Test Space Background

To properly explore the desired sample space there were a few quantities that needed to be found. The supporting paper that accompanies the example simulation that our sensitivity study draws from outlines the connection between the electron fraction, $Y_{e}$, and number luminosity, $L^{n}_{\nu}$ (Bliss Eq 6). The number luminosity is given by the For each simulation run we sought to test a wide range of electron fractions. To accomplish this we reworked the relevant equation to solve for electron antineutrino energy,

$\left<E_{\bar{\nu}}\right>$ $=$ $\frac{L_{\bar{\nu}} Y_{e} \left<E_{\nu}\right>}{L_{\nu}(1-Y_{e})} \frac{\left<\sigma_{\bar{\nu} p}\right>}{\left<\sigma_{\nu n}\right>}$

where $L_{\nu}$ and $L_{\bar{\nu}}$ are the neutrino and antineutrino energy luminosity respectively, $\left<E_{\nu}\right>$ is neutrino energy, $\frac{\left<\sigma_{\bar{\nu} p}\right>}{\left<\sigma_{\nu n}\right>}$ is the cross sections ratio for electron neutrino absorption on neutrons and electron antineutrino absorption on protons respectively. As described in the paper the number luminosity is a free quantity allowing for us to fix $L_{\nu}$ and $L_{\bar{\nu}}$ as well as $\left<E_{\nu}\right>$. Thus for any desired $Y_{e}$ we need only solve for the corresponding $\left<E_{\bar{\nu}}\right>$. Many papers on the subject of neutrino driven winds specify a realistic $Y_{e}$ between $\sim 0.4$ and $\sim 0.65$ (Bliss) (Tejas). For this reason we elected to increase the granularity for $Y_{e}$ values in this range. We also decided to test the space with very extreme fractions to both verify that the effect of neutrino interactions.

The base simulation has the following default parameters. From these parameters we inferred the $\frac{\left<\sigma_{\bar{\nu} p}\right>}{\left<\sigma_{\nu n}\right>}$,

We then fixed the other prevalent parameters to allow for a creation of a test space,

The following $Y_{e}$ and corresponding $\left<E_{\bar{\nu}}\right>$ were calculated,