nmma: An extended Bayesian framework for Nuclear Multimessenger Astronomy in the Era of Next-Generation Detectors

Technical Summary: nmma: An extended Bayesian framework for Nuclear Multimessenger Astronomy in the Era of Next-Generation Detectors

Problem Statement
The joint analysis of gravitational waves (GWs), electromagnetic (EM) transients, and nuclear physics is essential for breaking degeneracies in multimessenger astronomy. However, Bayesian inference for these combined datasets faces a critical bottleneck: computational cost scales prohibitively with parameter space dimensionality. Previous implementations of the Nuclear Multimessenger Astronomy (nmma) framework relied on pre-computed tables of Equations of State (EoS) to map nuclear parameters to macroscopic neutron star (NS) properties. While sufficient for current detectors, this approach suffers from an inherent resolution limit that will be insufficient for the high-precision, high-frequency detections expected from next-generation GW observatories like the Einstein Telescope (ET) and Cosmic Explorer. Furthermore, existing EM modeling tools often lack the speed required for stochastic sampling, and the integration of nuclear physics parameters directly into the inference loop remains computationally expensive.

Methodology
The authors present a major overhaul of the nmma framework, designed as a modular, extensible Bayesian inference tool that aligns closely with the architecture of the popular Bilby package. The core methodological advancements include:

1. Nuclear Physics Emulation: Instead of sampling from pre-computed EoS tables, the framework now employs machine learning (ML) emulators (specifically feed-forward neural networks) to map microphysical nuclear parameters directly to macroscopic NS properties (mass $M$, radius $R$, tidal deformability $\Lambda$) at runtime. This allows for direct sampling of the continuous nuclear parameter space.
2. Accelerated EM Surrogates: The framework integrates Fiesta, a high-precision surrogate model for EM transients. This includes:
   • Kilonova (KN): A neural-network surrogate trained on radiation-transport simulations (Possis) to model lightcurves.
   • GRB Afterglow: Surrogates for Gaussian jet models to predict afterglow lightcurves, drastically reducing the computational burden compared to running full hydrodynamic codes like afterglowpy or pyblastafterglow during sampling.
3. Waveform Acceleration: The GW analysis utilizes the IMRPhenomXAS_NRTidalv3 approximant accelerated via multibanding techniques to ensure rapid likelihood evaluations.
4. Modular Architecture: The codebase has been restructured to treat nmma as a "thin wrapper" around Bilby, facilitating the seamless integration of new data types (e.g., supernovae) and sampling algorithms.

Key Contributions

• Direct Nuclear Parameter Inference: For the first time, the framework enables simultaneous Bayesian sampling of nuclear physics parameters alongside GW, kilonova, and afterglow parameters, rather than relying on discrete EoS indices.
• Significant Speed-ups: By combining ML emulators for nuclear physics and EM surrogates, the authors achieve a 20- to 60-fold reduction in computational time compared to previous nmma versions (Pang et al. 2023), while utilizing more detailed physical models.
• Unified Multimessenger Analysis: The framework successfully combines GW strain data, kilonova lightcurves, and GRB afterglow data within a single likelihood function, allowing for the joint constraint of astrophysical, nuclear, and cosmological parameters.
• Cosmological Integration: The framework supports sampling arbitrary flat $\Lambda$CDM cosmological parameters, enabling the derivation of the Hubble parameter ($H_0$) from multimessenger events.

Results
The authors validated the upgraded framework through three primary applications:

1. Re-analysis of GW170817/AT2017gfo/GRB 170817A:

   • The new implementation reproduced the posterior distributions of key system parameters (chirp mass, mass ratio, luminosity distance, inclination, tidal deformability) consistent with previous studies, despite using different physical models and surrogates.
   • The inclusion of the GRB afterglow helped break the distance-inclination degeneracy, though the results were sensitive to the specific modeling of the ejecta and the GRB jet geometry.
   • The analysis highlighted tensions in current kilonova models, particularly regarding the late-time infrared flux and the electron fraction ($Y_e$) of wind ejecta, suggesting a need for refined models of lanthanide-poor regimes.

2. Constraining Nuclear Parameters:

   • By sampling microphysical EoS parameters (symmetry energy slope $L_{sym}$, curvature $K_{sym}$, incompressibility $K_{sat}$, and speed of sound at high densities), the study demonstrated the ability to constrain the nuclear equation of state.
   • The results showed that GW data alone favor softer EoSs, while the inclusion of NICER constraints and kilonova data shifts the posterior toward stiffer EoSs. The inclusion of GRB afterglow data moderated this stiffening trend.

3. Hypothetical Future Detection (Next-Generation Era):

   • Using a simulated event detected by a triangular Einstein Telescope network with a Rubin Observatory kilonova follow-up, the authors demonstrated the potential to constrain the Hubble parameter ($H_0$) and nuclear parameters simultaneously.
   • In a scenario with a well-measured redshift (from host galaxy identification), the framework recovered $H_0 = 68 \pm 4$ km s$^{-1}$ Mpc$^{-1}$, consistent with the injected value.
   • The study noted that without explicit redshift information, constraints on $H_0$ and nuclear parameters remain weak due to degeneracies, particularly for symmetric binary systems.

Significance and Claims
The paper claims that the upgraded nmma framework provides a necessary infrastructure for the "Era of Next-Generation Detectors." Its primary significance lies in enabling efficient, high-dimensional Bayesian inference that was previously computationally intractable. By integrating ML surrogates for both nuclear physics and EM transients, the framework allows researchers to:

• Move beyond discrete EoS tables to continuous nuclear parameter spaces.
• Perform joint analyses of GW and EM data with robust uncertainty quantification.
• Prepare for the data deluge expected from third-generation detectors, where current software infrastructure would be overwhelmed.

The authors remain modest regarding the immediate competitiveness of their constraints on $H_0$ or nuclear parameters compared to state-of-the-art studies, noting that the derived limits are currently limited by model systematics and the single-event nature of the demonstration. However, they emphasize that the framework opens a viable pathway for obtaining strong, robust, and independent constraints when analyzing multiple future events, particularly asymmetric low-mass mergers. The work also identifies current limitations, such as the need for rotation corrections in NS structure models and the eventual transition to GPU-based likelihood evaluations to fully exploit next-generation computing capabilities.