Destabilization of high-mass neutron stars by the emergence of $d^{*}$-hexaquarks

We study the effects of the first nontrivial hexaquark, $d^{*}(2380)$, on the equation of state of dense neutron star matter and investigate the consequences of its existence for neutron stars. The matter in the core regions of neutron stars is described using density-dependent relativistic mean-field theory. Our results show that within the parameter spaces examined in our paper, (i) the critical density at which the $d^{*}$ condensate emerges lies between 4 and 5 times the nuclear saturation density, (ii) $d^{*}$ hexaquarks are found to exist only in rather massive neutron stars, (iii) only relatively small fractions of the matter in the core of a massive neutron star may contain hexaquarks.

Figure 1

Pressure as a function of the energy density for the DD2 (a), GM1L (b), and SW4L (c) parametrizations, considering $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=1.05$ (left) and $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=1.25$ (right). The color bar represents the ratio of the dibaryon number density to the total baryon number density.

Figure 2

Mass-radius relationship shown for the DD2 (a), GM1L (b), and SW4L (c) parametrizations with different combinations of $x_{\omega d^{*}}$ and $x_{\sigma d^{*}}$. The orange (light-blue) curve corresponds to $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=1.25$ ($x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=1.05$). The presence of the $d^{*}$-hexaquark destabilizes NS, resulting in stable, very short branches (black short lines) of stellar configurations containing dibaryons. The enlarged area in each panel shows the effect of the combination of $x_{\omega d^{*}}$ and $x_{\sigma d^{*}}$ for stars close to the maximum mass configuration. The red circles indicate the stars considered in Fig. 4.

Figure 3

Dynamical neutron mass and the associated number density due to the instabilities discussed in the text for a representative truncated EoS. In particular, we present the results for SW4L parametrization, and $x_{\sigma d^{*}}=0.7$, $x_{\omega d^{*}}=-0.9$, $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=1.05$. We show the neutron dynamical mass, in units of the bare neutron mass, $M_n^{*}/M_n$, and the neutron number density, in units of the baryonic number density, $n_n/n$, as a function of the baryonic number density, in units of $n_0$. The dashed line indicates the onset of the $d^{*}$. This truncated EoS represents globally the behavior of all truncated EoS in this work.

Figure 4

Particle populations of the maximum-mass stellar configurations for the DD2 (a), GM1L (b), and SW4L (c) parametrizations, considering $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=1.05$, $x_{\omega d^{*}}=-0.4$, and $x_{\sigma d^{*}}=0.3$, with a total mass of $M=1.95M_{\odot }$, $M=1.87M_{\odot }$, and $M=1.77M_{\odot }$, respectively.

Figure 5

Onset of the dibaryon population in the $x_{\omega d^{*}}–x_{\sigma d^{*}}$ plane for DD2 (a), GM1L (b), and SW4L (c), considering meson-$\mathrm{\Delta }$ coupling constants of $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=1.05$ (left panel) and $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=1.25$ (right panel). The color bar shows the baryon density $n$, in units of $n_0$, at which the $d^{*}(2380)$ appears for each parametrization. The white lines show the maximum masses of NS as a function of $x_{\omega d^{*}}$ and $x_{\sigma d^{*}}$.

Figure 6

Ratio between the stellar mass containing dibaryons, $M_d^{*}$, and the maximum stellar mass, $M_{\max }$. This ratio is analyzed in the $x_{\omega d^{*}}–x_{\sigma d^{*}}$ plane for two different scenarios: one with $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=1.05$ on the left-hand side and the other with $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=1.25$ on the right-hand side. The analysis considers the DD2 and GM1L parametrizations. The color bar shows the $M_d^{*}$ proportion in the maximum-mass stellar configuration. The white lines show the maximum masses as a function of $x_{\omega d^{*}}$ and $x_{\sigma d^{*}}$. (The ratio $M_d^{*}/M_{\max }$ for the SW4L parametrization is below the precision of our calculations and, therefore, is not presented in the figure.)

Figure 7

Ratio between the stellar mass containing ${\mathrm{\Delta }}^{-}$ particles, $M_{{\mathrm{\Delta }}^{-}}$, and the maximum stellar mass, $M_{\max }$, in the $x_{\omega d^{*}}–x_{\sigma d^{*}}$ plane for $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=1.05$ on the left-hand-side and $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=1.25$ on the right-hand side). The analysis considers the DD2, GM1L, and SW4L parametrizations. The color bar shows the ${\mathrm{\Delta }}^{-}$ mass fraction in the maximum-mass stellar configurations. The dark and white lines show the maximum masses of NS as a function of $x_{\omega d^{*}}$ and $x_{\sigma d^{*}}$.