Constraining Hamiltonians from chiral effective field theory with neutron-star data

TL;DR

The paper tackles constraining low-energy constants (LECs) in a $N^2LO$ chiral EFT Hamiltonian using neutron-star (NS) observations, addressing the computational challenge that direct inference would require solving the EOS with AFDMC and the TOV equations for each model. It introduces emulators: a parametric matrix model (PMM) for AFDMC neutron-matter energies and a multilayer perceptron (MLP) for TOV solutions, integrated into the PyCBC framework to perform Bayesian inference over the six spectral LECs $(d_{11}, d_{22}, d_{3}, d_{4}, d_{6}, d_{7})$ (with long-range pion-nucleon LECs fixed) and leveraging NN-scattering priors as GW priors. The PMM–MLP pipeline, together with a nuclear meta-model and a speed-of-sound extension, yields NS EOSs described by $13$ parameters, enabling efficient exploration of the LEC space. Results show that current NS data provide modest constraints on these LECs, while next-generation GW detectors could dramatically tighten them, demonstrating the complementary information content between NS observations and terrestrial NN scattering data. This work thus establishes a practical pathway to infer EFT couplings directly from astrophysical data, enhancing our understanding of dense matter and nuclear forces.}

Abstract

Multi-messenger observations of neutron stars (NSs) and their mergers have placed strong constraints on the dense-matter equation of state (EOS). The EOS, in turn, depends on microscopic nuclear interactions that are described by nuclear Hamiltonians. These Hamiltonians are commonly derived within chiral effective field theory (EFT). Ideally, multi-messenger observations of NSs could be used to directly inform our understanding of EFT interactions, but such a direct inference necessitates millions of model evaluations. This is computationally prohibitive because each evaluation requires us to calculate the EOS from a Hamiltonian by solving the quantum many-body problem with methods such as auxiliary-field diffusion Monte Carlo (AFDMC), which provides very accurate and precise solutions but at a significant computational cost. Additionally, we need to solve the stellar structure equations for each EOS which further slows down each model evaluation by a few seconds. In this work, we combine emulators for AFDMC calculations of neutron matter, built using parametric matrix models, and for the stellar structure equations, built using multilayer perceptron neural networks, with the \texttt{PyCBC} data-analysis framework to enable a direct inference of coupling constants in an EFT Hamiltonian using multi-messenger observations of NSs. We find that astrophysical data can provide informative constraints on two-nucleon couplings despite the high densities probed in NS interiors.

Figures (6)

• Figure 1: Priors (red) and posteriors of the analysis of astrophysical data for all six spectral LECs in neutron matter. The priors are results of fits to NN scattering data. The posterior for current astrophysical data includes gravitational-wave, maximum-mass, and NICER data (blue). We also show posteriors from analyses of simulated signals as expected to be observed by third-generation detectors for symmetric binaries with component masses of $1.0M_{\odot}$ (black) and $1.4M_{\odot}$ (green).
• Figure 2: Percent error of the MLP neural network emulators for M$_{\rm TOV}$ (red), the radius (blue), and the tidal deformability (green) of a $1.4$M$_{\odot}$ neutron star. In all panels, we show histograms for 70,000 validation samples.
• Figure 3: Mass-radius curves drawn from the GW posterior where the maximum-mass and NICER likelihoods are applied. The EOS are colored according to their posterior probability normalized to the highest value. We also show the four NICER contours at 95% credible level.
• Figure 4: Phase shifts for the $^3P_1$ partial wave at the 90% CI for the prior (blue) and the posterior obtained from the analysis of the $1.0-1.0$$M_\odot$ injection (red). We also show the results of the Nijmegen partial-wave analysis Stoks:1993tb for comparison (black).
• Figure 5: Examples of solutions to the TOV equations using the high-fidelity solver (lines) and the emulator predictions (points). Left: Mass--radius relations. Right: Mass--tidal-deformability curves.