The effects of $phi$-meson on properties of hyperon stars are studied systematically in the framework of the density dependent relativistic mean field (DDRMF) model. The $phi$-meson shifts hyperon threshold to a higher density and reduces the hyperon fractions in neutron star cores. It also strongly stiffens the equation of state (EoS) calculated with various DDRMF effective interactions and increases the maximum mass of hyperon stars, but only a few effective interactions survive under the constraints from recent astrophysical observations. In the DDRMF model, the conformal limit of sound velocity is still in a strong tension with the fact that the maximum mass of neutron stars obtained in theoretical calculations reaches about two solar masses. Based on different interior composition assumptions, we discuss the possibility of the secondary object of GW190814 as a neutron star. When $phi$-meson is considered, DD-ME2 and DD-MEX support that the secondary object of GW190814 is a hyperon star rapidly rotating with Kepler frequency.
New effective $Lambda N$ interactions are proposed for the density dependent relativistic mean field model. The multidimensionally constrained relativistic mean field model is used to calculate ground state properties of eleven known $Lambda$ hypernuclei with $Age 12$ and the corresponding core nuclei. Based on effective $NN$ interactions DD-ME2 and PKDD, the ratios $R_sigma$ and $R_omega$ of scalar and vector coupling constants between $Lambda N$ and $NN$ interactions are determined by fitting calculated $Lambda$ separation energies to experimental values. We propose six new effective interactions for $Lambda$ hypernuclei: DD-ME2-Y1, DD-ME2-Y2, DD-ME2-Y3, PKDD-Y1, PKDD-Y2 and PKDD-Y3 with three ways of grouping and including these eleven hypernuclei in the fitting. It is found that the two ratios $R_sigma$ and $R_omega$ are correlated well and there holds a good linear relation between them. The statistical errors of the ratio parameters in these effective interactions are analyzed. These new effective interactions are used to study the equation of state of hypernuclear matter and neutron star properties with hyperons.
