HCN and CO line diagnostics provide new insight into the OH megamaser ( OHM ) phenomenon , suggesting a dense gas trigger for OHMs . We identify three physical properties that differentiate OHM hosts from other starburst galaxies : ( 1 ) OHMs have the highest mean molecular gas densities among starburst galaxies ; nearly all OHM hosts have \bar { n } ( { H } _ { 2 } ) = 10 ^ { 3 } – 10 ^ { 4 } cm ^ { -3 } ( OH line-emitting clouds likely have n ( { H } _ { 2 } ) > 10 ^ { 4 } cm ^ { -3 } ) . ( 2 ) OHM hosts are a distinct population in the nonlinear part of the IR-CO relation . ( 3 ) OHM hosts have exceptionally high dense molecular gas fractions , L _ { HCN } / L _ { CO } > 0.07 , and comprise roughly half of this unusual population . OH absorbers and kilomasers generally follow the linear IR-CO relation and are uniformly distributed in dense gas fraction and L _ { HCN } , demonstrating that OHMs are independent of OH abundance . The fraction of non-OHMs with high mean densities and high dense gas fractions constrains beaming to be a minor effect : OHM emission solid angle must exceed 2 \pi steradians . Contrary to conventional wisdom , IR luminosity does not dictate OHM formation ; both star formation and OHM activity are consequences of tidal density enhancements accompanying galaxy interactions . The OHM fraction in starbursts is likely due to the fraction of mergers experiencing a temporal spike in tidally driven density enhancement . OHMs are thus signposts marking the most intense , compact , and unusual modes of star formation in the local universe . Future high redshift OHM surveys can now be interpreted in a star formation and galaxy evolution context , indicating both the merging rate of galaxies and the burst contribution to star formation .