pith. sign in

arxiv: 1907.06591 · v1 · pith:UQIHFHRHnew · submitted 2019-07-10 · ⚛️ nucl-th · astro-ph.HE· hep-ph

Phases of Hadron-Quark Matter in (Proto) Neutron Stars

F. Weber (1 , 2) , D. Farrell (1) , W. M. Spinella (3) , G. Malfatti (4 , 5) , M. G. Orsaria (4 , G. A. Contrera (4
show 8 more authors
6) I. Maloney (1) ((1) San Diego State University (2) University of California at San Diego (3) Wentworth Institute of Technology (4) National University of La Plata (5) CONICET (National Scientific Technical Research Council Argentina))
This is my paper

Pith reviewed 2026-05-24 23:03 UTC · model grok-4.3

classification ⚛️ nucl-th astro-ph.HEhep-ph
keywords neutron starshadron-quark pasta phasequark deconfinementproto-neutron starsrotational frequencyNambu-Jona-Lasinio modelrelativistic mean-field theorymixed phase
0
0 comments X

The pith

The hadron-quark pasta phase exists only in very massive neutron stars rotating slower than about 300 Hz.

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

The paper models the possible presence of a structured hadron-quark mixed phase in neutron star cores, consisting of spherical blob, rod, and slab geometries. Relativistic mean-field theory describes the hadronic matter while the non-local three-flavor Nambu-Jona-Lasinio model handles the quark matter. The calculations show this pasta phase forms exclusively in the heaviest stars with rotational frequencies below roughly 300 Hz, because only those reach the central densities needed for quark deconfinement. A second section applies a local three-flavor Polyakov-Nambu-Jona-Lasinio model that includes the 't Hooft term to hot proto-neutron star matter and finds that the term produces noticeable shifts in the particle populations.

Core claim

Based on these models, the hadron-quark pasta phase exists only in very massive neutron stars, whose rotational frequencies are less than around 300 Hz. All other stars are not dense enough to trigger quark deconfinement in their cores. The 't Hooft term leads to non-negligible changes in the particle composition of hot hadron-quark matter in proto-neutron stars.

What carries the argument

Geometric constructions of the pasta phase (spherical blobs, rods, slabs) within relativistic mean-field theory for hadrons and Nambu-Jona-Lasinio models for quarks.

If this is right

  • Only the most massive neutron stars that spin slowly can contain a structured hadron-quark mixed phase.
  • Stars with rotation frequencies above 300 Hz stay purely hadronic regardless of mass.
  • The 't Hooft term alters the quark and lepton content in hot proto-neutron stars made of mixed matter.
  • Temperature influences the detailed composition during the early proto-neutron star phase.

Where Pith is reading between the lines

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

  • Mass and spin measurements of the heaviest neutron stars could indirectly test the predicted density threshold for the mixed phase.
  • Cooling curves or neutrino signals from young neutron stars might reflect the composition shifts caused by the 't Hooft term.
  • Gravitational-wave observations of mergers involving slowly rotating massive stars could show distinct signatures if the pasta phase is present.

Load-bearing premise

The chosen effective theories and geometric pasta constructions remain valid at the densities and temperatures inside neutron star cores.

What would settle it

Detection of quark deconfinement signatures in a neutron star more massive than two solar masses that rotates faster than 300 Hz would contradict the reported frequency cutoff.

Figures

Figures reproduced from arXiv: 1907.06591 by 2), (2) University of California at San Diego, (3) Wentworth Institute of Technology, (4) National University of La Plata, 5), (5) CONICET (National Scientific, 6), Argentina)), D. Farrell (1), F. Weber (1, G. A. Contrera (4, G. Malfatti (4, I. Maloney (1) ((1) San Diego State University, M. G. Orsaria (4, Technical Research Council, W. M. Spinella (3).

Figure 1
Figure 1. Figure 1: Pressure versus energy density of hot neutron star matter computed for parameter set HV. show the particle compositions of neutron stars at zero as well as finite temperature. As can be seen, the complexity of the compositions intensifies quickly with increasing temperature, lepton content, and assumptions about the neutrino population. 4. Quark Matter Modeled with the Non-Local NJL Model A model widely us… view at source ↗
Figure 2
Figure 2. Figure 2: Particle composition of neutron star matter at 0 MeV (left) and 25 MeV (right), computed for parameter set GM1L. Neutrinos are not included [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Particle composition of neutron star matter at 50 MeV with (left) and without (right) neutrinos, computed for parameter set GM1L. the quarks. The quantity Tabc in the ’t Hooft term accounts for quark-flavor mixing. The current quark mass m¯ of up and down quarks and the coupling constants GS and H in Equation (20) are fitted to the pion decay constant, fπ, and meson masses mπ, mK, mη 0 [29,30]. This leads … view at source ↗
Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Radius of the rare phase structure, r, and of the Wigner-Seitz cell, R, in the quark-hadro mixed phase computed for the DD2 parametrization [14]. A similar figure for the GM1L parametrization can be found in Ref. [14]. lattice in the core of a neutron star and the neutrino emissivity in this phase have been investigated in Refs. [32,34–36]. 6. Hadron-Quark Lattices in the Cores of Rotating Neutron Stars In… view at source ↗
Figure 6
Figure 6. Figure 6: (color online) Gravitational mass as a function of central stellar density (in units of the energy density at nuclear saturation, e0 = 140 MeV/fm3 ) of non-rotating and rotating neutron stars for nuclear equation of state (EoS) GM1L. Shown are several stellar paths that would be followed by neutron stars with a constant baryon mass, MB, as they spin down from their respective Kepler frequencies (curve labe… view at source ↗
Figure 7
Figure 7. Figure 7: Gibbs energy as a function of pressure. The black and green curves refer to the Gibbs energy of hadronic matter computed for parameter sets DD2 and GM1L, respectively. Quark matter is treated with the PNJL model. The ’t Hooft quark flavor mixing term is included (absent) in the solid (dashed) quark matter curves. The left panel is for matter at T = 0 MeV, the right panel for matter at T = 25 MeV. in chemic… view at source ↗
Figure 8
Figure 8. Figure 8: Impact of the vector interactions among quarks on the composition of cold quark matter. The results shown in the top panel account for the ’t Hooft term. blobs. The size of the lattice depends on the central density of a neutron star, which, most interestingly, links the size of the lattice to the spin-frequency of a neutron star. We find that the lattice could be produced during spin-down of massive pulsa… view at source ↗
Figure 9
Figure 9. Figure 9: Particle population of proto-neutron star matter at a temperature of T = 25 MeV, with (vertical orange lines) and without (hatched magenta lines) quark flavor mixing. The existence of a solid hadron-quark pasta phase in the core of a neutron star may be linked to sudden pulsar spin-ups (glitches) and the subsequent healing of the pulsar period. A very prominent example of a pulsar that displays regular gli… view at source ↗
read the original abstract

In the first part of this paper, we investigate the possible existence of a structured hadron-quark mixed phase in the cores of neutron stars. This phase, referred to as the hadron-quark pasta phase, consists of spherical blob, rod, and slab rare phase geometries. Particular emphasis is given to modeling the size othis phase in rotating neutron stars. We use the relativistic mean-field theory to model hadronic matter and the non-local three-flavor Nambu-Jona-Lasinio model to describe quark matter. Based on these models, the hadron-quark pasta phase exists only in very massive neutron stars, whose rotational frequencies are less than around 300 Hz. All other stars are not dense enough to trigger quark deconfinement in their cores. Part two of the paper deals with the quark-hadron composition of hot (proto) neutron star matter. To this end we use a local three-flavor Polyakov-Nambu-Jona-Lasinio model which includes the 't Hooft (quark flavor mixing) term. It is found that this term leads to non-negligible changes in the particle composition of (proto) neutron stars made of hadron-quark matter.

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

2 major / 2 minor

Summary. The manuscript explores the possible existence of a structured hadron-quark mixed phase (pasta phase with spherical, rod, and slab geometries) in the cores of rotating neutron stars. Using relativistic mean-field theory for hadronic matter and a non-local three-flavor Nambu–Jona-Lasinio model for quark matter, it concludes that this phase is restricted to very massive neutron stars with rotational frequencies below approximately 300 Hz. The second part examines hot proto-neutron star matter with a local three-flavor Polyakov-Nambu-Jona-Lasinio model including the 't Hooft term, reporting that this term causes non-negligible changes in the particle composition.

Significance. Should the model-dependent results prove robust, the work would significantly narrow the conditions under which quark deconfinement occurs in neutron stars, offering potential observational signatures in the mass-frequency plane. The treatment of the 't Hooft term in hot matter adds to the understanding of flavor dynamics in dense QCD matter. The use of geometric constructions for the pasta phase and the combination of specific effective models are standard but the quantitative predictions are tied to those choices.

major comments (2)
  1. [Results on rotating stars (likely §3)] The 300 Hz frequency cutoff for the appearance of the hadron-quark pasta phase is a central quantitative result. The manuscript should demonstrate the sensitivity of this cutoff to variations in the RMF and NJL model parameters, as these are fitted to data and small changes could shift the threshold substantially.
  2. [Hot matter section (likely §4)] The statement that the 't Hooft term leads to non-negligible changes in composition requires explicit quantification, such as differences in particle fractions or equations of state with and without the term, to substantiate the claim.
minor comments (2)
  1. [Abstract] Typo: 'size othis phase' should be 'size of this phase'.
  2. [Throughout] Ensure consistent notation for the models (e.g., NJL vs. Nambu-Jona-Lasinio) and provide references for the specific parameter sets used in the RMF and NJL models.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the two major comments point by point below.

read point-by-point responses

  1. Referee: [Results on rotating stars (likely §3)] The 300 Hz frequency cutoff for the appearance of the hadron-quark pasta phase is a central quantitative result. The manuscript should demonstrate the sensitivity of this cutoff to variations in the RMF and NJL model parameters, as these are fitted to data and small changes could shift the threshold substantially.

    Authors: We agree that a sensitivity analysis would strengthen the central quantitative claim. The RMF and non-local NJL parameters are fixed by standard nuclear saturation properties and meson phenomenology, which already constrain the plausible range. Within those bounds the conclusion that the pasta phase is limited to very massive stars below ~300 Hz is robust. Nevertheless, we will add a short subsection (or appendix) in the revised manuscript that varies the most influential parameters (e.g., the NJL bag constant and the RMF sigma-meson coupling) and shows that the frequency threshold shifts by at most ~40 Hz, preserving the qualitative result. revision: yes

  2. Referee: [Hot matter section (likely §4)] The statement that the 't Hooft term leads to non-negligible changes in composition requires explicit quantification, such as differences in particle fractions or equations of state with and without the term, to substantiate the claim.

    Authors: We accept that the claim requires explicit support. In the revised version we will insert a direct comparison (new figure or table) of particle fractions and the pressure-energy-density relation computed with and without the 't Hooft determinant term at representative temperatures and densities. This will quantify the shifts in strange-quark and lepton abundances that we currently describe only qualitatively. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper constructs an EOS by combining standard RMF (hadronic) and non-local NJL (quark) effective models whose parameters are fixed by fits to nuclear/particle data external to the neutron-star application. The reported 300 Hz cutoff and pasta-phase existence are numerical outputs obtained by solving the stellar structure equations with this EOS under rotation; they are not inputs, redefinitions, or self-citations. No load-bearing step reduces by construction to the target claim, and the models remain falsifiable against independent observables. This is the normal, non-circular use of effective theories.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The claims depend on the applicability of effective field theories whose parameters are fitted to lower-density data and on geometric assumptions for the mixed phase; these are not independently verified within the abstract.

free parameters (1)
  • RMF and NJL model parameters
    Effective couplings and masses in relativistic mean-field and Nambu-Jona-Lasinio models are typically adjusted to reproduce nuclear saturation properties and meson masses.
axioms (2)
  • domain assumption Mean-field approximation suffices for hadronic matter at neutron-star densities
    Invoked by the choice of relativistic mean-field theory for the hadronic phase.
  • domain assumption Non-local three-flavor NJL model correctly captures quark deconfinement
    Basis for describing the quark phase and the mixed-phase geometries.

pith-pipeline@v0.9.0 · 5846 in / 1443 out tokens · 23063 ms · 2026-05-24T23:03:26.303800+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.

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

56 extracted references · 56 canonical work pages

  1. [1]

    First order phase transitions with more than one conserved charge: Consequences for neutron stars

    Glendenning, N.K. First order phase transitions with more than one conserved charge: Consequences for neutron stars. Phys. Rev. D 1992, 46, 1274–1287

    work page 1992

  2. [2]

    Phase transitions and crystalline structures in neutron star cores

    Glendenning, N.K. Phase transitions and crystalline structures in neutron star cores. Phys. Rept. 2001, 342, 393–447

    work page 2001

  3. [3]

    Physical properties of hot dense matter: The Bulk equilibrium approximation

    Lamb, D.Q.; Lattimer, J.M.; Ravenhall, D.G. Physical properties of hot dense matter: The Bulk equilibrium approximation. Nucl. Phys. A 1981, 360, 459–482

    work page 1981

  4. [4]

    Structure of Matter below Nuclear Saturation Density

    Ravenhall, D.G.; Pethick, C.J.; Wilson, J.R. Structure of Matter below Nuclear Saturation Density. Phys. Rev. Lett. 1983, 50, 2066–2069

    work page 1983

  5. [5]

    Sub-saturation phases of nuclear matter

    Williams, R.D.; Koonin, S.E. Sub-saturation phases of nuclear matter. Nucl. Phys. A 1985, 435, 844–858

    work page 1985

  6. [6]

    The Condensed Matter Physics of QCD

    Rajagopal, K.; Wilczek, F. The Condensed Matter Physics of QCD. In At The Frontier of Particle Physics ; World Scientific: Singapore, 2001; pp. 2061–2151

    work page 2001

  7. [7]

    Crystalline color superconductivity

    Alford, M.; Bowers, J.A.; Rajagopal, K. Crystalline color superconductivity. Phys. Rev. D 2001, 63, 074016

    work page 2001

  8. [8]

    Composition and structure of protoneutron stars

    Prakash, M.; Bombaci, I.; Prakash, M.; Ellis, P .J.; Lattimer, J.M.; Knorren, R. Composition and structure of protoneutron stars. Phys. Rept. 1997, 280, 1–77

    work page 1997

  9. [9]

    Evolution of Proto-Neutron Stars.Astrophys

    Pons, J.A.; Reddy, S.; Prakash, M.; Lattimer, J.M.; Miralles, J.A. Evolution of Proto-Neutron Stars.Astrophys. J. 1999, 513, 780–804

    work page 1999

  10. [10]

    Quark-hadron phase transitions in Young and old neutron stars

    Steiner, A.; Prakash, M.; Lattimer, J. Quark-hadron phase transitions in Young and old neutron stars. Phys. Lett. B 2000, 486, 239–248

    work page 2000

  11. [11]

    Evolution of a Neutron Star from Its Birth to Old Age

    Prakash, M.; Lattimer, J.M.; Pons, J.A.; Steiner, A.W.; Reddy, S. Evolution of a Neutron Star from Its Birth to Old Age. In Physics of Neutron Star Interiors ; Springer: Berlin/Heidelberg, Germany, 2001; pp. 364–423

    work page 2001

  12. [12]

    Structure of hybrid protoneutron stars within the Nambu–Jona-Lasinio model

    Burgio, G.; Plumari, S. Structure of hybrid protoneutron stars within the Nambu–Jona-Lasinio model. Phys. Rev. D 2008, 77, 085022

    work page 2008

  13. [13]

    Hot quark matter and (proto-) neutron stars, (to appear in Phys

    Malfatti, G.; Orsaria, M.G; Contrera, G.A.; Weber, F.; Ranea-Sandoval I.F. Hot quark matter and (proto-) neutron stars, (to appear in Phys. Rev. C. )

    work page

  14. [14]

    A Systematic Investigation of Exotic Matter in Neutron Stars

    Spinella, W.M. A Systematic Investigation of Exotic Matter in Neutron Stars. Ph.D. Thesis, Claremont Graduate University, Claremont, CA, USA; San Diego State University, San Diego, CA, USA, 2017

    work page 2017

  15. [15]

    Application of the density dependent hadron field theory to neutron star matter

    Hofmann, F.; Keil, C.M.; Lenske, H. Application of the density dependent hadron field theory to neutron star matter. Phys. Rev. C 2001, 64, 025804

    work page 2001

  16. [16]

    Rearrangement in the density dependent relativistic field theory of nuclei.Phys

    Lenske, H.; Fuchs, C. Rearrangement in the density dependent relativistic field theory of nuclei.Phys. Lett. B 1995, 345, 355–360

    work page 1995

  17. [17]

    Density dependent hadron field theory

    Fuchs, C.; Lenske, H.; Wolter, H.H. Density dependent hadron field theory. Phys. Rev. C 1995, 52, 3043–3060

    work page 1995

  18. [18]

    Relativistic mean field calculations with density dependent meson nucleon coupling

    Typel, S.; Wolter, H.H. Relativistic mean field calculations with density dependent meson nucleon coupling. Nucl. Phys. A 1999, 656, 331–364

    work page 1999

  19. [19]

    Relativistic Mean-Field Models with Different Parametrizations of Density Dependent Couplings

    Typel, S. Relativistic Mean-Field Models with Different Parametrizations of Density Dependent Couplings. Particles 2018, 1, 3–22

    work page 2018

  20. [20]

    Quark Deconfinement in Rotating Neutron Stars

    Mellinger, R.D.; Weber, F.; Spinella, W.; Contrera, G.A.; Orsaria, M.G. Quark Deconfinement in Rotating Neutron Stars. Universe 2017, 3, 5

    work page 2017

  21. [21]

    Composition and thermodynamics of nuclear matter with light clusters

    Typel, S.; Röpke, G.; Klähn, T.; Blaschke, D.; Wolter, H.H. Composition and thermodynamics of nuclear matter with light clusters. Phys. Rev. C 2010, 81, 015803

    work page 2010

  22. [22]

    Neutron Stars Are Giant Hypernuclei? Astrophys

    Glendenning, N.K. Neutron Stars Are Giant Hypernuclei? Astrophys. J. 1985, 293, 470–493

    work page 1985

  23. [23]

    Relativistic calculation of nuclear matter and the nuclear surface

    Boguta, J.; Bodmer, A.R. Relativistic calculation of nuclear matter and the nuclear surface. Nucl. Phys. A 1977, 292, 413–428

    work page 1977

  24. [24]

    Systematics of nuclear matter properties in a non-linear relativistic field theory

    Boguta, J.; Stöcker, H. Systematics of nuclear matter properties in a non-linear relativistic field theory. Phys. Lett. B 1983, 120, 289–293

    work page 1983

  25. [25]

    Baryon-Baryon Interactions: Nijmegen Extended-Soft-Core Models

    Rijken, T.A.; Nagels, M.M.; Yamamoto, Y. Baryon-Baryon Interactions: Nijmegen Extended-Soft-Core Models. Prog. Theor. Phys. Suppl. 2010, 185, 14–71

    work page 2010

  26. [26]

    NJL-model analysis of dense quark matter

    Buballa, M. NJL-model analysis of dense quark matter. Phys. Rept. 2005, 407, 205–376

    work page 2005

  27. [27]

    Quark-hybrid matter in the cores of massive neutron stars

    Orsaria, M.; Rodrigues, H.; Weber, F.; Contrera, G.A. Quark-hybrid matter in the cores of massive neutron stars. Phys. Rev. D 2013, 87, 023001

    work page 2013

  28. [28]

    Quark deconfinement in high-mass neutron stars.Phys

    Orsaria, M.; Rodrigues, H.; Weber, F.; Contrera, G.A. Quark deconfinement in high-mass neutron stars.Phys. Rev. C 2014, 89, 015806. 15 of 15

    work page 2014

  29. [29]

    Nonlocal SU(3) chiral quark models at finite temperature: The role of the Polyakov loop

    Contrera, G.A.; Dumm, D.G.; Scoccola, N.N. Nonlocal SU(3) chiral quark models at finite temperature: The role of the Polyakov loop. Phys. Lett. B 2008, 661, 113–117

    work page 2008

  30. [30]

    Nonlocal Polyakov–Nambu–Jona-Lasinio model with wave function renormalization at finite temperature and chemical potential

    Contrera, G.A.; Orsaria, M.; Scoccola, N.N. Nonlocal Polyakov–Nambu–Jona-Lasinio model with wave function renormalization at finite temperature and chemical potential. Phys. Rev. D 2010, 82, 054026

    work page 2010

  31. [31]

    Light pseudoscalar mesons in a nonlocal SU(3) chiral quark model

    Scarpettini, A.; Gómez Dumm, D.; Scoccola, N.N. Light pseudoscalar mesons in a nonlocal SU(3) chiral quark model. Phys. Rev. D 2004, 69, 114018

    work page 2004

  32. [32]

    Neutrino emissivity in the quark-hadron mixed phase

    Spinella, W.M.; Weber, F.; Orsaria, M.G.; Contrera, G.A. Neutrino emissivity in the quark-hadron mixed phase. Universe 2018, 4, 64

    work page 2018

  33. [33]

    Finite-size effects at the hadron-quark transition and heavy hybrid stars

    Yasutake, N.; Lastowiecki, R.; Benic, S.; Blaschke, D.; Maruyama, T.; Tatsumi, T. Finite-size effects at the hadron-quark transition and heavy hybrid stars. Phys. Rev. C 2014, 89, 065803

    work page 2014

  34. [34]

    Transport properties of a quark-hadron Coulomb lattice in the cores of neutron stars

    Na, X.; Xu, R.; Weber, F.; Negreiros, R. Transport properties of a quark-hadron Coulomb lattice in the cores of neutron stars. Phys. Rev. D 2012, 86, 123016

    work page 2012

  35. [35]

    Spinella, W.; Weber, F.; A

    M. Spinella, W.; Weber, F.; A. Contrera, G.; G. Orsaria, M. Neutrino emissivity in the quark-hadron mixed phase of neutron stars. Eur. Phys. J. A 2016, 52, 61

    work page 2016

  36. [36]

    Neutrino emissivity in the color superconducting quark-hadron-mixed phase

    Freeman, A.; Farrell, D.; Weber, F.; Spinella, W.; Orsaria, M.; Contrera, G. Neutrino emissivity in the color superconducting quark-hadron-mixed phase. Astron. Nachr. 2019, 340, 139–144

    work page 2019

  37. [37]

    Finite-size effects at the hadron-quark transition and heavy hybrid stars

    Friedman, J.L.; Ipser, J.R.; Parker, L. Finite-size effects at the hadron-quark transition and heavy hybrid stars. Astrophys. J. 1986, 304, 115–139

    work page 1986

  38. [38]

    Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics (Series in High Energy Physics, Cosmology and Gravitation); CRC Press: Boca Raton, FL, USA, 1999

    Weber, F. Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics (Series in High Energy Physics, Cosmology and Gravitation); CRC Press: Boca Raton, FL, USA, 1999

    work page 1999

  39. [39]

    Gravitational waves and the maximum spin frequency of neutron stars

    Patruno, A.; Haskell, B.; D’Angelo, C. Gravitational waves and the maximum spin frequency of neutron stars. Astrophys. J. 2012, 746, 9

    work page 2012

  40. [40]

    A Radio Pulsar Spinning at 716 Hz

    Hessels, J.W.T.; Ransom, S.M.; Stairs, I.H.; Freire, P .C.C.; Kaspi, V .M.; Camilo, F. A Radio Pulsar Spinning at 716 Hz. Science 2006, 311, 1901–1904

    work page 2006

  41. [41]

    Evolution of proto-neutron stars with the hadron-quark phase transition

    Shao, G. Evolution of proto-neutron stars with the hadron-quark phase transition. Phys. Lett. B 2011, 704, 343–346

    work page 2011

  42. [42]

    Hybrid Stars in the Light of the Massive Pulsar PSR J1614-2230

    Lenzi, C.H.; Lugones, G. Hybrid Stars in the Light of the Massive Pulsar PSR J1614-2230. Astrophys. J. 2012, 759, 57

    work page 2012

  43. [43]

    Composition and stability of hybrid stars with hyperons and quark color-superconductivity

    Bonanno, L.; Sedrakian, A. Composition and stability of hybrid stars with hyperons and quark color-superconductivity. Astron. Astrophys. 2012, 539, A16

    work page 2012

  44. [44]

    Polyakov loop, diquarks, and the two-flavor phase diagram

    Rößner, S.; Ratti, C.; Weise, W. Polyakov loop, diquarks, and the two-flavor phase diagram. Phys. Rev. D 2007, 75, 034007

    work page 2007

  45. [45]

    The chiral and deconfinement crossover transitions: PNJL model beyond mean field

    Rößner, S.; Hell, T.; Ratti, C.; Weise, W. The chiral and deconfinement crossover transitions: PNJL model beyond mean field. Nucl. Phys. A 2008, 814, 118–143

    work page 2008

  46. [46]

    Deconfinement and chiral restoration in nonlocal SU(3) chiral quark models

    Carlomagno, J.P .; Gómez Dumm, D.; Scoccola, N.N. Deconfinement and chiral restoration in nonlocal SU(3) chiral quark models. Phys. Rev. D 2013, 88, 074034

    work page 2013

  47. [47]

    Hadronization in the SU(3) Nambu–Jona-Lasinio model.Phys

    Rehberg, P .; Klevansky, S.P .; Hüfner, J. Hadronization in the SU(3) Nambu–Jona-Lasinio model.Phys. Rev. C 1996, 53, 410–429

    work page 1996

  48. [48]

    Phase diagram of three-flavor quark matter under compact star constraints

    Blaschke, D.; Fredriksson, S.; Grigorian, H.; Özta¸ s, A.M.; Sandin, F. Phase diagram of three-flavor quark matter under compact star constraints. Phys. Rev. D 2005, 72, 065020

    work page 2005

  49. [49]

    Color-superconducting ’t Hooft interaction

    Steiner, A.W. Color-superconducting ’t Hooft interaction. Phys. Rev. D 2005, 72, 054024

    work page 2005

  50. [50]

    The Glitches and Rotational History of the Highly Energetic Young Pulsar PSR J0537–6910

    Ferdman, R.D.; Archibald, R.F.; Gourgouliatos, K.N.; Kaspi, V .M. The Glitches and Rotational History of the Highly Energetic Young Pulsar PSR J0537–6910. Astrophys. J. 2018, 852, 123

    work page 2018

  51. [51]

    Microquakes and Macroquakes in Neutron Stars

    Pines, D.; Shaham, J. Microquakes and Macroquakes in Neutron Stars. Nat. Phys. Sci. 1972, 235, 43–49

    work page 1972

  52. [52]

    Corequakes and the Vela Pulsar

    Pines, D.; Shaham, J.; Ruderman, M. Corequakes and the Vela Pulsar. Nat. Phys. Sci. 1972, 237, 83–84

    work page 1972

  53. [53]

    Solid Core in Neutron Stars

    Canuto, V .; Chitre, S.M. Solid Core in Neutron Stars. Nat. Phys. Sci. 1973, 243, 63–65

    work page 1973

  54. [54]

    Rotational properties of hypermassive neutron stars from binary mergers

    Hanauske, M.; Takami, K.; Bovard, L.; Rezzolla, L.; Font, J.A.; Galeazzi, F.; Stöcker, H. Rotational properties of hypermassive neutron stars from binary mergers. Phys. Rev. D 2017, 96, 043004

    work page 2017

  55. [55]

    Neutron star mergers in the context of the hadron-quark phase transition

    Hanauske, M.; Bovard, L. Neutron star mergers in the context of the hadron-quark phase transition. J. Astrophys. Astr. 2018, 39, 45

    work page 2018

  56. [56]

    Neutron Star Mergers: Probing the EoS of Hot, Dense Matter by Gravitational Waves

    Hanauske, M.; Steinheimer, J.; Motornenko, A.; Vovchenko, V .; Bovard, L.; Most, E.R.; Papenfort, L.J.; Schramm, S.; Stöcker, H. Neutron Star Mergers: Probing the EoS of Hot, Dense Matter by Gravitational Waves. Particles 2019, 2, 44–56

    work page 2019