Breakdown of hydrodynamic universality in causal first-order viscous neutron star oscillations

Abstract: Hydrodynamic modeling of viscous neutron stars requires a choice of theory of relativistic hydrodynamics. That distinct formulations contain the same physical content in the long-wavelength limit is referred to as ``hydrodynamic universality.'' It has been recently shown that hydrodynamic universality can break down in radial neutron star oscillations: causality and finite-size effects restrict access to the long-wavelength universal hydrodynamic regime in sufficiently viscous stars. We show that this breakdown occurs for a broad range of causal hydrodynamic frames in Bemfica--Disconzi--Noronha--Kovtun (BDNK) theory. Increasing viscosity collectively pushes this class of causal frames away from the BDNK regime of validity, eventually forcing all to lie outside it at bulk viscosities in the range $ζ\sim10^{30}$--$10^{31}\mathrm{g}/\mathrm{cm}/\mathrm{s}$. This breakdown of universality is accompanied by material changes in the oscillation mode structure: non-hydrodynamic modes become damped on timescales comparable to those of hydrodynamic modes, the first overtone can become longer lived than the fundamental mode, and unphysical instabilities with sub-millisecond timescales can emerge. Even in regimes where universality has broken down, we find that the inviscid threshold of gravitational collapse remains unchanged in BDNK theory. These results provide evidence that first-order theories of relativistic hydrodynamics may be insufficient for modeling sufficiently viscous neutron stars.