Exploring Composition Mixing in Kilonova Ejecta with Ray-by-ray Simulations

TL;DR

This study assesses the impact of composition mixing on $r$-process nucleosynthesis and kilonova observables in binary neutron star merger ejecta by incorporating a gradient-based mixing scheme into ray-by-ray radiation-hydrodynamics with the SkyNet nuclear network. Mixing operates where electron-fraction gradients are steep, smoothing $Y_e$ and free-neutron profiles mainly at intermediate angles while leaving equatorial regions largely intact. The global heavy-element yields and kilonova light curves show only minor changes due to mixing, with the second and third $r$-process peaks aligning with solar residuals and first-peak/rare-earth elements underproduced, similar to prior studies. The work suggests that, within this modeling framework, mixing is not a major source of uncertainty for predicting $r$-process yields or kilonova signatures, and highlights directions for future 3D, longer-timescale simulations and more accurate opacities.

Abstract

Binary neutron star merger (BNSM) ejecta are considered a primary repository of $r$-process nucleosynthesis and a source of the observed heavy-element abundances. We implement composition mixing into ray-by-ray radiation-hydrodynamic simulations of BNSM ejecta, coupled with an online nuclear network (NN). We model mixing via a gradient-based mixing approximation that evolves simultaneously with the hydrodynamics. We find that mixing occurs in regions where the electron fraction changes rapidly. While mixing smooths composition gradients in transition regions, it has a negligible impact on the heavy-element yields. This is because the primary $r$-process site (the equatorial ejecta) is initially homogeneous in free neutrons, leaving no strong gradients for mixing to act upon. In each angular ray, the abundances of the most produced elements are robust under mixing, while the less abundant ones are more affected. The total global abundances change only slightly from mixing, since each angular ray contributes its most abundant elements. Furthermore, the predicted kilonova light curves show only minor reddening, with differences below the detectability of state-of-the-art telescopes. In general, we do not observe significant effects from mixing in the time span of the $r$-process. Consequently, mixing only leads to minor variations in abundances and light curves in ray-by-ray simulations.

Figures (12)

• Figure 1: Initial conditions of the ejecta. The radial coordinate is the Lagrangian mass coordinate per unit polar angle, and the angular coordinate is the polar angle. The pole is in the vertical direction, and the equator is in the horizontal direction. From left to right and top to bottom, the quarter-spheres are density, electron fraction, entropy, and temperature, respectively. The rays in the polar regions are compressed in this plot since they have very low masses.
• Figure 2: Evolution of the spatial distribution of the electron fraction $Y_e$. The radial coordinate is the Lagrangian mass coordinate per unit polar angle, and the angular coordinate is the polar angle. The top and bottom panels are the evolution of the no-mixing and mixing models, respectively. The three columns correspond to $t = 0.01,\ 0.1,\ \mathrm{and}\ 1\ \mathrm{s}$. The $Y_e$ distribution near the equator is robust under mixing, but in the rays with polar angles $\sim 60^\circ$, where $Y_e$ has a greater radial gradient, mixing smooths its distribution. The gray solid contour marks the surface of velocity of $0.1c$. As the ejecta expand and accelerate, the mass enclosed by this low-velocity surface decreases, indicating that a greater amount of ejecta has achieved velocities $>0.1c$.
• Figure 3: Evolution of the spatial distribution of the free-neutron abundance $Y_\mathrm{n}$. The coordinates, panels, and the gray contour follow Fig. \ref{['fig: Ye_map']}. Similar to $Y_e$, mixing influences $Y_\mathrm{n}$ the most at $\sim 60^\circ$, smoothing the jagged features in the no-mixing model. Free neutrons have already been exhausted at 1 s.
• Figure 4: Final abundances of rays at polar angle $\theta = 30^\circ,\ 62^\circ,\ \mathrm{and}\ 90^\circ$ with reference to the mass number $A$. The relative residual in the bottom panel is defined as the absolute abundance difference divided by twice the average abundance of the mixing and no-mixing models. Mixing makes noticeable differences in the low-abundance elements of each ray, but the peaks are consistent.
• Figure 5: The combined global abundances with solar $r$-process residual abundances from Prantzos2020, normalized at $A=195$. The axes are defined the same as Fig. \ref{['fig: Y_angle']}. The abundances of the mixing and no-mixing models are consistent except for some light elements with $A<50$. The global yield is dominated by the angular rays where specific elements are produced most efficiently, which effectively dilutes the minor abundance differences found in other rays. The abundances of the second- and third-peak elements are comparable to the solar $r$-process abundances, but the first-peak and rare-earth elements are underproduced.