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Using parametric equations of state (relativistic polytropes and a simplequark bag model) to model dense-matter phase transitions, we study global,measurable astrophysical parameters of compact stars such as their allowedradii and tidal deformabilities. We also investigate the influence of stiffnessof matter before the onset of the phase transitions on the parameters of thepossible exotic dense phase. The aim of our study is to compare the parameterspace of the dense matter equation of state permitting phase transitions to asub-space compatible with current observational constraints such as the maximumobservable mass, tidal deformabilities of neutron star mergers, radii ofconfigurations before the onset of the phase transition, and to givepredictions for future observations. We studied solutions of theTolman-Oppenheimer-Volkoff equations for a flexible set of parametric equationsof state. We compare tidal deformabilities of stars with weak and strong phasetransitions with the results of the GW170817 neutron star merger. Specifically,we study characteristic phase transition features in the $\Lambda_1-\Lambda_2$relation, and estimate the deviations of our results from the approximateformul{\ae} for $\tilde{\Lambda}-R(M_1)$ and $\Lambda$-compactness proposed inthe literature. We find constraints on the hybrid equations of state to producestable neutron stars on the twin branch. For the exemplary equations of statemost of the high-mass twins occur for the minimum values of the density jump$\lambda = 1.33-1.54$; corresponding values of the square of the speed of soundare $\alpha = 0.7-0.37$. We compare results with observations of gravitationalwaves and with the theoretical causal limit and find that the minimum radius ofa twin branch is 9.5 - 10.5 km. For these solutions, the phase transitionoccurs below 0.56 [fm$^{-3}$].

Tidal deformability and other global parameters of compact stars with strong phase transitions