Building Neutron Stars with the MUSES Calculation Engine

Abstract: Exploring the equation of state of dense matter is an essential part of interpreting the observable properties of neutron stars. We present here the first results for dense matter in the zero-temperature limit generated by the MUSES Calculation Engine, a composable workflow management system that orchestrates calculation and data processing stages comprising a collection of software modules designed within the MUSES framework. The modules presented in this work calculate equations of state using algorithms spanning three different theories/models: (1) Crust Density Functional Theory, valid starting at low densities, (2) Chiral Effective Field Theory, valid around saturation density, and (3) the Chiral Mean Field model, valid beyond saturation density. Lepton contributions are added through the Lepton module to each equation of state, ensuring charge neutrality and the possibility of $\beta$-equilibrium. Using the Synthesis module, we match the three equations of state using different thermodynamic variables and different methods. We then couple the complete equation of state to a novel full-general-relativity solver (QLIMR) module that calculates neutron star properties. We find that the matching performed using different thermodynamic variables affects differently the range obtained for neutron star masses and radii (although never beyond a few percent difference). We also investigate the universality of equation of state-independent relations for our matched stars. Finally, for the first time, we use the Flavor Equilibration module to estimate bulk viscosity and flavor relaxation charge fraction and rates (at low temperature) for Chiral Effective Field Theory and the Chiral Mean Field model.

• The paper presents the MUSES Calculation Engine, a modular framework integrating nuclear physics models to compute neutron star properties from crust to core.
• It employs innovative matching techniques using hyperbolic tangent functions to smoothly connect EoS modules, with schemes affecting radii variations by up to 10%.
• The study paves the way for future work on finite-temperature effects and heavy-ion collision extensions, enhancing insights for multi-messenger astronomy.

Overview of "Building Neutron Stars with the MUSES Calculation Engine"

The paper "Building Neutron Stars with the MUSES Calculation Engine" presents a comprehensive framework for modeling the equation of state (EoS) of neutron stars from crust to core, through a modular and systematic approach dubbed the MUSES Calculation Engine. Utilizing a range of nuclear physics models, this work offers a complete methodology to tackle the computational challenges associated with neutron star physics, including the calculation of macroscopic observables such as masses and radii, and the exploration of neutron star properties under various theoretical frameworks.

MUSES Calculation Engine and Its Components

The MUSES (Modular Unified Solver of the Equation of State) Calculation Engine is introduced as an innovative tool designed to integrate multiple EoS modules seamlessly. This tool encompasses a suite of software products intended to efficiently manage and execute complex workflows, potentially driving advancements in the field of nuclear astrophysics. The framework is divided into three major software development goals:

1. Independent software modules for calculating EoSs and physical observables.
2. A framework for module interoperability.
3. A management system for multi-module workflow orchestration.

EoS Modules:

• Crust-DFT: Captures the low-density regime using Density Functional Theory, emphasizing the crust region composed primarily of nuclei and nucleons.
• Chiral Effective Field Theory ($\chi$EFT): Focuses on the intermediate densities corresponding to the outer core of neutron stars, employing many-body perturbation theory.
• Chiral Mean Field (CMF++): Describes the high-density inner core, incorporating hyperons, $\Delta$ baryons, and quarks, and addressing phase transitions such as deconfinement.

Observational Modules:

• QLIMR: Calculates macroscopic properties like mass, radii, and tidal deformabilities of neutron stars.
• Flavor Equilibration: Addresses the out-of-equilibrium states by estimating relaxation times and bulk viscosity, relevant for neutron star mergers.

Methodology and Results

Within the MUSES framework, the paper explores the process of matching different EoSs using thermodynamic variables, offering insights into how these matching techniques impact the predicted properties of neutron stars. Smooth matching across overlapping regions is executed through hyperbolic tangent functions. The implications of using various matching variables—such as pressure ($P$), energy density ($\varepsilon$), or speed of sound squared ($c_s^2$)—are thoroughly analyzed, highlighting the necessity for careful parameter tuning to ensure thermodynamic stability and causality.

Findings reveal that the choice of matching variables significantly affects the neutron star properties. For instance, different matching schemes result in variations up to 10% in neutron star radii, despite minimal differences in maximum mass. The study also reaffirms the robustness of EoS-independent relations like I-Love-Q relations, illustrating their insensitivity to the specific details of the EoS or matching method used but revealing notable deviations in tidal deformabilities.

Implications and Future Directions

The MUSES Calculation Engine facilitates the exploration of dense matter EoSs and their compliance with nuclear and astrophysical constraints, offering a path forward in neutron star research. The framework's modular design allows for flexibility in parameter choices and fosters collaboration. As a broader implication, this research strengthens the bridge between theory and observational data, potentially refining our understanding of the post-merger dynamics in neutron star mergers.

Future work aims to extend this framework's capabilities to include finite-temperature effects, enabling the study of dynamic scenarios such as neutron star mergers and supernovae. Moreover, by expanding the suite to incorporate heavy-ion collision EoSs, the tool will pave the way for multi-messenger astronomy applications, providing deep insights into the intricate behaviors of matter under extreme conditions.

In summary, the paper presents a substantial contribution to the field of neutron star physics, outlining an advanced computational framework that opens new avenues for understanding the dense matter equation of state across the crust and core of neutron stars. The MUSES Calculation Engine stands as a pivotal tool in decoding the mysteries of these cosmic entities, offering precision and flexibility in modeling their complex inner workings.