[Paper Review] Simulating bulk viscosity in neutron stars. II. Evolution in spherical symmetry

Giovanni Camelio, Lorenzo Gavassino+3 more|arXiv (Cornell University)|Apr 25, 2022

Pulsars and Gravitational Waves Research4 citations

TL;DR

This study compares multi-component fluid, Hiscock-Lindblom, and Maxwell-Cattaneo models for bulk viscosity in neutron stars using a new one-dimensional, general-relativistic hydrodynamic code, hydro-bulk-1D. It finds that bulk stress models approximate the multi-component fluid well for small perturbations and single-particle-fraction systems, but reaction luminosity dominates dynamics over bulk stress, making its inclusion critical for accurate simulations.

ABSTRACT

Out-of-equilibrium reactions between different particle species are the main processes contributing to bulk viscosity in neutron stars. In this work, we numerically compare three different approaches to the modeling of bulk viscosity: the multi-component fluid with reacting particle species and two bulk stress formalism based on the Müller-Israel-Stewart theory, namely the Hiscock-Lindblom and the Maxwell-Cattaneo models, whose flux-conservative formulation in radial gauge-polar slicing coordinates and spherical symmetry is derived in a companion paper. To our knowledge, this is the first time that a neutron star is simulated with the complete Hiscock-Lindblom model of bulk viscosity. We find that the Hiscock-Lindblom and Maxwell-Cattaneo models are good approximations of the multi-component fluid for small perturbations and when the non-equilibrium equation of state of the fluid depends on only one independent particle fraction. For more than one independent particle fraction and for large perturbations, the bulk stress approximation is still valid but less accurate. In addition, we include the energy loss due to the luminosity of the reactions in the bulk stress formulation. We find that the energy loss due to bulk viscosity has a larger effect on the dynamics than the bulk stress or the variation in particle composition per se. The new one-dimensional, general-relativistic hydrodynamic code developed for this work, hydro-bulk-1D, is publicly available.

Motivation & Objective

• To compare three approaches to modeling bulk viscosity in neutron stars: multi-component fluid, Hiscock-Lindblom, and Maxwell-Cattaneo formulations.
• To assess the validity and accuracy of bulk stress approximations (Müller-Israel-Stewart theory) under varying conditions, including multiple particle fractions and large perturbations.
• To implement and validate the complete Hiscock-Lindblom model in spherical symmetry for the first time in neutron star simulations.
• To investigate the impact of reaction luminosity on neutron star dynamics within bulk stress formulations.
• To develop and publicly release hydro-bulk-1D, a one-dimensional, general-relativistic hydrodynamic code for simulating bulk viscosity effects.

Proposed method

• Developed hydro-bulk-1D, a new one-dimensional, general-relativistic hydrodynamic code with flux-conservative formulations of bulk viscosity in radial gauge-polar slicing coordinates.
• Implemented the full Hiscock-Lindblom model and the Maxwell-Cattaneo model within the Müller-Israel-Stewart formalism for bulk viscosity in spherical symmetry.
• Tracked particle species and their reactions (direct and modified Urca) in the multi-component fluid approach to model non-equilibrium processes.
• Incorporated reaction luminosity into the bulk stress formulations for the first time, accounting for energy loss from particle reactions.
• Used a relativistic linearized damping time formula derived in Appendix C to analyze oscillation behavior across regimes.
• Validated results against known correspondences between multi-component fluid and bulk stress models (Gavassino et al., 2021), especially in frozen, quasi-stationary, and intermediate regimes.

Experimental results

Research questions

• RQ1 How accurately do the Hiscock-Lindblom and Maxwell-Cattaneo bulk stress models reproduce the dynamics of a multi-component fluid with reacting particle species in neutron stars?
• RQ2 What is the impact of including reaction luminosity in bulk stress formulations on the overall evolution and temperature profile of neutron stars?
• RQ3 How does the accuracy of bulk stress models degrade when multiple independent particle fractions are present or under large perturbations?
• RQ4 What are the numerical challenges associated with implementing the Hiscock-Lindblom model compared to the Maxwell-Cattaneo model in spherical symmetry?
• RQ5 In what regimes is the multi-component fluid approach more advantageous than bulk stress models for simulating bulk viscosity in neutron stars?

Key findings

• The Hiscock-Lindblom and Maxwell-Cattaneo models are accurate approximations of the multi-component fluid for small perturbations and when the equation of state depends on only one independent particle fraction.
• For systems with more than one independent particle fraction or large perturbations, the bulk stress approximation remains qualitatively correct but loses quantitative accuracy due to the breakdown of the relaxation-time approximation.
• The inclusion of reaction luminosity in bulk stress models has a larger influence on neutron star dynamics than the bulk stress itself, as it reduces temperature and delays thermal equilibration.
• The largest effect of bulk viscosity in violent, far-from-equilibrium dynamics is indirect: energy loss from reactions allows the fluid to remain farther from equilibrium, prolonging non-equilibrium behavior.
• The Hiscock-Lindblom model exhibits greater numerical noise than the Maxwell-Cattaneo model due to an additional derivative in its source term involving surface-vanishing quantities.
• The multi-component fluid approach is more robust and numerically simpler than Müller-Israel-Stewart models, especially when the system is driven far from equilibrium or involves multiple chemical species.