Physical Conditions for Synthesis of Sc, Ti, and V in Neutrino-driven Supernovae

TL;DR

This study tackles the origin of Sc, Ti, and V abundance ratios in very metal-poor stars by examining neutrino-process nucleosynthesis in CCSNe. The authors use a parameterized, hydrodynamics-free approach in a metal-free $13\,M_\odot$ progenitor's Si-burning layer, scanning constant $T$, $\rho$, $F_\nu$, and $t_{\rm nuc}$ and comparing to SAGA data. They find that reproducing the observed [Sc/Ti] and [V/Ti] requires a neutrino exposure of $\sigma_\nu \sim 10^{35}$ erg cm$^{-2}$ and a temperature window of $2.0$–$3.2$ GK, with weak density dependence. The results imply that realistic 3D, long-term simulations with initial asphericities are necessary to realize these conditions and robustly connect explosion physics to observed abundances.

Abstract

We present the results of simulations of nucleosynthesis in a core-collapse supernova (CCSN) including the neutrino process. Using the Si layer of $13M_\odot$ zero-metal progenitor as the initial composition, we calculate the nucleosynthesis by adopting the temperature, density, neutrino flux, and duration of nucleosynthesis as arbitrary parameters and compare the results with the observed abundances ratio of Sc, Ti, and V in very metal-poor (VMP) stars taken from the Stellar Abundances for Galactic Archaeology (SAGA) database. As a result, for the first time, we identify the quantitative requirements on local physical conditions. To reproduce the abundances ratios in the VMP stars, the explosive nucleosynthesis should take place under the neutrino exposure, which is time integration of neutrino flux, of $σ_ν\sim 10^{35}\,\mathrm{erg~cm^{-2}}$ and temperature of $2.0\,\mathrm{GK}\leq T \leq 3.2\,\mathrm{GK}$. The dependence on the density and each value of the neutrino flux and the duration of nucleosynthesis is weak. We also discuss whether the quantitative requirements are realized during the explosion. Although the requirements are difficult to be realized in the one-dimensional simulations, the non-monotonic thermal evolution shown in recent three-dimensional simulations may satisfy them. Because the evolution is likely caused by turbulent motion stemming from the initial asphericity of the progenitor, it is important to calculate the long-term three-dimensional supernova explosion of multi-dimensional metal-free progenitor models and follow the nucleosynthesis self-consistently.

Figures (4)

• Figure 1: Abundance distribution of a zero-metal $13M_\odot$ progenitor model (dashed line) and the ejecta after explosive nucleosynthesis (solid line; a 1D thermal bomb model with $1~\mathrm{B}$, Tominaga07). The colors represent the species of nuclei. The gray dashed line indicates $Y_e$ distribution of the progenitor. The shaded region indicates the initial composition.
• Figure 2: Gray scale is the normalized number density of the VMP stars as functions of [Sc/Ti] and [V/Ti]. The abundance ratios of 441 VMP stars are taken from the SAGA database suda08suda11Yamada13suda17. The contours represent 50%, 90%, and 99% of the total from the inside to outside. The [Sc/Ti] and [V/Ti] of the models with constant $\rho$ ($=10^{7}\,\mathrm{g~cm^{-3}}$), $F_\nu$ ($=2.65\times10^{36}\,\mathrm{erg~cm^{-2}~s^{-1}}$), $t_\mathrm{nuc}$ ($=0.1\,\mathrm{s}$), and various $T$ (filled circles connected with lines). The abundance ratios in an adopted progenitor star and an explosion model of the same progenitor star without neutrino exposure calculated in Tominaga07 are shown using a magenta open circle and a black circle, respectively. The models with the same $\rho$, $F_\nu$, and $t_{\rm nuc}$ are connected lines. The colors of the circles and lines represent $T$ and $\rho$.
• Figure 3: [Sc/Ti] and [V/Ti] of the models with $F_\nu=2.65\times10^{36}\,\mathrm{erg~cm^{-2}~s^{-1}}$, $t_\mathrm{nuc}=0.1\,\mathrm{s}$ and various $T$ and $\rho$. Colors of lines correspond to density, from $\rho=10^5\,\mathrm{g~cm^{-3}}$ to $10^8\,\mathrm{g~cm^{-3}}$. Solid and dashed lines indicate the models with and without neutrinos, respectively. The black lines show the [Sc/Ti] and [V/Ti] values at the boundary of 90% contour line.
• Figure 4: Abundance ratios [Sc/Ti] and [V/Ti] of the models with various $T$, $\rho$, $F_\nu$, and $t_{\rm nuc}$ (filled circles connected with lines). The same $F_\nu$ and $t_{\rm nuc}$ are adopted for the models in each panel. The colors of the circles and lines represent $T$ and $\rho$, respectively. The magenta open circles, background gray scale, and contours are the same as those in Figure \ref{['fig:saga_wnu-wonu']}.