Why can hadronic stars convert into strange quark stars with larger radii

TL;DR

This paper investigates the conditions under which hadronic stars can convert into larger-radius strange quark stars, emphasizing the energy considerations and providing criteria for such conversions based on equations of state.

Contribution

It introduces a criterion for the exothermic conversion of hadronic stars into larger-radius strange quark stars, considering microphysics and energy balances, and compares different formation scenarios.

Findings

Conversion can be exothermic if the increase in nuclear binding energy outweighs the gravitational energy loss.

A sufficient and necessary condition for larger-radius strange quark star formation is provided.

The study compares different quark star formation schemes and discusses observational discriminants.

Abstract

The total binding energy of compact stars is the sum of the gravitational binding energy $(BE)_g$ and the nuclear binding energy $(BE)_n$, the last being related to the microphysics of the interactions. While the first is positive (binding) both for hadronic stars and for strange quark stars, the second is large and negative for hadronic stars (anti-binding) and either small and negative (anti-binding) or positive (binding) for strange quark stars. A hadronic star can convert into a strange quark star with a larger radius because the consequent reduction of $(BE)_g$ is over-compensated by the large increase in $(BE)_n$. Thus, the total binding energy increases due to the conversion and the process is exothermic. Depending on the equations of state of hadronic matter and quark matter and on the baryonic mass of the star, the contrary is obviously also possible, namely the conversion of hadronic stars into strange quark stars having smaller radii, a situation more often discussed in the literature. We provide a condition that is sufficient and in most of the phenomenologically relevant cases also necessary in order to form strange quark stars with larger radii while satisfying the exothermicity request. Finally, we compare the two schemes in which quark stars are produced (one having large quark stars and the other having small quark stars) among themselves and with the third-family scenario and we discuss how present and future data can discriminate among them.