Smooth equations of state for high-accuracy simulations of neutron star binaries

Alana Gudinas; Francois Foucart; Francois Hebert; Harald P. Pfeiffer; Lawrence E. Kidder; Mark A. Scheel; Matthew D. Duez

REVIEW 3 major objections 5 minor 36 references

Smooth equations of state for high-accuracy simulations of neutron star binaries

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Smooth spectral equations of state allow high-accuracy neutron-star merger simulations at lower computational cost than piecewise polytropes, while the choice of low-density behavior sets an efficiency-accuracy tradeoff.

desk verdict A practical, credible implementation paper showing smooth spectral EOS improve the cost/accuracy trade-off in SpEC neutron star simulations, though the headline error numbers rest on an unverified convergence-order assumption. read the letter →

arxiv 1908.05277 v1 pith:VJLTWYHR submitted 2019-08-14 gr-qc astro-ph.HE

Francois Foucart , Matthew D. Duez , Alana Gudinas , Francois Hebert , Lawrence E. Kidder , Harald P. Pfeiffer , Mark A. Scheel This is my paper · ORCID

classification gr-qcastro-ph.HE PACS 04.25.dg04.40.Dg26.30.Hj98.70.-f

keywords spectralequationofstateneutronstarmergersgravitationalwavesnumericalrelativitypiecewisepolytropesmoothnessbinarystarsmethods

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to show that switching the equation of state used in neutron-star merger simulations from the common piecewise polytrope to a smooth 'spectral' form removes a numerical obstacle to high-order convergence, improving accuracy and lowering cost at the same time. The authors implement such equations of state in their spectral-method general-relativistic code and compare them against the standard SLy piecewise polytrope. At one orbit of evolution, the smoother spectral equation of state reaches an orbital-phase error near 0.0045 rad while the piecewise polytrope sits near 0.014 rad, at lower CPU cost at the highest resolution. They also find that not every spectral equation of state is equally efficient: a version using an unphysical low-density behavior ($\Gamma_0 = 2$) converges faster and costs about half as much at high resolution as a more realistic low-density version ($\Gamma_0 = 1.35692$). If these results hold, smooth spectral equations of state are a practical route to the high-accuracy waveforms needed to calibrate the semi-analytic models used in gravitational-wave parameter estimation.

What carries the argument

The load-bearing object is a spectral equation of state: the adiabatic index $\Gamma = d\ln P/d\ln \rho$ is expanded in powers of $x = \ln(\rho/\rho_0)$, so the cold pressure is $P(x) = P_0 \exp(\int_0^x \Gamma(\tilde x)\,d\tilde x)$, and thermodynamic consistency fixes the internal energy through an integral that is evaluated with a small precomputed table plus six-point Gaussian quadrature. Two details make it work: forcing $\gamma_0 = \Gamma_0$ and $\gamma_1 = 0$ pushes the only nonsmooth feature of $P$ into the third derivative, and choosing $\Gamma_0 = 2$ makes the density approach zero linearly at the star's surface, which the authors find is far easier for the adaptive spectral grid to resolve than the realistic low-density index $1.35692$. This compact parametrization costs about 10-20% more per time step than a piecewise polytrope, but the smoothness lets the code take fewer, larger time steps and reach smaller phase error.

What would settle it

Run the same $1.36\,M_\odot$ equal-mass binary at four resolutions with both a piecewise-polytrope and the smooth spectral equation of state, measure the orbital-phase error versus resolution to read off the actual convergence order, and recompute the error comparison with that measured order; if the spectral equation of state no longer shows roughly a factor-of-three smaller error at comparable cost, the central cost-accuracy claim is refuted.

Watch

Extended reading notes

Core claim

The central claim is that smoothness of the equation of state, not just its physical content, controls the cost and accuracy of high-order neutron-star simulations. By representing the adiabatic index as $\Gamma(x) = \gamma_0 + \gamma_2 x^2 + \gamma_3 x^3$ in $x = \ln(\rho/\rho_0)$ and imposing $\gamma_0 = \Gamma_0$ and $\gamma_1 = 0$ at the matching density, the authors construct equations of state whose pressure and internal energy are continuous through their second derivatives, leaving only a discontinuity in the third derivative. In their code, this smoothness removes the spurious numerical features that piecewise polytropes inject at the transition density and at the stellar surface, so the adaptive spectral grid can resolve the star with fewer basis functions and a larger time step. The paper's quantitative evidence is a set of equal-mass, nonspinning 1.36-solar-mass binary runs: at $t = 1000\, GM_\odot/c^3$, the smoother spectral equation of state gives an orbital-phase error of about 0.0045 rad versus 0.014 rad for the SLy piecewise polytrope, with a lower cost at the highest resolution. The same comparison across spectral variants shows the $\Gamma_0 = 2$ low-density form is the most cost-effective, while the more realistic $\Gamma_0 = 1.35692$ low-density form requires roughly twice as many time steps at high resolution.

Load-bearing premise

The load-bearing premise is that these simulations converge at second order: the paper estimates errors by extrapolating from three resolutions under the assumption that halving the grid spacing quarters the error, but the code is designed to be third-order in the asymptotic regime and no convergence-order measurement is shown.

Editorial extensions

If this is right

High-accuracy gravitational-wave templates for calibrating semi-analytic models can be produced at lower CPU cost, so systematic checks across many equations of state become more affordable.
The Γ0 = 2 spectral equation of state is the most cost-effective option for waveform generation, but it is unphysical below roughly 10^14 g/cm^3, so the efficiency gain comes with a realism tradeoff.
Frequent spectral mesh refinement (about every 5 GM⊙/c³) is required to realize the accuracy gain; with the slower trigger the smooth-equation-of-state advantage shrinks.
These equations of state are not intended for matter outflows, neutrino interactions, or post-merger accretion disks, because they ignore composition and temperature structure beyond a simple Γ-law.
Because orbital-phase error tracks gravitational-wave phase error, the factor-of-several accuracy improvement translates directly into more reliable tidal-deformability extraction.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The tests cover only equal-mass, nonspinning binaries; if the smoothness advantage survives unequal masses or spins, the savings for building parameter-estimation waveform banks would extend well beyond the demonstrated case.
A natural next step, not taken in the paper, is to apply the same third-derivative smoothing to tabulated nuclear-theory equations of state by fitting Γ(ρ) to global neutron-star properties rather than local values; the paper's MCMC construction of spectral models is a template for that.
Because the efficiency difference between Γ0 = 2 and Γ0 = 1.35692 is attributed to how the surface density vanishes, one could test that explanation directly by measuring convergence order across a sequence of low-density polytropic indices.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

This is a solid implementation paper that makes a credible pragmatic case for using smooth spectral EOS in neutron star merger simulations with SpEC. What's genuinely new is the specific smoothness modification (γ0=Γ0, γ1=0) that pushes the EOS discontinuity from the first to the third derivative of pressure, the efficient quadrature-tabulation hybrid for the internal energy integral, and the first head-to-head cost/accuracy comparison of spectral versus piecewise-polytropic EOS in a production code. The paper also shows that not all spectral EOS are equal: the Γ0=2 version is less realistic at low density but significantly cheaper and more accurate than the more physical Γ0=1.35 version. That trade-off is honestly discussed.

The main quantitative claim—that spectral EOS achieve a given phase accuracy at lower cost, with a factor-of-a-few improvement in orbital-phase error—is plausible and probably correct. The evidence, however, has real soft spots. The phase-error estimates come from Richardson extrapolation assuming second-order convergence, but the code is described as third-order in the asymptotic regime, and no convergence-order measurement is reported. If the actual order differs between the PP and spectral runs (which is plausible, since the PP EOS has a first-derivative discontinuity), the reported numbers could shift. The authors say 'from previous experience' second-order gives conservative estimates, but that's not quantified. Interestingly, the likely direction of the bias favors their conclusion: a smoother EOS would tend to have a higher convergence order, so assuming second order would overestimate its error, while the PP error might be underestimated if it converges at a lower order. Still, they should measure it.

There are minor issues too: in Sec. III.D.1 the text says the 0.0045 rad error is for SLyΓ2 when it should be SLyΓ1.35, and all results come from single runs of one equal-mass configuration in one code. The appendix tables of fitted EOS parameters are useful, but no public data or code is provided.

This paper is for numerical relativists who need accurate waveforms for calibrating semi-analytical models, and for code developers dealing with EOS implementations. It's a worthier referee than many; the main request I'd make is a small convergence study to validate the Richardson assumption, and fixing the typos. I'd send it to review.

Referee Report

3 major / 5 minor

Summary. This paper describes the implementation of Lindblom-style spectral equations of state in the Spectral Einstein Code (SpEC), with a modification enforcing continuity of the first and second derivatives of the pressure at the matching density by setting gamma0 = Gamma0 and gamma1 = 0. The authors fit the spectral EOS parameters to the SLy EOS via MCMC, generating grids of EOSs with specified maximum mass and 1.35-solar-mass radius, and then compare the cost and accuracy of short equal-mass, nonspinning neutron-star binary evolutions using SLyPP, a spectral EOS with Gamma0 = 1.35692 (SLyGamma1.35), and one with Gamma0 = 2 (SLyGamma2). The central empirical claim is that the smoother spectral EOSs yield smaller orbital-phase errors than piecewise-polytropic EOSs at comparable or lower computational cost, and that among spectral EOSs the Gamma0 = 2 variant is cheaper and more accurate than the more physically realistic Gamma0 = 1.35692 variant. The paper also reports that frequent spectral adaptive-mesh-refinement triggering is important for these EOSs, and it provides parameter tables for the generated EOS grids.

Significance. If the central comparison is correct, this is a practically important result for numerical relativity: smoother EOSs would allow cheaper production of the high-accuracy inspiral waveforms needed to calibrate semi-analytical waveform models for gravitational-wave parameter estimation. The paper is particularly valuable for its concrete implementation details, its large appendix of tabulated spectral EOS parameters, and its unusually explicit discussion of the limitations and regimes of applicability of the proposed EOSs. The claims are falsifiable and the comparison is grounded in actual SpEC simulations rather than in the fitting procedure itself. The main risk is that every quantitative accuracy statement rests on an assumed second-order Richardson extrapolation, while the paper itself states that the underlying algorithm should be third-order and that the exact convergence order is difficult to assess. Because the central claim is plausible and the identified gaps are addressable with additional convergence measurements and longer runs, the paper merits major revision rather than rejection.

major comments (3)

[Section III.D] The quantitative accuracy comparison relies entirely on Richardson extrapolation 'by assuming second order convergence of the simulations,' but Section III.B states that the two-grid algorithm 'should provide third-order accurate evolutions' in the asymptotic regime and that the exact order is 'difficult to assess.' No convergence-order measurement is reported for any of the three EOSs. The headline numbers (Delta-phi = 0.0045 rad for the spectral EOS vs. 0.014 rad for SLyPP at t = 1000) are therefore not directly measured errors but outputs of an assumed-order extrapolation. If the observed order differs from 2, and especially if it differs between the smooth spectral EOS and the piecewise-polytropic EOS, the inferred infinite-resolution phase is biased and the factor-of-three accuracy gap could change or even reverse. The appeal to 'previous experience' that second order is conservative is not quantified. I request at least four resolutions per EOS with a measured phase-versus-Delta-x convergence fit, or alternatively error estimates reported under both p = 2 and p = 3 assumptions to show that the conclusions are robust.
[Section III.A and Section IV] The accuracy and cost comparisons are based on simulations evolved only to t = 1000 (roughly one orbit), and the paper states in Section IV that production of full waveforms 'is in progress.' The abstract's claim that spectral equations of state 'allow for high-accuracy simulations at a lower computational cost' is thus supported only for a short inspiral window, not for a full merger waveform. Phase errors can accumulate and interact with the merger dynamics differently for different EOSs, so the advertised advantage should either be demonstrated over a substantially longer inspiral (or up to merger) or the claim should be explicitly restricted to the early-inspiral regime tested here.
[Section III.D.3] The conclusion that SLyGamma2 is cost-superior to SLyGamma1.35 rests on the number of time steps as a proxy for cost, with the assertion that the cost per time step is nearly identical for the two simulations. However, no direct CPU-hour comparison is given for this particular pair after the updated grid choices, despite the paper's own caveat in Section III.D that time-step ratio is only a good proxy when the cost of a step is roughly identical. Since the SLyGamma1.35 simulation required about twice as many time steps, a small increase in cost per step could affect the quantitative cost ranking. I ask for a direct CPU-hour measurement on the same machine, or a sensitivity test showing that per-step cost differences are negligible for the two spectral EOSs.

minor comments (5)

[Section III.D.1] The sentence reporting 'Delta-phi = 0.0045 rad for SLyGamma2' appears to be a typo: the comparison in that subsection is between SLyGamma1.35 and SLyPP, and Figure 4 is described as showing SLyGamma135 and SLyPP. This should be corrected to SLyGamma1.35.
[Section II.C] The text refers to 'Gamma_0 = 1.35962' in one place, while all tables and the rest of the text use Gamma_0 = 1.35692. This inconsistency should be fixed.
[Table II caption] The caption of Table II states 'Gamma_0 = 1.35602', but the entries and the text use 1.35692. This is a typographical error.
[Section II.C] 'Marko-Chain Monte-Carlo' should read 'Markov Chain Monte-Carlo.'
[Section III.D] The statement that the orbital-phase error scales as the gravitational-wave phase error 'at least when neglecting the error due to extrapolation of the gravitational wave signal to null-infinity' is plausible but not quantified; a brief justification or a reference would help the reader assess the reliability of using orbital phase as a waveform-accuracy proxy.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the accuracy and cost claims are measured from simulations, not encoded in the fitting of the spectral EOS parameters.

full rationale

The paper's central claims are that spectral equations of state enable more accurate neutron-star-binary evolutions at lower computational cost than piecewise-polytrope EOS, and that not all spectral EOS are equally efficient. These conclusions come from direct SpEC simulations at multiple resolutions, with orbital-phase errors estimated via Richardson extrapolation. The spectral EOS parameters are indeed fitted (via MCMC) to match target stellar properties such as R1.35 and Mmax of SLy, but those fitted properties are not the predicted quantities; the predicted quantities are convergence behavior, phase error, time-step count, and CPU cost, all of which are empirical outputs of the simulations. The Richardson-extrapolation error estimator is an internal convergence diagnostic, not a renamed input, and the stated assumption of second-order convergence is a correctness/robustness concern rather than a circular step. The self-citations to prior work [37] for the error-estimation practice and for the earlier observation that piecewise polytropes are inaccurate in SpEC are supportive but not load-bearing: the present paper reproduces the comparison with its own independent simulations. No equation in the paper reduces to its inputs by construction, and no load-bearing conclusion is imported solely from a self-citation. Therefore no significant circularity is found.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central performance claim rests on modeling simplifications (cold beta-equilibrium matter, Gamma-law thermal extension, no composition dependence), a causality check rather than a causality-guaranteeing construction, and a numerical-error estimation procedure whose convergence order is assumed rather than measured. The EOS parameters of the two SLy-like models are fitted via MCMC to match target stellar properties, but the cost and accuracy outcomes are measured rather than imposed.

free parameters (6)

Gamma0 = 2 and 1.35692 (two families)
Low-density adiabatic index, chosen by hand to represent either a numerically convenient or a more physically realistic low-density behavior.
rho0 = 1.0118e-4 (SLyGamma2), 8.2235e-5 (SLyGamma1.35), varied in Appendix tables
Reference density at which the spectral expansion is anchored; selected via MCMC to match target neutron star radius and maximum mass.
P0 = 3.3625e-7 (SLyGamma2), 2.5632e-7 (SLyGamma1.35), varied in Appendix tables
Reference pressure at rho0; selected via MCMC along with the other EOS parameters to match target stellar properties.
gamma2 = 0.4029 (SLyGamma2), 0.9297 (SLyGamma1.35)
Quadratic spectral coefficient in the adiabatic index expansion; fitted via MCMC to match SLy-like radius and maximum mass.
gamma3 = -0.1008 (SLyGamma2), -0.2523 (SLyGamma1.35)
Cubic spectral coefficient in the adiabatic index expansion; fitted via MCMC to match SLy-like stellar properties.
Gamma_th = 1.75
Adiabatic index of the thermal component added to the cold EOS; chosen by hand, and the authors note that different choices can affect post-merger ejecta.

assumptions (5)

domain assumption Neutron star matter is in neutrinoless beta-equilibrium, composition-independent, and described as an ideal fluid (Eqs. 2-4).
Invoked in Section II.A to close the hydrodynamic system; excludes composition, neutrinos, and magnetic fields, which limits applicability to outflows and disks.
domain assumption Cold EOS plus a Gamma-law thermal component with Gamma_th = 1.75 adequately captures temperature dependence for inspiral and merger waveforms.
Section II.A, Eqs. (13)-(14); the authors state the impact on pre-merger evolution is expected to be negligible but do not quantify it.
domain assumption Verifying causality cs < 1 up to the central density of the maximum-mass star is sufficient to guarantee causal behavior in simulations.
Section II.A after Eq. (22); the chosen formalism does not enforce causality by construction, so the check is a verification over a limited density range.
ad hoc to paper Richardson extrapolation assuming second-order convergence yields conservative estimates of phase error.
Section III.D; no convergence-order measurement is given, and the code is described as third-order in the asymptotic regime, so the assumed order is a load-bearing numerical assumption.
standard math The first law of thermodynamics for adiabatic evolutions, Eq. (5), connects pressure and internal energy.
Used in Section II.A to derive the spectral EOS energy integral; standard thermodynamic identity.

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Cite this review

Pith. "Pith review of Smooth equations of state for high-accuracy simulations of neutron star binaries." pith.science (2026). https://pith.science/paper/VJLTWYHR

@misc{pith2026190805277,
  author       = {Pith},
  title        = {Pith review of: Smooth equations of state for high-accuracy simulations of neutron star binaries},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VJLTWYHR}},
  note         = {Machine review of arXiv:1908.05277}
}

read the original abstract

High-accuracy numerical simulations of merging neutron stars play an important role in testing and calibrating the waveform models used by gravitational wave observatories. Obtaining high-accuracy waveforms at a reasonable computational cost, however, remains a significant challenge. One issue is that high-order convergence of the solution requires the use of smooth evolution variables, while many of the equations of state used to model the neutron star matter have discontinuities, typically in the first derivative of the pressure. Spectral formulations of the equation of state have been proposed as a potential solution to this problem. Here, we report on the numerical implementation of spectral equations of state in the Spectral Einstein Code. We show that, in our code, spectral equations of state allow for high-accuracy simulations at a lower computational cost than commonly used `piecewise polytrope' equations state. We also demonstrate that not all spectral equations of state are equally useful: different choices for the low-density part of the equation of state can significantly impact the cost and accuracy of simulations. As a result, simulations of neutron star mergers present us with a trade-off between the cost of simulations and the physical realism of the chosen equation of state.

Figures

Figures reproduced from arXiv: 1908.05277 by the authors.

**Figure 2.** FIG. 2. Mass-radius relationships for the equations of state from [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** FIG. 3. Density profile of a [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. Error in the orbital phase of an equal mass NSNS binary [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: FIG. 5. Error in the orbital phase of an equal mass NSNS binary [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: FIG. 6. Error in the orbital phase of an equal mass NSNS binary evo [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: FIG. 7. Number of time steps taken as a function of time for equal [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

36 extracted references · 5 canonical work pages

[1]

B. P. Abbott et al. (Virgo, LIGO Scientiﬁc), Phys. Rev. Lett. 119, 161101 (2017), arXiv:1710.05832 [gr-qc]

arXiv 2017
[2]

The LIGO Scientiﬁc Collaboration, the Virgo Collaboration, B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and et al., ArXiv e-prints (2018), arXiv:1805.11581 [gr-qc]

arXiv 2018
[3]

The LIGO Scientiﬁc Collaboration, the Virgo Collaboration, B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and et al., ArXiv e-prints (2018), arXiv:1805.11579 [gr-qc]

arXiv 2018
[4]

J. S. Read, C. Markakis, M. Shibata, K. Ury ¯u, J. D. E. Creighton, and J. L. Friedman, Phys. Rev. D 79, 124033 (2009), arXiv:0901.3258 [gr-qc]

arXiv 2009
[5]

Hinderer, B

T. Hinderer, B. D. Lackey, R. N. Lang, and J. S. Read, Phys. Rev. D 81, 123016 (2010), arXiv:0911.3535 [astro-ph.HE]

arXiv 2010
[6]

Del Pozzo, T

W. Del Pozzo, T. G. F. Li, M. Agathos, C. Van Den Broeck, and S. Vitale, Phys. Rev. Lett. 111, 071101 (2013), arXiv:1307.8338 [gr-qc]

arXiv 2013
[7]

´E. ´E. Flanagan and T. Hinderer, Phys. Rev. D 77, 021502 (2008), arXiv:0709.1915

arXiv 2008
[8]

Kiuchi, K

K. Kiuchi, K. Kawaguchi, K. Kyutoku, Y . Sekiguchi, M. Shi- bata, and K. Taniguchi, Phys. Rev. D 96, 084060 (2017), arXiv:1708.08926 [astro-ph.HE]

arXiv 2017

Show all 36 references

[9]

Dietrich, D

T. Dietrich, D. Radice, S. Bernuzzi, F. Zappa, A. Perego, B. Brgmann, S. V . Chaurasia, R. Dudi, W. Tichy, and M. Uje- vic, Class. Quant. Grav. 35, 24LT01 (2018), arXiv:1806.01625 [gr-qc]

2018 arXiv
[11]

Kiuchi, K

K. Kiuchi, K. Kyohei, K. Kyutoku, Y . Sekiguchi, and M. Shi- bata, (2019), arXiv:1907.03790 [astro-ph.HE]

2019 arXiv
[12]

Radice, L

D. Radice, L. Rezzolla, and F. Galeazzi, Mon. Not. Roy. Astr. Soc. 437, L46 (2014), arXiv:1306.6052 [gr-qc]

2014 arXiv
[13]

J. S. Read, B. D. Lackey, B. J. Owen, and J. L. Friedman, Phys. Rev. D 79, 124032 (2009), arXiv:0812.2163 [astro-ph]

2009 arXiv
[14]

The Spectral Einstein Code,

“The Spectral Einstein Code,” http://www. black-holes.org/SpEC.html
[15]

Bugner, T

M. Bugner, T. Dietrich, S. Bernuzzi, A. Weyhausen, and B. Br ¨ugmann, Phys. Rev. D 94, 084004 (2016), arXiv:1508.07147 [gr-qc]

2016 arXiv
[16]

L. E. Kidder, S. E. Field, F. Foucart, E. Schnetter, S. A. Teukol- sky, A. Bohn, N. Deppe, P. Diener, F. H ´ebert, J. Lippuner, J. Miller, C. D. Ott, M. A. Scheel, and T. Vincent, J. Comput. Phys. 335, 84 (2017), arXiv:1609.00098 [astro-ph.HE]

2017 arXiv
[17]

Lindblom, (2010), arXiv:1009.0738 [astro-ph.HE]

L. Lindblom, (2010), arXiv:1009.0738 [astro-ph.HE]

2010 arXiv
[18]

Lindblom, Phys

L. Lindblom, Phys. Rev. D97, 123019 (2018), arXiv:1804.04072 [astro-ph.HE]

2018 arXiv
[19]

Hotokezaka, K

K. Hotokezaka, K. Kiuchi, K. Kyutoku, H. Okawa, Y . Sekiguchi, M. Shibata, and K. Taniguchi, Phys. Rev. D 87, 024001 (2013), arXiv:1212.0905 [astro-ph.HE]

2013 arXiv
[20]

Hebeler, J

K. Hebeler, J. M. Lattimer, C. J. Pethick, and A. Schwenk, Ap.J. 773, 11 (2013), arXiv:1303.4662 [astro-ph.SR]

2013 arXiv
[21]

Shibata, S

M. Shibata, S. Fujibayashi, K. Hotokezaka, K. Kiuchi, K. Kyu- toku, Y . Sekiguchi, and M. Tanaka, Phys. Rev. D96, 123012 (2017), arXiv:1710.07579 [astro-ph.HE]

2017 arXiv
[22]

Radice, A

D. Radice, A. Perego, F. Zappa, and S. Bernuzzi, The As- trophysical Journal Letters 852, L29 (2018), arXiv:1711.03647 [astro-ph.HE]

2018 arXiv
[23]

Demorest, T

P. Demorest, T. Pennucci, S. Ransom, M. Roberts, and J. Hes- sels, Nature 467, 1081 (2010), arXiv:1010.5788 [astro-ph.HE]

2010 arXiv
[24]

Antoniadis, P

J. Antoniadis, P. C. C. Freire, N. Wex, T. M. Tauris, R. S. Lynch, M. H. van Kerkwijk, M. Kramer, C. Bassa, V . S. Dhillon, T. Driebe, J. W. T. Hessels, V . M. Kaspi, V . I. Kondratiev, N. Langer, T. R. Marsh, M. A. McLaughlin, T. T. Pennucci, S. M. Ransom, I. H. Stairs, J. va...

2013 arXiv
[25]

J. W. York, Phys. Rev. Lett. 82, 1350 (1999)

1999
[26]

H. P. Pfeiffer and J. W. York Jr., Phys. Rev. Lett. 95, 091101 (2005)

2005
[27]

H. P. Pfeiffer, L. E. Kidder, M. A. Scheel, and S. A. Teukolsky, Comput. Phys. Commun. 152, 253 (2003), gr-qc/0202096

2003 arXiv
[28]

Foucart, L

F. Foucart, L. E. Kidder, H. P. Pfeiffer, and S. A. Teukolsky, Phys. Rev. D 77, 124051 (2008), arXiv:arXiv:0804.3787 [gr- qc]

2008 arXiv
[29]

R. Haas, C. D. Ott, B. Szil´agyi, J. D. Kaplan, J. Lippuner, M. A. Scheel, K. Barkett, C. D. Muhlberger, T. Dietrich, M. D. Duez, F. Foucart, H. P. Pfeiffer, L. E. Kidder, and S. A. Teukolsky, Phys. Rev. D D93, 124062 (2016), arXiv:1604.00782 [gr-qc]

2016 arXiv
[30]

H. P. Pfeiffer, D. A. Brown, L. E. Kidder, L. Lindblom, G. Lovelace, and M. A. Scheel, Class. Quantum Grav. 24, S59 (2007), gr-qc/0702106. 11

2007 arXiv
[31]

M. D. Duez, F. Foucart, L. E. Kidder, H. P. Pfeiffer, M. A. Scheel, and S. A. Teukolsky, Phys. Rev. D 78, 104015 (2008), arXiv:0809.0002 [gr-qc]

2008 arXiv
[32]

Foucart, M

F. Foucart, M. B. Deaton, M. D. Duez, L. E. Kidder, I. Mac- Donald, C. D. Ott, H. P. Pfeiffer, M. A. Scheel, B. Szil ´agyi, and S. A. Teukolsky, Phys. Rev. D 87, 084006 (2013), arXiv:1212.4810 [gr-qc]

2013 arXiv
[33]

Lindblom, M

L. Lindblom, M. A. Scheel, L. E. Kidder, R. Owen, and O. Rinne, Class. Quantum Grav. 23, S447 (2006), gr- qc/0512093

2006
[34]

Szil ´agyi, Int

B. Szil ´agyi, Int. J. Mod. Phys. D 23, 1430014 (2014), arXiv:1405.3693 [gr-qc]

2014 arXiv
[35]

Radice and L

D. Radice and L. Rezzolla, Astron.Astrophys. 547, A26 (2012), arXiv:1206.6502 [astro-ph.IM]

2012 arXiv
[36]

D. A. Hemberger, M. A. Scheel, L. E. Kidder, B. Szil ´agyi, G. Lovelace, N. W. Taylor, and S. A. Teukolsky, Class. Quan- tum Grav. 30, 115001 (2013), arXiv:1211.6079 [gr-qc]

2013 arXiv
[37]

Foucart et al

F. Foucart et al. , Phys. Rev. D99, 044008 (2019), arXiv:1812.06988 [gr-qc]. Appendix A: List of spectral equations of state 12 TABLE II. List of spectral equations of state with Γ0 = 1.35602. Radii are in kilometers and masses in M⊙. R1.35 NS and Λ1.35 NS are the radius and t...

2019 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

B. P. Abbott et al. (Virgo, LIGO Scientiﬁc), Phys. Rev. Lett. 119, 161101 (2017), arXiv:1710.05832 [gr-qc]

arXiv 2017

[2] [2]

The LIGO Scientiﬁc Collaboration, the Virgo Collaboration, B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and et al., ArXiv e-prints (2018), arXiv:1805.11581 [gr-qc]

arXiv 2018

[3] [3]

The LIGO Scientiﬁc Collaboration, the Virgo Collaboration, B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and et al., ArXiv e-prints (2018), arXiv:1805.11579 [gr-qc]

arXiv 2018

[4] [4]

J. S. Read, C. Markakis, M. Shibata, K. Ury ¯u, J. D. E. Creighton, and J. L. Friedman, Phys. Rev. D 79, 124033 (2009), arXiv:0901.3258 [gr-qc]

arXiv 2009

[5] [5]

Hinderer, B

T. Hinderer, B. D. Lackey, R. N. Lang, and J. S. Read, Phys. Rev. D 81, 123016 (2010), arXiv:0911.3535 [astro-ph.HE]

arXiv 2010

[6] [6]

Del Pozzo, T

W. Del Pozzo, T. G. F. Li, M. Agathos, C. Van Den Broeck, and S. Vitale, Phys. Rev. Lett. 111, 071101 (2013), arXiv:1307.8338 [gr-qc]

arXiv 2013

[7] [7]

´E. ´E. Flanagan and T. Hinderer, Phys. Rev. D 77, 021502 (2008), arXiv:0709.1915

arXiv 2008

[8] [8]

Kiuchi, K

K. Kiuchi, K. Kawaguchi, K. Kyutoku, Y . Sekiguchi, M. Shi- bata, and K. Taniguchi, Phys. Rev. D 96, 084060 (2017), arXiv:1708.08926 [astro-ph.HE]

arXiv 2017