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From hadrons to quarks in neutron stars: a review

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abstract

We review the equation of state of matter in neutron stars from the solid crust through the liquid nuclear matter interior to the quark regime at higher densities. We focus in detail on the question of how quark matter appears in neutron stars, and how it affects the equation of state. After discussing the crust and liquid nuclear matter in the core we briefly review aspects of microscopic quark physics relevant to neutron stars, and quark models of dense matter based on the Nambu--Jona-Lasinio framework, in which gluonic processes are replaced by effective quark interactions. We turn then to describing equations of state useful for interpretation of both electromagnetic and gravitational observations, reviewing the emerging picture of hadron-quark continuity in which hadronic matter turns relatively smoothly, with at most only a weak first order transition, into quark matter with increasing density. We review construction of unified equations of state that interpolate between the reasonably well understood nuclear matter regime at low densities and the quark matter regime at higher densities. The utility of such interpolations is driven by the present inability to calculate the dense matter equation of state in QCD from first principles. As we review, the parameters of effective quark models -- which have direct relevance to the more general structure of the QCD phase diagram of dense and hot matter -- are constrained by neutron star mass and radii measurements, in particular favoring large repulsive density-density and attractive diquark pairing interactions. We describe the structure of neutron stars constructed from the unified equations of states with crossover. Lastly we present the current equations of state -- called "QHC18" for quark-hadron crossover -- in a parametrized form practical for neutron star modeling.

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representative citing papers

Scalar diquarks in the QCD vacuum

hep-ph · 2026-06-22 · unverdicted · novelty 6.0

A first-principles FRG approach to two-flavor QCD derives low-energy constants for the pion, sigma-meson and scalar diquark without parameters beyond QCD itself, including new diquark properties for color-superconducting models.

Crust glass formation reveals the neutron star birth properties in IGR J17480-2446

astro-ph.HE · 2026-06-20 · unverdicted · novelty 6.0

Accretion-induced failure of the neutron star crystal crust produces a glass layer that explains the observed cooling, fixes the accreted mass at 2.4e-6 solar masses, and indicates birth properties typical of recycled neutron stars, potentially from electron-capture supernova formation.

Axial Oscillations of Viscous Neutron Stars

gr-qc · 2026-04-14 · unverdicted · novelty 6.0

Causal viscous relativistic hydrodynamics applied to neutron stars yields new axial mode families without perfect-fluid counterparts, including mode avoidance and long-lived modes.

Primordial Neutron Stars

astro-ph.CO · 2026-04-09 · unverdicted · novelty 6.0

Large initial baryon asymmetry allows Hubble patches to collapse into primordial neutron stars arrested by nuclear pressure, requiring later entropy dilution to match observed Y_B and BBN.

Hybrid Stars with Post-Merger Rotation Profiles

gr-qc · 2026-06-16 · unverdicted · novelty 5.0

Differential rotation in hybrid stars with deconfinement phase transition allows quasi-toroidal configurations with quark matter rings and leads to degeneracies in rotational profiles at mass-radius curve intersections.

Nucleosynthesis in the fast ejecta of a neutron star merger

astro-ph.HE · 2026-05-15 · unverdicted · novelty 5.0

Free neutrons survive r-process freeze-out in fast ejecta of neutron star mergers and their beta-decay heating produces a visible early kilonova precursor for mass fractions above ~0.05.

Gradient-Produced Neutrinos

hep-ph · 2026-04-23 · unverdicted · novelty 5.0

Steep matter-density gradients in neutron stars can produce neutrino-antineutrino pairs analogous to the Schwinger effect.

FRG analysis of dense two-color QCD within the linear sigma model

hep-ph · 2026-06-30 · unverdicted · novelty 4.0

FRG analysis in the linear sigma model for QC2D shows enhanced meson U(1)_A anomaly couplings with increasing mu_q but suppressed topological susceptibility following chiral restoration at high density or temperature.

A quarkyonic matter model

hep-ph · 2026-05-31 · unverdicted · novelty 4.0

The IdylliQ model uses quark saturation to generate stiff equations of state and effective baryon repulsions that mitigate hyperon softening in neutron star matter.

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