Related Publication(s): r-Process network calculations from the paper "Neutrino Capture and the R-Process" Meyer, McLaughlin, and Fuller, Phys. Rev. C, 58, 3696-3710 (1998).

The following movies illustrate a number of aspects of the r-process in neutrino-driven winds. The calculations shown began with material at a radius of 5.6 km and a temperature T₉=40. The wind element expanded exponentially on a timescale of 0.3 seconds. The expansion was homologous such that the outflow velocity was always proportional to the radial distance from the center of the nascent neutron star. The entropy was constant throughout the expansion at 110k per nucleon. The electron neutrinos had a temperature of 3.5 MeV and a luminosity 10⁵¹ ergs/s while the electron antineutrinos had a temperature 4.0 MeV and a luminosity 4 x 10⁵¹ ergs/s. In the reference calculation, the neutrinos were turned off once the matter temperature reached T₉=10. At this point, the neutrinos had set the electron fraction Y_e to 0.23.

Reference calculation

Author(s): Bradley Meyer

This movie shows the abundance per nucleon of nuclei with the given mass number during the r-process. The calculation begins at T₉=T/10⁹ K = 40 with only neutrons and protons. As time progresses and the temperature drops below T₉=10, nucleons assemble into ⁴He nuclei then into heavier mass nuclides. Once T₉ falls below about 4, the QSE among the heavy nuclei begins to break down. Charged-particle reactions freeze out, and flow to higher mass number occurs via nuclear beta decay. This is the classical r-process phase. The peaks in the r-process distribution at A=130 and A=195 build up as the r-process path passes through closed neutron shells. Here beta-decay rates become slow, causing a "traffic jam" in the flow upward in mass. Notice in particular the dramatic smoothing of the r-process abundance curve at late time. This occurs as the nuclei fall out of equilibrium under exchange of free neutrons.

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Full network, NSE, QSE

Author(s): Bradley Meyer

This movie shows the elemental abundances for the calculation. The white curve is the actual network abundance distribution. The green curve is the NSE abundance distribution computed at the same temperature, density, and electron fraction. The red curve is the QSE abundance distribution at the same temperature, density, electron fraction, and abundance of heavy nuclei. The matter begins with pure neutrons and protons. As the temperature falls, nucleons assemble into higher-mass nuclei. The network follows NSE down to about T₉=6.5. Below this temperature, the reactions that assemble heavy nuclei from alpha particles become too slow to maintain the NSE. Nevertheless, the most abundant nuclei remain in a nearly exact QSE down to about T₉=5. At this point, the QSE begins to favor Sn isotopes (Z=50), but the charged-particle reactions that would carry the actual network abundances are too slow, so the network and QSE abundances diverge. With decreasing temperature, the network and QSE abundances increasingly diverge. By the end of the movie, the network, QSE, and NSE abundances are all very different. The network nuclear populations have now largely broken down into (n,gamma)-(gamma,n) equilibrium in which isotopes of a given element are in equilibrium under exchange of free neutrons but isotopes of different elements are completely out of equilibrium with each other.

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QSE Clusters

Author(s): Bradley Meyer

This movie shows the equilibria among the nuclear species under the exchange of light particles (neutrons, protons, and alphas). The limits of the network are shown as the solid lines. The intersection of the dashed lines gives the most abundant heavy nucleus. The color indicates how well the given nuclide is in equilibrium with the most abundant species. A nuclide is plotted if its mass fraction is greater than 10^-20. Notice how the system first builds up a large equilibrium among all the nuclides. As the temperature falls, however, certain nuclear reactions become too slow to maintain this equilibrium so that the large equilibrium breaks down into smaller ones. Constraints appear on the nuclear populations, and the system descends the "hierarchy of statistical equilibria". Of particular interest are the equilibrium rows that develop. These are the (n,γ)-(γ,n) equilibria of the classical r-process phase of the expansion.

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