Gravitational wave echoes from interacting quark stars

We show that interacting quark stars (IQSs) composed of interacting quark matter (IQM), including the strong interaction effects such as perturbative QCD corrections and color superconductivity, can be compact enough to feature a photon sphere that is essential to the signature of gravitational wave echoes. We utilize an IQM equation of state unifying all interacting phases by a simple reparametrization and rescaling, through which we manage to maximally reduce the number of degrees of freedom into one dimensionless parameter lambda over line that characterizes the relative size of strong interaction effects. It turns out that gravitational wave echoes are possible for IQSs with lambda over line greater than or similar to 10 at large center pressure. Rescaling the dimension back, we illustrate its implication on the dimensional parameter space of the effective bag constant Beff and the superconducting gap Delta with variations of the perturbative QCD parameter a4 and the strange quark mass ms in their empirical range. We calculate the rescaled gravitational wave echo frequencies we obtain a simple scaling relation for the minimal echo frequency fmin echo approximate to 5.76 the large lambda over line limit. f over line echo associated with IQSs, from which pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Beff/(100 MeV)4 kHz at