The Surface Tension of Quark Matter in a Geometrical Approach

TL;DR

This paper introduces a geometrical method to estimate the surface tension of quark matter using equations of state, providing more precise values that support quark star formation and exploring temperature effects.

Contribution

It presents a novel geometrical approach to calculate quark matter surface tension based on the equation of state, with applications to specific models and temperature dependence analysis.

Findings

Estimated surface tension: 7-30 MeV/fm^2

Small surface tension favors quark star formation

Surface tension decreases with increasing temperature

Abstract

The surface tension of quark matter plays a crucial role for the possibility of quark matter nucleation during the formation of compact stellar objects, because it determines the nucleation rate and the associated critical size. However, this quantity is not well known and the theoretical estimates fall within a wide range, $\gamma_0 \approx 5-300 MeV/fm^2$. We show here that once the equation of state is available one may use a geometrical approach to obtain a numerical value for the surface tension that is consistent with the model approximations adopted. We illustrate this method within the two-flavor linear \sigma model and the Nambu--Jona-Lasinio model with two and three flavors. Treating these models in the mean-field approximation, we find $\gamma_0 \approx 7-30 MeV/fm^2$. Such a relatively small surface tension would favor the formation of quark stars and may thus have significant astrophysical implications. We also investigate how the surface tension decreases towards zero as the temperature is raised from zero to its critical value.