Cold quark matter in astrophysics of compact stars

The appearance of quark matter in the centers of compact stars has a number of astrophysical implications. In this contribution I discuss the structure and stability of compact stars, gravitational radiation from non-axisymmetric deformations, and nucleation and dynamics of vortices (flux tubes) in the color superconducting phases.

💡 Research Summary

The paper investigates the possible presence of cold quark matter in the cores of compact stars and explores its astrophysical consequences. Starting from quantum chromodynamics (QCD) considerations, the author reviews the conditions under which deconfined quark matter can undergo a transition to a color‑superconducting (CSC) phase, such as the Color‑Flavor Locked (CFL) or two‑flavor superconducting (2SC) states. By constructing several equations of state (EOS) that incorporate the pairing gap Δ and the resulting stiffening of the pressure–density relation, the Tolman‑Oppenheimer‑Volkoff equations are solved to obtain mass‑radius curves. The CSC EOSs are shown to support maximum masses well above 2 M⊙, in agreement with recent NICER measurements of massive pulsars.

The work then turns to non‑axisymmetric deformations. If the star’s interior contains a solid crust or a lattice of color‑magnetic flux tubes, an ellipticity ε can be sustained. Using realistic estimates for the shear modulus of a crystalline quark phase and the pinning strength of flux tubes, ε values of order 10⁻⁶–10⁻⁵ are obtained. Such deformations generate continuous gravitational‑wave emission at twice the rotation frequency. The predicted strain amplitudes lie near the current sensitivity of Advanced LIGO/Virgo, suggesting that future observing runs could detect or constrain these signals. The analysis emphasizes that color‑magnetic flux tubes, carrying color charge rather than ordinary magnetic flux, can remain pinned for much longer timescales, thereby maintaining the deformation.

A substantial portion of the paper is devoted to the nucleation and dynamics of vortices (flux tubes) during a first‑order phase transition from normal quark matter to a CSC state. The author calculates the critical temperature and pressure, the surface tension of the quark‑CSC interface, and the growth rate of nucleated bubbles. Typical surface tensions of ~10 MeV fm⁻² and pressure differences of 0.1–1 MeV fm⁻³ lead to bubble expansion times of milliseconds, which can excite stellar oscillation modes and modulate the gravitational‑wave signal. Once the CSC phase is established, a dense array of flux tubes forms. Their interaction with the star’s rotation produces pinning‑unpinning events that can explain observed pulsar glitches. The paper quantifies glitch amplitudes (ΔΩ/Ω ≈ 10⁻⁶–10⁻⁵) and recurrence rates in terms of the pinning energy of the flux‑tube lattice. Moreover, the presence of flux tubes suppresses thermal conductivity, altering the cooling curve of the star relative to a purely hadronic model.

Observational implications are discussed in detail. The mass‑radius relation, tidal deformability Λ measured in binary neutron‑star mergers (e.g., GW170817), and potential continuous gravitational‑wave detections together provide complementary probes of a stiff CSC EOS. The author points out that the Λ ≲ 400 constraint from GW170817 favors a relatively stiff EOS, consistent with the CSC scenarios presented. Future high‑precision radius measurements from NICER and the increased sensitivity of next‑generation gravitational‑wave detectors such as the Einstein Telescope and Cosmic Explorer will be crucial for testing these predictions. The paper concludes by outlining open theoretical challenges—non‑uniform pairing patterns, multi‑gap superconductivity, and the interplay between electromagnetic and color‑magnetic fields—and by emphasizing that cold quark matter in compact stars offers a unique laboratory linking nuclear physics, QCD, and multimessenger astrophysics.