$D_L$ is the luminosity distance in Mpc. We integrate over the velocity width of the CO (1–0) lines as measured using the IRAM 30m [@French2015]. In Table \[table:hcn\], we present the 3$\sigma$ upper limits on the HCN (1–0) and HCO$^+$ (1–0) line luminosities for the two post-starburst targets.

We compare the $L^{\prime}($HCN$)$ upper limits to the SFRs and CO line luminosities in Figure \[fig:hcn\]. For comparison, we also show the rest of the @French2015 post-starburst sample, as well as comparison samples of star-forming and early type galaxies with both HCN and CO measurements [@Gao2004; @Crocker2012]. For the early type galaxies, SFRs are from @Davis2014, and we use the conversion factor from main beam temperature to flux density of 4.73 Jy/K from @Young2011. While the post-starbursts have high CO luminosities for their SFRs, the observed offset does not persist for the denser HCN-traced gas; their $L^{\prime}($HCN$)$ upper limits are consistent with their low SFRs. The $L^{\prime}($HCN$)$/$L^{\prime}($CO$)$ ratios for post-starbursts are low compared to the star-forming galaxies and most of the CO-detected early types.

Similarly, we compare the HCO$^+$ upper limits to the SFRs for the post-starburst targets in Figure \[fig:hco\_plus\]. The comparison samples of star-forming and starbursting galaxies are from @Gracia2008 