The Surface Tension of Magnetized Quark Matter

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 ${\gamma }_0\approx 10-300MeV/f{\mathrm{m}}^2$ but, very recently, different model applications have reduced these numerical values to fall within the range ${\gamma }_0\approx 5-30MeV/f{\mathrm{m}}^2$ 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 $eB\approx 3-30m_{\pi }^2$ ($B\approx 10^{19}-10^{20}G$) 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 $0<eB\lesssim 10m_{\pi }^2$, it only reaches values which are still relatively small. For $eB\approx 5m_{\pi }^2$ the B=0 surface tension value drops by about 30% while for $eB\gtrsim 10m_{\pi }^2$ 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.

Comments: 12 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1207.5186