State of matter for quark stars

It depends on the state of matter at supra-nuclear density to model pulsar's structure, which is unfortunately not certain due to the difficulties in physics. In cold quark matter at realistic baryon densities of compact stars (with an average value of $\sim 2-3\rho_0$), the interaction between quarks is so strong that they would condensate in position space to form quark-clusters. We argue that quarks in quark stars are grouped in clusters, then we apply two phenomenological models for quark stars, the polytropic model and Lennard-Jones model. Both of the two models have stiffer EoS, and larger maximum mass for quark stars (larger than 2 $M_\odot$). The gravitational energy releases during the AIQ process could explain the observed energy of three supergiant flares from soft gamma-ray repeaters ($\sim 10^{47}$ ergs).