that are considered to contribute OH megamasers is conservatively restricted to the range where strong OH emission has actually been detected (cf. Fig. 2 of Baan et al 1992a); adopting $H_o=100$ km s$^{-1}$Mpc$^{-1}$, this range is $5{\times}10^9<L_{60}<2{\times}10^{12}L_{\odot}$. Within this range, $f_m$ takes on non-zero values as follows, $f_m=0.05$ for $5{\times}10^9<L_{60}<2{\times}10^{10}L_{\odot}$, $f_m=0.2$ for $2{\times}10^{10}<L_{60}<2{\times}10^{11}L_{\odot}$, and $f_m=0.5$ for $2{\times}10^{11}<L_{60}<2{\times}10^{12}L_{\odot}$ (from Baan 1989, Baan et al 1992b). Since these probabilities are likely to be a result of viewing angle, the derived luminosity function should be considered as an “effective OH luminosity function” that provides the probability of detection for randomly oriented sources, rather than an an accurate accounting of the number of OH emitting galaxies. The constant of proportionality $C_1$ in $L_{OH}= C_1 L_{60}^2$ is $4.5{\times}10^{-21}L_{\odot}^{-1}$, and a fiducial $L_{OH}^*$ can be defined to be $L_{OH}^*= C_1L_{60}^{*2}= 0.10L_{\odot}$.

Figure \[OHLumfnct.fig\] shows the numerically computed luminosity function for OH megamasers in logarithmically spaced bins of 0.1 Dex. For reference, the 60 $\mu$m luminosity ($L_{60}=\sqrt{L_{OH}/C_1}$) is indicated on the top axis. Since the bright OH megamasers that are likely to be useful in cosmological studies lie well above $L_{OH}^*$, the approximation in Eq.(\[phiapprox.eq\]) can be used to verify the numerical estimate in the range of 