Fission and the $r$-process nucleosynthesis of translead nuclei in neutron star mergers

We study the impact of fission on the production and destruction of translead nuclei during the $r$-process nucleosynthesis occurring in neutron-star mergers. Abundance patterns and rates of nuclear energy production are obtained for different ejecta conditions using three sets of stellar reaction rates, one of which is based on microscopic and consistent calculations of nuclear masses, fission barriers, and collective inertias. We show that the accumulation of fissioning material during the $r$ process can strongly affect the free neutron abundance after the $r$-process freeze-out. This leads to a significant impact on the abundances of heavy nuclei that undergo $\alpha$ decay or spontaneous fission, affecting the radioactive energy production by the ejecta at timescales relevant for kilonova emission.

Figure 1

Highest fission barrier ($B_f$), and energy windows for $\beta$-delayed fission ($B_f-Q_{\beta }$) and neutron-induced fission ($B_f-S_n$) predicted by $\text{FRDM}+\text{TF}$ (top panels), HFB14 (middle panels), and BCPM (bottom panels) as a function of proton and neutron number. $B_f$ and $S_n$ values correspond to the nucleus with $Z$ protons and $N$ neutrons, while $Q_{\beta }$ values correspond to the FRDM prediction for the $(Z-1,N+1)$ parental nucleus. All the quantities are in MeV. Red circles indicate the $r$-process nuclei produced at $t\approx 10\mathrm{s}$ in the hot dynamical ejecta nucleosynthesis.

Figure 2

Evolution of the different thermodynamic variables (from top to bottom): mass density, temperature, entropy, and free neutron number density $n_n$. The different curves represent the predictions obtained with BCPM (dashed lines), HFB14 (dotted lines), and $\text{FRDM}+\text{TF}$ (solid lines) for three different trajectories: dynamical hot (red curves), dynamical cold (blue curves), and accretion disk (purple curves) (see text for details).

Figure 3

Abundances as functions of mass number predicted by BCPM, HFB14, and $\text{FRDM}+\text{TF}$ at 1 Gyr for the three different ejecta conditions: dynamical hot (top panel), dynamical cold (middle panel), and accretion disk (bottom panel). As a reference, black dots show the renormalized solar $r$-process abundances.

Figure 4

Abundances as functions of mass number predicted by $\text{FRDM}+\text{TF}$, HFB14, and BCPM at four different times. Each row represent a different type of ejecta: dynamical hot (top panels), dynamical cold (middle panels), and accretion disk (bottom panels). Insets show the abundances prediction in ${log}_{10}$ scale for particular mass regions. At $t=1$ day, mass number $A=254$ is marked with a gray vertical dotted line. Black dots represent solar $r$-process abundances, which are renormalized by the same factor in all plots.

Figure 5

Abundances (in ${log}_{10}$ scale) at freeze-out predicted by $\text{FRDM}+\text{TF}$ (top panel), HFB14 (middle plot), and BCPM (bottom plot) in the hot dynamical ejecta. Black squares represent stable nuclei.

Figure 6

Contribution of single channels in Eq. (2) to $d{Y}_n/dt$ obtained with different reaction rates in the hot dynamical scenario. The exact neutron abundance $Y_n$ (black circles) are compared with those predicted by Eq. (4) assuming quasiequilibrium (green line).

Figure 7

Impact of single fission channels on the abundances of nuclei with $A\gtrsim 250$ at 1 d (top panels) and on the evolution of $A=254$ abundances (bottom panels) for the hot dynamical ejecta. The different curves show the abundances predicted when different fission channels are suppressed: $\beta$-delayed fission ($\beta$fis, red dashed line), spontaneous fission ($\mathit{sf}$, yellow dashed line) and neutron-induced fission ($(n,f)$, gray dashed line). The purple solid line corresponds to standard calculations, when all the fission are included. Left, middle, and right panels correspond to $\text{FRDM}+\text{TF}$, HFB14, and BCPM, respectively.

Figure 8

Neutron-induced fission (black circles) and neutron capture (green triangles) stellar reaction rates predicted at $T=0.64$ GK (solid lines, solid symbols) and $T=0,12$ GK (dotted lines, hollow symbols) by $\text{FRDM}+\text{TF}$ (left panel), HFB14 (middle panel), and BCPM (right panel).

Figure 9

Evolution of the total $220\le A\le 230$ abundance predicted by $\text{FRDM}+\text{TF}$ (solid lines), HFB14 (dotted lines), and BCPM (dashed lines) for different trajectories.

Figure 10

Radioactive energy emitted by $\beta$ decay (gray lines), $\alpha$ decay (blue lines), and fission (red lines) as a function of time for different ejecta conditions: dynamical hot (solid lines), dynamical cold (dash-dotted lines), and accretion disk (dotted lines). Top, middle, and bottom panel shows the results predicted by $\text{FRDM}+\text{TF}$, HFB14, and BCPM, respectively.

Figure 11

Top: Ejecta heating rate as a function of time predicted with BCPM (dash lines), HFB14 (dotted lines), and $\text{FRDM}+\text{TF}$ (solid lines) for different scenarios. Bottom: Evolution of the ratio between ejecta heating rates for different scenarios: $\text{FRDM}+\text{TF}$/BCPM (solid lines) and HFB14/BCPM (dotted lines).