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The X-ray astronomy mission eXTP (enhanced X-ray Timing Polarimetry) is designed to study matter under extreme conditions of density, gravity and magnetism. Primary goals are the determination of the equation of state (EoS) of matter at supranuclear density, the physics in extremely strong magnetic fields, the study of accretion in strong-field gravity (SFG) regime. Primary targets include isolated and binary neutron stars, strong magneticfield systems like magnetars, and stellar-mass and supermassive black holes. In this paper we report about key observations and simulations with eXTP on the primary objectives involving accretion under SFG regimes and determination of NS-EoS.

We construct isoentropic equations of state (EOSs) of $$\beta $$ β -stable dense hadronic matter considering the possibility that a quark deconfinement phase transition can take place. These conditions can be actually realized in different astrophysical contexts like core-collapse supernovae (CCSNe), during the early stages of the evolution of a newly formed neutron star (protoneutron star, PNS) or in the postmerger compact object formed in binary neutron star (BNS) mergers. We consider four different EOSs to describe the hadronic phase: three EOSs from relativistic mean field theory and one EOS recently derived from microscopic calculations in the framework of the Brueckner–Hartree–Fock approach. We combine these hadronic EOSs with a quark matter EOS obtained from a modified MIT-Bag model which takes into account some perturbative corrections in the grand canonical potential due to the quark–quark interaction. The two phases are then joined up through a Gibbs construction. For each model we study thermal and neutrino trapping effects on the matter composition and consequently on the EOS. We finally determine the PNS static structure integrating the Tolman–Oppenheimer–Volkoff equations. We find that the thermal contribution and particularly the effect of neutrino trapping play an important role on the full EOS. The latter can get softer or stiffer according to the strangeness content in the hadronic phase. These effects are thus crucial to provide a proper description of the dynamical evolution of both the postmerger compact object formed in a BNS merger or the PNS formed in a CCSN.