Hybrid stars may have an inverted structure

We propose a new stellar structure of compact stars, the ``cross stars" that consist of a hadronic matter core and a quark matter crust, with an inverted structure compared to the conventional hybrid stars. This distinct stellar structure naturally arises from the quark matter to hadronic matter transition associated with the chemical potential crossing, in the context of the quark matter hypothesis that either strange or up-down quark matter is the ground state of baryonic matter at low pressure. We find that the interplay between the hadronic matter and quark matter compositions of cross stars can help to reconcile the small radii constraints indicated by the LIGO/Virgo GW170817 event, the large radii constraints set for massive compact stars by recent NICER X-ray observations, and the recent observation of the most-massive pulsar PSR J0952-0607. This leaves more space open for the equation of states of both hadronic matter and quark matter.