Learning about neutron star composition from the slope of the mass-radius diagram

TL;DR

This study uses two relativistic mean-field EoS datasets—one nucleonic and one including hyperons—to investigate how the slope of the neutron-star mass–radius relation, $dM/dR$, encodes information about core composition under GW170817 and NICER constraints. By computing $dM/dR$ along the TOV sequence from $1.0M_{\odot}$ to $M_{\max}$, the authors find that most nucleonic EoS exhibit $dM/dR<0$, while hyperonic EoS largely do not, with only a tiny fraction showing the opposite. A positive $dM/dR$ near $1.4M_{\odot}$ would indicate non-nucleonic degrees of freedom, and the sign of $dM/dR|_M$ at fixed masses correlates with the symmetry-energy parameters, especially the curvature $K_{\rm sym}$. Bayesian evidence combining GW170817 and NICER data favors nucleonic EoS over hyperonic ones, particularly without back-bending, suggesting current observations disfavor hyperons in NS cores; tighter future data could further clarify the role of non-nucleonic degrees of freedom.

Abstract

The slope of the neutron star mass-radius curve, $dM/dR$, is studied to understand the information it may carry about the composition of neutron stars, particularly with regard to the presence of non-nucleonic degrees of freedom. This study uses two large sets of relativistic mean-field equations of state with either nucleonic or nucleonic and hyperonic degrees of freedom, and imposes constraints obtained from GW170817 and the pulsars PSR J0030+0451 and PSR J0740+6620. It is shown that: i) some mass-radius curves are characterized by a negative slope from one solar mass up to the maximum mass; ii) other equations of state (EoS) have a positive slope for a given range of masses below the maximum star mass. Within the set of models considered, the first set includes only a very small number of hyperonic EoS: less than 0.5\% of the total number of hyperonic stars and approximately one third of the nucleonic EoS. We have also analyzed the sign of the slope for neutron star masses of 1.2, 1.4 and 1.8$M_\odot$. Only approximately 1\% of hyperonic equations of state (EoS) predict a negative slope for 1.4$M_\odot$ stars, whereas over 90\% of nucleonic stars have a negative slope at this mass. Finally, almost all stars have a negative slope at 1.8$M_\odot$. A positive slope at 1.4$M_\odot$ may indicate the presence of non-nucleonic degrees of freedom within neutron stars. The nuclear matter property that distinguishes the different scenarios most clearly is the curvature of the symmetry energy. Nucleonic EoSs with a positive slope $dM/dR$ predict the highest values, which can exceed 100 MeV.

Figures (4)

• Figure 1: Mass-radius relations for different sets of models. The full probability distributions have been plotted. To complement these plots the 90% CI of several NS properties are given in Table \ref{['tab:1']}. Colors indicate the slope of the mass-radius curve: blue for $dM/dR < 0$ and red for $dM/dR \not < 0$. Light shades represent nucleonic sets, while dark shades represent hyperonic sets. Left panel: Sets without back-bending ($dM/dR < 0$). Middle panel: Sets with back-bending ($dM/dR \not < 0$). Right panel: All sets combined. The total number of 17,537 nucleonic EoS are distributed by 11,495 exhibiting $dM/dR < 0$ and 6,042 with $dM/dR \not < 0$. From the 16,146 EoS hyperonic EoS, only 77 satisfy $dM/dR < 0$ while 16,069 $dM/dR \not < 0$.
• Figure 2: The pressure (left), speed-of-sound squared (middle), and the renormalized trace anomaly (right) as a function of baryonic density for the four sets displayed in Fig. \ref{['fig:1']}. Full distributions are given. Colors indicate the slope of the mass-radius curve: blue for $dM/dR < 0$ and red for $dM/dR \not < 0$. Light shades represent nucleonic sets, while dark shades represent hyperonic sets.
• Figure 3: The PDFs of the $dM/dR|_{M}$ sign (positive/negative) at specific $M$ values for nucleonic (solid) and hyperonic (dashed) datasets. Purple indicates positive $dM/dR|_{M}$ values while green indicates negative values. The number of hyperonic EoS satisfying positive/negative ($+/-$) $dM/dR|_{M}$ is summarized in Table \ref{['tab:new']}. Note that for $M=1.8\, M_\odot$ the purple dashed distribution is missing because there are no hyperonic EoS with a positive $dM/dR$ for this mass, see Table \ref{['tab:new']}.
• Figure 4: Log-likelihood (see Eq. \ref{['eq:log_lik']}) of the hyperonic (dark colors) and hadronic (light colors) sets for $dM/dR < 0$ (blue) and $dM/dR \not < 0$ (red). The $\log \mathcal{L}^{\rm GW}$ is displayed on the left, $\log \mathcal{L}^{\rm NICER}$ on the center, while the total log-likelihood $\log \mathcal{L}$ is on the right.