pith. sign in

arxiv: 2605.18560 · v1 · pith:DVMHZVBDnew · submitted 2026-05-18 · ⚛️ nucl-th · astro-ph.HE

Astrophysics equation of state inference with Bayesian chiral effective field theory uncertainties

Melissa Mendes , Hannah G\"ottling , Anna Hensel , Isak Svensson , Kai Hebeler , Achim Schwenk , Nathan Rutherford , Anna Watts This is my paper

Pith reviewed 2026-05-20 07:59 UTC · model grok-4.3

classification ⚛️ nucl-th astro-ph.HE
keywords nuclear equation of statechiral effective field theoryBayesian inferenceneutron starssymmetry energyGW170817NICER observationspQCD constraints
0
0 comments X

The pith

Astrophysical observations with Bayesian chiral effective field theory uncertainties show stiffening of the equation of state above three times nuclear saturation density and constrain the symmetry energy slope L to 43-57 MeV.

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

The paper combines Bayesian priors for the equation of state near saturation density, drawn from chiral effective field theory uncertainties, with constraints from gravitational-wave events, NICER X-ray observations of pulsars, and mass measurements. Although the uncertainty tails permit wider pressure ranges than earlier analyses, most of those ranges are ruled out by the data, yielding mass-radius posteriors that remain consistent with prior results. A clear stiffening emerges in the equation of state at densities greater than or equal to three times saturation density, while perturbative QCD constraints add little once astrophysics is included. The authors exploit the correlation between pure neutron matter and beta-equilibrium matter to extract the symmetry energy slope L directly from the astrophysical posterior.

Core claim

Within broad prior ranges from Bayesian chiral effective field theory uncertainties, the equation of state exhibits clear stiffening at n greater than or equal to 3 n0 after incorporating LIGO/Virgo, NICER, and pulsar data. Perturbative QCD constraints have negligible impact on the final posterior. Using the strong correlation between pure neutron matter and beta-equilibrium matter, the symmetry energy slope parameter L is inferred to lie in the 68 percent credible intervals 42.6-52 MeV for piecewise-polytrope extensions and 44.2-56.7 MeV for speed-of-sound extensions, with the posterior driven primarily by GW170817 together with NICER observations of PSR J0740+6620, PSR J0437-4715, and PSR

What carries the argument

The strong correlation, computed in chiral effective field theory, between the equation of state of pure neutron matter and that of beta-equilibrium matter, which permits inference of the symmetry energy slope L from astrophysical posteriors.

If this is right

  • The final equation of state and neutron-star mass-radius posteriors stay consistent with earlier work despite the broader priors.
  • Perturbative QCD constraints do not meaningfully narrow the posterior once astrophysical data are included.
  • The inferred L values arise from the combination of GW170817 with the listed NICER pulsar observations.
  • The precise numerical range for L depends modestly on whether a piecewise-polytrope or speed-of-sound parametrization is used for the high-density extension.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Neutron-star observations can serve as an independent route to nuclear symmetry-energy parameters without requiring new low-density experiments.
  • The observed stiffening may limit the density at which a transition to deconfined quark matter could occur inside the most massive stars.
  • Additional gravitational-wave events or higher-precision NICER data could shrink the credible interval on L by a factor of two or more.

Load-bearing premise

The strong correlation between pure neutron matter and beta-equilibrium matter computed in chiral effective field theory remains valid when the equation of state is extended to the densities probed by astrophysical observations.

What would settle it

A direct chiral effective field theory calculation or lattice result at densities above 3 n0 that shows the correlation between pure neutron matter and beta-equilibrium matter breaking down by more than the current uncertainty band would falsify the extracted L range.

Figures

Figures reproduced from arXiv: 2605.18560 by Achim Schwenk, Anna Hensel, Anna Watts, Hannah G\"ottling, Isak Svensson, Kai Hebeler, Melissa Mendes, Nathan Rutherford.

Figure 1
Figure 1. Figure 1: Pressure-energy density prior distributions for the PP (left panel) and CS (right panel) extensions with Bayesian χEFT uncertainties up to 1.5n0 (GP-N3LO, blue regions) and uniformly sampled in the previous N3LO range (N3LO, black dashed lines). The dark (light, lighter) blue regions and dashed black (grey, lighter grey) lines encompass the 68% (95% and 99.7%) credible intervals for the GP-N3LO and N3LO ca… view at source ↗
Figure 2
Figure 2. Figure 2: Visual representation of the “minimum” (red dashed line) and “maximum” (blue dashed line) pQCD-com￾patible extensions to an EOS (green) in the number density– chemical potential (n–µ) plane. The pQCD limit is in red. Orange arrows indicate the c 2 s = 1 lines. or lower limit of the allowed pressure range. These ex￾tensions are illustrated in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Mass-radius prior distributions for the PP (left panel) and CS (right panel) extensions with Bayesian χEFT uncertainties up to 1.5n0 without pQCD extensions (GP-N3LO, blue regions), with pQCD extensions (GP-N3LO with pQCD extension, solid red and orange lines), and uniformly sampled in the previous N3LO range (N3LO, black dashed lines). The dark (light) blue regions, the solid red (orange), and the inner (… view at source ↗
Figure 4
Figure 4. Figure 4: Same as [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Mass-radius posterior distributions showing the 2D histogram for the PP (left panel) and CS (right panel) extensions with Bayesian χEFT uncertainties up to 1.5n0 with pQCD extensions (GP-N3LO with pQCD extension, upper panels) and uniformly sampled in the previous N3LO range (N3LO, lower panels). The dark shaded hexagons indicate a lower number of mass-radius samples, while the lighter shaded hexagons indi… view at source ↗
Figure 6
Figure 6. Figure 6: Pressure-energy density posterior distributions for the PP (left panel) and CS (right panel) extensions with Bayesian χEFT uncertainties up to 1.5n0 with pQCD extensions (GP-N3LO, blue regions) and uniformly sampled in the previous N3LO range (N3LO, black dashed lines). The dark (light) blue regions and the inner (outer) black dashed lines encompass the 68% (95%) credible intervals. The vertical thin lines… view at source ↗
Figure 7
Figure 7. Figure 7: Prior (dashed lines) and posterior distributions (filled contours) for the pressure at 1, 1.5, 2, 3 and 4ε0 with Bayesian χEFT uncertainties up to 1.5n0 with pQCD extensions (GP-N3LO) versus uniformly sampled (N3LO) for the PP extension (left panel), CS extension (middle panel), and a comparison between PP and CS extensions for GP-N3LO (right panel). 1.0 2.0 3.0 4.0 ε [ε0] 0 0.2 0.4 0.6 0.8 1.0 1.2 c 2 s G… view at source ↗
Figure 8
Figure 8. Figure 8: Same as [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Prior (unfilled) and posterior (filled) distributions for the L parameter based on the GP-N3LO EOS with the PP (green) and CS (yellow) high-density extensions. The posterior distributions include all astrophysics data consid￾ered in this work. We also give the 68% credible interval as colored horizontal bars (unfilled prior and filled posterior), as well as comparisons to previous L ranges (for details see… view at source ↗
Figure 10
Figure 10. Figure 10: Distributions for the L parameter for the GP-N3LO EOS with the PP (left) and CS (right) high-density extensions, as in [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
read the original abstract

We investigate Bayesian chiral effective field theory ($\chi$EFT) uncertainties, which assign a statistical interpretation to equation of state (EOS) distributions near nuclear saturation density, n$_0$, as well as constraints from perturbative quantum chromodynamics (pQCD) to Bayesian EOS inference from LIGO/Virgo, NICER and pulsar mass observations. The tails of the $\chi$EFT uncertainties allow for broader pressure ranges in our priors, but large parts of these are excluded by the astrophysical observations, so that the EOS and the resulting mass-radius posteriors are still very consistent with our earlier work. Within our broad prior ranges, we observe a clear stiffening of the EOS at $n \gtrsim 3 n_0$. Moreover, the impact of the pQCD constraints on the posterior EOS and mass-radius range is negligible due to the astrophysics constraints. Exploiting the strong correlation between pure neutron matter and matter in beta equilibrium, we infer the symmetry energy slope parameter $L$ from astrophysics. For the $68\%$ credible interval, we obtain $L=42.6-52$ MeV and $L=44.2-56.7$ MeV using piecewise-polytrope and speed-of-sound high-density extensions, respectively. The $L$ posterior is mainly driven by the combination of GW170817 LIGO/Virgo and PSR J0740+6620, PSR J0437-4715, and PSR J0614-3329 NICER observations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper performs Bayesian inference of the neutron-star equation of state that incorporates statistical uncertainties from chiral effective field theory near nuclear saturation density, combines them with astrophysical constraints from LIGO/Virgo, NICER, and pulsar mass measurements, and applies perturbative QCD at high density. It reports that astrophysical data exclude most of the prior tails, that the EOS stiffens at n ≳ 3 n0, that pQCD has negligible effect on the posterior, and that the symmetry-energy slope L can be inferred from the astrophysical posterior by exploiting the χEFT correlation between pure neutron matter and beta-equilibrium matter, yielding 68 % credible intervals L = 42.6–52 MeV (piecewise-polytrope extension) and L = 44.2–56.7 MeV (speed-of-sound extension).

Significance. If the central claims hold, the work supplies updated, statistically interpreted EOS and L constraints that remain consistent with earlier results while employing broader χEFT priors. The finding that astrophysics dominates over pQCD and that the EOS stiffens at moderate densities above saturation is of direct interest to nuclear astrophysics and neutron-star modeling.

major comments (1)
  1. [Abstract and L-inference results] The L inference reported in the abstract and results section exploits the strong correlation between pure neutron matter and beta-equilibrium matter that was previously computed in χEFT near saturation. This correlation is then applied to the posterior EOS after it has been extended to n ≳ 3 n0 with piecewise-polytrope or speed-of-sound parametrizations. The manuscript does not demonstrate that the correlation coefficient remains unchanged once the low-density χEFT form is replaced by these phenomenological extensions, which are only loosely constrained by pQCD at much higher densities. Because this assumption is load-bearing for the quoted L credible intervals, a sensitivity test or explicit justification is required.
minor comments (1)
  1. [Abstract] The abstract states that the χEFT uncertainties 'assign a statistical interpretation' to the EOS distributions; a brief sentence clarifying how the truncation-error model is converted into a probability distribution would improve readability for readers outside the χEFT community.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive major comment. We address the point directly below and have incorporated revisions to strengthen the presentation of the L-inference procedure.

read point-by-point responses

  1. Referee: [Abstract and L-inference results] The L inference reported in the abstract and results section exploits the strong correlation between pure neutron matter and beta-equilibrium matter that was previously computed in χEFT near saturation. This correlation is then applied to the posterior EOS after it has been extended to n ≳ 3 n0 with piecewise-polytrope or speed-of-sound parametrizations. The manuscript does not demonstrate that the correlation coefficient remains unchanged once the low-density χEFT form is replaced by these phenomenological extensions, which are only loosely constrained by pQCD at much higher densities. Because this assumption is load-bearing for the quoted L credible intervals, a sensitivity test or explicit justification is required.

    Authors: We agree that an explicit check of the correlation under the high-density extensions would improve clarity. The correlation between pure neutron matter and beta-equilibrium matter is taken from χEFT calculations performed near saturation density; in our framework the EOS below the matching density (approximately 2 n0) is still drawn from the χEFT prior (updated by astrophysical data), while the piecewise-polytrope and speed-of-sound extensions are applied only above this density. Because L is fixed by the slope of the symmetry energy at n0, the high-density parametrization cannot retroactively alter the low-density correlation. Nevertheless, to address the referee’s concern we have added a new appendix containing a sensitivity study in which the transition density is varied between 1.5 n0 and 3 n0 and the L posterior is recomputed for both extensions. The resulting 68 % credible intervals shift by less than 2 MeV, remaining within the originally quoted ranges. A short paragraph justifying this robustness has also been inserted in Section 4. We therefore regard the quoted L intervals as reliable, but the added material makes the underlying assumption transparent. revision: yes

Circularity Check

0 steps flagged

No significant circularity; L inference applies independent χEFT correlation to external astrophysical posterior

full rationale

The derivation combines Bayesian χEFT priors (with their computed correlation between pure neutron matter and beta-equilibrium matter) and independent astrophysical likelihoods from GW170817, NICER pulsars, and mass measurements. The high-density extensions (piecewise polytrope or speed-of-sound) are phenomenological and constrained by pQCD at very high density, but the central posterior and L intervals are driven by the external data rather than by re-deriving the low-density correlation inside the same fit. The correlation itself is a prior theoretical result from χEFT, not fitted to the present astrophysical observations or redefined by construction within this paper. Self-citations to prior χEFT work are present but not load-bearing for the final claim, as the astrophysical constraints are external and falsifiable. This is the normal, non-circular case of using established theoretical inputs to interpret new data.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on (1) the statistical interpretation of χEFT truncation errors as a prior, (2) the validity of the pure-neutron-matter to beta-equilibrium correlation at densities above saturation, and (3) the modeling choices for the high-density extension (piecewise polytrope or speed-of-sound). No new particles or forces are introduced.

free parameters (1)
  • high-density extension parameters
    Piecewise-polytrope or speed-of-sound parameters above the χEFT matching density are chosen or fitted within the Bayesian framework.
axioms (2)
  • domain assumption χEFT truncation errors can be assigned a statistical interpretation that remains valid when the EOS is matched to astrophysical data
    Invoked when constructing the Bayesian prior from χEFT uncertainty bands.
  • domain assumption The correlation between pure neutron matter and beta-equilibrium matter computed at low density persists into the density regime constrained by observations
    Required for inferring L directly from the posterior.

pith-pipeline@v0.9.0 · 5830 in / 1629 out tokens · 37323 ms · 2026-05-20T07:59:57.466946+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Exploiting the strong correlation between pure neutron matter and matter in beta equilibrium, we infer the symmetry energy slope parameter L from astrophysics. For the 68% credible interval, we obtain L=42.6-52 MeV and L=44.2-56.7 MeV using piecewise-polytrope and speed-of-sound high-density extensions, respectively.

  • IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    The region 0.5n0 < n ≤ 1.5n0 is described by a probability distribution derived from χEFT calculations... Two different general high-density extensions are used beyond 1.5n0: a piecewise-polytropic (PP) or a speed-of-sound (CS) model

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

80 extracted references · 80 canonical work pages · 3 internal anchors

  1. [1]

    P., Abbott, R., Abbott, T

    Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2019, Properties of the Binary Neutron Star Merger GW170817, Phys. Rev. X, 9, 011001, doi: 10.1103/PhysRevX.9.011001

    work page doi:10.1103/physrevx.9.011001 2019

  2. [2]

    ApJL , year = 2020, month = mar, volume =

    Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2020, GW190425: Observation of a Compact Binary Coalescence with Total Mass∼3.4 M ⊙, Astrophys. J. Lett., 892, L3, doi: 10.3847/2041-8213/ab75f5

    work page doi:10.3847/2041-8213/ab75f5 2020

  3. [3]

    2025, Equation of state and Fermi liquid properties of dense matter based on chiral effective field theory interactions, Phys

    Alp, F., Dietz, Y., Hebeler, K., & Schwenk, A. 2025, Equation of state and Fermi liquid properties of dense matter based on chiral effective field theory interactions, Phys. Rev. C, 112, 055802, doi: 10.1103/ls3l-dn1y

    work page doi:10.1103/ls3l-dn1y 2025

  4. [4]

    Antoniadis, J., Freire, P. C. C., Wex, N., et al. 2013, A Massive Pulsar in a Compact Relativistic Binary, Sci., 340, 1233232, doi: 10.1126/science.1233232

    work page doi:10.1126/science.1233232 2013

  5. [5]

    E., et al

    Basu, A., Graber, V., Lower, M. E., et al. 2025, Probing Neutron Star Interiors and the Properties of Cold Ultra-dense Matter with the SKA, Open J. Astrophys., 8, 54253, doi: 10.33232/001c.154253

    work page doi:10.33232/001c.154253 2025

  6. [6]

    The Ground state of matter at high densities: Equation of state and stellar models

    Baym, G., Pethick, C., & Sutherland, P. 1971, The Ground state of matter at high densities: Equation of state and stellar models, Astrophys. J., 170, 299, doi: 10.1086/151216

    work page doi:10.1086/151216 1971

  7. [7]

    2023, Inference of the sound speed and related properties of neutron stars, Phys

    Brandes, L., Weise, W., & Kaiser, N. 2023, Inference of the sound speed and related properties of neutron stars, Phys. Rev. D, 107, 014011, doi: 10.1103/PhysRevD.107.014011 12

    work page doi:10.1103/physrevd.107.014011 2023

  8. [8]

    X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue

    Buchner, J., Georgakakis, A., Nandra, K., et al. 2014, X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue, Astron. Astrophys., 564, A125, doi: 10.1051/0004-6361/201322971

    work page internal anchor Pith review doi:10.1051/0004-6361/201322971 2014

  9. [9]

    Reviews of Modern Physics , keywords =

    Chatziioannou, K., Cromartie, H. T., Gandolfi, S., et al. 2025, Neutron stars and the dense matter equation of state, Rev. Mod. Phys., 97, 045007, doi: 10.1103/ymsq-cfcw

    work page doi:10.1103/ymsq-cfcw 2025

  10. [10]

    , keywords =

    Choudhury, D., Salmi, T., Vinciguerra, S., et al. 2024, A NICER View of the Nearest and Brightest Millisecond Pulsar: PSR J0437–4715, Astrophys. J. Lett., 971, L20, doi: 10.3847/2041-8213/ad5a6f

    work page doi:10.3847/2041-8213/ad5a6f 2024

  11. [11]

    T., Fonseca, E., Ransom, S

    Cromartie, H. T., Fonseca, E., Ransom, S. M., et al. 2020, Relativistic Shapiro delay measurements of an extremely massive millisecond pulsar, Nature Astr., 4, 72, doi: 10.1038/s41550-019-0880-2

    work page doi:10.1038/s41550-019-0880-2 2020

  12. [12]

    Nature Astronomy , keywords =

    Cruise, M., Guainazzi, M., Aird, J., et al. 2025, The NewAthena mission concept in the context of the next decade of X-ray astronomy, Nature Astr., 9, 36, doi: 10.1038/s41550-024-02416-3

    work page doi:10.1038/s41550-024-02416-3 2025

  13. [13]

    2010, Shapiro Delay Measurement of A Two Solar Mass Neutron Star, Nature, 467, 1081, doi: 10.1038/nature09466

    Hessels, J. 2010, Shapiro Delay Measurement of A Two Solar Mass Neutron Star, Nature, 467, 1081, doi: 10.1038/nature09466

    work page doi:10.1038/nature09466 2010

  14. [14]

    , keywords =

    Dittmann, A. J., Miller, M. C., Lamb, F. K., et al. 2024, A More Precise Measurement of the Radius of PSR J0740+6620 Using Updated NICER Data, Astrophys. J., 974, 295, doi: 10.3847/1538-4357/ad5f1e

    work page doi:10.3847/1538-4357/ad5f1e 2024

  15. [15]

    J., Melendez, J

    Drischler, C., Furnstahl, R. J., Melendez, J. A., & Phillips, D. R. 2020a, How Well Do We Know the Neutron-Matter Equation of State at the Densities Inside Neutron Stars? A Bayesian Approach with Correlated Uncertainties, Phys. Rev. Lett., 125, 202702, doi: 10.1103/PhysRevLett.125.202702

    work page doi:10.1103/physrevlett.125.202702

  16. [16]

    2019, Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation, Phys

    Drischler, C., Hebeler, K., & Schwenk, A. 2019, Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation, Phys. Rev. Lett., 122, 042501, doi: 10.1103/PhysRevLett.122.042501

    work page doi:10.1103/physrevlett.122.042501 2019

  17. [17]

    S., & Arthuis, P

    Drischler, C., McElvain, K. S., & Arthuis, P. 2026, Many-body perturbation theory for the nuclear equation of state up to fifth order, https://arxiv.org/abs/2603.24532

    work page arXiv 2026

  18. [18]

    A., Furnstahl, R

    Drischler, C., Melendez, J. A., Furnstahl, R. J., & Phillips, D. R. 2020b, Quantifying uncertainties and correlations in the nuclear-matter equation of state, Phys. Rev. C, 102, 054315, doi: 10.1103/PhysRevC.102.054315

    work page doi:10.1103/physrevc.102.054315

  19. [19]

    R., Machleidt, R., & Nosyk, Y

    Entem, D. R., Machleidt, R., & Nosyk, Y. 2017, High-quality two-nucleon potentials up to fifth order of the chiral expansion, Phys. Rev. C, 96, 024004, doi: 10.1103/PhysRevC.96.024004

    work page doi:10.1103/physrevc.96.024004 2017

  20. [20]

    Epelbaum, E., Krebs, H., & Meißner, U. G. 2015, Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order, Eur. Phys. J. A, 51, 53, doi: 10.1140/epja/i2015-15053-8

    work page doi:10.1140/epja/i2015-15053-8 2015

  21. [21]

    Essick, R., Tews, I., Landry, P., Reddy, S., & Holz, D. E. 2020, Direct Astrophysical Tests of Chiral Effective Field Theory at Supranuclear Densities, Phys. Rev. C, 102, 055803, doi: 10.1103/PhysRevC.102.055803

    work page doi:10.1103/physrevc.102.055803 2020

  22. [22]

    2021, Astrophysical Constraints on the Symmetry Energy and the Neutron Skin of 208Pb with Minimal Modeling

    Essick, R., Tews, I., Landry, P., & Schwenk, A. 2021, Astrophysical Constraints on the Symmetry Energy and the Neutron Skin of 208Pb with Minimal Modeling

    work page 2021

  23. [23]

    Assumptions, Phys. Rev. Lett., 127, 192701, doi: 10.1103/PhysRevLett.127.192701

    work page doi:10.1103/physrevlett.127.192701

  24. [24]

    W., von Neumann-Cosel, P., Bacca, S., et al

    Fearick, R. W., von Neumann-Cosel, P., Bacca, S., et al. 2023, Electric dipole polarizability of 40Ca, Phys. Rev. Res., 5, L022044, doi: 10.1103/PhysRevResearch.5.L022044

    work page doi:10.1103/physrevresearch.5.l022044 2023

  25. [25]

    doi:10.1111/j.1365-2966.2009.14548.x , eprint =

    Feroz, F., Hobson, M. P., & Bridges, M. 2009, MULTINEST: an efficient and robust Bayesian inference tool for cosmology and particle physics, Mon. Not. Roy. Astron. Soc., 398, 1601, doi: 10.1111/j.1365-2966.2009.14548.x

    work page doi:10.1111/j.1365-2966.2009.14548.x 2009

  26. [26]

    T., Ellis, J

    Fonseca, E., Pennucci, T. T., Ellis, J. A., et al. 2016, The NANOGrav Nine-year Data Set: Mass and Geometric Measurements of Binary Millisecond Pulsars, Astrophys. J., 832, 167, doi: 10.3847/0004-637X/832/2/167

    work page doi:10.3847/0004-637x/832/2/167 2016

  27. [27]

    , keywords =

    Fonseca, E., Cromartie, H. T., Pennucci, T. T., et al. 2021, Refined Mass and Geometric Measurements of the High-mass PSR J0740+6620, Astrophys. J. Lett., 915, L12, doi: 10.3847/2041-8213/ac03b8

    work page doi:10.3847/2041-8213/ac03b8 2021

  28. [28]

    S., Kurkela, A., & Vuorinen, A

    Fraga, E. S., Kurkela, A., & Vuorinen, A. 2014, Interacting quark matter equation of state for compact stars, Astrophys. J. Lett., 781, L25, doi: 10.1088/2041-8205/781/2/L25

    work page doi:10.1088/2041-8205/781/2/l25 2014

  29. [29]

    2023a, Constraints on Strong Phase Transitions in Neutron Stars, Astrophys

    Vuorinen, A. 2023a, Constraints on Strong Phase Transitions in Neutron Stars, Astrophys. J., 955, 100, doi: 10.3847/1538-4357/aceefb

    work page doi:10.3847/1538-4357/aceefb

  30. [30]

    2023b, Ab-initio QCD Calculations Impact the Inference of the Neutron-star-matter Equation of State, Astrophys

    Gorda, T., Komoltsev, O., & Kurkela, A. 2023b, Ab-initio QCD Calculations Impact the Inference of the Neutron-star-matter Equation of State, Astrophys. J., 950, 107, doi: 10.3847/1538-4357/acce3a

    work page doi:10.3847/1538-4357/acce3a

  31. [31]

    2026, Constrained Gaussian-process-bridge Prior for Neutron-star Equation-of-state Inference, Astrophys

    Gorda, T., Komoltsev, O., Kurkela, A., & Sunde, E. 2026, Constrained Gaussian-process-bridge Prior for Neutron-star Equation-of-state Inference, Astrophys. J., 1002, 40, doi: 10.3847/1538-4357/ae552a 13

    work page doi:10.3847/1538-4357/ae552a 2026

  32. [32]

    Matter, Phys. Rev. Lett., 127, doi: 10.1103/physrevlett.127.162003

    work page doi:10.1103/physrevlett.127.162003

  33. [33]

    Neutron star crust and outer core equation of state from chiral effective field theory with quantified uncertainties

    Vuorinen, A. 2021b, Cold quark matter at N 3LO: Soft contributions, Phys. Rev. D, 104, doi: 10.1103/physrevd.104.074015 G¨ ottling, H., Hoff, L., Hebeler, K., & Schwenk, A. 2025, Neutron star crust and outer core equation of state from chiral effective field theory with quantified uncertainties, https://arxiv.org/abs/2512.19593

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.104.074015 2025

  34. [34]

    Watts, A. L. 2019, Equation of state sensitivities when inferring neutron star and dense matter properties, Mon. Not. Roy. Astron. Soc., 485, 5363, doi: 10.1093/mnras/stz654

    work page doi:10.1093/mnras/stz654 2019

  35. [35]

    M., Pethick, C

    Hebeler, K., Lattimer, J. M., Pethick, C. J., & Schwenk, A. 2013, Equation of state and neutron star properties constrained by nuclear physics and observation, Astrophys. J., 773, 11, doi: 10.1088/0004-637X/773/1/11

    work page doi:10.1088/0004-637x/773/1/11 2013

  36. [36]

    2025, Cross-Comparison of Sampling Algorithms for Pulse Profile Modeling of PSR J0740+6620, https://arxiv.org/abs/2502.13682

    Buchner, J. 2025, Cross-Comparison of Sampling Algorithms for Pulse Profile Modeling of PSR J0740+6620, https://arxiv.org/abs/2502.13682

    work page arXiv 2025

  37. [37]

    , keywords =

    Hoogkamer, M., Rutherford, N., Huppenkothen, D., et al. 2026, Equation-of-state-informed pulse profile modeling, Phys. Rev. D, 113, 063049, doi: 10.1103/z2hd-w9sy

    work page doi:10.1103/z2hd-w9sy 2026

  38. [38]

    2022, Ab initio predictions link the neutron skin of 208Pb to nuclear forces, Nature Phys., 18, 1196, doi: 10.1038/s41567-022-01715-8

    Hu, B., Jiang, W., Miyagi, T., et al. 2022, Ab initio predictions link the neutron skin of 208Pb to nuclear forces, Nature Phys., 18, 1196, doi: 10.1038/s41567-022-01715-8

    work page doi:10.1038/s41567-022-01715-8 2022

  39. [39]

    , keywords =

    Keller, J., Hebeler, K., & Schwenk, A. 2023, Nuclear Equation of State for Arbitrary Proton Fraction and Temperature Based on Chiral Effective Field Theory and a Gaussian Process Emulator, Phys. Rev. Lett., 130, 072701, doi: 10.1103/PhysRevLett.130.072701

    work page doi:10.1103/physrevlett.130.072701 2023

  40. [40]

    Kiniet al., A NICER View of PSR J0030+0451: Up- dated Constraints from Six Years of NICER Observations, arXiv (2026), arXiv:2602.23743 [astro-ph.HE]

    Kini, Y., Mauviard, L., Salmi, T., et al. 2026, A NICER View of PSR J0030+0451: Updated Constraints from Six Years of NICER Observations, https://arxiv.org/abs/2602.23743

    work page arXiv 2026

  41. [41]

    Koehn, H., Rose, H., Pang, P. T. H., et al. 2025, From Existing and New Nuclear and Astrophysical Constraints to Stringent Limits on the Equation of State of Neutron-Rich Dense Matter, Phys. Rev. X, 15, 021014, doi: 10.1103/PhysRevX.15.021014

    work page doi:10.1103/physrevx.15.021014 2025

  42. [42]

    2022, How Perturbative QCD Constrains the Equation of State at Neutron-Star

    Komoltsev, O., & Kurkela, A. 2022, How Perturbative QCD Constrains the Equation of State at Neutron-Star

    work page 2022

  43. [43]

    Densities, Phys. Rev. Lett., 128, doi: 10.1103/physrevlett.128.202701

    work page doi:10.1103/physrevlett.128.202701

  44. [44]

    2024, Equation of state at neutron-star densities and beyond from perturbative QCD, Phys

    Komoltsev, O., Somasundaram, R., Gorda, T., et al. 2024, Equation of state at neutron-star densities and beyond from perturbative QCD, Phys. Rev. D, 109, 094030, doi: 10.1103/PhysRevD.109.094030

    work page doi:10.1103/physrevd.109.094030 2024

  45. [45]

    2020, Nonparametric constraints on neutron star matter with existing and upcoming gravitational wave and pulsar observations, Phys

    Landry, P., Essick, R., & Chatziioannou, K. 2020, Nonparametric constraints on neutron star matter with existing and upcoming gravitational wave and pulsar observations, Phys. Rev. D, 101, 123007, doi: 10.1103/PhysRevD.101.123007

    work page doi:10.1103/physrevd.101.123007 2020

  46. [46]

    Lattimer, J. M. 2021, Neutron Stars and the Nuclear Matter Equation of State, Annu. Rev. Nucl. Part. Sci., 71, 433, doi: 10.1146/annurev-nucl-102419-124827

    work page doi:10.1146/annurev-nucl-102419-124827 2021

  47. [47]

    Lattimer, J. M. 2023, Constraints on Nuclear Symmetry Energy Parameters, Particles, 6, 30, doi: 10.3390/particles6010003

    work page doi:10.3390/particles6010003 2023

  48. [48]

    L., Zhang, G., et al

    Li, A., Watts, A. L., Zhang, G., et al. 2025, Dense matter in neutron stars with eXTP, Sci. China Phys. Mech. Astron., 68, 119503, doi: 10.1007/s11433-025-2761-4

    work page doi:10.1007/s11433-025-2761-4 2025

  49. [49]

    E., Tews, I., Carlson, J., et al

    Lynn, J. E., Tews, I., Carlson, J., et al. 2016, Chiral Three-Nucleon Interactions in Light Nuclei, Neutron-α Scattering, and Neutron Matter, Phys. Rev. Lett., 116, 062501, doi: 10.1103/PhysRevLett.116.062501

    work page doi:10.1103/physrevlett.116.062501 2016

  50. [50]

    , keywords =

    Mauviard, L., Guillot, S., Salmi, T., et al. 2025, A NICER View of the 1.4 M ⊙ Edge-on Pulsar PSR J0614-3329, Astrophys. J., 995, 60, doi: 10.3847/1538-4357/ae145d

    work page doi:10.3847/1538-4357/ae145d 2025

  51. [51]

    C., Lamb, F

    Miller, M. C., Lamb, F. K., Dittmann, A. J., et al. 2019, PSR J0030+0451 Mass and Radius from NICER Data and Implications for the Properties of Neutron Star

    work page 2019

  52. [52]

    Matter, Astrophys. J. Lett., 887, L24, doi: 10.3847/2041-8213/ab50c5

    work page doi:10.3847/2041-8213/ab50c5 2041

  53. [53]

    C., Lamb, F

    Miller, M. C., Lamb, F. K., Dittmann, A. J., et al. 2021, The Radius of PSR J0740+6620 from NICER and XMM-Newton Data, Astrophys. J. Lett., 918, L28, doi: 10.3847/2041-8213/ac089b

    work page doi:10.3847/2041-8213/ac089b 2021

  54. [54]

    , keywords =

    Miller, M. C., Dittmann, A. J., Holt, I. M., et al. 2026, The Radius of PSR J0437–4715 from NICER Data, Astrophys. J. Lett., 1000, L48, doi: 10.3847/2041-8213/ae5057

    work page doi:10.3847/2041-8213/ae5057 2026

  55. [55]

    2025, Inferring the neutron star equation of state with nuclear-physics informed semiparametric models, Class

    Ng, S., Legred, I., Suleiman, L., et al. 2025, Inferring the neutron star equation of state with nuclear-physics informed semiparametric models, Class. Quant. Grav., 42, 205008, doi: 10.1088/1361-6382/ae1094

    work page doi:10.1088/1361-6382/ae1094 2025

  56. [56]

    Classical and Quantum Gravity , year = 2010, month = oct, volume = 27, number = 19, eid =

    Punturo, M., Abernathy, M., Acernese, F., et al. 2010, The Einstein Telescope: a third-generation gravitational wave observatory, Class. Quant. Grav., 27, 194002, doi: 10.1088/0264-9381/27/19/194002

    work page doi:10.1088/0264-9381/27/19/194002 2010

  57. [57]

    2025, The Astrophysical J ournal, 981, 99, doi: 10.3847/1538-4357/adb42f

    Qi, L., Zheng, S., Zhang, J., et al. 2025, PSR J1231–1411 Revisited: Pulse Profile Analysis of X-Ray Observation, Astrophys. J., 981, 99, doi: 10.3847/1538-4357/adb42f 14

    work page doi:10.3847/1538-4357/adb42f 2025

  58. [58]

    2025, NEoST: A Python package for nested sampling of the neutron star equation of state, J

    Raaijmakers, G., Rutherford, N., Timmerman, P., et al. 2025, NEoST: A Python package for nested sampling of the neutron star equation of state, J. Open Source Softw., 10, 6003, doi: 10.21105/joss.06003

    work page doi:10.21105/joss.06003 2025

  59. [59]

    E., Watts, A

    Raaijmakers, G., Riley, T. E., Watts, A. L., et al. 2019, A Nicer View of PSR J0030+0451: Implications for the Dense Matter Equation of State, Astrophys. J. Lett., 887, L22, doi: 10.3847/2041-8213/ab451a

    work page doi:10.3847/2041-8213/ab451a 2019

  60. [60]

    K., Riley, T

    Raaijmakers, G., Greif, S. K., Riley, T. E., et al. 2020, Constraining the Dense Matter Equation of State with Joint Analysis of NICER and LIGO/Virgo

    work page 2020

  61. [61]

    Measurements, Astrophys. J. Lett., 893, L21, doi: 10.3847/2041-8213/ab822f

    work page doi:10.3847/2041-8213/ab822f 2041

  62. [62]

    K., Hebeler, K., et al

    Raaijmakers, G., Greif, S. K., Hebeler, K., et al. 2021, Constraints on the Dense Matter Equation of State and Neutron Star Properties from NICER’s Mass–Radius Estimate of PSR J0740+6620 and Multimessenger

    work page 2021

  63. [63]

    Observations, Astrophys. J. Lett., 918, L29, doi: 10.3847/2041-8213/ac089a

    work page doi:10.3847/2041-8213/ac089a 2041

  64. [64]

    S., Lackey, B

    Read, J. S., Lackey, B. D., Owen, B. J., & Friedman, J. L. 2009, Constraints on a phenomenologically parametrized neutron-star equation of state, Phys. Rev. D, 79, doi: 10.1103/physrevd.79.124032

    work page doi:10.1103/physrevd.79.124032 2009

  65. [65]

    2021, Implications of PREX-2 on the Equation of State of Neutron-Rich Matter, Phys

    Piekarewicz, J. 2021, Implications of PREX-2 on the Equation of State of Neutron-Rich Matter, Phys. Rev. Lett., 126, 172503, doi: 10.1103/PhysRevLett.126.172503

    work page doi:10.1103/physrevlett.126.172503 2021

  66. [66]

    Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO

    Reitze, D., Adhikari, R. X., Ballmer, S., et al. 2019, Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO, in Bull. Am. Astron. Soc., Vol. 51, 35, doi: 10.48550/arXiv.1907.04833

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1907.04833 2019

  67. [67]

    , keywords =

    Riley, T. E., Watts, A. L., Bogdanov, S., et al. 2019, A NICER View of PSR J0030+0451: Millisecond Pulsar Parameter Estimation, Astrophys. J. Lett., 887, L21, doi: 10.3847/2041-8213/ab481c

    work page doi:10.3847/2041-8213/ab481c 2019

  68. [68]

    , keywords =

    Riley, T. E., Watts, A. L., Ray, P. S., et al. 2021, A NICER View of the Massive Pulsar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy, Astrophys. J. Lett., 918, L27, doi: 10.3847/2041-8213/ac0a81

    work page doi:10.3847/2041-8213/ac0a81 2021

  69. [69]

    , keywords =

    Rutherford, N., Mendes, M., Svensson, I., et al. 2024, Constraining the Dense Matter Equation of State with New NICER Mass–Radius Measurements and New Chiral Effective Field Theory Inputs, Astrophys. J. Lett., 971, L19, doi: 10.3847/2041-8213/ad5f02

    work page doi:10.3847/2041-8213/ad5f02 2024

  70. [70]

    , keywords =

    Salmi, T., Vinciguerra, S., Choudhury, D., et al. 2022, The Radius of PSR J0740+6620 from NICER with NICER Background Estimates, Astrophys. J., 941, 150, doi: 10.3847/1538-4357/ac983d

    work page doi:10.3847/1538-4357/ac983d 2022

  71. [71]

    , keywords =

    Salmi, T., Vinciguerra, S., Choudhury, D., et al. 2023, Atmospheric Effects on Neutron Star Parameter Constraints with NICER, Astrophys. J., 956, 138, doi: 10.3847/1538-4357/acf49d

    work page doi:10.3847/1538-4357/acf49d 2023

  72. [72]

    , keywords =

    Salmi, T., Choudhury, D., Kini, Y., et al. 2024a, The Radius of the High-mass Pulsar PSR J0740+6620 with 3.6 yr of NICER Data, Astrophys. J., 974, 294, doi: 10.3847/1538-4357/ad5f1f

    work page doi:10.3847/1538-4357/ad5f1f

  73. [73]

    , keywords =

    Salmi, T., Deneva, J. S., Ray, P. S., et al. 2024b, A NICER View of PSR J1231-1411: A Complex Case, Astrophys. J., 976, 58, doi: 10.3847/1538-4357/ad81d2

    work page doi:10.3847/1538-4357/ad81d2

  74. [74]

    Nested Sampling , volume =

    Skilling, J. 2004, Nested Sampling, AIP Conf. Proc., 735, 395, doi: 10.1063/1.1835238

    work page doi:10.1063/1.1835238 2004

  75. [75]

    2025, Inferring three-nucleon couplings from multi-messenger neutron-star observations, Nature Commun., 16, 9819, doi: 10.1038/s41467-025-64756-6

    Somasundaram, R., Svensson, I., De, S., et al. 2025, Inferring three-nucleon couplings from multi-messenger neutron-star observations, Nature Commun., 16, 9819, doi: 10.1038/s41467-025-64756-6

    work page doi:10.1038/s41467-025-64756-6 2025

  76. [76]

    2026, Bayesian approach for many-body uncertainties in nuclear structure: Many-body perturbation theory for finite nuclei, Phys

    Svensson, I., Tichai, A., Hebeler, K., & Schwenk, A. 2026, Bayesian approach for many-body uncertainties in nuclear structure: Many-body perturbation theory for finite nuclei, Phys. Rev. C, 113, 024303, doi: 10.1103/y8kt-mgf5

    work page doi:10.1103/y8kt-mgf5 2026

  77. [77]

    2018, Constraining the speed of sound inside neutron stars with chiral effective field theory interactions and observations, Astrophys

    Tews, I., Carlson, J., Gandolfi, S., & Reddy, S. 2018, Constraining the speed of sound inside neutron stars with chiral effective field theory interactions and observations, Astrophys. J., 860, 149, doi: 10.3847/1538-4357/aac267

    work page doi:10.3847/1538-4357/aac267 2018

  78. [78]

    2013, Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory, Phys

    Tews, I., Kr¨ uger, T., Hebeler, K., & Schwenk, A. 2013, Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory, Phys. Rev. Lett., 110, 032504, doi: 10.1103/PhysRevLett.110.032504

    work page doi:10.1103/physrevlett.110.032504 2013

  79. [79]

    2025, Neutron matter from local chiral effective field theory interactions at large cutoffs, Phys

    Tews, I., Somasundaram, R., Lonardoni, D., et al. 2025, Neutron matter from local chiral effective field theory interactions at large cutoffs, Phys. Rev. Res., 7, 033024, doi: 10.1103/r314-6r62

    work page doi:10.1103/r314-6r62 2025

  80. [80]

    , keywords =

    Vinciguerra, S., Salmi, T., Watts, A. L., et al. 2024, An Updated Mass-Radius Analysis of the 2017-2018 NICER Data Set of PSR J0030+0451, Astrophys. J., 961, 62, doi: 10.3847/1538-4357/acfb83

    work page doi:10.3847/1538-4357/acfb83 2024