Quark-hadron pasta phase in neutron stars: the role of medium-dependent surface and curvature tensions

We investigate the properties of the hadron-quark mixed phase, often termed the \textit{pasta} phase, expected to exist in the cores of massive neutron stars. To construct the equations of state (EoS), we combine an analytical representation based on the APR EoS for hadronic matter with the MIT bag model featuring vector interactions for quark matter. For modeling the mixed phase, we utilize the compressible liquid drop model that consistently accounts for finite-size and Coulomb effects. Unlike most previous analyses that treated surface tension as a constant free parameter and neglected curvature tension, we employ microphysical calculations using the multiple reflection expansion formalism to determine these parameters, while also ensuring their self-consistency with the EoS. We construct an extensive set of mixed hybrid EoSs by varying model parameters, solve the stellar structure equations to obtain neutron star mass-radius relationships, and select the models that satisfy current astrophysical constraints. Our findings closely align with calculations using a constant surface tension in terms of EoS stiffness and resulting stellar structure. However, they reveal significant differences in the types of geometric structures and their prevalence ranges within the mixed phase. Specifically, curvature effects enhance the emergence of tubes and bubbles at high densities despite the large value of surface tension, while suppressing the existence of drops and rods at low densities.