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
$\bar{\lambda}$ that characterizes the relative size of strong interaction
effects. It turns out that gravitational wave echoes are possible for IQSs with
$\bar{\lambda}\gtrsim10$ at large center pressure. Rescaling the dimension
back, we illustrate its implication on the dimensional parameter space of
effective bag constant $B_{\rm eff}$ and the superconducting gap $\Delta$ with
variations of the perturbative QCD parameter $a_4$ and the strange quark mass
$m_s$. We calculate the rescaled GW echo frequencies $\bar{f}_\text{echo}$
associated with IQSs, from which we obtain a simple scaling relation for the
minimal echo frequency $f_\text{echo}^{\rm min}\approx 5.76 {\sqrt{B_{\rm
eff}/\text{(100 MeV)}^4}} \,\,\, \rm kHz$ at the large $\bar{\lambda}$ limit.
Chen Zhang