Inferring three-nucleon couplings from multi-messenger neutron-star observations

Abstract

Understanding the interactions between nucleons in dense matter is an important challenge in theoretical physics. Effective field theories have emerged as the dominant approach to address this problem at low energies, with many successful applications to the structure of nuclei and the properties of dense nucleonic matter. However, how far into the interior of neutron stars these interactions can describe dense matter is an open question. Here, we develop a framework that enables the inference of three-nucleon couplings in dense matter directly from astrophysical neutron star observations. We apply this formalism to the LIGO/Virgo gravitational-wave event GW170817 and the X-ray measurements from NASA's Neutron Star Interior Composition Explorer and establish direct constraints for the couplings that govern three-nucleon interactions in chiral effective field theory. Furthermore, we demonstrate how next-generation observations of a population of neutron star mergers can offer stringent constraints on three-nucleon couplings, potentially at a level comparable to those from laboratory data. Our work directly connects the microscopic couplings in quantum field theories to macroscopic observations of neutron stars, providing a way to test the consistency between low-energy couplings inferred from terrestrial and astrophysical data.

Figures (7)

• Figure 1: Validation results for our machine-learning--based emulators. In both panels, the color of the curves corresponds to the percentage uncertainty in the emulators' prediction. Panel (a) shows $70$ results for the neutron-matter EOS up to $2n_\textrm{sat}$ predicted by a PMM built using a training set of $30$ different samples. At nuclear saturation density, individual validation uncertainties $\Delta_{\rm sat}$ are below 0.3%, with the average uncertainty being 0.04%. In Panel (b), we show about 60,000 tidal deformability-mass curves predicted by an ensemble of 50 neural networks trained on the 5-parameter EOS model. The uncertainty at $1.4 M_{\odot}$, $\Delta_{1.4}$, is at most 2.5 % with an average of 0.02 %. We note that less than 0.1% of EOSs have emulator uncertainties of around 2%, making these very rare occurrences. Source data for this figure are provided as a Source Data file.
• Figure 2: Constraints from GW170817 and NICER data. Panel (a) shows the posterior distribution function of the LEC $c_1$. Panel (c) shows the posterior distribution function of the LEC $c_3$. In panels (a) and (c), results are shown for the 2- (blue), 5- (orange), and 7-parameter (green) models. The quoted errors are for the 7-parameter model evaluated at the 90$\%$ confidence level. Panel (b) depicts the correlation between $c_1$ and $c_3$ and displays iso-probability contours at the $68\%$ and $90\%$ confidence levels. The laboratory values for $c_1$ and $c_3$ from pion-nucleon ($\pi N$) scattering experiments are shown in gray. Source data for this figure are provided as a Source Data file.
• Figure 3: Evolution of the obtained constraints on $c_3$. We show the prior on $c_3$ (purple) as well as the present astrophysical constraints, which include GW170817 and the NICER X-ray observations of millisecond pulsars but exclude simulated data from next-generation GW observatories. The inferred $c_3$ for our population study is then shown as a function of the number of events observed by a network of next-generation GW detectors for the 2-parameter (blue), 5-parameter (orange-dashed) and 7-parameter (green) EOS models. We observe that the constraints are well converged at 20 observations. For the 7-parameter model, the diamond error bar is obtained by analyzing 20 observations using parameter estimation on zero-noise injections, whereas the circle error-bars are obtained within a Fisher matrix approximation. We compare the resulting constraints to the injected value and to the uncertainties in the laboratory result from $\pi$N scattering (black). All error bars represent $90\%$ confidence levels. Source data for this figure are provided as a Source Data file.
• Figure 4: Compound emulator uncertainty. The figure shows the accuracy of our emulators where the validation is performed using both high-fidelity solvers: MBPT and the full TOV solver. The quoted average error for $1.4 M_{\odot}$, $\langle\Delta_{1.4}\rangle = 0.2\%$, is an estimate of the total compound emulator uncertainty including both the PMM and the neural network, instead of only the latter. Source data for this figure are provided as a Source Data file.
• Figure 5: Updated constraints from NICER Reanalysis I. Panel (a) shows the posterior distribution function of the LEC $c_1$. Panel (c) shows the posterior distribution function of the LEC $c_3$. Panel (b) depicts the correlation between $c_1$ and $c_3$ and displays iso-probability contours at the $68\%$ and $90\%$ confidence levels. These distributions are obtained by applying constraints from GW170817 and results from the recent reanalysis of NICER X-ray observations of PSR J0030 Vinciguerra:2023qxq. Here, we use the mode with mass and radius of about $[1.4M_{\odot},11.5~\textrm{km}]$, i.e., using the hot-spot model ST+PDT. Source data for this figure are provided as a Source Data file.