The Surface Tension of Magnetized Quark Matter

TL;DR

This paper investigates how strong magnetic fields and temperature affect the surface tension of magnetized quark matter, which is important for understanding phase transitions in compact stellar objects like hybrid stars and magnetars.

Contribution

It provides the first analysis of the magnetic field and thermal effects on the surface tension of magnetized quark matter using the Nambu--Jona-Lasinio model.

Findings

Surface tension oscillates around its zero-field value with magnetic field.

At moderate fields, surface tension decreases by about 30%.

High magnetic fields (>10 m_pi^2) increase surface tension, suppressing phase conversion.

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 and also for the existence of a mixed phase within hybrid stars. However, despite its importance, this quantity does not have a well established numerical value. Some early estimates have predicted that, at zero temperature, the value falls within the wide range $\gamma_0\approx10-300{\rm\ MeV/fm^2}$ but, very recently, different model applications have reduced these numerical values to fall within the range $\gamma_0\approx5-30{\rm\ MeV/fm^2}$ which would favor the phase conversion process as well as the appearance of a mixed phase in hybrid stars. In magnetars one should also account for the presence of very high magnetic fields which may reach up to about $ eB\approx 3-30\, m_\pi^2$ ($B \approx 10^{19}-10^{20} \,G$) at the core of the star so that it may also be important to analyze how the presence of a magnetic field affects the surface tension. With this aim we consider magnetized two flavor quark matter, described by the Nambu--Jona-Lasinio model. We show that although the surface tension oscillates around its B=0 value, when $0 < eB \lesssim 10 \, m_\pi^2$, it only reaches values which are still relatively small. For $eB \approx 5\, m_\pi^2$ the B=0 surface tension value drops by about 30% while for $eB \gtrsim 10\, m_\pi^2$ it quickly raises with the field intensity so that the phase conversion and the presence of a mixed phase should be suppressed if extremely high fields are present. We also investigate how thermal effects influence the surface tension for magnetized quark matter.