Pasta nucleosynthesis: Molecular dynamics simulations of nuclear statistical equilibrium

Background: Exotic nonspherical nuclear pasta shapes are expected in nuclear matter at just below saturation density because of competition between short-range nuclear attraction and long-range Coulomb repulsion.

Purpose: We explore the impact nuclear pasta may have on nucleosynthesis during neutron star mergers when cold dense nuclear matter is ejected and decompressed.

Methods: We use a hybrid CPU/GPU molecular dynamics (MD) code to perform decompression simulations of cold dense matter with 51 200 and 409 600 nucleons from $0.080{\mathrm{fm}}^{-3}$ down to $0.00125{\mathrm{fm}}^{-3}$. Simulations are run for proton fractions $Y_P=$ 0.05, 0.10, 0.20, 0.30, and 0.40 at temperatures $T=$ 0.5, 0.75, and 1.0 MeV. The final composition of each simulation is obtained using a cluster algorithm and compared to a constant density run.

Results: Size of nuclei in the final state of decompression runs are in good agreement with nuclear statistical equilibrium (NSE) models for temperatures of $1\mathrm{MeV}$ while constant density runs produce nuclei smaller than the ones obtained with NSE. Our MD simulations produces unphysical results with large rod-like nuclei in the final state of $T=0.5\mathrm{MeV}$ runs.

Conclusions: Our MD model is valid at higher densities than simple nuclear statistical equilibrium models and may help determine the initial temperatures and proton fractions of matter ejected in mergers.

Figure 1

Distribution of cluster masses for $T=0.75\mathrm{MeV}$ (top row) and $T=1.0\mathrm{MeV}$ (bottom row) for proton fractions $Y_P=$ 0.05, 0.10, 0.20, 0.30, and 0.40 (columns) from simulations of $51200$ nucleons at a density of $n=0.00125{\mathrm{fm}}^{-3}$. The mass fraction of free neutrons $m_n$ is indicated.

Figure 2

Distribution of charge for $T=0.75\mathrm{MeV}$ (top row) and $T=1.0\mathrm{MeV}$ (bottom row) for proton fractions $Y_P=$ 0.05, 0.10, 0.20, 0.30, and 0.40 (columns) from simulations of $51200$ nucleons at a density of $n=0.00125{\mathrm{fm}}^{-3}$. The mass fraction of free neutrons $m_n$ is indicated.

Figure 3

Atomic number $Z$ and neutron number $N$ of nuclides for simulations at $T=$ 0.75 MeV with $Y_P=$ 0.05, 0.10, 0.20, 0.30, and 0.40 described in Sec. 3b.

Figure 4

Atomic number $Z$ and neutron number $N$ of nuclides for simulations at $T=$ 1.0 MeV with $Y_P=$ 0.05, 0.10, 0.20, 0.30, and 0.40 described in Sec. 3b.

Figure 5

Distribution of cluster masses for $T=0.5\mathrm{MeV}$ for proton fractions $Y_P=$ 0.05, 0.10, 0.20, 0.30, and 0.40 from simulations of $51200$ nucleons at a density of $n=0.00125{\mathrm{fm}}^{-3}$. The mass fraction of free neutrons $m_n$ is indicated.

Figure 6

Distribution of charge for $T=0.5\mathrm{MeV}$ for proton fractions $Y_P=$ 0.05, 0.10, 0.20, 0.30, and 0.40 from simulations of $51200$ nucleons at a density of $n=0.00125{\mathrm{fm}}^{-3}$.

Figure 7

Charge fractions (left) and mass fractions (right-hand side) for simulations of 409 600 particles at $T=$ 0.5, 0.75, and 1.0 MeV with $Y_P=$ 0.05 as described in Sec. 3d. The mass fraction of free neutrons $m_n$ is indicated on the left-hand panels.

Figure 8

Performance of the iumd GPU code for the 15 simulations described in Secs. 3b and 3c. All computations were performed using 51 200 particles with 32 GPU nodes on Big Red II.

Figure 9

Performance of the iumd GPU code for the three simulations described in Sec. 3d. All simulations were performed using 409 600 particles, $Y_P=0.05$, with 128 GPU nodes on Big Red II.