\begin{table}%t1
\caption{\label{tab1}Selected properties of our He-core white dwarf   sequences at the  point of maximum  effective temperature:  metallicity of progenitor star, stellar  mass, mass of hydrogen in the outer layers, $M_{\rm H}$, and surface hydrogen abundance by mass.}
\small%\centerline
 {
\begin{tabular}{@{}cccc}
\hline
\hline
&&& \\[-8pt]
$Z$ &$M/M_{\odot}$ & $M_{\rm H}/M_{\odot} [10^{-3}]$ & $X_{\rm H}$\\
\hline
0.03  &  0.220           &  2.07  &  0.490 \\
      &  0.250           &  1.51  &  0.531 \\ 
      &  0.303           &  0.98  &  0.658 \\
      &  0.358           &  0.56  &  0.658 \\
      &  0.400           &  0.40  &  0.658 \\
      &  0.452           &  0.27  &  0.658 \\
      &  0.513$^{\dag}$  &  0.20  &  0.658 \\
      &  0.522$^{\dag}$  &  0.17  &  0.658 \\
\hline
0.04  &  0.212           &  1.96  &  0.464 \\
      &  0.272           &  1.17  &  0.622 \\
      &  0.283           &  1.04  &  0.622 \\
      &  0.289           &  0.98  &  0.622 \\
      &  0.299           &  0.88  &  0.622 \\
      &  0.306           &  0.81  &  0.622 \\
      &  0.319           &  0.72  &  0.621 \\
      &  0.337           &  0.60  &  0.622 \\
      &  0.365           &  0.48  &  0.625 \\
      &  0.403           &  0.35  &  0.623 \\
      &  0.445           &  0.26  &  0.617 \\
\hline
0.05  &  0.207           &  2.26  &  0.430 \\
      &  0.273           &  1.06  &  0.588 \\
      &  0.288           &  0.91  &  0.588 \\
      &  0.295           &  0.84  &  0.588 \\
      &  0.301           &  0.78  &  0.588 \\
      &  0.311           &  0.72  &  0.588 \\ 
      &  0.323           &  0.63  &  0.588 \\
      &  0.348           &  0.51  &  0.588 \\
      &  0.368           &  0.43  &  0.585 \\
      &  0.401           &  0.34  &  0.588 \\
      &  0.445           &  0.25  &  0.588 \\
\hline
\end{tabular}}
\medskip
$^{\dag}$ These sequences  were obtained by artificially suppressing the core helium flash at the RGB.  They are discussed in~Sect.~4.3.
\end{table}