\begin{table}%t2
\caption{\label{tab:bounds}Bounds to parameter space and solutions.}
%\centerline
 {\small \begin{tabular}{cccccc}
\hline \hline\noalign{\smallskip}
Case(s) &
$\begin{array}{c} \Delta_{\tilde{n}} \\
\mbox{(in $\mu$Hz)} \end{array}$ &
$\displaystyle \frac{\Delta_{\tilde{\l}}}{\Delta_{\tilde{n}}}$ &
$\displaystyle \frac{\Delta_{\tilde{m}}}{\Delta_{\tilde{n}}}$ &
$\displaystyle \frac{\Omega}{\Delta_{\tilde{n}}}$ &
$\displaystyle \frac{\alpha}{\Delta_{\tilde{n}}}$ \\
\noalign{\smallskip}\hline\noalign{\smallskip}
\multicolumn{6}{c}{Bounds to parameter space} \\
%\hline
1   & 11.5--19.2 & 0.5--0.9 & 0.01--0.05 & 0.6--1.0 & 2.5--3.5 \\
2,3 & 9.6--19.2  & 0.5--0.9 & 0.00--0.05 & 0.8--1.2 & 2.8--3.8 \\
4,5 & 9.6--19.2  & 0.5--0.9 & 0.00--0.05 & 0.8--1.2 & 1.0--2.0 \\
\hline\noalign{\smallskip}
\multicolumn{6}{c}{Solutions} \\
%\hline
1$^\star$ & 17.26 & 0.660 & 0.0288 & 0.827 & 2.92 \\
2 & 15.25 & 0.767 & 0.0205 & 0.955 & 3.35 \\
4 & 16.01 & 0.755 & 0.0076 & 0.919 & 1.64 \\
5 & 16.01 & 0.758 & 0.0074 & 0.921 & 1.65 \\
\hline
\end{tabular}}
\medskip
Bounds of the parameter space used in the mode identification scheme
and corresponding exact solutions.  These bounds were chosen so as to include the solutions. $^\star$ These parameters correspond to a polytropic model with a polytropic index of~3 and the same mass and equatorial radius as the model used in cases~2, 4 and~5 (\ie\ $M = 25 M_{\odot}$ and $R_{{\rm eq}} = 7.46~R_{\odot}$).
%\vspace*{-3mm}
\end{table}