\begin{table}%t1
\par
   \caption{\label{Tab_un-dimensioned}Definition of the main non-dimensional variables.}   
    %\centerline
 {\begin{tabular}{@{}r@{~~}c@{~~}ll@{}}    
\hline\hline
Symbol$^{{a}}$ &  & Definition & Quantity\\   
\hline
$\Dn$~  &$=$& $D /\Do$                & distance of the axis apex to the Sun \\
$\Ln$~  &$=$& $L(D) / L(\Do)$         & flux rope length \\
$\Ptn$ &$=$& $\frac{\varpi(D)}{\varpi(\Do)} \frac{\Pt(D)}{\Pt(\Do)}$ & total pressure at the flux rope boundary \\
$\ron$ &$=$& $\ro/\Ro$                & radial coordinate of the reference field \\
$\rn$~  &$=$& $(\Ptn)^{1/4} ~ r/\Ro$  & radial coordinate\\
$\Bn$~  &$=$& $(\Ptn)^{-1/2}~ B/\Bco$ & magnetic field strength at $r$ \\
$\Bnc$ &$=$& $(\Ptn)^{-1/2}~ \Bc/\Bco$& magnetic field strength at the center\\
$\sn$~  &$=$& $\Ln~(\Ptn)^{1/4}$      & size factor \\
$\aon$ &$=$& $\ao \Ro$                & amount of twist for the GH field \\
$\Aon$ &$=$& $\Ao /\Ro$               & axial field extension for the SP field  \\
\hline
    \end{tabular}}
\par
    \smallskip
$^{{a}}$  The non-dimensional variables (with a \~\ on top) are normalized at the reference field, that is labeled with a ``o'' subscript. The reference field is at a distance~$\Do$ from the Sun, it has a radius~$\Ro$ and a central field strength $\Bco$. The value of $B$ taken at the flux rope center have a ``$c$'' subscript. GH means Gold \& Hoyle and SP ``split'' (see Sects.~\ref{N-GH} and~\ref{N-SP}).
   \end{table}