Low-Resolution Sodium D Absorption is a Bad Proxy for Extinction

Dust extinction is generally the least tractable systematic uncertainty in astronomy, and particularly in supernova science. Often in the past, studies have used the equivalent width of Na I D absorption measured from low-resolution spectra as proxies for extinction, based on tentative correlations that were drawn from limited data sets. We show here, based on 443 low-resolution spectra of 172 Type Ia supernovae for which we have measured the dust extinction as well as the equivalent width of Na I D, that the two barely correlate. We briefly examine the causes for this large scatter that effectively prevents one from inferring extinction using this method.