Hyperon Puzzle: Hints from Quantum Monte Carlo Calculations

The onset of hyperons in the core of neutron stars and the consequent softening of the equation of state have been questioned for a long time. Controversial theoretical predictions and recent astrophysical observations of neutron stars are the grounds for the so-called hyperon puzzle. We calculate the equation of state and the neutron star mass-radius relation of an infinite systems of neutrons and $\mathrm{\Lambda }$ particles by using the auxiliary field diffusion Monte Carlo algorithm. We find that the three-body hyperon-nucleon interaction plays a fundamental role in the softening of the equation of state and for the consequent reduction of the predicted maximum mass. We have considered two different models of three-body force that successfully describe the binding energy of medium mass hypernuclei. Our results indicate that they give dramatically different results on the maximum mass of neutron stars, not necessarily incompatible with the recent observation of very massive neutron stars. We conclude that stronger constraints on the hyperon-neutron force are necessary in order to properly assess the role of hyperons in neutron stars.

Figure 1

Equations of state. Green solid curve refers to the PNM EOS calculated with the $\mathrm{AV}8’+\mathrm{UIX}$ potential. The red dotted curve represents the EOS of hypermatter with hyperons interacting via the two-body $\mathrm{\Lambda }N$ force alone. The blue dashed curve is obtained including the three-body hyperon-nucleon potential in the parametrization (I). Shaded regions represent the uncertainties on the results as reported in the text. The vertical dotted lines indicate the $\mathrm{\Lambda }$ threshold densities ${\rho }_{\mathrm{\Lambda }}^{th}$. In the inset, neutron and lambda fractions corresponding to the two HNM EOSs.

Figure 2

Mass-radius relations. The key is the same as of Fig. 1. Full dots represent the predicted maximum masses. Horizontal bands at $\sim 2M_{\odot }$ are the observed masses of the heavy pulsars PSR J1614-2230 [18] and PSR $\mathrm{J}0348+0432$ [19]. The grey shaded region is the excluded part of the plot due to causality.