$r$-process Heating Feedback on Disk Outflows from Neutron Star Mergers

Abstract

Neutron star mergers produce $r$-process elements, with yields that are sensitive to the kinematic and thermodynamic properties of the ejecta. These ejecta properties are potentially affected by dynamically-important feedback from $r$-process heating, which is usually not coupled to the hydrodynamics in post-merger simulations modeling the ejecta launching and expansion. The multi-messenger detection of GW170817 showed the importance of producing reliable ejecta predictions, to maximize the diagnostic potential of future events. In this paper, we develop a prescription for including $r$-process heating as a source term in the hydrodynamic equations. This prescription depends on local fluid properties and on the $Y_{e}$ history as recorded by dedicated tracer particles, which exchange information with the grid using the Cloud-in-Cell method. The method is implemented in long-term viscous hydrodynamic simulations of accretion disk outflows to investigate its feedback on ejecta properties. We find that $r$-process heating can increase the unbound disk ejecta mass by $\sim 10\%$ relative to a baseline case that only considers alpha particle recombination. Nuclear heating also enhances the radial velocity of the ejecta with $Y_e < 0.25$ by up to a factor of two, while concurrently suppressing marginally-bound convective ejecta.

Figures (11)

• Figure 1: Specific nuclear energy release rates $\dot\varepsilon_{\rm nuc}$ as functions of temperature for 50 sample parametrized expansion trajectories with different initial $Y_e$ (see text for details). Our heating prescription interpolates the heating rate based on temperature and $Y_{e}$, using the instantaneous fluid temperature (as a proxy for time) and two trajectories whose $Y_{e, T6}$ (i.e. the $Y_{e}$ value when it first reached temperature 6 GK) bracket the value that the fluid element has.
• Figure 2: Snapshots of density in our fiducial model at various times, as labeled, comparing a baseline case with no $r$-process heating (top row, model al03nH) and one that includes our heating rate prescription with default settings (bottom row, model al03T4). Both models share the color map at the same time. The model with nuclear heating produces an outflow with more spherical morphology and on a shorter timescale than the model without $r$-process heating.
• Figure 3: Left: energy evolution for selected models. Solid and dashed lines represent the total kinetic and internal energy in the simulation domain for each model, respectively. Right: total heating rates as functions of time for various models in different colors, as indicated in the legend.
• Figure 4: The upper four panels depict the distribution of tracers from 100 ms to 16 s (left to right) for model al03T4. The color map represents each tracer's $Y_{e, T6}$ value. The empty region in the left panel (at t = 0.1 s) corresponds to the initial torus, where temperature exceeds 6 GK. In this high-temperature region, tracers are not yet assigned with their $Y_{e, T6}$ value. Heating rate is also not required under such conditions. The lower panels display the specific nuclear heating rate derived from tracers corresponding to the upper panels. Heating regions (outflows) are shown in red, while cooling regions (inflows) are in blue.
• Figure 5: Time evolution of the $Y_{e}$ (upper panel) and radial velocity (lower panel) for model al03T4. Grey lines in the background represent all unbound tracers. 10 representative unbound tracers are highlighted in color, selected to cover a range of $Y_{e,T6}$ values, with colors assigned according to the color map. Dotted points mark the time when each tracer first passes through $T = 6$ GK, indicating the onset of its contribution to nuclear heating or cooling.