OPAL type I opacity tables [@Rogers2002]. The varying parameter values of the models in the grid are given in Table \[tab:mesa\].

For each of the models in our grid we also computed the asymptotic period spacing $$\Delta\Pi_l = \frac{\Pi_0}{\sqrt{l(l+1)}},
\label{eq:1}$$ with $$\Pi_0
= 2\pi^2\left(\int_{r_1}^{r_2}N\frac{\mathrm{d}r}{r}\right)^{-1},
\label{eq:2}$$ as derived by @Tassoul1980 for high-order gravity modes. Here $l$ is the spherical degree of the pulsation mode, $r$ is the distance from the stellar center, $N$ is the Brunt-Väisälä frequency and the boundaries of the mode trapping region are marked by $r_1$ and $r_2$ [@Aerts2010]. While $\Delta\Pi_l$ is smaller for larger values of $l$ (Eq.\[eq:1\]), $\Delta\Pi_l$ also changes as the star evolves. We have therefore calculated the probability of observing different spacing values using the stellar ages in our grid models. As shown in Fig.\[fig:Spacing\_dist\], we typically expect $\Delta\Pi_l$ values on the order of 3100$s$ and 1800$s$ for $l=1$ and $l=2$ respectively, which in turn implies $\Pi_0$ is on the order of $4400\,s$. In addition, there are strong linear correlations for $\Delta\Pi_l$ between models with different values of $M$, $Z$, $X$, $f_{\rm ov}$ and $\alpha_{\rm ov}$, assuming a fixed hydrogen abundance $X_c$ in the convective core.

As shown by @Bouabid2013 and as observed by 