Heavy baryons in hot stellar matter with light nuclei and hypernuclei

The production of light nuclei and hypernuclei together with heavy baryons, both hyperons and $\mathrm{\Delta }$ baryons, in low-density matter as found in stellar environments such as supernova or binary mergers is studied within relativistic mean-field models. Five light nuclei were considered together with three light hypernuclei. The presence of both hyperons and $\mathrm{\Delta }$ baryons shift the dissolution of clusters to larger densities and increase the abundance of clusters. This effect is larger the smaller the charge fraction and the higher the temperature. The couplings of the $\mathrm{\Delta }$ baryons were chosen imposing that the nucleon effective mass remains finite inside neutron stars.

Figure 1

Mass-Radius relations (left) and nucleon effective mass as a function of the density (right) for several sets of values for the $x_{\sigma \mathrm{\Delta }}$, $x_{\omega \mathrm{\Delta }}$ couplings, fixing $x_{\rho \mathrm{\Delta }}=1$, and the two RMF models considered, DD2 and FSU2H. The black curves correspond to the EoS without the $\mathrm{\Delta }$ baryons. The horizontal bands, from top to bottom, indicate the mass and radius uncertainties associated with the PSR J0740 $+$ 6620 [40] (blue), PSR J0348 $+$ 0432 [41] (brown), and the two independent analysis of the NICER data of the PSR J0030 $+$ 0451, $M=1.{44}_{-0.14}^{+0.15}{\mathrm{M}}_{\odot }$ with $R=13.{02}_{-1.06}^{+1.24}\mathrm{km}$ [42] (green), and $M=1.{34}_{-0.16}^{+0.15}{\mathrm{M}}_{\odot }$ with $R=12.{71}_{-1.19}^{+1.14}\mathrm{km}$ [43] (red).

Figure 2

Unbound nucleon (red) and light cluster (blue) fractions for the DD2 model in a calculation with (thick lines) and without (thin lines) (a) hyperons and (b) hyperons and $\mathrm{\Delta }$ isobars as a function of the temperature for a fixed charge fraction of $Y_Q=0.1$, and density of $n_B=0.1$ ${\mathrm{fm}}^3$. The scalar cluster-meson coupling is fixed to $x_s=0.93$. The $\mathrm{\Delta }$ couplings are fixed to $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=x_{\rho \mathrm{\Delta }}=1$.

Figure 3

Unbound nucleon and light cluster fractions as a function of the temperature in a calculation with hyperons and $\mathrm{\Delta }$ isobars for the DD2 (thin lines) and FSU2H (thick lines) models, and a fixed charge fraction of $Y_Q=0.1$, and density of $n_B=0.1{\mathrm{fm}}^{-3}$. The $\mathrm{\Delta }$ couplings are fixed to $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=1.2$, $x_{\rho \mathrm{\Delta }}=1$.

Figure 4

Unbound nucleon and hyperon fractions as a function of the temperature in a calculation with (thick lines) and without (thin lines) $\mathrm{\Delta }$ isobars for the DD2 model, and a fixed charge fraction of $Y_Q=0.1$ and density $n_B=0.1{\mathrm{fm}}^{-3}$. The scalar cluster-meson coupling fraction is set to $x_s=0.93$. The $\mathrm{\Delta }$ abundances are also displayed with thick pink lines. Light clusters are present in the calculation but their fractions are not shown. The $\mathrm{\Delta }$ couplings are fixed to $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=x_{\rho \mathrm{\Delta }}=1$.

Figure 5

Total mass fraction $Y_{\mathrm{tot}}$ of the light clusters as a function of the density at $T=50\mathrm{MeV}$ (left) and the dissolution density of the clusters, $n_d$, as a function of the temperature (right) for a calculation without hyperons and $\mathrm{\Delta }s$ (dashed), with hyperons and without $\mathrm{\Delta }s$ (solid), and with hyperons and $\mathrm{\Delta }s$ (dash-dotted). The charge fraction is fixed to $Y_Q=0.3$ (orange) and 0.1 (blue), and the DD2 model is considered.

Figure 6

Mass fractions of the $\mathrm{\Lambda }$, $\mathrm{\Sigma }$, and $\mathrm{\Xi }$ hyperons (green), and $\mathrm{\Delta }$ isobars (orange) (top panel), and mass fractions of the light clusters (blue), and light hypernuclei (pink) (bottom panel), as a function of the density for $T=50\mathrm{MeV}$ and $x_s=0.93$, with $Y_Q=0.3$ (left) and 0.1 (right). The calculations are performed for the DD2 RMF model with (thick lines) and without (thin lines) $\mathrm{\Delta }$ particles. The mass fractions of the unbound nucleons are shown in red in both panels.

Figure 7

Mass fractions of the $\mathrm{\Lambda }$, $\mathrm{\Sigma }$, and $\mathrm{\Xi }$ hyperons (green), and $\mathrm{\Delta }$ isobars (orange) (top panel), and mass fractions of the light clusters (blue) and light hypernuclei (pink) (bottom panel), within the DD2 model (thin) and FSU2H model (thick) as a function of the density for $T=50\mathrm{MeV}$ and $Y_Q=0.1$. The $\mathrm{\Delta }$ couplings are fixed to $x_{\sigma \mathrm{\Delta }}=x_{\omega \mathrm{\Delta }}=1.2,x_{\rho \mathrm{\Delta }}=1$. The mass fractions of the unbound nucleons are shown in red in both panels.

Figure 8

Total fraction of $\mathrm{\Delta }$ isobars, $Y_{\mathrm{\Delta }}$ as a function of the density for $T=50\mathrm{MeV}$ and a charge fraction of $Y_Q=0.3$. The $\sigma$-cluster meson fractions are $x_s=0.93$ (DD2) and $x_s=0.91$ (FSU2H), and several $\mathrm{\Delta }$ couplings are considered.