Constraints on the high-density nuclear equation of state from the phenomenology of compact stars and heavy-ion collisions

A new scheme for testing nuclear matter equations of state (EoSs) at high densities using constraints from neutron star (NS) phenomenology and a flow data analysis of heavy-ion collisions is suggested. An acceptable EoS shall not allow the direct Urca process to occur in NSs with masses below $1.5{M}_{\ensuremath{\bigodot}}$, and also shall not contradict flow and kaon production data of heavy-ion collisions. Compact star constraints include the mass measurements of $2.1\ifmmode\pm\else\textpm\fi{}0.2{M}_{\ensuremath{\bigodot}}$ ($1\ensuremath{\sigma}$ level) for PSR J0751+1807 and of $2.0\ifmmode\pm\else\textpm\fi{}0.1{M}_{\ensuremath{\bigodot}}$ from the innermost stable circular orbit for 4U 1636--536, the baryon mass---gravitational mass relationships from Pulsar B in J0737--3039 and the mass-radius relationships from quasiperiodic brightness oscillations in 4U 0614+09 and from the thermal emission of RX J1856--3754. This scheme is applied to a set of relativistic EoSs which are constrained otherwise from nuclear matter saturation properties. We demonstrate on the given examples that the test scheme due to the quality of the newly emerging astrophysical data leads to useful selection criteria for the high-density behavior of nuclear EoSs.