\begin{table}%t1
\caption{Parameters of computed 2D~models for progenitor stars with different
  masses. $\Omega_{{\rm i}}$ is the angular velocity of the Fe-core,
  which is assumed to rotate uniformly, prior to collapse, $\theta_0$ and
  $\theta_1$ are the polar angles of the lateral grid boundaries, and
  $N_{\theta}$ is the number of grid points in the lateral
  direction. $t_{\rm 2D}$ denotes the time (relative to the bounce
  time) when the simulation was started or continued in 2D.
}
\small%\centerline
{
\begin{tabular}{llllllclll}
\hline
\hline
Model$~^\ast$ & Progenitor
      & $\Omega_{{\rm i}}$ & $[\theta_0,\theta_1]$
      & $N_{\theta}$ & Resolution & Collapse & $t_{\rm 2D}$
      &  Perturbation & Boundary \\
      &
      & (rad~s$^{-1}$)            & (degrees)
      &              & (degrees)  & in 2D~   & [ms]
      & (\%)         & conditions \\
\hline
s112\_32     & s11.2   & --   & $[46.8,133.2]$ & 32 & 2.70 & {}--{} & 6.4 &
     $v,\pm1$    & periodic   \\
s112\_64     & s11.2   & --   & $[46.8,133.2]$ & 64 & 1.35 & {}--{} & 7.3 &
     $v,\pm1$    & periodic   \\
s112\_128\_f & s11.2   & --   & $[0,180]$      & 128& 1.41 & {}--{} & 6.4 &
     $v,\pm1$    & reflecting \\
s15\_32~$^\dagger$
            & s15s7b2 & --   & $[46.8,133.2]$ & 32 & 2.70 & {}--{} & 6.5 &
     $v,\pm1$    & periodic   \\
s15\_64\_p  & s15s7b2 & --   & $[46.8,133.2]$ & 64 & 1.35 & {}+{}  & $-$175 &
     $\rho,\pm2$ & periodic   \\
s15\_64\_r  & s15s7b2 & 0.5 & $[0,90]$       & 64 & 1.41 & {}+{}  & $-$175 &
     $\rho,\pm1$ & reflecting \\
s20\_32     & s20.0   & --   & $[46.8,133.2]$ & 32 & 2.70 & {}--{} & 6.5 &
     $v,\pm1$    & periodic \\
\hline\noalign{\smallskip}
s15\_mix~$^\ddagger$
            & s15s7b2 & --   & {}--{}       & 1  & {}--{} & {}--{} &  &
     {}--{}      & {}--{} \\
\hline
\end{tabular}}
\smallskip
 $^\ast$ Models s112\_32, s112\_64, s15\_32, s15\_64\_p, s15\_64\_r, and
  s20\_32 were discussed in overview in \cite{burram03}.
\\
  $^\dagger$ This is Model~s15Gio\_32.b from \cite{burram06:I}. 
  Different from the other models presented in this paper, Model~s15\_32
  was computed with an older implementation of the gravitational potential,
  which contained a slightly different treatment of the relativistic 
  corrections in the potential (see also the comment in Table~\ref{table:evol}).
  This affects only the neutrino luminosities
  and average neutrino energies by a few percent. We have corrected
  this difference in our plots for the luminosities and mean energies. The
  correction was calculated as $\Delta L = L_{\rm 1D,new}
  - L_{\rm 1D,old}$, where~$L_{\rm 1D,new}$ and~$L_{\rm 1D,old}$ are the luminosities of the 1D~simulations with
  the "new'' and "old'' versions of the gravitational potential,
  respectively. Then the corrected luminosity is given by $L_{\rm 2D,corr} =
  L_{\rm 2D,old} + \Delta L$, where $L_{\rm 2D,old}$ is the
  luminosity of the 2D~model which was simulated with the old version
  of the gravitational potential. For the average neutrino energies
  the procedure is analogous.
\\
  $^\ddagger$ This model was calculated in 1D~using the mixing
  algorithm described in Appendix~\ref{app:ns_mix} for treating
  effects from PNS~convection.
\label{tab:2d_models}
\end{table}