Constraining the speed of sound inside neutron stars with chiral effective field theory interactions and observations

Abstract: The dense matter equation of state (EOS) determines neutron star (NS) structure but can be calculated reliably only up to one to two times the nuclear saturation density, using accurate many-body methods that employ nuclear interactions from chiral effective field theory constrained by scattering data. In this work, we use physically motivated ansatzes for the speed of sound $c_S$ at high density to extend microscopic calculations of neutron-rich matter to the highest densities encountered in stable NS cores. We show how existing and expected astrophysical constraints on NS masses and radii from X-ray observations can constrain the speed of sound in the NS core. We confirm earlier expectations that $c_S$ is likely to violate the conformal limit of $c_S^2\leq c^2/3 $, possibly reaching values closer to the speed of light $c$ at a few times the nuclear saturation density, independent of the nuclear Hamiltonian. If QCD obeys the conformal limit, we conclude that the rapid increase of $c_S$ required to accommodate a $2 $ M$\odot$ NS suggests a form of strongly interacting matter where a description in terms of nucleons will be unwieldy, even between one and two times the nuclear saturation density. For typical NSs with masses in the range $1.2-1.4~$ M$\odot$, we find radii between $10$ and $14$ km, and the smallest possible radius of a $1.4$ M$_{\odot}$ NS consistent with constraints from nuclear physics and observations is $8.4$ km. We also discuss how future observations could constrain the EOS and guide theoretical developments in nuclear physics.

• The paper shows that neutron star sound speed may exceed the conformal limit, implying a rapid stiffening of the equation of state.
• It employs chiral EFT up to nuclear saturation density combined with two-solar-mass and radius constraints to delineate neutron star structure.
• The integration of theoretical predictions and observations offers a framework to explore dense matter phase transitions in neutron star cores.

Constraining the Speed of Sound Inside Neutron Stars with Chiral Effective Field Theory Interactions and Observations

The paper by Tews et al. addresses the complex problem of deriving the equation of state (EOS) for neutron stars (NS) by integrating chiral effective field theory (EFT) predictions with astronomical observations. Sound velocity in dense matter is a critical factor in determining the EOS, which in turn significantly influences NS structure, especially their mass-radius relationship. Chiral EFT, rooted in Quantum Chromodynamics, is utilized to calculate the EOS reliably up to 1-2 times nuclear saturation density. Beyond this range, uncertainties become prohibitive, necessitating alternative methods to extend the EOS to the high densities found in neutron-star cores.

The investigation leverages astrophysical constraints, including the gravitational detectability of two-solar-mass NSs, as well as observed NS radii from X-ray sources, to propose limits on the speed of sound. The sound velocity, $c_S$, is modeled with physically motivated ansatzes, scrutinizing whether it surpasses the conformal limit of $c_S^2 \leq c^2/3$, which would imply a regime dominated by strongly interacting matter.

Key Numerical Results and Claims

• The constraint analysis indicates that the sound speed likely violates the conformal limit, potentially reaching velocities close to the speed of light at several times nuclear saturation density.
• Chiral EFT Hamiltonians predict maximal polytropic indices that necessitate a rapid stiffening of the EOS at higher densities to accommodate observed NS masses.
• The analysis suggests that for a neutron star to host a $2 M_{\odot}$ profile, the rapid increase in $c_S$ occurs perhaps signaling a breakdown in nucleonic description, prompting instead a focus on quark-gluon activities at these densities.
• The radii of typical NSs (1.2-1.4 $M_{\odot}$) are determined to fall within the range of 10 to 14 km, and the minimum possible radius for a $1.4 M_{\odot}$ NS, consistent with nuclear constraints and observations, is computed to be 8.4 km.

Theoretical and Practical Implications

The research extends theoretical frameworks in nuclear physics, emphasizing the role of chiral EFT interactions at densities over $2 n_0$ and ultimately contributing to the delineation of phase transitions within the NS core, potentially involving deconfined quark matter. Practically, the model informs gravitational wave astronomy and electromagnetic observations by suggesting methodologies for deducing core properties of NS.

The results assert the relevance of EOS constraints in guiding post-EFT theories, intended to reconcile tension between QCD expectations and neutron-matter constraints. Future developments could assess exotic phases in the NS core using advanced simulations, which foreseeably would include further gravitational wave observations informing sound velocity profiles beyond saturation.

Speculation on Future AI Developments

Future developments in AI, particularly in data assimilation, pattern recognition, and soft-body simulations, may prove invaluable in refining models of neutron-star interiors with comprehensive datasets. Advanced AI tools could analyze observational data adeptly and optimize parameterizations of nuclear matter EOS that incorporate multifaceted physical inputs. AI could prioritize evidence integration from terrestrial experiments and astrophysical surveys, accommodating higher-order correlations and nonlinear dynamics inherent in neutron star structures. Such capabilities may offer profound insights into the fundamental interactions governing the high-density regime of the universe, ultimately bridging chiral EFT potency with astronomical data fidelity.