Stellar properties indicating the presence of hyperons in neutron stars

TL;DR

The paper tackles the challenge of identifying hyperons in neutron-star matter by introducing curvature-based and derivative-based diagnostics of macroscopic observables. It defines the curvature of the mass-radius relation $\kappa_R$ and the second derivative of the tidal deformability $\frac{d^2\lambda}{dM^2}$ as robust indicators that differentiate hyperonic from purely nucleonic EoSs across a broad model ensemble, while slopes $dR/dM$ and $d\Lambda/dM$ relative to $M_{\max}$ provide additional discrimination. Analysis of an extensive EoS sample shows that hyperons are associated with strongly negative $\kappa_R$ in the $1.0$–$2.0\,M_\odot$ range and with reduced $\frac{d^2\lambda}{dM^2}$ for $1.4$–$1.85\,M_\odot$, with slopes at $M_{\mathrm{ref}}=1.6\,M_\odot$ offering a complementary diagnostic when compared to $M_{\max}$. The work outlines practical measurement requirements and discusses limitations, including potential degeneracies with quark matter, proposing a path forward for using multi-mass neutron-star observations to probe non-nucleonic degrees of freedom and address the hyperon puzzle.

Abstract

We describe distinctive stellar features indicating the presence of hyperons in neutron stars as compared to purely nucleonic systems. A strongly negative curvature of the mass-radius relation $R(M)$ is characteristic of hyperons, which can be determined from measurements of neutron stars with three different masses. Similarly, a reduced second derivative of the tidal deformability as function of mass λ(M) points to hyperonic degrees of freedom in NS matter. The slopes of such curves R(M) and λ(M) can distinguish a hyperonic equation of state from purely nucleonic models if they appear increased (decreased for λ(M)) relative to the maximum mass of neutron stars.

Figures (8)

• Figure 1: Mass-radius relations of NSs considered in this study for hyperonic EoSs (blue) and purely nucleonic EoSs (gray). Dashed curves indicate EoSs with $M_\mathrm{max}<2.0~M_\odot$.
• Figure 2: Curvature $\kappa_R$ as function of mass for purely nucleonic (gray) and hyperonic (blue) EoSs. Dashed curves indicate EoSs with $M_\mathrm{max}<2.0~M_\odot$. For numerical reasons the curves terminate slightly before $M_\mathrm{max}$.
• Figure 3: Curvature $\kappa_R$ evaluated at a fixed mass of 1.6 $M_\odot$ as function the radius $R_{1.6}=R(1.6M_\odot)$ for purely nucleonic (gray) and hyperonic (blue) EoSs (crosses; asterisks for EoSs with $M_\mathrm{max}<2.0~M_\odot$). Radius measurements at $M=1.6M_\odot$ and $M=(1.6\pm0.25)M_\odot$ yield an estimate of $\kappa_R(1.6M_\odot)$ (dots). Error bars indicating corresponding precision for an assumed radius uncertainty of $\delta R=100$ meters (only for hyperonic models).
• Figure 4: Second derivative of $\lambda(M)$ with respect to mass $M$ for hyperonic EoSs (blue) and purely nucleonic EoSs (gray). Dashed curves indicate models with $M_\mathrm{max}<2.0~M_\odot$.
• Figure 5: Second derivative of $\lambda(M)$ with respect to mass $M$ at fixed mass $M=1.6~M_\odot$ as function of $\lambda(M=1.6~M_\odot)$. Symbols and colors have same meaning as in Fig. \ref{['fig:kappaerr']}. See main text for details.