We derive dust masses ( M _ { dust } ) from the spectral energy distributions of 58 post-starburst galaxies ( PSBs ) .
There is an anticorrelation between specific dust mass ( M _ { dust } / M _ { \star } ) and the time elapsed since the starburst ended , indicating that dust was either destroyed , expelled , or rendered undetectable over the \sim 1 Gyr after the burst .
The M _ { dust } / M _ { \star } depletion timescale , 205 ^ { +58 } _ { -37 } Myr , is consistent with that of the CO-traced M _ { H _ { 2 } } / M _ { \star } , suggesting that dust and gas are altered via the same process .
Extrapolating these trends leads to the M _ { dust } / M _ { \star } and M _ { H _ { 2 } } / M _ { \star } values of early-type galaxies ( ETGs ) within 1-2 Gyr , a timescale consistent with the evolution of other PSB properties into ETGs .
Comparing M _ { dust } and M _ { H _ { 2 } } for PSBs yields a calibration , log M _ { H _ { 2 } } = 0.45 log M _ { dust } + 6.02 , that allows us to place 33 PSBs on the Kennicutt-Schmidt ( KS ) plane , \Sigma SFR - \Sigma M _ { H _ { 2 } } .
Over the first \sim 200-300 Myr , the PSBs evolve down and off of the KS relation , as their star formation rate ( SFR ) decreases more rapidly than M _ { H _ { 2 } } .
Afterwards , M _ { H _ { 2 } } continues to decline whereas the SFR levels off .
These trends suggest that the star-formation efficiency bottoms out at 10 ^ { -11 } yr ^ { -1 } and will rise to ETG levels within 0.5-1.1 Gyr afterwards .
The SFR decline after the burst is likely due to the absence of gas denser than the CO-traced H _ { 2 } .
The mechanism of the M _ { dust } / M _ { \star } and M _ { H _ { 2 } } / M _ { \star } decline , whose timescale suggests active galactic nucleus ( AGN ) or low-ionization nuclear emission-line region ( LINER ) feedback , may also be preventing the large CO-traced molecular gas reservoirs from collapsing and forming denser star forming clouds .