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REVIEW 3 major objections 5 minor 67 references

Inference of Neutron Star Mass Distributions and the Dense Matter Equation of State from Multi-messenger Observations

T0 review · 3 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read This paper claims that whether the neutron-star maximum mass gets a flat prior directly or is derived as a nuisance parameter changes the inferred maximum mass, from 2.09 to 2.15 solar masses for polytropic equations of state.

desk verdict The paper's headline Mmax shift is a prior effect, real in their setup but overlapping at 90% CL; the novelty claim is oversold, and the reparametrization behind it needs justification before the central result is accepted. read the letter →

arxiv 2512.12130 v3 pith:XMW33DCW submitted 2025-12-13 astro-ph.HE

Mahmudul Hasan Anik , Andrew W. Steiner , Richard O'Shaughnessy This is my paper · ORCID
classification astro-ph.HE
keywords neutronstarmaximummassequationofstatedistributionBayesianinferencemulti-messengerastronomygravitationalwaveslow-massX-raybinariespriordependence
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 builds a single Bayesian model that combines gravitational-wave detections, electromagnetic mass-radius measurements, and radio-timing masses of neutron stars in three binary classes—double neutron stars, neutron-star–white-dwarf systems, and low-mass X-ray binaries—to infer both the dense-matter equation of state and the neutron-star mass distribution at once. The authors' new claim is that the inferred maximum neutron-star mass depends on where the prior is placed: if the prior is set uniform on the maximum mass itself rather than on an equation-of-state parameter that only indirectly determines it, the posterior for the maximum mass shifts upward (for polytropic equations of state, from 2.09 to 2.15 solar masses at 90% confidence). The same prior choice also moves the inferred mean mass of low-mass X-ray binaries from about 1.51 to 1.62 solar masses. A careful reader cares because the number quoted as "the maximum neutron-star mass" is partly an artifact of prior parametrization, not purely a statement about the data.

What carries the argument

The load-bearing object is the Jacobian change-of-variables identity (Eq. 17), P(Mmax) = (∂p_Nk/∂Mmax) P(p_Nk), used to replace one EoS parameter by Mmax so that Mmax can be given a flat prior. The paper applies it to two EoS families—a three-segment piecewise polytrope and a three-segment fixed-sound-speed model—matched to a low-density crust EoS. The identity is what converts a vague "the EoS parameters are uncertain" statement into a concrete "the maximum mass itself is uniformly uncertain" statement, and it is the mechanism that produces the reported upward shift in Mmax and in the LMXB population mean.

What would settle it

Re-run the polytropic analysis after explicitly computing the Jacobian ∂p_Nk/∂Mmax along the posterior samples; if the posterior for Mmax under the flat-Mmax prior matches what you get by directly sampling p_Nk and then weighting by 1/|∂Mmax/∂p_Nk| at every point, the shift is real. Alternatively, replace the single-parameter mapping with a two-parameter high-density EoS in which Mmax is non-monotone; if the flat-Mmax prior no longer shifts Mmax, the effect is an artifact of the parametrization.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central finding is that reparametrizing the equation of state so that the observable neutron-star maximum mass Mmax carries a uniform prior—instead of being a derived function of EoS parameters with uniform priors—shifts the posterior Mmax to larger values. Specifically, for piecewise-polytropic EoSs the 90% maximum-mass posterior changes from Mmax = 2.09+0.18−0.07 Msun to Mmax = 2.15+0.19−0.10 Msun, and for linear sound-speed EoSs from 2.09+0.33−0.07 to 2.16+0.27−0.12. The paper also finds distinct, EoS-dependent mass distributions for the three populations, with the low-mass X-ray binary population mean shifting from 1.51 to 1.62 Msun (68%) under the flat-Mmax

Load-bearing premise

The argument rests on assuming that the neutron-star maximum mass is a one-to-one, monotonically increasing function of a single equation-of-state parameter with all others fixed; if that map is not invertible over the prior range, the 'flat Mmax prior' models are not actually flat in Mmax and the reported shift may be an artifact.

Editorial extensions

If this is right

  • If correct, the commonly quoted neutron-star maximum mass from multi-messenger inference is prior-dependent at the ~0.06 solar-mass level; comparisons among studies must state their prior convention.
  • Joint inference of EoS and mass distribution is necessary: a separate analysis of Mmax from population alone and EoS alone can disagree for reasons that are partly prior effects.
  • The flat-Mmax prior also changes the inferred LMXB mean mass, so conclusions about neutron-star formation and accretion histories based on LMXB masses carry an EoS-prior sensitivity.
  • The upper bound of Mmax remains weakly constrained (support up to ~2.5–2.9 Msun depending on model), so future measurements of very massive pulsars, not just more average-mass stars, are the lever arm.

Reading between the lines

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

  • Editorial inference: the shift suggests that analyses that put uniform priors on pressure/sound-speed parameters may systematically under-report Mmax, because they effectively put a non-uniform, peaked prior on the maximum mass; re-running published analyses with a flat-Mmax prior would test this across data sets.
  • Editorial inference: if the assumed monotone one-to-one map between the EoS parameter and Mmax (needed for Eq. 17) fails, the reported shift could be a numerical artifact; a direct check of the Jacobian over the full prior volume would settle this.
  • Editorial inference: a testable extension is to apply the same reparametrization to an EoS family that allows phase transitions or a second high-density parameter, where Mmax may not be monotone; if the shift disappears, the effect is specific to smooth polytropes, not to the prior location in general.
  • Editorial inference: the correlation plot (Figure 6) hints that LMXB skewness and Mmax are entangled in some models; a future analysis that conditions on a fixed observed Mmax (e.g., from a 2.1+ Msun pulsar) would isolate how much population inference can say about the EoS ceiling.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper constructs a joint Bayesian inference of neutron-star mass distributions and the dense-matter equation of state (EoS) using three subpopulations (double neutron stars, NS–white-dwarf binaries, and low-mass X-ray binaries), combining radio-timing mass measurements, electromagnetic mass–radius constraints, and the gravitational-wave events GW170817 and GW190425. Two high-density EoS parametrizations are used: a linear sound-speed model and a piecewise polytrope. The main methodological addition is in §3.3: a reparametrization that replaces one EoS parameter with the maximum mass Mmax and assigns Mmax a uniform prior. The authors report that this prior reweighting shifts the inferred Mmax from 2.09 Msun to 2.15 Msun for polytropic EoSs and changes the LMXB population mean from 1.51 to 1.62 Msun. They also report population-specific mass distributions and correlations between Mmax and the LMXB skewness.

Significance. If the technical construction is valid, the paper provides a useful and reproducible study of prior sensitivity in a joint EoS-population inference, with a heterogeneous modern data set and publicly available code and data. The population-specific mass distributions are broadly consistent with earlier work, and the simultaneous treatment of EoS and mass-distribution parameters is a worthwhile contribution. However, the headline claim—that a uniform prior on Mmax shifts the posterior—is a prior-consequence rather than a new empirical measurement, and its quantitative magnitude is not robustly established because the reparametrization's validity is unverified and a hard lower bound on Mmax is imposed. The paper is therefore not acceptable in its current form, but the concerns are addressable within the scope of a revision.

major comments (3)
  1. [§3.3, Eqs. (17)–(18)] The change of variables replaces one EoS parameter p_Nk by Mmax and reweights by ∂p_Nk/∂Mmax. This is valid only if p_Nk is a single-valued, monotone function of Mmax with nonzero derivative for every fixed value of the remaining parameters over the sampled range. The paper does not state which parameter is eliminated, nor does it check invertibility. For the piecewise polytrope NP, Mmax is a nonlocal functional of the adiabatic indices and transition densities and can be non-monotonic in a high-density exponent; the same applies to the sound-speed parameters in NL. If the Jacobian changes sign or becomes small, the induced prior on Mmax is not flat and the ML/MP posteriors do not realize the claimed uniform-Mmax prior. Since the headline result is exactly the NL→ML and NP→MP shift (2.09→2.15 Msun and 1.51→1.62 Msun for μ_lmxb), an unverified Jacobian makes the central claim an artifact.
  2. [§3.2/§4.1, Fig. 3] The text states that a cutoff at 2 Msun reflects an imposed constraint Mmax≥2 Msun, but this constraint is not in Table 4 or in Eq. (15). It is unclear whether the hard lower bound is applied to all four models or only to ML/MP, what the support of the Mmax prior is, and how the boundary interacts with the Jacobian in Eq. (17) near 2 Msun. Because the NL/ML and NP/MP comparisons are the central result, the shift could be partly produced by the hard cutoff rather than by the uniform-Mmax prior. Please specify the full Mmax prior (support and density) for the transformed runs and repeat the analysis with the lower bound relaxed (or with a data-motivated, not hard-imposed, bound).
  3. [§5, Eq. (14)] The paper acknowledges selection effects ('GW detection being more sensitive to massive binaries, optical observations being more favorable for compact objects') but no selection function appears in the likelihood. The claim that categorizing by companion type 'avoids numerous subtleties associated with selection effects' is not supported: GW-selected DNS and radio-timing DNS enter with the same population distribution, with no detection-probability factor. Selection bias in the GW channel can distort the DNS population and, via the Mmax–LMXB-skewness correlation (Fig. 6), the Mmax and LMXB-mean posteriors. A quantitative check (e.g., a simple detection-weighting or a sensitivity test removing GW events) is needed before the population-specific shifts can be interpreted.
minor comments (5)
  1. [Eq. (14)] The EM mass–radius term uses n_em inside a product over populations i=2,3, but n_em is defined as the total number of EM stars. This notation appears to double-count or misindex the EM likelihood; please define n_em per population or rewrite the product explicitly.
  2. [§2.3, Eq. (5)] The pressure formula introduces parameters b and β, but Table 4 lists only a, α, S, and L. State how b and β are determined (presumably from S=a+b+16 and L=3(aα+bβ)), or include them in the parameter table.
  3. [Table 6] The table header says 'Maximum a posteriori (MAP)' but the entries are quoted as central values with 68% bounds. Specify whether the central value is the posterior mode, median, or mean.
  4. [§4.2.4, Fig. 6] The text says 'there is a negative and positive correlation between them for NL and NP' but does not specify which is which; the caption should identify the sign for each model.
  5. [Abstract and §1] The phrase 'for the first time' overstates the result: the shift is a consequence of the prior reparametrization, not a new observation. The paper is transparent about this in §5, but the abstract and introduction should be reframed as a prior-sensitivity study.

Circularity Check

1 steps flagged · score 4.0 of 10

Headline Mmax prior-shift is a self-defined prior effect; mass-distribution inference is data-grounded.

  1. self definitional [Abstract and §3.3 'Changing parameters' (Eqs. 16–18); Fig. 3 and Table 5]
    "we show for the first time that using a uniform prior on the observable NS maximum mass, rather than a nuisance parameter in the unknown high-density EoS, shifts the posterior maximum mass to larger values. For polytropic EoSs, the maximum mass posterior changes from Mmax=2.09+0.18−0.07 Msun to 2.15+0.19−0.10 Msun at 90% confidence level."

    By Bayes (Eq. 13), the posterior of Mmax depends directly on its prior. Eqs. 16–18 deliberately replace the induced Mmax prior (from uniform EoS parameters) with an imposed uniform P(Mmax), so the claimed 'shift' of the Mmax posterior is the necessary consequence of the prior change the authors designed, not an inference forced by data. The conclusion concedes the result 'depends critically on how we propagate prior knowledge.' Additionally, Eq. 17 is valid only if p_Nk is a single-valued monotone function of Mmax with other parameters fixed — never demonstrated — and the imposed 'Mmax >= 2Msun' cutoff (Fig. 3) fixes the lower bound, so the comparison may be partly a Jacobian/boundary artifact.

full rationale

The paper's joint inference of NS mass distributions and the EoS is grounded in external data: 26 DNS, 32 NS-WD, 14 LMXB mass measurements, NICER J0740+6620 and J0030+0451, qLMXB/PRE mass-radius constraints, and GW170817/GW190425 likelihoods. These ingredients (including the Al-Mamun et al. 2021 GW likelihood and Steiner et al. 2018 globular-cluster data) are published, externally reproducible inputs, so the mass-distribution, radius, and tidal-deformability results are not circular. The self-citations (Steiner et al. 2013, 2015, 2016, 2018; Al-Mamun et al. 2021; BAMR/O2SCL) provide the EoS models, data, likelihoods, and code — real evidence, not a uniqueness chain. The one claim that reduces largely to its own input is the headline prior-shift: Eqs. 16–18 change the prior on Mmax and, by Bayes' theorem (Eq. 13), the posterior on Mmax must respond; the abstract's 'for the first time' result (2.09 -> 2.15 Msun) is the designed consequence of that prior choice. The paper is transparent about this (conclusion: 'the specific quantitative result... depends critically on how we propagate prior knowledge'), and the direction of the shift is data-dependent, so this is a partial, modest circularity rather than a fabricated inference. A correctness caveat compounds it: Eq. 17 requires Mmax to be a single-valued, monotone function of the replaced parameter p_Nk at fixed other parameters, and invertibility is never demonstrated, so the 'flat Mmax prior' may not actually be flat, making the comparison partly a Jacobian/boundary artifact.

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

The central analysis introduces no new particles, forces, or conserved quantities; it uses standard EoS parametrizations and population models. The main free parameters are the EoS parameters, population shape parameters, and per-star nuisance masses; the Mmax lower bound is a hand-imposed constraint.

free parameters (6)
  • Low-density EoS parameters (a, α, S, L) = posterior distributions inferred
    Uniform priors in Table 4; S and L constrained by Eq (7). These are fitted to the data.
  • High-density EoS parameters (γ1,γ2,γ3,Γ1,Γ2 for NP; c_s,1..3, Γ1,Γ2 for NL) = posterior distributions inferred
    Parameters of the piecewise polytrope / linear sound-speed EoS; fitted jointly.
  • Mass distribution shape parameters (μ_i, σ_i, α_i) = Table 6 MAPs, e.g. μ_dns≈1.39–1.41 Msun, μ_lmxb≈1.51–1.71 Msun depending on model
    Three skewed-normal populations; fitted to mass data and EoS constraints.
  • Individual NS masses M_i,j (70 stars) = posterior per-star masses
    Nuisance parameters for each star's true mass; required by hierarchical model.
  • GW parameters (M_det, q, z, m'_1) = posteriors
    Parameters for GW170817/GW190425; fitted.
  • Imposed lower bound Mmax ≥ 2 Msun = 2.0 Msun
    Hard constraint applied in all models (Fig. 3); chosen, not inferred.
assumptions (6)
  • domain assumption NSs are non-rotating, non-accreting, isotropic, spherically symmetric; EoS models are simple P–ϵ relations uninformative of microphysics.
    Section 2 opening; standard simplification but can bias radii/tides.
  • domain assumption Mass distributions do not evolve and are independent of evolution paths within each population.
    Section 2.1; load-bearing for pooling stars of different ages/accretion histories.
  • domain assumption GW170817 and GW190425 follow the same DNS mass distribution as galactic DNS.
    Section 2.1 and Conclusions; a misclassification would bias DNS moments.
  • standard math Asymmetric normal distribution (Eq 3) accurately maps 68% mass limits to a noise model.
    Appendix A derives c,d from l,u; assumes the true error distribution has this exact shape.
  • ad hoc to paper Mmax is a monotone invertible function of the last EoS parameter p_Nk with others fixed.
    Section 3.3 Eq (17)-(18); required for the flat-Mmax reparametrization; not demonstrated.
  • ad hoc to paper The Mmax ≥ 2 Msun hard lower bound is an acceptable outside constraint.
    Section 4.1; truncates posteriors and can inflate Mmax if data allow lower values.

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Cite this review

Pith. "Pith review of Inference of Neutron Star Mass Distributions and the Dense Matter Equation of State from Multi-messenger Observations." pith.science (2026). https://pith.science/paper/XMW33DCW

@misc{pith2026251212130,
  author       = {Pith},
  title        = {Pith review of: Inference of Neutron Star Mass Distributions and the Dense Matter Equation of State from Multi-messenger Observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XMW33DCW}},
  note         = {Machine review of arXiv:2512.12130}
}
abstract

We construct a combined model to incorporate neutron star (NS) mass measurements with electromagnetic mass-radius constraints and gravitational-wave observations using Bayesian inference. We use different mass distributions for three populations depending on the companion stars: double neutron stars, NS - white dwarfs, and low-mass X-ray binaries (LMXB). To observe the effects of different parametrizations, we use two equation of state (EoS) models: a piecewise polytrope and a fixed sound-speed model at high densities in combination with a low-density EoS. Our results show that the mass distributions of these NS populations are distinct and sensitive to the EoS prior choices. In addition, we show for the first time that using a uniform prior on the observable NS maximum mass, rather than a nuisance parameter in the unknown high-density EoS, shifts the posterior maximum mass to larger values. For polytropic EoSs, the maximum mass posterior changes from $M_\mathrm{max}=2.09_{-0.07}^{+0.18} M_\odot$ to $2.15_{-0.10}^{+0.19} M_\odot$ at 90% confidence level. This change in prior also impacts the shape of the mass distribution for NSs in LMXB, shifting the posterior for the population mean from $\mu_\mathrm{lmxb} = 1.51_{-0.13}^{+0.13} M_\odot$ to $1.62_{-0.12}^{+0.15} M_\odot$ at 68% confidence level.

Figures

Figures reproduced from arXiv: 2512.12130 by the authors.

Figure 2
Figure 2. shows the posterior of the NS radius as a function of the gravitational mass for each EoS. The mass-radius curves for ML and NL indicate smaller radii for low-mass stars and larger radii for high-mass stars. While MP closely follows this trend with a tighter lower bound for low-mass stars, NP exhibits a rather neutral behavior where low- and high-mass stars have fairly sim￾ilar radii. The peak in each curve represen… view at source ↗
Figure 3
Figure 3. The posterior distributions of the NS maximum mass. The modes are reported at the peaks and the means (µmax of Mmax) are given in the inset. sive stars. The model NL accommodates higher Mmax with its widest distribution and support up to 2.9 M⊙. Conversely, NP has the narrowest width and support with its peak close to NL. A similar argument can be made for the pair ML and MP. The difference in these distribution sha… view at source ↗
Figure 4
Figure 4. Tidal deformability as a function of NS mass for each model, with 68% (purple) and 95% (orange) confidence levels. The color map shows locally normalized densities [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: The normalized mass distributions of NS populations (row-wise), grouped by the EoS models (column-wise). The contour lines represent 68% (purple) and 95% (orange) confidence levels. The statistics are reported in table 6. 4.2.2. Low-Mass X-ray Binaries For NS hosted in…
Figure 6
Figure 6. Figure 6: Correlation between the maximum mass and the skewness of the LMXB mass distribution for each EoS model, with 68% (purple) and 95% (orange) confidence levels. NS population for all events; the EoS models employed) and arrives at a systematically much larger maximum NS m…

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Works this paper leans on

67 extracted references · 9 canonical work pages

  1. [1]

    P., et al

    Abbott, B. P., et al. 2017, Phys. Rev. Lett., 119, 161101, doi: 10.1103/PhysRevLett.119.161101

    doi:10.1103/physrevlett.119.161101 2017

  2. [2]

    P., et al

    Abbott, B. P., et al. 2020, The Astrophysical Journal Letters, 892, L3, doi: 10.3847/2041-8213/ab75f5

    doi:10.3847/2041-8213/ab75f5 2020

  3. [3]

    2021, Phys

    Adhikari, D., Albataineh, H., Androic, D., et al. 2021, Phys. Rev. Lett., 126, 172502, doi: 10.1103/PhysRevLett.126.172502

    doi:10.1103/physrevlett.126.172502 2021

  4. [4]

    2022, Phys

    Adhikari, D., Albataineh, H., Androic, D., et al. 2022, Phys. Rev. Lett., 129, 042501, doi: 10.1103/PhysRevLett.129.042501

    doi:10.1103/physrevlett.129.042501 2022

  5. [5]

    W., N¨ attil¨ a, J., et al

    Al-Mamun, M., Steiner, A. W., N¨ attil¨ a, J., et al. 2021, Phys. Rev. Lett., 126, 061101, doi: 10.1103/PhysRevLett.126.061101

    doi:10.1103/physrevlett.126.061101 2021

  6. [6]

    O., & Berti, E

    Alsing, J., Silva, H. O., & Berti, E. 2018, MNRAS, 478, 1377, doi: 10.1093/mnras/sty1065

    doi:10.1093/mnras/sty1065 2018

  7. [7]

    Anik, M. H. 2025, Inference of Neutron Star Mass Distributions and the Equation of State from Multi-messenger Observations, 1.0.0 Zenodo, doi: 10.5281/zenodo.17842420

    work page doi:10.5281/zenodo.17842420 2025

  8. [8]

    M., Ozel, F., et al

    Antoniadis, J., Tauris, T. M., Ozel, F., et al. 2016, arXiv e-prints, arXiv:1605.01665, doi: 10.48550/arXiv.1605.01665

    arXiv doi:10.48550/arxiv.1605.01665 2016

Show all 67 references
  1. [9]

    H., Koester, D., et al

    Antoniadis, J., van Kerkwijk, M. H., Koester, D., et al. 2012, MNRAS, 423, 3316, doi: 10.1111/j.1365-2966.2012.21124.x

    2012

  2. [10]

    Antoniadis, J., Freire, P. C. C., Wex, N., et al. 2013, Science, 340, 448, doi: 10.1126/science.1233232

    2013 doi

  3. [11]

    T., Brazier, A., et al

    Arzoumanian, Z., Baker, P. T., Brazier, A., et al. 2018, ApJ, 859, 47, doi: 10.3847/1538-4357/aabd3b

    2018 doi

  4. [12]

    D., Freire, P

    Barr, E. D., Freire, P. C. C., Kramer, M., et al. 2017, MNRAS, 465, 1711, doi: 10.1093/mnras/stw2947

    2017 doi

  5. [13]

    G., van Kerkwijk, M

    Bassa, C. G., van Kerkwijk, M. H., Koester, D., & Verbunt, F. 2006, A&A, 456, 295, doi: 10.1051/0004-6361:20065181

    2006 doi

  6. [14]

    J., Freire, P

    Berezina, M., Champion, D. J., Freire, P. C. C., et al. 2017, MNRAS, 470, 4421, doi: 10.1093/mnras/stx1518

    2017 doi

  7. [15]

    Bhat, N. D. R., Bailes, M., & Verbiest, J. P. W. 2008, PhRvD, 77, 124017, doi: 10.1103/PhysRevD.77.124017

    2008 doi

  8. [16]

    2025, Phys

    Biswas, B., & Rosswog, S. 2025, Phys. Rev. D, 112, 023045, doi: 10.1103/8lv3-1ywb

    2025 doi

  9. [17]

    2010, MNRAS, 401, 2517, doi: 10.1111/j.1365-2966.2009.15828.x

    Rebolo, R. 2010, MNRAS, 401, 2517, doi: 10.1111/j.1365-2966.2009.15828.x

    2010

  10. [18]

    J., Lorimer, D

    Champion, D. J., Lorimer, D. R., McLaughlin, M. A., et al. 2005, MNRAS, 363, 929, doi: 10.1111/j.1365-2966.2005.09499.x 14

    2005

  11. [19]

    Chatziioannou, K., & Farr, W. M. 2020, Phys. Rev. D, 102, 064063, doi: 10.1103/PhysRevD.102.064063

    2020 doi

  12. [20]

    Cognard, I., Freire, P. C. C., Guillemot, L., et al. 2017, ApJ, 844, 128, doi: 10.3847/1538-4357/aa7bee

    2017 doi

  13. [21]

    W., et al

    Corongiu, A., Kramer, M., Stappers, B. W., et al. 2007, A&A, 462, 703, doi: 10.1051/0004-6361:20054385

    2007 doi

  14. [22]

    T., Fonseca, E., Ransom, S

    Cromartie, H. T., Fonseca, E., Ransom, S. M., et al. 2020, Nature Astronomy, 4, 72, doi: 10.1038/s41550-019-0880-2

    2020 doi

  15. [23]

    S., Freire, P

    Deneva, J. S., Freire, P. C. C., Cordes, J. M., et al. 2012, ApJ, 757, 89, doi: 10.1088/0004-637X/757/1/89

    2012 doi

  16. [24]

    N., Lentati, L., et al

    Desvignes, G., Caballero, R. N., Lentati, L., et al. 2016, MNRAS, 458, 3341, doi: 10.1093/mnras/stw483

    2016 doi

  17. [25]

    2024, Phys

    Fan, Y.-Z., Han, M.-Z., Jiang, J.-L., Shao, D.-S., & Tang, S.-P. 2024, Phys. Rev. D, 109, 043052, doi: 10.1103/PhysRevD.109.043052

    2024 doi

  18. [26]

    M., & Chatziioannou, K

    Farr, W. M., & Chatziioannou, K. 2020, Research Notes of the AAS, 4, 65, doi: 10.3847/2515-5172/ab9088

    2020 doi

  19. [27]

    2019, The Astrophysical Journal, 876, 18, doi: 10.3847/1538-4357/ab12e3

    Farrow, N., Zhu, X.-J., & Thrane, E. 2019, The Astrophysical Journal, 876, 18, doi: 10.3847/1538-4357/ab12e3

    2019 doi

  20. [28]

    D., Stairs, I

    Ferdman, R. D., Stairs, I. H., Kramer, M., et al. 2010, ApJ, 711, 764, doi: 10.1088/0004-637X/711/2/764

    2010 doi

  21. [29]

    D., Stairs, I

    Ferdman, R. D., Stairs, I. H., Kramer, M., et al. 2014, MNRAS, 443, 2183, doi: 10.1093/mnras/stu1223

    2014 doi

  22. [30]

    Finn, L. S. 1994, Phys. Rev. Lett., 73, 1878, doi: 10.1103/PhysRevLett.73.1878

    1994 doi

  23. [31]

    H., & Thorsett, S

    Fonseca, E., Stairs, I. H., & Thorsett, S. E. 2014, ApJ, 787, 82, doi: 10.1088/0004-637X/787/1/82

    2014 doi

  24. [32]

    2012, Phys

    Gandolfi, S., Carlson, J., & Reddy, S. 2012, Phys. Rev. C, 85, 032801, doi: 10.1103/PhysRevC.85.032801

    2012 doi

  25. [33]

    M., Tomsick, J

    Gelino, D. M., Tomsick, J. A., & Heindl, W. A. 2002, in American Astronomical Society Meeting Abstracts, Vol. 201, American Astronomical Society Meeting Abstracts, 54.05

    2002

  26. [34]

    2025, Physical Review D, 111, doi: 10.1103/physrevd.111.023029

    Golomb, J., Legred, I., Chatziioannou, K., & Landry, P. 2025, Physical Review D, 111, doi: 10.1103/physrevd.111.023029

    2025 doi

  27. [35]

    2022, The Astrophysical Journal, 926, 79, doi: 10.3847/1538-4357/ac43bc

    Golomb, J., & Talbot, C. 2022, The Astrophysical Journal, 926, 79, doi: 10.3847/1538-4357/ac43bc

    2022 doi

  28. [36]

    A., Cameron, P

    Jacoby, B. A., Cameron, P. B., Jenet, F. A., et al. 2006, ApJL, 644, L113, doi: 10.1086/505742

    2006 doi

  29. [37]

    2023, Phys

    Keller, J., Hebeler, K., & Schwenk, A. 2023, Phys. Rev. Lett., 130, 072701, doi: 10.1103/PhysRevLett.130.072701

    2023 doi

  30. [38]

    D., & Thorsett, S

    Kiziltan, B., Kottas, A., Yoreo, M. D., & Thorsett, S. E. 2013, The Astrophysical Journal, 778, 66, doi: 10.1088/0004-637x/778/1/66

    2013 doi

  31. [39]

    2022, Physical Review Letters, 128, doi: 10.1103/physrevlett.128.202701

    Komoltsev, O., & Kurkela, A. 2022, Physical Review Letters, 128, doi: 10.1103/physrevlett.128.202701

    2022 doi

  32. [40]

    H., Manchester, R

    Kramer, M., Stairs, I. H., Manchester, R. N., et al. 2006, Science, 314, 97, doi: 10.1126/science.1132305

    2006 doi

  33. [41]

    Landry, P., & Read, J. S. 2021, The Astrophysical Journal Letters, 921, L25, doi: 10.3847/2041-8213/ac2f3e

    2021 doi

  34. [42]

    2018, arXiv e-prints, arXiv:1805.10457, doi: 10.48550/arXiv.1805.10457

    Lange, J., O’Shaughnessy, R., & Rizzo, M. 2018, arXiv e-prints, arXiv:1805.10457, doi: 10.48550/arXiv.1805.10457

    2018 doi arXiv

  35. [43]

    2021, The Astrophysical Journal, 923, 97, doi: 10.3847/1538-4357/ac34f0

    Li, Y.-J., Tang, S.-P., Wang, Y.-Z., et al. 2021, The Astrophysical Journal, 923, 97, doi: 10.3847/1538-4357/ac34f0

    2021 doi

  36. [44]

    S., Freire, P

    Lynch, R. S., Freire, P. C. C., Ransom, S. M., & Jacoby, B. A. 2012, ApJ, 745, 109, doi: 10.1088/0004-637X/745/2/109

    2012 doi

  37. [45]

    G., Stovall, K., Freire, P

    Martinez, J. G., Stovall, K., Freire, P. C. C., et al. 2015, ApJ, 812, 143, doi: 10.1088/0004-637X/812/2/143

    2015 doi

  38. [46]

    C., Lamb, F

    Miller, M. C., Lamb, F. K., Dittmann, A. J., et al. 2019, ApJL, 887, L24, doi: 10.3847/2041-8213/ab50c5

    2019 doi

  39. [47]

    C., Lamb, F

    Miller, M. C., Lamb, F. K., Dittmann, A. J., et al. 2021, ApJL, 918, L28, doi: 10.3847/2041-8213/ac089b Mu˜ noz-Darias, T., Casares, J., & Mart ´ ınez-Pais, I. G. 2005, ApJ, 635, 502, doi: 10.1086/497420 N¨ attil¨ a, J., Miller, M. C., Steiner, A. W., et al. 2017, A&A, 608, A3...

    2021 doi

  40. [48]

    J., Stairs, I

    Nice, D. J., Stairs, I. H., & Kasian, L. E. 2008, in American Institute of Physics Conference Series, Vol. 983, 40 Years of Pulsars: Millisecond Pulsars, Magnetars and More, ed. C. Bassa, Z. Wang, A. Cumming, & V. M. Kaspi, 453–458, doi: 10.1063/1.2900273 ¨Ozel, F., Psaltis, D...

    2008 doi

  41. [49]

    M., Stairs, I

    Ransom, S. M., Stairs, I. H., Archibald, A. M., et al. 2014, Nature, 505, 520, doi: 10.1038/nature12917

    2014 doi

  42. [50]

    L., Orosz, J

    Rawls, M. L., Orosz, J. A., McClintock, J. E., et al. 2011, ApJ, 730, 25, doi: 10.1088/0004-637X/730/1/25

    2011 doi

  43. [51]

    J., Hobbs, G., Coles, W., et al

    Reardon, D. J., Hobbs, G., Coles, W., et al. 2016, MNRAS, 455, 1751, doi: 10.1093/mnras/stv2395

    2016 doi

  44. [52]

    E., Watts, A

    Riley, T. E., Watts, A. L., Bogdanov, S., et al. 2019, ApJL, 887, L21, doi: 10.3847/2041-8213/ab481c

    2019 doi

  45. [53]

    E., Watts, A

    Riley, T. E., Watts, A. L., Ray, P. S., et al. 2021, ApJL, 918, L27, doi: 10.3847/2041-8213/ac0a81

    2021 doi

  46. [54]

    2010, The Astrophysical Journal, 719, 722, doi: 10.1088/0004-637X/719/1/722

    Schwab, J., Podsiadlowski, P., & Rappaport, S. 2010, The Astrophysical Journal, 719, 722, doi: 10.1088/0004-637X/719/1/722

    2010 doi

  47. [55]

    2020, Phys

    Shao, D.-S., Tang, S.-P., Jiang, J.-L., & Fan, Y.-Z. 2020, Phys. Rev. D, 102, 063006, doi: 10.1103/PhysRevD.102.063006

    2020 doi

  48. [56]

    Stairs, I. H. 2006, Journal of Physics G Nuclear Physics, 32, S259, doi: 10.1088/0954-3899/32/12/S32 15

    2006 doi

  49. [57]

    Steeghs, D., & Jonker, P. G. 2007, ApJL, 669, L85, doi: 10.1086/523848

    2007 doi

  50. [58]

    W., Gandolfi, S., Fattoyev, F

    Steiner, A. W., Gandolfi, S., Fattoyev, F. J., & Newton, W. G. 2015, Phys. Rev. C, 91, 015804, doi: 10.1103/PhysRevC.91.015804

    2015 doi

  51. [59]

    W., Heinke, C

    Steiner, A. W., Heinke, C. O., Bogdanov, S., et al. 2018, MNRAS, 476, 421, doi: 10.1093/mnras/sty215

    2018 doi

  52. [60]

    W., Lattimer, J

    Steiner, A. W., Lattimer, J. M., & Brown, E. F. 2013, The Astrophysical Journal Letters, 765, L5, doi: 10.1088/2041-8205/765/1/L5

    2013 doi

  53. [61]

    W., Lattimer, J

    Steiner, A. W., Lattimer, J. M., & Brown, E. F. 2016, The European Physical Journal A, 52, 18

    2016

  54. [62]

    Stovall, K., Freire, P. C. C., Antoniadis, J., et al. 2019, ApJ, 870, 74, doi: 10.3847/1538-4357/aaf37d

    2019 doi

  55. [63]

    2025, Physical Review Research, 7, doi: 10.1103/r314-6r62

    Tews, I., Somasundaram, R., Lonardoni, D., et al. 2025, Physical Review Research, 7, doi: 10.1103/r314-6r62

    2025 doi

  56. [64]

    E., & Chakrabarty, D

    Thorsett, S. E., & Chakrabarty, D. 1999, The Astrophysical Journal, 512, 288, doi: 10.1086/306742

    1999 doi

  57. [65]

    Valentim, R., Rangel, E., & Horvath, J. E. 2011, Monthly Notices of the Royal Astronomical Society, 414, 1427, doi: 10.1111/j.1365-2966.2011.18477.x van Leeuwen, J., Kasian, L., Stairs, I. H., et al. 2015, ApJ, 798, 118, doi: 10.1088/0004-637X/798/2/118

    2011

  58. [66]

    M., Nice, D

    Weisberg, J. M., Nice, D. J., & Taylor, J. H. 2010, ApJ, 722, 1030, doi: 10.1088/0004-637X/722/2/1030

    2010 doi

  59. [67]

    Wysocki, D., O’Shaughnessy, R., Wade, L., & Lange, J. 2020, arXiv preprint arXiv:2001.01747 16 APPENDIX A.SKEWED AND ASYMMETRIC NORMAL DISTRIBUTIONS The probability distribution functionϕand the cumulative distribution function Φ of the normal distributionN(µ, σ) in equation (...

    2020 arXiv

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