\begin{table}%t2
\caption{\label{tmod1}Characteristics of the 15~$M_{\odot}$ models with varying $\delta_{\rm NN}$ at the end of core He~burning.}
\par
%\centering
\par
\begin{tabular}{crrrccc}
\hline \hline \noalign{\smallskip}
$\delta_{\rm NN}$ & \multicolumn{1}{c}{$\tau_{\rm MS}$} & \multicolumn{1}{c}{$\tau_{\rm CHeB}$} & \multicolumn{1}{c}{$M_{\rm CO}$\tablefootmark{a}} & \multicolumn{1}{c}{$X({\rm C})$\tablefootmark{b}} & \multicolumn{1}{c}{C/O\tablefootmark{c}} & Case\tablefootmark{d} \\
  & \multicolumn{1}{c}{[Myr]} & \multicolumn{1}{c}{[Myr]} & \multicolumn{1}{c}{[$M_{\odot}$]} &  &  & \\
\hline
 --0.009 & 8.224 & 1.344 & 3.84 & 4.4e-10 & -- & III \\
 --0.008 & 8.285 & 1.276 & 3.83 & 2.9e-10 & -- &  \\
 --0.007 & 8.308 & 1.200 & 3.38 & 8.5e-10 & -- &  \\
 --0.006 & 8.401 & 1.168 & 3.61 & 4.2e-07 & -- & \\
  \hline
--0.005 & 8.480 & 1.130 & 3.59 & 5.9e-06 & 3.0e-05 & II \\
 --0.004 & 8.672 & 0.933 & 3.60 & 3.2e-05 & 5.2e-05 & \\
 --0.003 & 8.790 & 0.905 & 3.60 & 1.3e-04 & 1.7e-04 & \\
 --0.002 & 9.046 & 0.892 & 3.61 & 5.6e-04 & 6.4e-04 & \\
 \hline
 --0.001 & 9.196 & 0.888 & 3.70 & 0.013 & 0.014 & I \\
 0          & 9.640 & 0.802 & 3.65 & 0.355 & 0.550 & \\
+0.001 & 9.937 & 0.720 & 3.61 & 0.695 & 2.278 & \\
+0.002 & 10.312 & 0.684 & 3.62 & 0.877 & 7.112 & \\
 \hline
+0.003 & 10.677 & 0.664 & 3.62 & 0.958 & 22.57 & IV \\
+0.004 & 10.981 & 0.659 & 3.62 & 0.981 & 52.43 & \\
+0.005 & 11.241 & 0.660 & 3.61 & 0.992 & 123.9 & \\
+0.006 & 11.447 & 0.661 & 3.55 & 0.996 & 270.2 & \\
\hline
\end{tabular}
\tablefoot {\tablefoottext{a}{Mass coordinate where the abundance of $^4$He drops below~10$^{-3}$;}
\tablefoottext{b}{here, $X({\rm C}) = X(^{12}{\rm C})$, the central value for the carbon mass fraction;}
\tablefoottext{c}{ratio of the carbon to oxygen mass fractions;}
\tablefoottext{d}{see~text, p.~\pageref{casepage} for the description of the different cases.}}
\end{table}