Tidal Deformation and Strain Accumulation of Solid Compact Stars

Abstract

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 μ = 1034 erg cm−3, we find a relative difference of approximately 30 % in tidal deformability between solid and fluid strangeon stars of 1.4 M⊙, corresponding to a ~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 $\rm Hz$, the strain in a large fraction of the stellar volume exceeds the adopted threshold σ = 10−3, and the elastic energy stored in the threshold-exceeding region reaches ~1046 erg at these frequencies. A solid-to-fluid transition would alter the tidal response and could imprint 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.