\begin{table}%t8 \caption{\label{Table: required Tbg for TA 10mK}Estimated required background temperatures to produce absorption lines with \mbox{$T_{\rm b}=-10$~mK} at an observing frequency of~550~GHz assuming \mbox{$T_{\rm ex} \ll T_{\rm bg}$}, and an opacity of one or~10$^{-3}$.} %\centering \par \begin{tabular}{lccrr} \hline \hline \noalign{\smallskip} Transition & Redshift & Opacity & $T_{\rm bg}$ & $T_{\rm CMB}$\\ & $z$ & $\tau$ & [K]& [K]\\ \hline H$_2$(2--0) & 18.3 & 1 & 58 & 53\\ & & 10$^{-3}$ & 260 \\ H$_2$(3--1) & 31.0 & 1 & 96 & 87\\ & & 10$^{-3}$ & 430 \\ H$_2$(4--2) & 43.4 & 1 & 132 & 121 \\ & & 10$^{-3}$ & 595 \\ H$_2$(5--3) & 55.4 & 1 & 168 & 154 \\ & & 10$^{-3}$ & 756 \\ HD(4--3) & 18.1 & 1 & 57 & 52 \\ & & 10$^{-3}$ & 257 \\ \par HD(5--4) & 22.7 & 1 & 71 & 65 \\ & & 10$^{-3}$ & 317 \\ HeH$^+$(4--3) & 13.4 & 1 & 43 & 39 \\ & & 10$^{-3}$ & 194& \\ HeH$^+$(5--4) & 16.7 & 1 & 54 & 48\\ & & 10$^{-3}$ & 240 & \\ \hline \end{tabular} \tablefoot {Note, that since the observing frequencies are the same for all transitions the source redshift is different for every transition. As~a comparison, the CMB~temperatures are listed for each redshift.} \end{table}