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This paper argues that rigid rotation can raise the maximum stable mass of a protoquark star by about 40%, and that this enhancement is largest in the hot, lepton-rich phase of its thermal evolution.

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2026-08-03 09:21 UTC pith:U3CHU3FX

load-bearing objection First isentropic rotating protoquark-star study with clear thermal ordering, but headline numbers rest on a single mass-maximizing parameter point with no posterior spread. the 3 major comments →

arxiv 2601.13941 v2 pith:U3CHU3FX submitted 2026-01-20 astro-ph.HE hep-phnucl-th

Rotational enhancement and stability of protoquark stars during thermal evolution

Adamu Issifu , Andreas Konstantinou , Prashant Thakur , Tobias Frederico This is my paper
classification astro-ph.HE hep-phnucl-th
keywords protoquark starsquark matterrotationthermal evolutionequation of stateTkin to |W| ratiomass-radius relationgravitational-wave instabilities
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper wants to establish how rotation and thermal history together shape protoquark stars—hypothetical compact objects made of self-bound quark matter. It argues that rigid rotation can boost the maximum stable mass by up to ~40% near the Keplerian mass-shedding limit, and that the ratio of rotational kinetic energy to gravitational binding energy reaches 0.18–0.19, putting these stars close to gravitational-wave-driven instabilities. It further claims that as a protoquark star cools and deleptonizes, its radius, moment of inertia, angular momentum, and quadrupole deformation decrease monotonically, so the most extreme configurations occur in the hot, lepton-rich stage. If true, this makes rotating protoquark stars distinguishable from hadronic protoneutron stars in the mass–radius–spin plane, and means future multimessenger interpretations must fold in both thermal state and rotation.

Core claim

The core discovery is that uniform rotation and thermal evolution jointly determine the structure of protoquark stars: rotation increases the maximum stable mass by up to ~40% at the Keplerian limit, while Tkin/|W| approaches 0.18–0.19, indicating enhanced susceptibility to non-axisymmetric gravitational-wave instabilities. Along the Kelvin–Helmholtz sequence, all global properties—radius, moment of inertia, angular momentum, quadrupole moment—peak in the hot, lepton-rich stages and decline monotonically as the star cools. The resulting sequences occupy a distinct region in the mass–radius–spin plane, and a single quark-matter equation of state can simultaneously accommodate low-mass, small-

What carries the argument

The central machinery is a chain of quasi-static equilibrium snapshots. For each evolutionary stage—labelled by fixed entropy per baryon and lepton fraction—the paper uses a temperature-dependent density-dependent quark mass equation of state and constructs uniformly rotating, general-relativistic stellar models by solving the stationary, axisymmetric Einstein equations. It then extracts global quantities (mass, radius, moment of inertia, angular momentum, quadrupole moment, polar redshift) and, crucially, the ratio Tkin/|W|, which serves as the diagnostic for centrifugal support and instability. This decomposition is what allows the paper to separate the effects of rotation from those of th

Load-bearing premise

The quantitative results hinge on the phenomenological temperature-dependent quark-mass ansatz of Eq. (24), with parameters C = 0.8 and sqrt(D) = 127.4 MeV chosen at the edge of a previous fit to yield the maximum stable quark-star mass; if real quark matter is stiffer or the mass scaling is different, the ~40% enhancement and the claimed agreement with observations shrink.

What would settle it

A direct contradiction would be a young, rapidly rotating compact remnant whose spin frequency is near the Keplerian limit but whose inferred Tkin/|W| falls well below 0.18, or a fast-spinning quark-star candidate whose maximum mass exceeds its nonrotating value by much less than the predicted ~40%; both are observable with current timing and gravitational-wave data.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Mass and radius constraints derived without accounting for spin will systematically underestimate what a quark-matter equation of state can support; the same EOS that explains low-mass objects can also reach high-mass pulsars once rotation is included.
  • Rapidly rotating protoquark stars are predicted to sit near the secular instability threshold (Tkin/|W| ~ 0.18–0.19), making them promising sources of continuous gravitational waves from non-axisymmetric modes.
  • Thermal history imposes a monotonic ordering: hot, lepton-rich stages are the largest, most massive, and most deformed, so observations of young remnants probe a different part of the mass–radius plane than cold, old pulsars.
  • Combined mass–radius–moment-of-inertia–quadrupole measurements offer a discriminator between quark and hadronic interiors, since quark stars are predicted to have larger radii, higher moments of inertia, and stronger quadrupole deformations at fixed mass and spin.
  • Keplerian frequencies are lower for hot, lepton-rich stars, so cold quark stars can rotate at higher absolute frequencies while staying farther from the mass-shedding limit.

Where Pith is reading between the lines

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

  • If the ~40% enhancement survives more realistic microphysics, rotation should be included in any attempt to identify quark matter via maximum-mass measurements; a fast-spinning quark-star candidate near 3 solar masses would be a direct test.
  • The quasi-static, isentropic treatment could be extended to differential rotation and magnetic fields; both would likely push the maximum mass and Tkin/|W| even higher, strengthening the gravitational-wave signal.
  • The predicted lower core temperature of quark matter compared with hadronic matter at fixed entropy could, in principle, be diagnosed through neutrino luminosities or cooling curves of a newborn remnant.
  • The Tkin/|W| values imply that protoquark stars may be a source class for current and future gravitational-wave detectors; follow-up searches for long-lived remnants in gravitational-wave data could test the prediction.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper presents a systematic study of rigidly rotating protoquark stars using the rns code and isentropic equations of state derived from the density-dependent quark mass (DDQM) model. The thermal evolution is approximated by four quasi-static stages: hot lepton-rich matter (sB=1, Yl=0.4), deleptonizing matter (sB=2, Yl=0.2), neutrino-transparent matter (sB=2, Yνe=0), and cold catalyzed quark matter (T=0). For each stage, sequences of rotating equilibrium configurations are constructed for polar-to-equatorial radius ratios from 1.0 to 0.5. The authors report that rotation increases the maximum mass by up to about 40%, with Tkin/|W| reaching 0.18–0.19 near the Keplerian limit, and that the maximum mass, equatorial radius, angular momentum, moment of inertia, and quadrupole moment decrease monotonically as the star cools, while the spin frequency at the maximum mass increases. They further claim that a single quark-matter EOS can simultaneously accommodate the HESS J1731–347, PSR J0030+0451, PSR J0740+6620, and GW170817 constraints, and that rotating protoquark stars occupy a distinct region of the mass–radius–spin plane compared with hadronic protoneutron stars.

Significance. If the results are robust, the paper would establish that rotation and thermal history are essential ingredients for interpreting quark-star candidates and that protoquark stars may be more susceptible to gravitational-wave instabilities than hadronic stars. The study uses the standard, publicly available rns code and provides a self-consistent thermodynamic derivation for the DDQM model at finite temperature; the four-stage sequence gives a clear, internally consistent demonstration of the cooling ordering for most global quantities. The complete energy decomposition (Fig. 8) is a useful addition. However, the quantitative claims are computed at a single parameter point deliberately chosen to maximize the mass, and the observational agreement in Fig. 1 is inherited from the Bayesian fit used to set the parameters in [27]. These two issues mean that the headline 40% enhancement and Tkin/|W| values are not yet demonstrated to be representative of the model's parameter space.

major comments (3)
  1. [Sec. II.1.2, Eq. (24), Table I] The parameters C=0.8 and sqrt(D)=127.4 MeV in Eq. (24) are 'deliberately chosen to yield the maximum possible stable quark star mass within the optimized parameter space identified in [27]' (Sec. II.1.2). All of the paper's headline quantitative results—the ~40% Mmax enhancement, Tkin/|W| ≈ 0.18–0.19, and the specific values in Table I—are computed at this single extremal point. No posterior spread or sensitivity to other parameter pairs from [27] is given. Because the parameter point sits at the edge of the fitted region, the reported numbers may be upper-envelope estimates rather than robust predictions. Please show how the rotational enhancement and stability indicators vary across the [27] posterior, or at least provide a few representative interior points, and soften the claims accordingly if the spread is large.
  2. [Sec. III, Fig. 1 and Sec. II.1.1] The agreement of the cold T=0 sequences with HESS J1731–347, PSR J0740+6620, PSR J0030+0451, and GW170817 is presented in Sec. III and Fig. 1 as evidence that 'a single QM EOS can accommodate current observational constraints' (Sec. IV). However, the DDQM parameters were determined in [27] by Bayesian inference using the same astrophysical constraints. The overlap in Fig. 1 is therefore a consistency check, not an independent prediction. The manuscript should explicitly state this and, more usefully, identify which of its results (e.g., the rotational enhancement or the thermal ordering of I, Q, and J) constitute genuine predictions that are not already encoded in the fit.
  3. [Abstract and Sec. III, Table I] The abstract states that 'all stellar properties peak during the lepton-rich stages and decrease monotonically as the star cools.' This is contradicted by the spin frequency ν at the maximum mass: Table I shows that at fixed rp/re=0.5, ν increases from 999.93 Hz (sB=1, Yl=0.4) to 1021.57, 1024.37, and 1043.31 Hz as the star cools to T=0. The text in Sec. III explicitly acknowledges this ('the ν at M rises with cooling'). Please revise the abstract and conclusions to exclude ν from the monotonic-decrease claim, or to list explicitly which properties (Mmax, Re, J, I, Q) do decrease monotonically.
minor comments (5)
  1. [Table I caption] 'delebrately' should be 'deliberately'.
  2. [Fig. 4 caption] 'rotational fattening' should be 'flattening'.
  3. [Fig. 1 panel labels] The panel label uses 'Y_e = 0' while the text and Table I use 'Yνe = 0'; please make the notation consistent.
  4. [Sec. II.1] The symbol for the number density is sometimes n_i (Eq. 2) and sometimes ρ_i (Eqs. 12–23). Please unify the notation.
  5. [Sec. III, Fig. 1] The comparison with hadronic protoneutron stars is only qualitative. A quantitative overlay or table of the hadronic sequences from [47] would make the claimed 'distinct signature in the mass–radius–spin plane' more compelling.

Circularity Check

1 steps flagged

Observational 'agreement' is inherited from a self-authored Bayesian fit to the same objects; headline numbers are computed at a deliberately mass-maximizing posterior point without uncertainty propagation, while the rotational structure computations themselves are genuine.

specific steps
  1. fitted input called prediction [Abstract; Sec. II.1–II.1.2 (adoption of [27] parameters); Sec. III, Fig. 1 discussion; Sec. IV (conclusion)]
    "The appropriate coupling constants were also adopted from [27], in which the authors determined the free model parameters of the DDQM… The EOS parameters are constrained using current astrophysical observations, including mass–radius measurements from HESS J1731–347 and PSR J0030+0451, the high-mass constraint from PSR J0740+6620, and mass-radius constraints from GW170817… The agreement of the cold, catalyzed configurations with the HESS J1731-347 and NICER PSR J0740+6620 constraints reflects the ability of the QM EOS to remain stiff at high densities."

    The abstract itself says the parameters were constrained using HESS J1731–347, PSR J0030+0451, PSR J0740+6620, and GW170817 — precisely the objects used as likelihood data in the Bayesian fit of [27] (co-authored by A. Issifu, a present author). The paper then adopts a point from that posterior and presents agreement with those same objects (Fig. 1; conclusion: a single QM EOS can accommodate current observational constraints) as a result (The agreement … reflects the ability of the QM EOS). The validation dataset is the fitting dataset, so this agreement is inherited by construction rather than newly predicted. The rotational sequences themselves are genuine RNS computations, so the circularity is partial and confined to the observational-validation claim.

full rationale

The derivation chain is: (i) DDQM EOS with temperature extension Eq. (24), parameters C = 0.8 and √D = 127.4 MeV taken from the Bayesian analysis [27]; (ii) rotating equilibria from the open-source RNS code solving Einstein's equations; (iii) global quantities (M, Re, J, I, Q, Zp, Tkin/|W|) from standard GR formulae. No step of this chain defines an output in terms of the quantity it is claimed to predict; the rotational enhancement (up to ~40%), Tkin/|W| ≈ 0.18–0.19, and the monotonic thermal ordering across the four evolution stages are computed outputs that could in principle have differed. The one exhibitable reduction by construction is the observational agreement in Fig. 1 / abstract / conclusions: those objects were the very data used to fit the DDQM parameters in [27], which has overlapping authorship, so the agreement is a postdiction of the fit marketed as validation. Separately, the parameter point is deliberately chosen to yield the maximum possible stable quark star mass within the [27] posterior, so the headline 40% and T/|W| values are upper-envelope numbers at the posterior edge, with no uncertainty propagation; the paper discloses this choice but does not quantify its impact — a representativeness concern rather than a definitional circularity, since the enhancement is genuinely computed from the rotating field equations. Given the central rotational computations are independent, the circularity score is moderate (5): partial circularity confined to the observational-validation claim.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The central quantitative claims rest on the DDQM parameters C and sqrt(D), selected from the edge of a Bayesian fit [27] to maximize Mmax; the hot-stage results additionally rest on a phenomenological temperature-dependent mass ansatz and a quasi-static isentropic staging. No new particles or forces are introduced.

free parameters (3)
  • C (DDQM linear density coefficient) = 0.8
    Repulsive interaction parameter in Eq. (1)/(24); adopted from Bayesian fit [27] and deliberately chosen to maximize Mmax.
  • sqrt(D) (DDQM confinement coefficient) = 127.4 MeV
    Parameter in Eq. (1)/(24) from [27]; chosen to maximize the quark star mass; drives magnitude of rotational enhancement.
  • Evolutionary stage conditions (sB, Yl) = sB=1,Yl=0.4; sB=2,Yl=0.2; sB=2,Yνe=0; T=0
    Four quasi-static snapshots chosen to represent Kelvin-Helmholtz evolution; values are representative inputs, not derived from a transport calculation.
axioms (5)
  • domain assumption Strange quark matter is the true ground state of nuclear matter and can form stable quark stars
    Intro cites [3-5]; underpins the entire protoquark star scenario.
  • domain assumption The DDQM effective-chemical-potential scheme restores thermodynamic consistency and the finite-size term V∂Ω0/∂V in Eq. (20) can be neglected
    Section II.1.2, Eqs. (19)-(23); needed for the pressure and energy-density expressions used in stellar structure.
  • ad hoc to paper The temperature-dependent quark mass ansatz Eq. (24) with f(T) describes hot quark matter
    Phenomenological extension from [28,35]; not derived from QCD; controls thermal stiffening/softening.
  • domain assumption Quasi-static isentropic snapshots with fixed sB and Yl capture the thermal evolution
    Used to build the four evolutionary stages; ignores dynamical cooling, neutrino transport, and differential rotation.
  • standard math Rigid rotation and axisymmetric stationary equilibria computed with rns are valid
    Standard GR stellar code [26]; central numerical method.

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read the original abstract

We present the first systematic study of rigidly rotating protoquark stars based on isentropic equations of state (EOS) within the density-dependent quark mass (DDQM) framework. Using a quasi-static equilibrium approach, we follow the Kelvin--Helmholtz evolution from hot, lepton-rich matter to a cold, catalyzed quark star (QS). Rotation substantially enhances the maximum stable mass (by up to $\sim 40\%$), equatorial radius, and key rotational observables, with the ratio of rotational kinetic to gravitational potential energy, $T_{\rm kin}/|W|$, reaching $0.18$--$0.19$ near the Keplerian limit, indicating a heightened susceptibility to gravitational-wave--emitting instabilities. Thermal evolution introduces a clear ordering: all stellar properties peak during the lepton-rich stages and decrease monotonically as the star cools. Compared to hadronic stars, rotating proto-QSs exhibit larger radii, higher moments of inertia, and stronger quadrupolar deformation, producing a distinct signature in the mass--radius--spin plane. The EOS parameters are constrained using current astrophysical observations, including mass--radius measurements from HESS~J1731--347 and PSR~J0030+0451, the high-mass constraint from PSR~J0740+6620, and mass-radius constraints inferred from GW170817. The results demonstrate that future multimessenger observations must account for both thermal history and rotation to identify quark matter (QM) in compact stars robustly.

Figures

Figures reproduced from arXiv: 2601.13941 by Adamu Issifu, Andreas Konstantinou, Prashant Thakur, Tobias Frederico.

Figure 1
Figure 1. Figure 1: FIG. 1. The gravitational mass [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The core temperature evolution of rotating proto stars examined along gravitational-mass sequences. The stars in the [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Variation of the ratio of the rotational frequency to [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Variation of the magnitude of the quadrupole moment [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Variation of the polar redshift [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The complete energy decomposition of rotating pro [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗

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Reference graph

Works this paper leans on

79 extracted references · 46 linked inside Pith

  1. [1]

    Witten, Cosmic Separation of Phases, Phys

    E. Witten, Cosmic Separation of Phases, Phys. Rev. D 30, 272 (1984)

    1984

  2. [2]

    Alcock, E

    C. Alcock, E. Farhi, and A. Olinto, Strange Stars, Astro- phys. J.310, 261 (1986)

    1986

  3. [3]

    A. R. Bodmer, Collapsed nuclei, Phys. Rev. D4, 1601 (1971)

    1971

  4. [4]

    Farhi and R

    E. Farhi and R. L. Jaffe, Phys. Rev. D30, 2379 (1984)

    1984

  5. [5]

    Weber, Strange quark matter and compact stars, Prog

    F. Weber, Strange quark matter and compact stars, Prog. Part. Nucl. Phys.54, 193 (2005), arXiv:astro-ph/0407155

    Pith/arXiv arXiv 2005

  6. [6]

    J. J. Drakeet al., Is RXJ1856.5-3754 a quark star?, As- trophys. J.572, 996 (2002), arXiv:astro-ph/0204159

    Pith/arXiv arXiv 2002

  7. [7]

    Doroshenko, V

    V. Doroshenko, V. Suleimanov, G. P¨ uhlhofer, and A. San- tangelo, A strangely light neutron star within a supernova remnant, Nature Astronomy6, 1444 (2022)

    2022

  8. [8]

    X.-D. Li, S. Ray, J. Dey, M. Dey, and I. Bombaci, On the Nature of the compact star in 4u 1728-34, Astrophys. J. Lett.527, L51 (1999), arXiv:astro-ph/9908274

    Pith/arXiv arXiv 1999

  9. [9]

    Di Clemente, A

    F. Di Clemente, A. Drago, and G. Pagliara, Is the Com- pact Object Associated with HESS J1731-347 a Strange Quark Star? A Possible Astrophysical Scenario for Its For- mation, Astrophys. J.967, 159 (2024), arXiv:2211.07485 [astro-ph.HE]

    arXiv 2024

  10. [10]

    J. M. Lattimer, M. Prakash, D. Masak, and A. Yahil, Rapidly Rotating Pulsars and the Equation of State, As- trophys. J.355, 241 (1990)

    1990

  11. [11]

    Stergioulas, W

    N. Stergioulas, W. Klu´ zniak, and T. Bulik, Keplerian frequencies and innermost stable circular orbits of rapidly rotating strange stars, Astronomy and Astrophysics352, L116 (1999), arXiv:astro-ph/9909152 [astro-ph]

    Pith/arXiv arXiv 1999

  12. [12]

    J. L. Zdunik, T. Bulik, W. Klu´ zniak, P. Haensel, and D. Gondek-Rosi´ nska, On the mass of moderately rotat- ing strange stars in the mit bag model and lmxbs, As- tronomy and Astrophysics359, 143 (2000), arXiv:astro- ph/0004278 [astro-ph]

    arXiv 2000

  13. [13]

    A. J. Romanowsky and C. S. Kochanek, Dynamics of stars and globular clusters in m87, Astrophys. J.553, 722 (2001), arXiv:astro-ph/0008062

    Pith/arXiv arXiv 2001

  14. [15]

    J. L. Zdunik and P. Haensel, Maximum rotation frequency of strange stars, Phys. Rev. D42, 710 (1990)

    1990

  15. [16]

    Prakash, E

    M. Prakash, E. Baron, and M. Prakash, Erratum: Rota- tion of stars containing strange quark matter [Phys. Lett. B 243 (1990) 175], Phys. Lett. B247, 632 (1990)

    1990

  16. [17]

    Gondek-Rosi´ nska, T

    D. Gondek-Rosi´ nska, T. Bulik, J. L. Zdunik, E. Gour- goulhon, S. Ray, J. Dey, and M. Dey, Rapidly rotating compact strange stars, Astronomy and Astrophysics363, 1005 (2000), arXiv:astro-ph/0007004 [astro-ph]

    Pith/arXiv arXiv 2000

  17. [18]

    Bhattacharyya, I

    S. Bhattacharyya, I. Bombaci, D. Logoteta, and A. V. Thampan, Fast spinning strange stars: possible ways to constrain interacting quark matter parameters, Mon. Not. Roy. Astron. Soc.457, 3101 (2016), arXiv:1601.06120 [astro-ph.HE]

    Pith/arXiv arXiv 2016

  18. [19]

    Gourgoulhon, P

    E. Gourgoulhon, P. Haensel, R. Livine, E. Paluch, S. Bonazzola, and J. A. Marck, Fast rotation of strange stars, Astron. Astrophys.349, 851 (1999), arXiv:astro- ph/9907225

    arXiv 1999

  19. [20]

    E. Zhou, A. Tsokaros, L. Rezzolla, and R. Xu, Maxi- 11 mum mass of axisymmetric rotating quark stars, Astron. Nachrichten338, 1044 (2017)

    2017

  20. [21]

    Szkudlarek, D

    M. Szkudlarek, D. Gondek-Rosi´ nska, L. Villain, and M. Ansorg, The Maximum Mass of Rotating Strange Stars, inElectromagnetic Radiation from Pulsars and Magnetars, Astronomical Society of the Pacific Conference Series, Vol. 466, edited by W. Lewandowski, O. Maron, and J. Kijak (2012) p. 231

    2012

  21. [22]

    Szkudlarek, D

    M. Szkudlarek, D. Gondek-Rosi´ nska, L. Villain, and M. Ansorg, Maximum Mass Of Differentially Rotat- ing Strange Quark Stars, Astrophys. J.879, 44 (2019), arXiv:1904.03759 [astro-ph.HE]

    Pith/arXiv arXiv 2019

  22. [23]

    E. Zhou, A. Tsokaros, K. Uryu, R. Xu, and M. Shibata, Differentially rotating strange star in general relativity, Phys. Rev. D100, 043015 (2019), arXiv:1902.09361 [astro- ph.HE]

    Pith/arXiv arXiv 2019

  23. [24]

    Zhou, Properties of relativistically rotating quark stars, inJournal of Physics Conference Series, Journal of Physics Conference Series, Vol

    E. Zhou, Properties of relativistically rotating quark stars, inJournal of Physics Conference Series, Journal of Physics Conference Series, Vol. 861 (2017) p. 012007

    2017

  24. [25]

    E. Zhou, A. Tsokaros, L. Rezzolla, R. Xu, and K. Ury¯ u, Uniformly rotating, axisymmetric, and triaxial quark stars in general relativity, Phys. Rev. D97, 023013 (2018)

    2018

  25. [26]

    Stergioulas and J

    N. Stergioulas and J. L. Friedman, Comparing Models of Rapidly Rotating Relativistic Stars Constructed by Two Numerical Methods, Astrophys. J.444, 306 (1995), arXiv:astro-ph/9411032 [astro-ph]

    Pith/arXiv arXiv 1995

  26. [27]

    The ther- modynamics of hot quark matter follows the formalism introduced in Sec

    in order to maximize the stellar mass. The ther- modynamics of hot quark matter follows the formalism introduced in Sec. IIB of [ 28], which focuses on static protoquark stars. The evolution is represented by a se- quence of equilibrium snapshots corresponding to four distinct stages. Within this framework, we compute the mass–radius relation, the distrib...

    Pith/arXiv arXiv 2026

  27. [28]

    The three-dimensional structure of the nucleon from lattice QCD

    and references therein) Ω0 =− X i γi 24π2 µ∗ i νi ν2 i − 3 2 m2 i + 3 2 m4 i ln µ∗ i +ν i mi , (3) with γi = 6 accounting for spin and color degeneracy. The corresponding Fermi momentum is νi = q µ∗2 i −m 2 i ,(4) leading to the number density ρi = γi 6π2 µ∗2 i −m 2 i 3/2 = γi ν3 i 6π2 .(5) The physical chemical potential is related to its effective count...

    1984

  28. [29]

    F. M. da Silva, A. Issifu, L. L. Lopes, L. C. N. Santos, and D. P. Menezes, Bayesian study of quark models in view of recent astrophysical constraints, Phys. Rev. D 109, 043054 (2024), arXiv:2309.16865 [nucl-th]

    Pith/arXiv arXiv 2024

  29. [30]

    Issifu, F

    A. Issifu, F. M. da Silva, and D. P. Menezes, Proto-strange quark stars from density-dependent quark mass model, Eur. Phys. J. C84, 463 (2024), arXiv:2311.12511 [nucl- th]

    Pith/arXiv arXiv 2024

  30. [31]

    Issifu, A

    A. Issifu, A. Konstantinou, F. M. da Silva, and T. Fred- erico, Rotational effects in quark stars: comparing differ- ent models (2025), arXiv:2511.20477 [astro-ph.HE]

    Pith/arXiv arXiv 2025

  31. [32]

    J.-y. Shen, Y. Zhang, B. Wang, and R.-K. Su, Slowly rotating proto strange stars in quark mass density- and temperature- dependent model, Int. J. Mod. Phys. A20, 7547 (2005), arXiv:gr-qc/0503015

    Pith/arXiv arXiv 2005

  32. [33]

    Madsen, Physics and astrophysics of strange quark matter, Lect

    J. Madsen, Physics and astrophysics of strange quark matter, Lect. Notes Phys.516, 162 (1999), arXiv:astro- ph/9809032

    arXiv 1999

  33. [34]

    Chen and L.-M

    K. Chen and L.-M. Lin, Fully general relativistic simula- tions of rapidly rotating quark stars: Oscillation modes and universal relations, Phys. Rev. D108, 064007 (2023), arXiv:2307.01598 [gr-qc]

    Pith/arXiv arXiv 2023

  34. [35]

    C. J. Xia, G. X. Peng, S. W. Chen, Z. Y. Lu, and J. F. Xu, Thermodynamic consistency, quark mass scaling, and properties of strange matter, Phys. Rev. D89, 105027 (2014), arXiv:1405.3037 [hep-ph]

    Pith/arXiv arXiv 2014

  35. [36]

    Issifu, F

    A. Issifu, F. M. da Silva, L. C. N. Santos, D. P. Menezes, and T. Frederico, Strongly interacting quark matter in massive quark stars, Classical and Quantum Gravity42, 125004 (2025)

    2025

  36. [37]

    X. J. Wen, X. H. Zhong, G. X. Peng, P. N. Shen, and P. Z. Ning, Thermodynamics with density and temperature dependent particle masses and properties of bulk strange quark matter and strangelets, Phys. Rev. C72, 015204 (2005), arXiv:hep-ph/0506050

    Pith/arXiv arXiv 2005

  37. [38]

    G. X. Peng, H. C. Chiang, and P. Z. Ning, Thermody- namics, strange quark matter, and strange stars, Phys. Rev. C62, 025801 (2000), arXiv:hep-ph/0003027

    Pith/arXiv arXiv 2000

  38. [39]

    B. C. Backes, E. Hafemann, I. Marzola, and D. P. Menezes, Density dependent quark mass model revisited: Thermo- dynamic consistency, stability windows and stellar prop- erties, J. Phys. G48, 055104 (2021), arXiv:2007.04494 [hep-ph]

    Pith/arXiv arXiv 2021

  39. [40]

    A. Deur, S. J. Brodsky, and G. F. de Teramond, The QCD Running Coupling, Nucl. Phys.90, 1 (2016), arXiv:1604.08082 [hep-ph]

    Pith/arXiv arXiv 2016

  40. [41]

    R. L. Workmanet al.(Particle Data Group), Review of Particle Physics, PTEP2022, 083C01 (2022)

    2022

  41. [42]

    Chen, C.-J

    H.-M. Chen, C.-J. Xia, and G.-X. Peng, Strangelets at finite temperature in a baryon density-dependent quark mass model, Phys. Rev. D105, 014011 (2022), arXiv:2110.09194 [hep-ph]

    Pith/arXiv arXiv 2022

  42. [43]

    G. B. Cook, S. L. Shapiro, and S. A. Teukolsky, Rapidly Rotating Neutron Stars in General Relativity: Realistic Equations of State, Astrophys. J.424, 823 (1994)

    1994

  43. [44]

    Komatsu, Y

    H. Komatsu, Y. Eriguchi, and I. Hachisu, Rapidly rotating general relativistic stars. i – numerical method and its application to uniformly rotating polytropes, Mon. Not. R. Astron. Soc.237, 355 (1989)

    1989

  44. [45]

    W. G. Laarakkers and E. Poisson, Quadrupole moments of rotating neutron stars, Astrophys. J.512, 282 (1999), arXiv:gr-qc/9709033

    Pith/arXiv arXiv 1999

  45. [46]

    Pappas and T

    G. Pappas and T. A. Apostolatos, Multipole moments of numerical spacetimes (2012), arXiv:1211.6299 [gr-qc]

    Pith/arXiv arXiv 2012

  46. [47]

    Konstantinou and S

    A. Konstantinou and S. M. Morsink, Universal relations for the increase in the mass and radius of a rotating neutron star, The Astrophysical Journal934, 139 (2022)

    2022

  47. [48]

    Konstantinou, The effect of a self-bound equation of state on the structure of rotating compact stars, The Astrophysical Journal997, 55 (2026)

    A. Konstantinou, The effect of a self-bound equation of state on the structure of rotating compact stars, The Astrophysical Journal997, 55 (2026)

    2026

  48. [49]

    F. M. da Silva, A. Issifu, L. C. N. Santos, T. Frederico, and D. P. Menezes, Hyperons and ∆’s in rotating protoneutron stars: Global properties, Phys. Rev. D112, 023007 (2025), arXiv:2504.05495 [hep-ph]

    Pith/arXiv arXiv 2025

  49. [50]

    Stergioulas, Rotating Stars in Relativity, Living Rev

    N. Stergioulas, Rotating Stars in Relativity, Living Rev. Rel.6, 3 (2003), arXiv:gr-qc/0302034

    Pith/arXiv arXiv 2003

  50. [51]

    Andersson, Gravitational waves from instabilities in relativistic stars, Class

    N. Andersson, Gravitational waves from instabilities in relativistic stars, Class. Quant. Grav.20, R105 (2003), arXiv:astro-ph/0211057

    Pith/arXiv arXiv 2003

  51. [52]

    Gondek-Rosinska, N

    D. Gondek-Rosinska, N. Stergioulas, T. Bulik, W. Kluz- niak, and E. Gourgoulhon, Lower limits on the maximum orbital frequency around rotating strange stars, Astron. Astrophys.380, 190 (2001), arXiv:astro-ph/0110209

    Pith/arXiv arXiv 2001

  52. [53]

    Rileyet al., A N ICER View of PSR J0030+0451: Millisecond Pulsar Parameter Estimation, Astrophys

    T. Rileyet al., A N ICER View of PSR J0030+0451: Millisecond Pulsar Parameter Estimation, Astrophys. J. Lett.887, L21 (2019)

    2019

  53. [54]

    Milleret al., PSR J0030+0451 Mass and Radius from N ICER Data and Implications for the Properties of Neutron Star Matter, Astrophys

    M. Milleret al., PSR J0030+0451 Mass and Radius from N ICER Data and Implications for the Properties of Neutron Star Matter, Astrophys. J. Lett.887, L24 (2019), arXiv:1912.05705 [astro-ph.HE]

    Pith/arXiv arXiv 2019

  54. [55]

    T. E. Rileyet al., A nicer view of the massive pulsar psr j0740+6620 informed by radio timing and xmm-newton spectroscopy, Astrophys. J. Lett.918(2021)

    2021

  55. [56]

    M. C. Milleret al., The Radius of PSR J0740+6620 from NICER and XMM-Newton Data, Astrophys. J. Lett.918, L28 (2021), arXiv:2105.06979 [astro-ph.HE]

    Pith/arXiv arXiv 2021

  56. [57]

    Choudhuryet al., A NICER View of the Nearest and Brightest Millisecond Pulsar: PSR J0437–4715, Astrophys

    D. Choudhuryet al., A NICER View of the Nearest and Brightest Millisecond Pulsar: PSR J0437–4715, Astrophys. J. Lett.971, L20 (2024)

    2024

  57. [58]

    Kumari and A

    M. Kumari and A. Kumar, Properties of strange quark matter and strange quark stars, Eur. Phys. J. C81, 791 (2021)

    2021

  58. [59]

    J. A. Pons, S. Reddy, M. Prakash, J. M. Lattimer, and J. A. Miralles, Evolution of protoneutron stars, Astrophys. 12 J.513, 780 (1999), arXiv:astro-ph/9807040

    Pith/arXiv arXiv 1999

  59. [60]

    Prakash, I

    M. Prakash, I. Bombaci, M. Prakash, P. J. Ellis, J. M. Lattimer, and R. Knorren, Composition and structure of protoneutron stars, Phys. Rept.280, 1 (1997), arXiv:nucl- th/9603042

    arXiv 1997

  60. [61]

    Issifu, K

    A. Issifu, K. D. Marquez, M. R. Pelicer, and D. P. Menezes, Exotic baryons in hot neutron stars, Mon. Not. Roy. As- tron. Soc.522, 3263 (2023), arXiv:2302.04364 [nucl-th]

    Pith/arXiv arXiv 2023

  61. [62]

    J. E. Horvath, L. S. Rocha, L. M. de S´ a, P. H. R. S. Moraes, L. G. Bar˜ ao, M. G. B. de Avellar, A. Bernardo, and R. R. A. Bachega, A light strange star in the rem- nant HESS J1731−347: Minimal consistency checks, As- tron. Astrophys.672, L11 (2023), arXiv:2303.10264 [astro- ph.HE]

    Pith/arXiv arXiv 2023

  62. [63]

    Lugones and J

    G. Lugones and J. E. Horvath, High-density QCD pairing in compact star structure, Astron. Astrophys.403, 173 (2003), arXiv:astro-ph/0211638

    Pith/arXiv arXiv 2003

  63. [64]

    Paschalidis and N

    V. Paschalidis and N. Stergioulas, Rotating Stars in Rel- ativity, Living Rev. Rel.20, 7 (2017), arXiv:1612.03050 [astro-ph.HE]

    Pith/arXiv arXiv 2017

  64. [65]

    Alford, P

    M. Alford, P. Jotwani, C. Kouvaris, J. Kundu, and K. Ra- jagopal, A Hot water bottle for aging neutron stars, Phys. Rev. D71, 114011 (2005), arXiv:astro-ph/0411560

    Pith/arXiv arXiv 2005

  65. [66]

    Oertel, M

    M. Oertel, M. Hempel, T. Kl¨ ahn, and S. Typel, Equations of state for supernovae and compact stars, Rev. Mod. Phys. 89, 015007 (2017), arXiv:1610.03361 [astro-ph.HE]

    Pith/arXiv arXiv 2017

  66. [67]

    Y. Li, J. Wang, Z. Wu, and D. Wen, Inferring the gravita- tional binding energy and moment of inertia of psr j0030 + 0451 and psr j0740 + 6620 from new universal relations, Classical and Quantum Gravity39, 035014 (2022)

    2022

  67. [68]

    H. O. Silva, A. M. Holgado, A. C´ ardenas-Avenda˜ no, and N. Yunes, Astrophysical and theoretical physics impli- cations from multimessenger neutron star observations, Phys. Rev. Lett.126, 181101 (2021), arXiv:2004.01253 [gr-qc]

    Pith/arXiv arXiv 2021

  68. [69]

    Kumar and P

    B. Kumar and P. Landry, Inferring neutron star properties from GW170817 with universal relations, Phys. Rev. D 99, 123026 (2019), arXiv:1902.04557 [gr-qc]

    Pith/arXiv arXiv 2019

  69. [70]

    S. Yang, D. Wen, J. Wang, and J. Zhang, Exploring the universal relations with the correlation analysis of neutron star properties, Phys. Rev. D105, 063023 (2022)

    2022

  70. [71]

    Bejger, T

    M. Bejger, T. Bulik, and P. Haensel, Moments of inertia of the binary pulsars J0737-3039A,B and the dense mat- ter EOS, Mon. Not. Roy. Astron. Soc.364, 635 (2005), arXiv:astro-ph/0508105

    Pith/arXiv arXiv 2005

  71. [72]

    Breu and L

    C. Breu and L. Rezzolla, Maximum mass, moment of inertia and compactness of relativistic stars, Mon. Not. Roy. Astron. Soc.459, 646 (2016), arXiv:1601.06083 [gr- qc]

    Pith/arXiv arXiv 2016

  72. [73]

    D. G. Ravenhall and C. J. Pethick, Neutron Star Moments of Inertia, Astrophys. J.424, 846 (1994)

    1994

  73. [74]

    Yagi and N

    K. Yagi and N. Yunes, Approximate Universal Relations for Neutron Stars and Quark Stars, Phys. Rept.681, 1 (2017), arXiv:1608.02582 [gr-qc]

    Pith/arXiv arXiv 2017

  74. [75]

    Cutler, Gravitational waves from neutron stars with large toroidal B fields, Phys

    C. Cutler, Gravitational waves from neutron stars with large toroidal B fields, Phys. Rev. D66, 084025 (2002), arXiv:gr-qc/0206051

    Pith/arXiv arXiv 2002

  75. [76]

    J. M. Lattimer and M. Prakash, Neutron star structure and the equation of state, Astrophys. J.550, 426 (2001), arXiv:astro-ph/0002232

    Pith/arXiv arXiv 2001

  76. [77]

    Burrows and J

    A. Burrows and J. M. Lattimer, The birth of neutron stars, Astrophys. J.307, 178 (1986)

    1986

  77. [78]

    Glendenning,Compact Stars

    N. Glendenning,Compact Stars. Nuclear Physics, Particle Physics and General Relativity.(1996)

    1996

  78. [79]

    J. M. Lattimer and M. Prakash, The physics of neutron stars, Science304, 536 (2004), arXiv:astro-ph/0405262

    Pith/arXiv arXiv 2004

  79. [80]

    C. M. Will, Testing general relativity with compact-body orbits: a modified Einstein–Infeld–Hoffmann framework, Class. Quant. Grav.35, 085001 (2018), arXiv:1801.08999 [gr-qc]

    Pith/arXiv arXiv 2018