Rapidly Spinning Massive Pulsars as an Indicator of Quark Deconfinement

TL;DR

The paper addresses how rapidly rotating millisecond pulsars constrain the dense-matter equation of state by studying rotating hybrid stars that undergo a deconfinement phase transition to color-superconducting quark matter. Using a hybrid EoS with a hadronic DD2npY-T sector and a 2SC quark sector connected via a Maxwell construction, and varying the vector coupling $η_V$ and diquark coupling $η_D$, the authors map static and rotating sequences up to the mass-shedding limit with the Rotating Neutron Star code, ensuring consistency with mass, radius, and tidal deformability constraints. Key findings include that rotation stiffens the star and can stabilize configurations with quark cores, the phase transition onset remains robust across rotation, and a revised Kepler relation introduces a parameter $C$ that yields tight upper radius bounds ($R_{1.4} ≤ 14.90$ km, $R_{0.7} < 11.49$ km). The analysis explains observed MSP clustering near $∼ 2$ kHz as a result of accretion-driven spin-up near the phase transition, and shows that a $T/W$ threshold around $0.08$ excludes highly deformed configurations, thus constraining the model parameter space. These results support quark deconfinement as a viable mechanism to reconcile heavy neutron stars with hyperon-rich EoSs and provide observationally testable signatures for future surveys such as SKA.

Abstract

We study rotating hybrid stars, with particular emphasis on the effect of spin on the deconfinement phase transition and star properties. Our analysis is based on a hybrid equation of state with a phase transition from hadronic matter containing hyperons to color-superconducting quark matter, where the quark phase is modeled within a relativistic density functional approach. By varying the strength of the vector repulsion and diquark pairing couplings in the microscopic quark Lagrangian, we construct a set of hybrid star sequences with different quark-matter onset densities. This framework ensures consistency with astrophysical and gravitational wave constraints on mass, radius, and tidal deformability.

Figures (3)

• Figure 1: Mass-radius diagram for a set of static (solid curves) and rotating stars with the Kepler frequency (dashed curves). The black and color curves depict the baryonic DD2npY-T EoS, while the color ones show hybrid stars for the fixed vector coupling $\eta_V=0.30$ and different values of the diquark coupling $\eta_D$. The radius corresponds to the equatorial radius. The allowed configurations for hybrid stars are located between the solid and dashed curves of the same color. This figure is adapted from the work of Gärtlein et al. (2025) Gartlein:2024cbj.
• Figure 2: The angular velocity as a function of the gravitational mass of compact stars. The solid blue curve represents the Kepler frequency, above which lies the gray-shaded area where no stationary rotating stars can be found. Black solid curves mark the separation between NSs (dark green area), hybrid stars (light green area), and black holes (pink beige area of unstable configurations). In comparison, the dashed curves represent the purely hadronic analogues. The circles with 1$\sigma$ confidence level error bars depict the measured mass and frequency of the most rapidly rotating MSPs with spin frequency f>200 Hz (the data are listed in Ref. Gartlein:2024cbj). The arrows, rather than error bars, represent the available upper limit on the mass estimate. Other independent mass measurements of the same object are depicted with gray dots. The color solid curves represent the evolution trajectories of the hybrid (solid) and hadronic (dashed) star of 1.2$M_{\odot}$ with the corresponding strength of the magnetic field. This figure is adapted from the work of Gärtlein et al. (2025) Gartlein:2024cbj.
• Figure 3: Left panel: Angular velocity $\Omega$ as a function of the ratio of rotational and gravitational energy. Right panel: Parameter plot of the hybrid EoS constrained via the $\Omega-T/W$ plot. This figure is adapted from the work of Gärtlein et al. (2025) Gartlein:2024cbj and shows an additional excluded (blue) area in the $\eta_V-\eta_D$ plain. The physical parameter space is constrained to the colorful area.