Nuclear "waffles"

Background: The dense neutron-rich matter found in supernovae and inside neutron stars is expected to form complex nonuniform phases, often referred to as nuclear pasta. The pasta shapes depend on density, temperature and proton fraction and determine many transport properties in supernovae and neutron star crusts. Purpose: To characterize the topology and compute two observables, the radial distribution function (RDF) g(r) and the structure factor S(q), for systems with proton fractions Yp=0.10,0.20,0.30, and 0.40 at about one-third of nuclear saturation density, n=0.050fm-3, and temperatures near kT=1MeV. Methods: We use two recently developed hybrid CPU/GPU codes to perform large scale molecular dynamics (MD) simulations with 51200 and 409600 nucleons. From the output of the MD simulations we obtain the two desired observables. Results: We compute and discuss the differences in topology and observables for each simulation. We observe that the two lowest proton fraction systems simulated, Yp=0.10 and 0.20, equilibrate quickly and form liquidlike structures. Meanwhile, the two higher proton fraction systems, Yp=0.30 and 0.40, take a longer time to equilibrate and organize themselves in solidlike periodic structures. Furthermore, the Yp=0.40 system is made up of slabs, lasagna phase, interconnected by defects while the Yp=0.30 systems consist of a stack of perforated plates, the nuclear waffle phase. Conclusions: The periodic configurations observed in our MD simulations for proton fractions Yp≥0.30 have important consequences for the structure factors S(q) of protons and neutrons, which relate to many transport properties of supernovae and neutron star crust. A detailed study of the waffle phase and how its structure depends on temperature, size of the simulation, and the screening length showed that finite-size effects appear to be under control and, also, that the plates in the waffle phase merge at temperatures slightly above 1.0MeV and the holes in the plates form a hexagonal lattice at temperatures slightly lower than 1.0MeV.