Table 2:

Bounds to parameter space and solutions.

Case(s)
$\begin{array}{c} \Delta_{\tilde{n}} \\
\mbox{(in $\mu$ Hz)} \end{array}$ $\displaystyle \frac{\Delta_{\tilde{\ell}}}{\Delta_{\tilde{n}}}$ $\displaystyle \frac{\Delta_{\tilde{m}}}{\Delta_{\tilde{n}}}$ $\displaystyle \frac{\Omega}{\Delta_{\tilde{n}}}$ $\displaystyle \frac{\alpha}{\Delta_{\tilde{n}}}$
Bounds to parameter space
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

Solutions
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
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 (i.e. $M = 25 M_{\odot}$ and $R_{{\rm eq}} = 7.46~R_{\odot}$).

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