Tidal deformation and strain accumulation of solid compact stars

The tidal deformability of compact stars encodes the equation of state of dense matter, and gravitational-wave observations such as GW170817 have begun to constrain it under the assumption of a fluid interior. Yet whether the interior of pulsar-like compact stars is fluid or solid remains largely untested, despite the distinct tidal responses the two states predict. In this work, based on the strangeon-star model, we develop a framework for modeling tidal deformation in solid compact stars. Adopting a shear modulus of $\mu = 10^{34}\,\mathrm{erg}\,\mathrm{cm}^{-3}$, we find a relative difference of approximately $40\%$ in tidal deformability between solid and fluid strangeon stars of $1.4\,M_\odot$, corresponding to a $\sim 10\%$ deviation from the universal I--Love relation. We further model the accumulation of internal strain during binary inspiral and find that it peaks near the stellar center. When the gravitational-wave frequency reaches several hundred $\rm Hz$, large-scale fracturing occurs and can release up to $\sim 10^{46}\,\mathrm{erg}$ of elastic energy, sufficient to power short $\gamma$-ray-burst precursors. This solid-to-fluid transition alters the tidal response and imprints on the waveform and phase of the emitted gravitational radiation. Combined with the precursor electromagnetic emission, these gravitational-wave signatures offer a multi-messenger avenue to test the solid nature of pulsar-like compact stars.