nuclear matter. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s1 | In the present work, we use the Chandrasekhar criterion of stellar instability by employing a large number of realistic equations of state (EoS) of neutron star matter. | method 0.77 | 0.91 | 0.03 | asserted 0.98 |
| s2 | We mainly focus on the critical point of transition from stable to unstable configuration. | contribution 0.83 | 0.33 | 0.04 | asserted 0.90 |
| s3 | This point corresponds to the maximum neutron star mass configuration. | interpretation 0.72 | 0.17 | 0.06 | asserted 1.00 |
| s4 | We calculate, in each case, the resulting compactness parameter, $\beta=GM/c^2R$, and the corresponding effective adiabatic index, $\gamma_{\rm cr}$. | method 0.85 | 0.96 | 0.05 | asserted 0.99 |
| s5 | The role of the trial function $\xi(r)$ is presented and discussed in details. | method 0.84 | 0.67 | 0.03 | asserted 0.63 |
| s6 | We found that it holds a model-independent relation between $\gamma_{\rm cr}$ and $\beta$. | result 1.00 | 0.95 | 0.74 | asserted 1.00 |
| s7 | This statement is strongly supported by the large number of EoS and it is also corroborated by using analytical solutions of the Einstein's field equations. | result 0.80 | 0.78 | 0.41 | asserted 0.99 |
| s8 | In addition, we present and discuss the relation between the maximum rotation rate and the adiabatic index close to the instability limit. | contribution 0.81 | 0.89 | 0.05 | asserted 0.82 |
| s9 | Accurate observational measurements of the upper bound of the neutron star mass and the corresponding radius, in connection with the present predictions, may help to impose constraints on the high density part of the neutron star equation of state. | interpretation 0.66 | 0.12 | 0.22 | hedged possibility 1.00 |
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The paper
Original abstract
The stellar equilibrium and collapse, including mainly white dwarfs, neutron stars and supper massive stars, is an interplay between general relativistic effects and the equation of state of nuclear matter. In the present work, we use the Chandrasekhar criterion of stellar instability by employing a large number of realistic equations of state (EoS) of neutron star matter. We mainly focus on the critical point of transition from stable to unstable configuration. This point corresponds to the maximum neutron star mass configuration. We calculate, in each case, the resulting compactness parameter, $\beta=GM/c^2R$, and the corresponding effective adiabatic index, $\gamma_{\rm cr}$. The role of the trial function $\xi(r)$ is presented and discussed in details. We found that it holds a model-independent relation between $\gamma_{\rm cr}$ and $\beta$. This statement is strongly supported by the large number of EoS and it is also corroborated by using analytical solutions of the Einstein's field equations. In addition, we present and discuss the relation between the maximum rotation rate and the adiabatic index close to the instability limit. Accurate observational measurements of the upper bound of the neutron star mass and the corresponding radius, in connection with the present predictions, may help to impose constraints on the high density part of the neutron star equation of state.
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References
How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers citing it
Uses its method or tool 1 paper
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For the EOS we will use the so-called spectral parameterization in terms of the adiabatic index $Γ(p)$, defined as [ref] [equation] where $ϵ$ is energy density and $p$ is pressure.
Determining the equation of state of neutron stars with Einstein Telescope using tidal effects and r-mode excitations from a population of binary inspirals · Spectral parametrization of the EOS · 0.90
Cites it as background 1 paper
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The adiabatic index, [equation] quantifies the stiffness of dense matter against adiabatic compression and plays a central role in the stability and oscillation properties of compact stars [ref] .
A self-consistent Higgs-portal framework for dark matter--admixed neutron stars: Collider-motivated benchmarks meet multimessenger constraints · Adiabatic index · 0.96
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