Debadri Bhattacharjee, Pradip Kumar Chattopadhyay, Kazuharu Bamba

Gravitational wave astronomy provides an exemplary avenue to study exotic compact stars with utmost precision. Recent analyses of GW170817 have reported possible post-merger gravitational wave echoes with a significance of $4.2σ$ and a dominant frequency near $72$ Hz. Such echoes may originate from ultracompact remnants possessing photon spheres that partially trap gravitational perturbations. In general relativity, photon-sphere formation requires the stellar compactness to lie within one-third and four-ninths, which is challenging even for a realistic equations of state. Here, we explore this possibility in quadratic curvature gravity with non-minimal matter coupling, considering strange stars described by the MIT bag model equation of state. By solving the modified Tolman-Oppenheimer-Volkoff equations, we obtain the mass-radius relations and identify configurations capable of supporting photon spheres and GW echoes. In the proposed framework, the modified Buchdahl limit allows more compact stellar solutions, while photon-sphere constraints restrict the viable parameter space. We find that increasing the bag constant, decreases the maximum mass and echo time, shifting the echo frequency toward the kHz regime. The echo constraints yield more stringent maximum mass-radius limits than hydrostatic equilibrium, suggesting a revised maximum mass bounds for strange stars. These results highlight the potential of post-merger strange stars as GW echo sources and demonstrate the role of echoes as probes of modified gravity and high-frequency gravitational waves.