Identifiability of $g$ mode Resonances in Eccentric Binary Neutron Stars with Multidetector Observations

Abstract

$g$ mode resonances in eccentric binary neutron star systems are potential probes of internal stratification, superfluidity, composition gradients, and the equation of state. Although such weak dynamical tidal signatures are unlikely to be resolved with current detector sensitivities, third generation observations may make them accessible, in which case identifying the weak resonant phase shift would provide information beyond the bulk adiabatic tidal deformability. We build a four class dataset in an eccentric harmonic framework, containing point particle, adiabatic tide, resonant $g$ mode, and pure noise samples, and use Einstein Telescope (ET) and Cosmic Explorer (CE) detector data to test whether this weak resonant phase signature can be identified from noisy time domain strain. The ET, CE, and ET+CE deep learning models reach accuracies of $0.655$, $0.815$, and $0.897$, respectively. On the same simulated samples, the matched filtering method reaches lower accuracies of $0.514$, $0.677$, and $0.689$. This result arises from the fact that the resonant correction manifests as a weak phase morphology difference superimposed on the adiabatic tidal background, whereas matched filtering is sensitive only to the overall similarity. Hence, in the presence of weak phase differences, the neural classifier employed in deep learning is better able to learn these local phase and morphology features from the complete time domain strain segment. The results indicate that joint third generation observations improve the identifiability of weak internal mode phase information.