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The interior of compact stars is usually divided into two major parts, theouter part called crust and the inner part called core. There are severalpossibilities for the composition of these parts. One is a hybrid star, inwhich the crust contains nuclear matter, while the inner core contains quarkmatter. Since at large baryon densities one can work with effective models, andnuclear and quark matter are usually described by different models, someunification of the two parts is needed. We show two different approaches for acomposite model and some recent developments in hybrid star constructions usingthe extended linear sigma model for modeling the quark matter at the core.

Hybrid star construction with the extended linear sigma model: preliminary results