\begin{table}%t1 \par \caption{\label{tab:qso_photometry}Average stacked QSO $100~\mu$m rest-frame luminosities for bins in redshift and $I$-band absolute magnitude. } \small%\centering \par \begin{tabular}{lllllll} \hline\hline\noalign{\smallskip} $N$ & $z_{\rm min}$ & $z_{\rm max}$ & $I_{\rm min}$ & $I_{\rm max}$ & $\nu L_\nu(100~\mu{\rm m})$ & SFD\\ & & & (AB) & (AB) & $/10^{12}~L_\odot$ & $/$($M_\odot$ yr$^{-1}$ Mpc$^{-3}$)\\ \hline\noalign{\smallskip} 6 & $0.05$ & $0.5$ &$-22$ & $-19$ & $0.126\pm 0.069$ & $(2.0\pm1.1)\times10^{-4}$\\ %% 72 & $0.05$ & $0.5$ &$-24$ & $-22$ & $0.115\pm 0.019$ & $(4.94\pm0.79)\times10^{-5}$\\ %% 29 & $0.05$ & $0.5$ &$-26$ & $-24$ & $0.31\pm 0.13 $ & $(3.6\pm1.5)\times10^{-6}$\\ %% 9 & $0.05$ & $0.5$ &$-28$ & $-26$ & $0.52\pm 0.38$ & $(8.8\pm6.4)\times10^{-8}$\\ %% 9 & $0.5$ & $1$ &$-22$ & $-19$ & $0.028\pm 0.065$ & $(0.5\pm1.2)\times10^{-4}$\\ %% 73 & $0.5$ & $1$ &$-24$ & $-22$ & $0.173\pm 0.034 $ & $(1.58\pm0.31)\times10^{-4}$\\ %% 38 & $0.5$ & $1$ &$-26$ & $-24$ & $0.400\pm 0.084 $ & $(6.1\pm1.3)\times10^{-5}$\\ %% 5 & $0.5$ & $1$ &$-28$ & $-26$ & $1.54\pm 0.24$ & $(4.06\pm0.63)\times10^{-6}$\\ %% 2 & $0.5$ & $1$ &$-32$ & $-28$ & $5.5\pm 4.5$ & $(4.9\pm4.0)\times10^{-8}$\\ %% 46 & $1$ & $2$ &$-24$ & $-22$ & $0.218\pm 0.090 $ & $(2.4\pm1.0)\times10^{-4}$\\ %% 223& $1$ & $2$ &$-26$ & $-24$ & $0.727\pm 0.092$ & $(5.38\pm0.69)\times10^{-4}$\\ %% 75 & $1$ & $2$ &$-28$ & $-26$ & $1.81\pm 0.26 $ & $(8.6\pm1.2)\times10^{-5}$\\ %% 32 & $1$ & $2$ &$-32$ & $-28$ & $5.1\pm 1.9 $ & $(8.6\pm3.2)\times10^{-7}$\\ %% 6 & $2$ & $4$ &$-24$ & $-22$ & $1\pm17$ & $(0.4\pm8)\times10^{-3}$\\ %% 52 & $2$ & $4$ &$-26$ & $-24$ & $1.05\pm 0.54 $ & $(3.9\pm2.0)\times10^{-4}$\\ %% 108& $2$ & $4$ &$-28$ & $-26$ & $3.47\pm 0.68 $ & $(3.30\pm0.65)\times10^{-4}$\\ %% 66 & $2$ & $4$ &$-32$ & $-28$ & $5.42\pm 0.76 $ & $(9.9\pm1.4)\times10^{-6}$\\ %% 1 & $4$ & $7$ &$-24$ & $-22$ & $1.7\pm 1.9 $ & $(2.1\pm2.4\times10^{-5}$\\ %% 1 & $4$ & $7$ &$-26$ & $-24$ & $2.0\pm 2.2 $ & $(1.9\pm2.1)\times10^{-5}$\\ %% 58 & $4$ & $7$ &$-28$ & $-26$ & $2.32\pm 0.46 $ & $(5.6\pm1.1)\times10^{-6}$\\ %% 64 & $4$ & $7$ &$-32$ & $-28$ & $4.25\pm 0.69$ & $(1.95\pm0.32)\times10^{-7}$\\ \hline \end{tabular} \tablefoot{An M~82 SED has been assumed, though the results are only very weakly dependent on the assumed SED. The first column gives the number of QSOs in the bin in question. The final column gives the comoving volume-averaged star formation densities of QSO host galaxies in each bin.} \end{table}