The maximum mass and radius of neutron stars and the nuclear symmetry energy (1101.1921v2)

Abstract: We calculate the equation of state of neutron matter with realistic two- and three-nucleon interactions using quantum Monte Carlo techniques, and illustrate that the short-range three-neutron interaction determines the correlation between neutron matter energy at nuclear saturation density and higher densities relevant to neutron stars. Our model also makes an experimentally testable prediction for the correlation between the nuclear symmetry energy and its density dependence -- determined solely by the strength of the short-range terms in the three neutron force. The same force provides a significant constraint on the maximum mass and radius of neutron stars.

• The paper shows how the three-neutron interaction crucially stiffens the neutron matter equation-of-state, directly influencing neutron star mass and radius.
• It employs the auxiliary field diffusion Monte Carlo method to solve the complex many-body nuclear Hamiltonian with realistic two- and three-nucleon forces.
• The study links nuclear symmetry energy and its density derivative to observable neutron star properties, offering key constraints for future experiments.

The Maximum Mass and Radius of Neutron Stars and the Nuclear Symmetry Energy

This paper, authored by S. Gandolfi, J. Carlson, and Sanjay Reddy, presents a detailed analysis of the equation of state (EoS) of neutron matter using quantum Monte Carlo (QMC) techniques to explore the impact of realistic two- and three-nucleon interactions on neutron stars. The paper precisely calculates the EoS, crucial for understanding neutron star properties, such as mass and radius. The authors emphasize the role of the short-range three-neutron (3n) interaction in dictating the correlation between neutron matter energy at nuclear saturation, density, and the conditions prevalent in neutron stars.

The neutron star EoS is critical in astrophysics because it directly influences the star’s mass and radius. The authors employ QMC methods, specifically the auxiliary field diffusion Monte Carlo (AFDMC) approach, to solve the non-perturbative many-body nuclear Hamiltonian and obtain results for neutron-rich systems. They highlight the significant impact of the 3n interaction, which is poorly constrained, on neutron star characteristics.

Through their calculations, the authors determine that the recent measurement of a neutron star mass of $M=1.97 \pm 0.04 M_{\rm solar}$ suggests a stiff high-density EoS. This measurement contrasts with smaller inferred radii for neutron stars, implying a transition from a soft to stiff EoS as density increases beyond nuclear saturation. This transition's microscopic determinant is the 3n force, a conclusion that aligns with the pivotal role attributed to three-body forces in nuclear physics and neutron star matter.

The impact of the nuclear symmetry energy, and its density dependence on neutron star properties, is another focal point of the paper. Utilizing empirical data suggesting a symmetry energy of about $32 \pm 2$ MeV, the authors implement a range of 3n force models to align with this value. They examine the parameter $L$, which represents the density derivative of the symmetry energy, finding it crucial in constraining the 3n interaction. Notably, the correlation between symmetry energy and its derivative is found to be largely invariant to variations in 3n force details once tuned to a specific symmetry energy value.

Practically, this research sets constraints on neutron star mass and radius estimates. The calculated EoS indicates an upper bound on neutron star mass and scope for narrower radius uncertainties, especially when factoring in higher density effects. The authors employ a causal EoS approach beyond a critical density $\rho_c$, derived from their QMC results, to gauge the upper-bound limits on mass and radius, affirming a maximally stiff EoS does not violate causality at high densities.

In summary, this paper emphasizes the significance of the 3n interaction in determining neutron star properties and highlights the potential for nuclear experiments to refine our understanding of EoS parameters. The findings have profound implications for astrophysics, offering empirical tests for neutron-rich nuclear matter's theoretical models and establishing a clearer relationship between nuclear symmetry energy and neutron star characteristics. Further work in both theoretical approaches and experimental methodologies is suggested to reduce uncertainties and expand knowledge in this domain.