Talent

Sensitivity studied of ⁴⁴Ti production in in core-collapse supernova environments.

Scientific Background

Recipe
Starting with a set parameter space of peak temperatures [T₉ = 4 - 7] and densities [$\rho$ = 10⁵ - 10⁷ g/cm³].

We use analytic adiabatic freeze-out trajectories (Hoyle et al. 1964; Fowler & Hoyle 1964) which satisfy the differential equations:

\begin{equation} \frac{dT}{dt} = \frac{-T}{3\tau} \hspace{1cm} \frac{d\rho}{dt} = -\frac{\rho}{\tau} \end{equation}

which obviously leads to:

\begin{equation} T(t) = T_0 exp(-t/3\tau) \hspace{1cm} \rho (t) = \rho_0 exp(-t/\tau) \end{equation} where $T_0$ and $\rho_0$ are the peak temperature and density in the supernova.

REFERENCES
Trends in 44Ti and 56Ni from Core-Collapse Supernovae