Domains and defects in nuclear pasta

Abstract

Nuclear pasta topology is an essential ingredient to determine transport properties in the inner crust of neutron stars. We perform semiclassical molecular dynamics simulations of nuclear pasta for proton fractions $Y_p$ = 0.30 and $Y_p$ = 0.40 near one-third of nuclear saturation density, $n$ = 0.05 fm$^{−3}$ , at a temperature $T$ = 1.0 MeV . Our simulations are, to our knowledge, the largest nuclear pasta simulations to date and contain up to 3 276 800 nucleons in the $Y_p$ = 0.30 and 819 200 nucleons in the $Y_p$ = 0.40 case. An algorithm to determine which nucleons are part of a given sub-domain in the system is presented. By comparing runs of different sizes we study finite-size effects, equilibration time, the formation of multiple domains and defects in the pasta structures, as well as the structure factor dependence on simulation size. Although we find qualitative agreement between the topological structure and the structure factors of runs with 51 200 nucleons and those with 819 200 nucleons or more, we show that simulations with hundreds of thousands of nucleons may be necessary to accurately predict pasta transport properties.