Irvin Martínez-Rodríguez

arXiv2026

Neutron Stars as Perfect Fluids: Extracting the Linearized Response Function

We develop an effective field theory framework for the conservative linear tidal response of a relativistic neutron star modeled as a perfect fluid with conserved particle number. Starting from the covariant fluid action in a curved background, we linearize about a static equilibrium configuration and obtain the quadratic action for fluid displacements coupled to metric perturbations. We then split the metric perturbation into induced and externally sourced parts, and integrate out the induced metric on a conservative matched domain using a symmetric Green kernel. The resulting effective fluid theory contains metric-mediated fluid interactions through a self-adjoint operator acting on the displacement, while the external perturbation acts as a tidal source. This self-adjoint structure permits a modal expansion of the pole sector: after projection onto conservative eigenmodes, the dynamics reduce to tidally driven oscillators with couplings fixed by relativistic inner products and overlap integrals. Matching these oscillator variables to the quadrupolar worldline theory gives analytic expressions for the modal dynamical tidal deformabilities in terms of mode frequencies, normalizations, and overlap integrals. We also identify a source-only non-pole sector generated by terms quadratic in the external perturbation. This sector does not affect the mode amplitudes, but its electric-quadrupolar projection can contribute to the full tidal response. This formulation clarifies which part of the relativistic tidal response is captured by explicit fluid modes and where a possible source-only non-pole contribution enters the worldline description.

gr-qc↗

arXiv2025

Modeling Tidal Disruptions with Dynamical Tides

Tidal disruption events (TDEs) occur when stars pass close enough to supermassive black holes to be torn apart by tidal forces. Traditionally, these events are studied with computationally intensive hydrodynamical simulations. In this paper, we present a fast, physically motivated two-stage model for TDEs. In the first stage, we model the star's tidal deformation using linear stellar perturbation theory, treating the star as a collection of driven harmonic oscillators. When the tidal energy exceeds a fraction $γ$ of the star's gravitational binding energy (with $γ\sim \mathcal O(1)$), we transition to the second stage, where we model the disrupted material as free particles. The parameter $γ$ is determined with a one-time calibration to the critical impact parameter obtained in hydrodynamical simulations. This method enables fast computation of the energy distribution ${\rm d} M/{\rm d}E$ and fallback rate ${\rm d} M/{\rm d} T$, while offering physical insight into the disruption process. We apply our model to MESA-generated profiles of middle-age main-sequence stars. Our code is available on GitHub.

astro-ph.HE↗