\begin{table}%t2 \caption{\label{samples}Related \textit{Spitzer}-selected $z\sim2$ ULIRGs samples.} %\centerline {\begin{tabular}{lcccccc} \hline\hline Sample & $N$ & $F_{\rm{24~\mu m}}$ & $\langle F_{\rm{24~\mu m}}\rangle$ & IR color selection & $r$ & density \\ \hline & & $\mu$Jy & $\mu$Jy & & Vega & deg$^{-2}$ \\ This work & 33 & \textgreater400 & 566 & $F_{\rm{3.6~\mu m}}$\textless $F_{\rm{4.5~\mu m}}$\textless $F_{\rm{5.8~\mu m}}$\textgreater $F_{\rm{8.0~\mu m}}$ & \textgreater23 & 65 \\ Lonsdale et al.\ (2008) & 61 & \textgreater400 & 819 & $F_{\rm{3.6~\mu m}}$\textless $F_{\rm{4.5~\mu m}}$\textless $F_{\rm{5.8~\mu m}}$\textgreater $F_{\rm{8.0~\mu m}}$ & \textgreater23 & 55 \\ Farrah et al.\ (2008) & 32 & \textgreater500 & 726 & $F_{\rm{3.6~\mu m}}$\textless $F_{\rm{4.5~\mu m}}$\textgreater $F_{\rm{5.8~\mu m}}$ and $F_{\rm{4.5~\mu m}}$\textgreater $F_{\rm{8.0~\mu m}}$ & \textgreater23 & 34 \\ Huang et al.\ (2009)$^{a}$ & 12 & \textgreater500 & 689 & 0~\textless~[3.6]--[4.5]~\textless~0.4 & & \\ & & & & --0.7~\textless~[3.6]--[8.0]~\textless~0.5 & \\ Magliocchetti et~al.\ (2007) & 793 & \textgreater350 & & & \textgreater25.5 & 200 \\ Yan et~al.\ (2005) & 52 & \textgreater900 & & $\log_{10}(\nu f_{\nu}(\rm{24~\mu m})/\nu {\textit f}_{\nu}(\rm{8~\mu m}))$~\textgreater~0.5 & & \\ & & & & $\log_{10}(\nu f_{\nu}(\rm{24~\mu m})/\nu {\textit f}_{\nu}(\rm{0.7~\mu m})$)~\textgreater~1.0 & & \\\hline \end{tabular}} \par \smallskip $^{a}$ The sample of \citet{Huan08} differs by only one source from the one of \citet{Youn09}. \end{table}