During the late stages of a binary neutron star inspiral, dynamical tides induced in each star by its companion become significant and should be included in complete gravitational-wave (GW) modeling. We investigate the coupling between the tidal field and quasinormal modes in hybrid stars and show that the discontinuity mode ($g$ mode) intrinsically associated with first-order phase transitions and buoyancy contributes non-negligibly compared with the fundamental $f$ mode. We find that the $g$-mode overlap integral can reach up to $\sim 10\%$ of the $f$-mode value for hybrid star masses in the range $1.4-2.0M_{\odot }$, with the largest values generally associated with larger density jumps. This leads to a GW phase shift due to the $g$ mode of $\mathrm{\Delta }{\varphi }_g\lesssim 0.1-1\mathrm{rad}$ (i.e., up to $\sim 5\%-10\%$ of $\mathrm{\Delta }{\varphi }_f$), with the largest shifts occurring for masses near the phase transition. At higher masses, the shifts remain smaller and nearly constant, with $\mathrm{\Delta }{\varphi }_g\lesssim 0.1\mathrm{rad}$ (roughly $\sim 1\%$ of $\mathrm{\Delta }{\varphi }_f$). These GW shifts may be relevant even at the design sensitivity of current second-generation GW detectors in the most optimistic cases. Moreover, if a $g$ mode is present and lies near the $f$-mode frequency, neglecting it in the GW modeling can lead to systematic biases in neutron star parameter estimation, resulting in radius errors of up to $1\%-2\%$. These results show the importance of dynamical tides to probe neutron stars’ equation of state, and to test the existence of dense-matter phase transitions.

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• First order phase transitions
• General relativity
• Gravitational waves
• Neutron stars & pulsars