Slowly Rotating Two-Fluid Neutron Stars: Coupled Frame-Dragging, Inertia Splitting, and Universal Relations

TL;DR

This paper develops a relativistic framework for analyzing the rotational behavior of two-fluid neutron stars, revealing intrinsic collective modes and how dark matter influences universal relations and rotational observables.

Contribution

It introduces a coupled set of equations for two-fluid neutron stars, defining effective moments of inertia and identifying intrinsic rotational eigenmodes, especially in the context of dark matter effects.

Findings

Two intrinsic collective rotational eigenmodes exist in two-fluid neutron stars.

Dark matter modifies the rotational response and universal relations.

Rotational-tidal universality depends on dark-sector microphysics.

Abstract

We develop a fully relativistic framework to study the rotational response of gravitationally coupled two-fluid neutron stars within the slow-rotation approximation. Treating the two components as independently conserved perfect fluids interacting only through spacetime curvature, we derive the coupled equilibrium and frame-dragging equations and exploit their linear structure to construct a basis decomposition of the rotational response. This formulation leads to a natural definition of the effective total moment of inertia, which generalizes the single-fluid concept and depends solely on the equilibrium background. It further reveals that the coupled system admits two intrinsic collective rotational eigenmodes, characterized by distinct eigen-moments of inertia, even in the absence of relative rotation between the fluids. Applying this framework to neutron stars containing dark matter, we explore how the presence of an additional gravitationally bound component modifies the global rotational response and its relation to tidal deformability. Our results demonstrate that the persistence or breakdown of rotational-tidal universality in two-fluid neutron stars is governed by dark-sector microphysics rather than by the mere presence of an additional component, and establish a unified framework for interpreting rotational observables, intrinsic mode structure, and universal relations in multi-component relativistic stars.