Nuclear Pasta Formation (1307.1678v1)

Abstract: The formation of complex nonuniform phases of nuclear matter, known as nuclear pasta, is studied with molecular dynamics simulations containing 51200 nucleons. A phenomenological nuclear interaction is used that reproduces the saturation binding energy and density of nuclear matter. Systems are prepared at an initial density of 0.10fm$^{-3}$ and then the density is decreased by expanding the simulation volume at different rates to densities of 0.01 fm$^{-3}$ or less. An originally uniform system of nuclear matter is observed to form spherical bubbles ("swiss cheese"), hollow tubes, flat plates ("lasagna"), thin rods ("spaghetti") and, finally, nearly spherical nuclei with decreasing density. We explicitly observe nucleation mechanisms, with decreasing density, for these different pasta phase transitions. Topological quantities known as Minkowski functionals are obtained to characterize the pasta shapes. Different pasta shapes are observed depending on the expansion rate. This indicates non equilibrium effects. We use this to determine the best ways to obtain lower energy states of the pasta system from MD simulations and to place constrains on the equilibration time of the system.

Overview of Nuclear Pasta Formation

The paper "Nuclear Pasta Formation" by Schneider et al. presents a detailed investigation into the formation of complex nonuniform nuclear matter phases, colloquially termed nuclear pasta. Utilizing molecular dynamics (MD) simulations, the authors explore these phases at subnuclear densities ranging from approximately $0.010 \, \text{fm}^{-3}$ to $0.10 \, \text{fm}^{-3}$, focusing on their formation mechanisms, morphological characteristics, and dependency on multiple variables such as temperature, density, and proton fraction.

Methodological Approach

The authors deploy MD simulations that involve 51,200 nucleons, coupled with phenomenological nuclear interactions. These simulations start with systems at a density of $0.10 \, \text{fm}^{-3}$, subsequently reducing the density by expanding the simulation volume at various rates. The interactions used in these simulations are designed to emulate the properties of nuclear matter, including its saturation binding energy and density. To characterize the pasta's topological attributes, Minkowski functionals are employed, providing a quantitative measure of shape evolution as density decreases.

Simulation Results and Characterization

The simulations reveal a sequence of morphological transitions with decreasing density:

• At higher densities, the formation of spherical bubbles ("swiss cheese") is observed.
• This "swiss cheese" transitions to structures such as hollow tubes, flat plates ("lasagna"), and thin rods ("spaghetti").
• At the lowest densities, nearly spherical nuclei are formed.

The dependency of the pasta shapes on the expansion rate illustrated the non-equilibrium effects prominent in such phase transitions. Furthermore, the utilization of Minkowski functionals enabled a precise characterization of the pasta shapes, supporting the determination of equilibration timescales and energy state optimization in the MD simulations.

Implications of Research

The implications of this research are noteworthy. These insights into nuclear matter organization at subnuclear densities bear relevance to several astrophysical phenomena, including supernovae and neutron star structure. The understanding of nuclear pasta phases contributes to theoretical developments in nuclear physics pertaining to the equation of state of nuclear matter and its influence on phenomena such as neutrino transport and neutron star magnetic field decay.

Practically, these findings open paths for refined modeling of neutron star properties, especially concerning their crustal behavior, shear modulus, and transport characteristics in supernovae environments. The exploration of non-equilibrium effects points to potential hysteresis in pasta shape transitions, which could impact bulk viscosity calculations essential for accurately modeling r-mode oscillations in rapidly rotating neutron stars.

Future Directions

The paper sets groundwork for further exploration into nuclear pasta equilibria and transitions, particularly emphasizing the need for simulations at varying proton fractions and temperatures. Future research may focus on the energetics and mechanical properties of nuclear pasta, investigating its role in astrophysical processes through enhanced computational simulations involving larger nucleon counts and incorporating additional interactions or quantum effects beyond classical MD methodologies.

Ultimately, the work by Schneider et al. enriches the understanding of exotic nuclear phases and paves the way for continued exploration into their wide-ranging implications on both stellar and quantum systems.