3D1D hydro-nucleosynthesis simulations. I. Advective-reactive post-processing method and its application to H ingestion into He-shell flash convection in rapidly accreting white dwarfs

We present two mixing models for post-processing of 3D hydrodynamic simulations applied to convective-reactive i-process nucleosynthesis in a rapidly accreting white dwarf (RAWD) with [Fe/H] = -2.6, in which H is ingested into a convective He shell during a He flash. A 1D advective two-stream model is formulated with physically motivated radial and horizontal mixing coefficients constrained by 3D hydrodynamic simulations. A more traditional approach uses diffusion coefficients calculated from the same simulations. All 3D simulations include the energy feedback of the $^{12}$C(p,$\gamma)^{13}$N reaction from the entrainment of stably stratified H. Global oscillations of shell H ingestion in two of the RAWD simulations cause bursts of entrainment of H and energy feedback into the flow. With the same nuclear network as in the 3D simulations, the 1D advective two-stream model reproduces the rate and location of the H burning within the He shell closely matching the 3D simulation predictions, as well as qualitatively displaying the asymmetry of the $X_{\mathrm{H}}$ profiles between the up- and downstream. With a full i-process network the advective mixing model captures the difference in the n-capture nucleosynthesis in the up- and downstream. For example, $^{89}$Kr and $^{90}$Kr with half-lives of 3.18 min and 32.3 s differ by a factor 2 - 10 in the two streams. In this particular application the diffusion approach provides globally the same abundance distribution as the advective two-stream mixing model. The resulting i-process yields from the diffusive and advective post-processing models are compared with observations of the exemplary CEMP-r/s star CS31062-050.