Relativistic hypernuclear compact stars with calibrated equations of state

Within the covariant density functional theory of hypernuclear matter we build a series of equations of state for hypernuclear compact stars, by calibrating the coupling constants of the $\Xi$-hyperon to the experimental binding energy of the single-$\Xi$ hypernuclei $^{15}_{\Xi^-}$C and $^{12}_{\Xi^-}$Be. Coupling constants of the $\Lambda$-hyperon to nucleons have been calibrated on a vast collection of experimental data on single $\Lambda$-hypernuclei and we employ those values. Uncertainties on the couplings of the $\Sigma$-hyperon to nuclear matter, due to lack of experimental data, are accounted for by allowing for a wide variation of the well depth of $\Sigma$ at rest in symmetric saturated nuclear matter. To account for uncertainties in the nucleonic sector at densities much larger than the saturation density, a rich collection of parametrizations is employed, some of them in agreement with existing constraints from nuclear physics and astrophysics. Neutron star properties are investigated with all these calibrated equations of state. The effects of the presence of hyperons on the radius, on the tidal deformability, on the moment of inertia, and on the nucleonic direct Urca process are discussed. The sensitivity of the hyperonic direct Urca processes to uncertainties in the nucleonic and hyperonic sectors is also addressed. It is shown that the relative variations of the radius, tidal deformability and moment of inertia from the values that characterize purely nucleonic stars are linearly correlated with the strangeness fraction. The maximum radius deviation, obtained for most massive neutron stars, is $\approx 10\%$. The reduction of the maximum mass, triggered by nucleation of strangeness, is estimated at $\approx 15 - 20\%$, out of which 5\% comes from insufficient information on the $\Sigma$-hyperon interactions.