Low-density nuclear matter with quantum molecular dynamics: The role of the symmetry energy

Abstract

We study the effect of isospin-dependent nuclear forces on the pasta phase in the inner crust of neutron stars. To this end we model the crust within the framework of quantum molecular dynamics (QMD). For maximizing the numerical performance, a newly developed code has been implemented on GPU processors. As a first application of the crust studies we investigate the dependence of the particular pasta phases on the isospin dependence of the interaction, including non-linear terms in this sector of the interactions. Our results indicate that in contrast to earlier studies the phase diagram of the pasta phase is not very sensitive to isospin effects. We show that the extraction of the isospin parameters like asymmetry energy and slope from numerical data is affected by higher-order terms in the asymmetry dependence of the energies per particle.Furthermore, a rapid transition from the pasta to a homogeneous phase is observed even for protonto-neutron ratios typical for a supernova environment.

Simulations of the Neutron Star Crust

“…Changing the isospin parameters of the interactions as done in the calculations for Fig. 4 does not significantly change this behaviour as discussed in Ref., 6 which is in contrast to other reported studies.…”

“…6 The left panel shows results to the simulation data with a quadratic function, whereas the right-hand panel contains the same data using a fit including a fourthorder dependence on δ. One can observe significant deviations from the often-used simple quadratic asymmetry dependence of the energy, demonstrating the need for higher-order terms in order to describe the asymmetry energy over a larger range correctly.…”

Studies of the neutron star crust

“…After establishing that the properties of saturated nuclear matter and nuclear binding energies have reasonable values (see [7]), a closer study of isospin-asymmetric matter follows. In order to test this aspect we calculate the isospin dependence of the energy density around nuclear saturation ρ 0 ≈ 0.165fm −3 .…”

“…This comes about as one can also express the value of χ the as number of connected regions plus the number of cavities minus the number of connecting tunnels [11]. Thus the figure shows the development of tunnels between nuclear slabs [7]. This result stresses the complexity of the pasta region as there are many competing nearly degenerate states of matter, therefore even for low temperatures the system might consist of a superposition of various structures.. One important aspect of studying the pasta phase of the neutron star crust is to investigate the transition from the pasta to the homogeneous matter of the stellar core.…”

“…In this work we follow closely the formulation developed in [6], extending this treatment by non-linear isospindependent interactions in order to study isospin effects in more detail. All terms are explicitly discussed in [7]. …”